Physics Accomplishments and Future Prospects of the BES Experiments at the BEPC Collider
PPhysics Accomplishmentsand Future Prospects of the BES Experiments at the BEPC Collider
Roy A. Briere , Frederick A. Harris and RyanE. Mitchell Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania,USA, 15213; email: [email protected] Department of Physics and Astronomy, The University of Hawaii, Honolulu,Hawaii, USA, 96734; email: [email protected] Department of Physics, Indiana University, Bloomington, Indiana, USA, 47405;email: [email protected] 0000. 00:1–30Copyright c (cid:13)
Keywords
BES, charm, charmonium, XYZ, tau, R scan, hadron physics
Abstract
The cornerstone of the Chinese experimental particle physics programconsists of a series of experiments performed in the tau-charm energyregion. China began building e + e − colliders at the Institute for HighEnergy Physics in Beijing more than three decades ago. Beijing Elec-tron Spectrometer, BES, is the common root name for the particlephysics detectors operated at these machines. The development of theBES program is summarized and highlights of the physics results acrossseveral topical areas are presented. a r X i v : . [ h e p - e x ] M a r ontents
1. BES AND TAU-CHARM ENERGY REGION PHYSICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. BEGINNINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33. THE BES EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44. τ MASS MEASUREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65. R SCAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86. LIGHT QUARK PHYSICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106.1. Glueballs and the light isoscalar spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116.2. S-wave KK , ππ and Kπ scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126.3. Studies of the X (1835) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136.4. Baryons in J/ψ and ψ (2 S ) decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147. CHARMONIUM PHYSICS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157.1. Masses of charmonium states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167.2. Radiative transitions between charmonium states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177.3. Decays of the J/ψ and ψ (2 S ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198. XYZ PHYSICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208.1. Discovery of charged Z c states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218.2. Emerging patterns and problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229. CHARM PHYSICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239.1. Studies of the ψ (3770) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239.2. Precision Semileptonic and Leptonic D Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249.3. CP Tagging of D ¯ D Pairs from the ψ (3770) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259.4. Beyond the D + and D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2510.FUTURE PROSPECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1. BES AND TAU-CHARM ENERGY REGION PHYSICS
The Beijing Spectrometer experiments, BESI, BESII, and BESIII, have a long historyof operation at the Beijing Electron Positron Colliders, BEPC and BEPCII, located atthe Institute for High Energy Physics, IHEP, in Beijing, China. BEPC and BEPCIIwere designed to operate in the tau-charm center-of-mass (CM) energy region from2 to 5 GeV. This region provides access to a broad range of physics topics, includingcharmonium and charm physics, hadron studies, determination of the tau mass, R measurements, and investigations of the still-mysterious XY Z particles.This energy region has been instrumental in understanding various aspects ofthe Standard Model of elementary particle physics. Figure 1 shows the cross sectionfor electron-positron annihilation to hadrons divided by the cross section to muons, R = σ ( e + e − → hadrons ) /σ ( e + e − → µ + µ − ), in the CM energy range from 1.3 to5.0 GeV. Except for the large J/ψ and ψ (2 S ) charmonium resonances, the regionbelow about 3.7 GeV is relatively flat with an R value determined approximately bythe number of kinematically accessible quark flavors (up, down, and strange) witheach quark coming in three “colors.” The R measurements provided some of the firstevidence for “color” in Quantum Chromodynamics (QCD) (1). CROSS SECTION( σ ): An effectivearea that, given theintegratedluminosity,determines thelikelihood an eventis produced. Units:cm or barns (1barn = 10 − cm ). The discovery of the
J/ψ (3), composed of a charm and an anti-charm quark ( c ¯ c )was instrumental in establishing the existence of charm and in convincing physicistsof the reality of the quark model (1). The region above 4.6 GeV is again relativelyflat, but at a higher value due to crossing the charm production threshold. J/ ψ ψ (2S) ψ (3770) ψ (4040) ψ (4160) ψ (4415) BESCollaboration/PhysicsLetters B677(2009)239–245
Fig.4. R values reported here together with previous measurements below 5 GeV. at 3.07 GeV, and 2 . ± . ± .
07 at 3.65 GeV, which are sum-marized in Table 1.As a cross check, the R values are determined using the relation R exp = N obshad − N bg σ µµ L ϵ trg ¯ ϵ had ( + δ ), (7) where ¯ ϵ had is the hadronic e ffi ciency averaged over all of the ISRspectrum, and ( + δ ) is the corresponding theoretical ISR fac-tor. The ISR scheme used to simulate ¯ ϵ had , ϵ and to calculate ( + δ ) and ( + δ obs ) are the same in order to keep the consis-tency between theoretical calculation and simulation. The R val-ues determined with Eq. (7) are 2 . ± . ± .
07 at 2.6 GeV,2 . ± . ± .
07 at 3.07 GeV, and 2 . ± . ± .
08 at 3.65 GeV.The mean R values obtained using Eqs. (2) and (7) are consistentto within 1%.A cross check is also made by selecting hadronic events with n ch ! R values atthe three energy points are 2 . ± . ± .
08, 2 . ± . ± . . ± . ± .
08, respectively. The differences in the mean R values determined by selecting hadronic events with n ch ! n ch !
4. Results and discussion
Tables 1 and 2 list the quantities used in the determination of R using Eq. (2) and the contributions to the total error. The re-sults are shown in Fig. 4, together with previous measurements.The errors on the R values reported here are about 3 . R values are consistent within errors with the prediction of pertur-bative QCD [4].Compared with our previous results [8,9], the measurementprecision has been improved due to three main refinements to theanalysis: (1) the simulation of BES including both of the hadronicand electromagnetic interactions with a GEANT3 based packageSIMBES that has a more detailed geometrical description and mat-ter definition for the sub-detectors; (2) large data samples aretaken at each energy point, with statistical errors smaller than1%; (3) the selected hadronic event sample is expanded to includeone-track events, which supplies more information to the tuning Table3 α s ( s ) determined from R values at 2.600, 3.070, and 3.650 GeV, and evolved to5 GeV. The first and second errors are statistical and systematic, respectively. Shownin the last two columns are the weighted averages of the three measurements at5 GeV and M Z . √ s ( GeV ) α ( ) s ( s ) α ( ) s (
25 GeV ) ¯ α ( ) s (
25 GeV ) α ( ) s ( M z ) .
60 0 . + . + . − . − . . + . + . − . − . .
07 0 . + . + . − . − . . + . + . − . − . . + . − . . + . − . .
65 0 . + . + . − . − . . + . + . − . − . of LUARLW, and results in the improved values of parameters andhadronic e ffi ciency.In another BESII work, parts of the data sample taken at3.65 GeV with a luminosity of 5.536 pb − and at 3.665 GeV with aluminosity of 998.2 nb − are used, the hadronic events with morethan 2-tracks ( n ch !
3) are selected, and the averaged R value is R = . ± . ± .
089 which has an error of 4 .
1% [36].Based on the R values in this work and the perturbativeQCD expansion that computes R QCD ( α s ) to O ( α s ) [37–39], thestrong running coupling constant α ( ) s ( s ) can be determinedat each energy point [40–43]. The obtained α ( ) s ( s ) values areevolved to 5 GeV, and the weighted average of the measurements ¯ α ( ) s (
25 GeV ) is listed in Table 3. When evaluated at the M Z scale,the resulting value is α ( ) s ( M Z ) = . + . − . , which agrees withthe world average value within the quoted errors [4]. Acknowledgements
The BES Collaboration thanks the staff of BEPC and comput-ing center for their hard efforts. BES Collaboration also thanksB. Andersson for helping in the development of generator LU-ARLW during 1998–1999. This work is supported in part bythe National Natural Science Foundation of China under con-tracts Nos. 19991480, 19805009, 19825116, 10491300, 10225524,10225525, 10425523, 10625524, 10521003, the Chinese Academyof Sciences under contract No. KJ 95T-03, the 100 Talents Pro-gram of CAS under Contract Nos. U-11, U-24, U-25, and theKnowledge Innovation Project of CAS under Contract Nos. U-602, U-34 (IHEP), the National Natural Science Foundation of
BESCollaboration/PhysicsLetters B677(2009)239–245
Fig.4. R values reported here together with previous measurements below 5 GeV. at 3.07 GeV, and 2 . ± . ± .
07 at 3.65 GeV, which are sum-marized in Table 1.As a cross check, the R values are determined using the relation R exp = N obshad − N bg σ µµ L ϵ trg ¯ ϵ had ( + δ ), (7) where ¯ ϵ had is the hadronic e ffi ciency averaged over all of the ISRspectrum, and ( + δ ) is the corresponding theoretical ISR fac-tor. The ISR scheme used to simulate ¯ ϵ had , ϵ and to calculate ( + δ ) and ( + δ obs ) are the same in order to keep the consis-tency between theoretical calculation and simulation. The R val-ues determined with Eq. (7) are 2 . ± . ± .
07 at 2.6 GeV,2 . ± . ± .
07 at 3.07 GeV, and 2 . ± . ± .
08 at 3.65 GeV.The mean R values obtained using Eqs. (2) and (7) are consistentto within 1%.A cross check is also made by selecting hadronic events with n ch ! R values atthe three energy points are 2 . ± . ± .
08, 2 . ± . ± . . ± . ± .
08, respectively. The differences in the mean R values determined by selecting hadronic events with n ch ! n ch !
4. Results and discussion
Tables 1 and 2 list the quantities used in the determination of R using Eq. (2) and the contributions to the total error. The re-sults are shown in Fig. 4, together with previous measurements.The errors on the R values reported here are about 3 . R values are consistent within errors with the prediction of pertur-bative QCD [4].Compared with our previous results [8,9], the measurementprecision has been improved due to three main refinements to theanalysis: (1) the simulation of BES including both of the hadronicand electromagnetic interactions with a GEANT3 based packageSIMBES that has a more detailed geometrical description and mat-ter definition for the sub-detectors; (2) large data samples aretaken at each energy point, with statistical errors smaller than1%; (3) the selected hadronic event sample is expanded to includeone-track events, which supplies more information to the tuning Table3 α s ( s ) determined from R values at 2.600, 3.070, and 3.650 GeV, and evolved to5 GeV. The first and second errors are statistical and systematic, respectively. Shownin the last two columns are the weighted averages of the three measurements at5 GeV and M Z . √ s ( GeV ) α ( ) s ( s ) α ( ) s (
25 GeV ) ¯ α ( ) s (
25 GeV ) α ( ) s ( M z ) .
60 0 . + . + . − . − . . + . + . − . − . .
07 0 . + . + . − . − . . + . + . − . − . . + . − . . + . − . .
65 0 . + . + . − . − . . + . + . − . − . of LUARLW, and results in the improved values of parameters andhadronic e ffi ciency.In another BESII work, parts of the data sample taken at3.65 GeV with a luminosity of 5.536 pb − and at 3.665 GeV with aluminosity of 998.2 nb − are used, the hadronic events with morethan 2-tracks ( n ch !
3) are selected, and the averaged R value is R = . ± . ± .
089 which has an error of 4 .
1% [36].Based on the R values in this work and the perturbativeQCD expansion that computes R QCD ( α s ) to O ( α s ) [37–39], thestrong running coupling constant α ( ) s ( s ) can be determinedat each energy point [40–43]. The obtained α ( ) s ( s ) values areevolved to 5 GeV, and the weighted average of the measurements ¯ α ( ) s (
25 GeV ) is listed in Table 3. When evaluated at the M Z scale,the resulting value is α ( ) s ( M Z ) = . + . − . , which agrees withthe world average value within the quoted errors [4]. Acknowledgements
The BES Collaboration thanks the staff of BEPC and comput-ing center for their hard efforts. BES Collaboration also thanksB. Andersson for helping in the development of generator LU-ARLW during 1998–1999. This work is supported in part bythe National Natural Science Foundation of China under con-tracts Nos. 19991480, 19805009, 19825116, 10491300, 10225524,10225525, 10425523, 10625524, 10521003, the Chinese Academyof Sciences under contract No. KJ 95T-03, the 100 Talents Pro-gram of CAS under Contract Nos. U-11, U-24, U-25, and theKnowledge Innovation Project of CAS under Contract Nos. U-602, U-34 (IHEP), the National Natural Science Foundation of e + e − Center-of-Mass Energy (GeV) R V a l u e Figure 1 R = σ ( e + e − → hadrons ) /σ ( e + e − → µ + µ − ) measurements as a function of e + e − CMenergy. Also shown are the positions of the
J/ψ , ψ (2 S ), and other higher masscharmonium states. Modified from Reference (2) with permission. The ψ (3770) is just above the threshold for producing open-charm D ¯ D mesonpairs, and it decays almost entirely to D ¯ D . A D meson is formed from a charmquark and a light (up, down) anti-quark. The complicated region above the ψ (3770)to about 4.5 GeV is the charm meson resonance region, containing additional ψ resonances and a rich variety of other states, including the intriguing XY Z states.Although it is not obvious from Fig. 1, the threshold for e + e − → τ + τ − is atapproximately 3.554 GeV. The τ lepton is the third charged lepton, in addition tothe electron and the muon. LUMINOSITY( L ): Measures the“strength” ofcolliding beams.Units: cm − s − . INTEGRATEDLUMINOSITY( (cid:82) L dt ): Theluminosity times thetotal time of thecollisions. Units:cm − or barns − .Number of eventsexpected is given by (cid:82) L dt × σ . Remarkably, all this physics is accessible at IHEP. BES has data sets at manyCM energies in this region and very large data sets at the
J/ψ (1.3 billion events), ψ (2 S ) (0.45 billion), and ψ (3770) (2.9 fb − ). These are the world’s largest exclusivecharmonium data sets and allow for many precision measurements.The BES experiments have published 267 physics papers up through the end of2015 and have provided an innumerable number of talks and technical papers. Indeciding what physics topics to cover here, we have chosen to give some priority tothose with the most citations. However, we also keep in mind that many citations aremade directly to the Particle Data Group (PDG) (4) listings, and that more recentpapers have had less time to be cited.
2. BEGINNINGS
The history of the development of high-energy physics in China is fascinating andis detailed in “Panofsky on Physics, Politics and Peace” (5) by Wolfgang K. H.Panofsky. In 1973, China had decided to build a 50 GeV proton accelerator near theMing Tombs outside Beijing. Panofsky was critical of this proposal since the machinewould be expensive and have less energy than similar machines in the US and Europe.He advised “that an electron-positron collider would be a much better initial venturefor China, because such a machine could serve a dual purpose of serving the economyby being a facility for synchrotron radiation, while at the same time allowing them • Physics Accomplishments of the BES Experiments 3 o enter a field that was just beginning to be explored in the West.”Following much consultation, the Chinese government agreed to sponsor the con-struction of the Beijing Electron-Positron Collider at IHEP. This involved collab-oration with the Stanford Linear Accelerator Center (SLAC). The Chinese sent adelegation of about 30 engineers and physicists to SLAC in 1982 to make the pre-liminary design of the machine. Subsequently, the Chinese authorized constructionof the BEPC, and cooperation with SLAC continued. Deng Xiaoping personallywielded a shovel at the groundbreaking ceremony on Oct. 7, 1984 and returned toIHEP on Oct. 24, 1988 to celebrate the completion of BEPC. Important dates aresummarized in Table 1.
Joint Committee of Cooperation in High-Energy Physics
In 1979, President Jimmy Carter and Chairman Deng Xiaoping signed the United States-China Agreementon Cooperation in Science and Technology. The first protocol under this agreement was in high-energyphysics, and a Joint Committee of Cooperation in High-Energy Physics (JCCHEP) has met annually since.In 2004, it celebrated its 25th anniversary. Panofsky and T. D. Lee, who had both participated since 1979and made valuable contributions, attended.
3. THE BES EXPERIMENTS
The Beijing Electron-Positron Collider, BEPC (6), originally operated from 1988until 1995; it was then upgraded, increasing the reliability of the machine and ap-proximately doubling its luminosity. The upgraded BEPC ran from 1998-2004, whena major upgrade to BEPCII was started. BEPCII is a two ring collider with 93bunches and currents of up to 0.91 A in each ring, and a design luminosity of 1 × cm − s − (7). Some parameters of the colliders are given in Table 2.The configurations of the BES detectors are similar, although the subsystemsthemselves are often quite different. For all three, the innermost subsystem is com-posed of drift chamber(s) to determine the momenta and trajectories of chargedparticles in the magnetic field. Next are time of flight (TOF) counters to determinetheir velocities, followed by electromagnetic shower counters to measure the energiesof photons and identify electrons. Outside the electromagnetic shower counter is thecoil of the magnet with the flux return instrumented with detectors to identify muonsby their penetration through the iron.BESI had a central drift chamber (CDC) surrounded by the main drift chamber(MDC). Its electromagnetic calorimeter was composed of self quenching streamertubes interleaved with lead. Details of BESI may be found in Ref. (8). BESI op-erated from 1989 until 1995, when it was upgraded to BESII, and BEPC was alsoupgraded. The upgrade replaced the CDC with a revamped MARKII vertex detectorand replaced the MDC and the barrel TOF system. BESII operated from 1998 until2004. Details on BESII may be found in Ref. (9).The current detector is BESIII, which is a new detector with a single small-celled,helium-based MDC, a plastic scintillator TOF system, a CsI(Tl) electromagneticcalorimeter, a 1.0 T superconducting magnet, and a muon counter with 9 resistive able 1 Timeline Dates Exp. Item1979 First meeting of JCCHEP1981 T.D. Lee and Panofsky suggest e + e − collider1982 Deng Xiaoping endorses e + e − collider4/24/1984 BEPC project officially approved10/7/1984 Ground breaking (Deng Xiaoping wields shovel)10/16/1988 First collisions in BEPC10/24/1988 Inaugural celebration; Deng Xiaoping attendsMay 1989 BESI BESI detector moves to interaction region6/22/1989 BESI J/ψ peak observed in BESIJan. 1990 BESI Data taking at
J/ψ beginsMay 1991 BESI 10 M
J/ψ events accumulated1991 BESI American scientists join; BESI becomes internationalNov. 1991 - Jan. 1992 BESI τ threshold scan1992 BESI Improved τ mass measurement announcedJan. 1992 - May 1993 BESI D s runs (10 pb − )1993 - 1995 BESI 4 M ψ (2 S ) accumulated1998 - 1999 BESII R -scan from 2 - 5 GeVNov. 1999 - May 2001 BESII 51 M J/ψ accumulatedNov. 2001 - Mar. 2002 BESII 14 M ψ (2 S ) accumulated2/14/2003 BEPCII approved4/30/2004 BEPC shuts down and upgrade begins6/5/2005 First BESIII Collaboration Meeting4/30/2008 BESIII BESIII moves to interaction region7/18/2008 BESIII First hadron events recorded4/14/2009 BESIII 106 M ψ (2 S ) events accumulated7/28/2009 BESIII 225 M J/ψ events accumulated6/27/2010 BESIII 0.975 fb − accumulated at ψ (3770)5/3/2011 BESIII 2.9 fb − accumulated at ψ (3770)3/31/2012 BESIII 0.45 B ψ (2 S ) events accumulated5/26/2012 BESIII 1.3 B J/ψ events accumulatedDec. 2012 - June 2013 BESIII initial
XY Z runningFeb. 2014 - May 2014 BESIII subsequent
XY Z runningDec. 2014 - Apr. 2015 BESIII R -scan from 2 - 3 GeV Table 2 Some BEPC and BEPCII parameters
Parameter BEPC Upgrade BEPCIIBeam energy (GeV) 1.1 - 2.7 1.0 - 2.8 1.0 - 2.3Design luminosity ( × ) (cm − s − ) 0 . × ) (cm − s − ) 0 .
007 0049 0 . • Physics Accomplishments of the BES Experiments 5 late chamber (RPC) layers in the barrel part and 8 in the end-cap portions in-terleaved in the steel of the flux return yoke. Details of BESIII may be found inRef. (10). Figure 2 shows a schematic view of the BESIII detector, and some detailson all three detectors are summarized in Table 3.
Be beampipe SC magnetMuonCounterDriftChamber CsI(Tl) calorimeterTOF
Figure 2
Schematic of BESIII detector. Shown are the beryllium beam pipe, main drift chamber,barrel and end-cap TOF counters, the barrel and end-cap CsI(Tl) electromagneticcalorimeters, the 1 T superconducting magnet, and the muon resistive plate chambersembedded in the magnet return yoke iron. The outer radius of the main drift chamber is0.81 m. τ MASS MEASUREMENTS
In the early 1990’s, the τ lepton appeared to violate the Standard Model. Accordingto theory, the τ lifetime ( τ τ ), τ mass ( m τ ), electronic branching fraction ( B ( τ → eν ¯ ν )) and weak coupling constant g τ are related to one another according to: B ( τ → eν ¯ ν ) τ τ = g τ m τ π , (1)up to small radiative and electroweak corrections (11). However, this relation ap-peared to be badly violated, and BES/BEPC was in an excellent position to measurethe τ lepton mass, one of the fundamental parameters of the Standard Model.In spring 1992, the BES collaboration, composed then of more than 100 Chinesephysicists from IHEP and about 40 American physicists, measured the mass to be1776 . +0 . − . ± . c by an energy scan over the τ production threshold using thereaction e + + e − → τ + τ − → e + ν e ¯ ν τ µ − ¯ ν µ ν τ (12). Approximately 5 pb − of data,distributed over 12 scan points, was collected. The mass was lower than the worldaverage value at that time by 7.2 MeV/ c , had improved precision by a factor of 7, able 3 Some BES detector parameters. Sub-system Parameter BESI BESII BESIIIBeam pipe Material Al BeMDC σ p /p @ 1 GeV/ c σ dE/dx c TOF-barrel σ t
330 ps 180 ps 80 psTOF-end-cap σ t ND ND 110 psEMC-barrel Construction Str. tubes/Pb Str. tubes/Pb CsI(Tl) σ E /E @ 1 GeV 24% 21% 2.5% σ pos (cm) 3.0 ND 0.6EMC-end-cap Construction Str. tubes/Pb Str. tubes/Pb CsI(Tl) σ E /E @ 1 GeV 21% 21% 5% σ pos (cm) 2.3 2.3 0.9Magnet Type conventional conventional superconductingField (T) 0.4 0.4 1Muon-barrel σ pos (cm) 6 6 2Muon-end-cap and greatly improved agreement with the Standard Model. This measurement waslater updated to be 1776 . +0 . . − . − . MeV/ c with more τ decay channels (13).The new BESIII detector and BEPCII accelerator called for an improved τ massmeasurement. A study was carried out before starting a new energy scan to optimizethe number and choice of scan points in order to provide the highest precision for agiven integrated luminosity (14). Beam Energy Measurement System
Extremely important in the threshold scan is to precisely determine the beam energy and the beam energyspread. For this, the beam energy measurement system (BEMS) (15) for BEPCII was used. Photons from aCO laser are collided head on with either the electron or the positron beam, and the maximum energies ofthe back scattered Compton photons are measured with high accuracy by a High Purity Germanium (HPGe)detector, whose energy scale is calibrated with photons from radioactive sources. The beam energies can bedetermined by the kinematics of Compton scattering (16).The τ scan experiment was done in December 2011. For energy calibration pur-poses, the J/ψ and ψ (cid:48) resonances were each scanned at seven energy points. About 24pb − of data, distributed over four scan points near τ pair production threshold, wascollected. The first point was below the mass of τ pairs, while the other three wereabove. However, running conditions were not optimal, so the running was stoppedbefore collecting the full data set. • Physics Accomplishments of the BES Experiments 7 o reduce the statistical error in the τ lepton mass, the analysis included 13 τ pair final states decaying into two charged particles ( ee , eµ , eπ , eK , µµ , µπ , µK , πK , ππ , KK , eρ , µρ and πρ ) plus accompanying neutrinos to satisfy lepton conservation.By a fit to the τ pair cross section data near threshold, shown in the left plot ofFig. 3, the mass of the τ lepton was determined to be (17): m τ = (1776 . ± . +0 . − . ) MeV /c . (2)The right plot of Fig. 3 shows the comparison of this result with values from thePDG; it is consistent with all of them, but has the smallest uncertainty. With thefull τ scan data set, BESIII should be able to do even better. σ i ¼ N i R data = MC ϵ i L i : ð Þ The measured cross sections at different scan points areconsistent with the theoretical values. In Fig. 6 (right plot),the dependence of ln L on m τ is almost symmetric as aconsequence of the large data sample obtained.
3. Systematic error estimation
Theoretical accuracy. — The systematic error associatedwith the theoretical τ pair production cross section isestimated by comparing the difference of the fitted m τ between two cases; in one case, the old τ pair productioncross- section formulas are used, in the other, the improvedversion formulas are used. The uncertainty due to this effectis at the level of − MeV =c . More details can be foundin Ref. [29]. Energy scale. — The m τ shift, Δ τ M ¼ð . $ . ð stat Þ $ . ð syst ÞÞ MeV =c [Eq. (12)] is taken as a systematic error.Combining statistical and systematic errors, two boundariescan be established: Δ m low τ ¼ . − . ¼ . MeV =c and Δ m high τ ¼ . þ . ¼ . MeV =c . We take thehigher value to form a negative systematic error and the lowervalue the positive systematic error. The systematic errors onthe m τ from this source are Δ m − τ ¼ . MeV =c and Δ m þ τ ¼ . MeV =c . Energy spread. — From Table II, δ BEMS w at the τ scan energypoints is determined from the BEMS to be ð . $ . Þ MeV. If we assume quadratic dependence of δ w on energy, we can also extrapolate the J= ψ and ψ energyspreads to the τ region, which yields δ w ¼ ð . $ . Þ MeV. The difference of energy spreads obtainedfrom these two methods is taken as a systematic uncer-tainty. The largest contribution to the energy spreaduncertainty comes from interference effects. Includinginterference, the difference between the extrapolated valueand the BEMS measurement is 0.056 MeV, and the overallsystematic error is taken as 0.057 MeV. The final energy spread at the τ scan energy points is ð . $ . $ . Þ MeV. The uncertainty of m τ from this item isestimated by refitting the data when the energy spread isset at its $ σ values, and the shifted value of the fitted m τ , $ . MeV =c , is taken as the systematic error.Table VII lists the fitted results with different energyspread values. Luminosity. — Both the Bhabha and the two-gamma lumi-nosities are used in fitting the τ mass, and the difference offitted τ masses is taken as the systematic error due touncertainty in the luminosity determination. The differenceis . MeV =c .The τ mass shift [Eq. (12)] is . MeV =c whendetermined with two-gamma luminosities. If Bhabha lumi-nosities are used instead, the mass shift is . MeV =c ,and the difference, . MeV =c , is also taken as a sys-tematical error due to the luminosity. The total systematicaluncertainty from luminosity determination is . MeV =c . Number of good photons. — It is required that there are noextra good photons in our final states. Bhabha events areselected as a control sample to study the efficiency differ-ence between data and MC of this requirement. Theefficiency for data is ð . $ . Þ % , and the efficiencyfor the MC simulation is ð . $ . Þ % , where the errorsare statistical. Correcting the number of observed eventsfrom data for the efficiency difference, we refit the τ mass,and the change of τ mass is . MeV =c , which is takenas the systematic uncertainty for this requirement. W (MeV) C r o ss S e c t i on ( nb ) ) (MeV/c τ m ) m a x l n ( L / L -2.0-1.5-1.0-0.50.0 FIG. 6. (left) The c.m. energy dependence of the τ pair cross section resulting from the likelihood fit (curve), compared to the data(Poisson errors), and (right) the dependence of the logarithm of the likelihood function on m τ , with the efficiency and backgroundparameters fixed at their most likely values. TABLE VII. The τ mass determined from fits with differentenergy spreads. δ BEMS w (MeV) τ mass (MeV =c )1.383 . þ . − . . þ . − . . þ . − . PRECISION MEASUREMENT OF THE MASS OF THE τ … PHYSICAL REVIEW D
CM Energy (MeV) C r o ss S ec t i o n ( nb ) σ i ¼ N i R data = MC ϵ i L i : ð Þ The measured cross sections at different scan points areconsistent with the theoretical values. In Fig. 6 (right plot),the dependence of ln L on m τ is almost symmetric as aconsequence of the large data sample obtained.
3. Systematic error estimation
Theoretical accuracy. — The systematic error associatedwith the theoretical τ pair production cross section isestimated by comparing the difference of the fitted m τ between two cases; in one case, the old τ pair productioncross- section formulas are used, in the other, the improvedversion formulas are used. The uncertainty due to this effectis at the level of − MeV =c . More details can be foundin Ref. [29]. Energy scale. — The m τ shift, Δ τ M ¼ð . $ . ð stat Þ $ . ð syst ÞÞ MeV =c [Eq. (12)] is taken as a systematic error.Combining statistical and systematic errors, two boundariescan be established: Δ m low τ ¼ . − . ¼ . MeV =c and Δ m high τ ¼ . þ . ¼ . MeV =c . We take thehigher value to form a negative systematic error and the lowervalue the positive systematic error. The systematic errors onthe m τ from this source are Δ m − τ ¼ . MeV =c and Δ m þ τ ¼ . MeV =c . Energy spread. — From Table II, δ BEMS w at the τ scan energypoints is determined from the BEMS to be ð . $ . Þ MeV. If we assume quadratic dependence of δ w on energy, we can also extrapolate the J= ψ and ψ energyspreads to the τ region, which yields δ w ¼ ð . $ . Þ MeV. The difference of energy spreads obtainedfrom these two methods is taken as a systematic uncer-tainty. The largest contribution to the energy spreaduncertainty comes from interference effects. Includinginterference, the difference between the extrapolated valueand the BEMS measurement is 0.056 MeV, and the overallsystematic error is taken as 0.057 MeV. The final energy spread at the τ scan energy points is ð . $ . $ . Þ MeV. The uncertainty of m τ from this item isestimated by refitting the data when the energy spread isset at its $ σ values, and the shifted value of the fitted m τ , $ . MeV =c , is taken as the systematic error.Table VII lists the fitted results with different energyspread values. Luminosity. — Both the Bhabha and the two-gamma lumi-nosities are used in fitting the τ mass, and the difference offitted τ masses is taken as the systematic error due touncertainty in the luminosity determination. The differenceis . MeV =c .The τ mass shift [Eq. (12)] is . MeV =c whendetermined with two-gamma luminosities. If Bhabha lumi-nosities are used instead, the mass shift is . MeV =c ,and the difference, . MeV =c , is also taken as a sys-tematical error due to the luminosity. The total systematicaluncertainty from luminosity determination is . MeV =c . Number of good photons. — It is required that there are noextra good photons in our final states. Bhabha events areselected as a control sample to study the efficiency differ-ence between data and MC of this requirement. Theefficiency for data is ð . $ . Þ % , and the efficiencyfor the MC simulation is ð . $ . Þ % , where the errorsare statistical. Correcting the number of observed eventsfrom data for the efficiency difference, we refit the τ mass,and the change of τ mass is . MeV =c , which is takenas the systematic uncertainty for this requirement. W (MeV) C r o ss S e c t i on ( nb ) ) (MeV/c τ m ) m a x l n ( L / L -2.0-1.5-1.0-0.50.0 FIG. 6. (left) The c.m. energy dependence of the τ pair cross section resulting from the likelihood fit (curve), compared to the data(Poisson errors), and (right) the dependence of the logarithm of the likelihood function on m τ , with the efficiency and backgroundparameters fixed at their most likely values. TABLE VII. The τ mass determined from fits with differentenergy spreads. δ BEMS w (MeV) τ mass (MeV =c )1.383 . þ . − . . þ . − . . þ . − . PRECISION MEASUREMENT OF THE MASS OF THE τ … PHYSICAL REVIEW D
CM Energy (MeV) C r o ss S ec t i o n ( nb ) mass (MeV) τ This workPDG12BABARKEDRBELLOPALCLEOBESII (96’)ARGUS +0.144-0.169 +0.160-0.160 +0.430-0.430 +0.300-0.280 +0.380-0.380 +1.900-1.900 +1.500-1.500 +0.310-0.280 +2.800-2.800
Figure 3 (Left plot) Cross section versus e + e CM energy. Cross section measurements are shown witherror bars; the smooth curve is the fit. (Right plot) Comparison of the measured ⌧ mass withthose from the PDG (17). The green band corresponds to the 1 limit of the BESIIImeasurement. Modified from Reference (16) with permission. Lepton Universality
A precision m ⌧ measurement is also required to check lepton universality. Lepton universality, a basicingredient in the minimal Standard Model, requires that the charged-current gauge coupling strengths forthe electron, muon, and tau leptons, g e , g µ , g ⌧ , should be identical: g e = g µ = g ⌧ . Lepton universalityimplies: ✓ g ⌧ g µ ◆ = ⌧ µ ⌧ ⌧ ⇣ m µ m ⌧ ⌘ B ( ⌧ ! e⌫ ¯ ⌫ ) B ( µ ! e⌫ ¯ ⌫ ) (1 + F W )(1 + F ) = 1 , (3)where F W and F are the weak and electromagnetic radiative corrections (10). Note ( g ⌧ /g µ ) depends on m ⌧ to the fifth power.Inserting the ⌧ mass value into Eq. 3, together with the values of ⌧ µ , ⌧ ⌧ , m µ , m ⌧ , B ( ⌧ ! e⌫ ¯ ⌫ ) and B ( µ ! e⌫ ¯ ⌫ ) from the PDG (17) and using the values of F W (-0.0003) and F (0.0001)) calculated fromreference (10), the ratio of squared coupling constants is determined to be: ✓ g ⌧ g µ ◆ = 1 . ± . , (4)which is consistent with unity.
5. R SCAN
The big news of 2012 was the discovery of the Higgs particle, the capstone of the StandardModel, at the Large Hadron Collider (LHC) at CERN in Geneva, Switzerland. However,before the discovery, fits in the Standard Model were able to predict its mass, becausehigher order terms in the model can include a massive virtual particle, such as the Higgs.Surprisingly, important in this fit is R scan data.Among the three input parameters generally used in global fits to electroweak data, Tau Mass (MeV/c ) Figure 3 (Left plot) Cross section versus e + e − CM energy. Cross section measurements are shownwith error bars; the smooth curve is the fit. (Right plot) Comparison of the measured τ mass with those from the PDG (4). The green band corresponds to the 1 σ limit of theBESIII measurement. Modified from Reference (17) with permission.
5. R SCAN
The big news of 2012 was the discovery of the Higgs particle, the capstone of the Stan-dard Model, at the Large Hadron Collider (LHC) at CERN in Geneva, Switzerland.However, before the discovery, fits in the Standard Model were able to predict itsmass, because higher order terms in the model can include a massive virtual particle,such as the Higgs. Surprisingly, important in this fit is R scan data.Among the three input parameters generally used in global fits to electroweakdata, the QED running coupling constant evaluated at the mass of the Z boson, epton Universality A precision m τ measurement is also required to check lepton universality. Lepton universality, a basicingredient in the minimal Standard Model, requires that the charged-current gauge coupling strengths forthe electron, muon, and tau leptons, g e , g µ , g τ , should be identical: g e = g µ = g τ . Lepton universalityimplies: (cid:18) g τ g µ (cid:19) = τ µ τ τ (cid:16) m µ m τ (cid:17) B ( τ → eν ¯ ν ) B ( µ → eν ¯ ν ) (1 + F W )(1 + F γ ) = 1 , (3)where F W and F γ are the weak and electromagnetic radiative corrections (11). Note ( g τ /g µ ) depends on m τ to the fifth power.Inserting the τ mass value into Eq. 3, together with the values of τ µ , τ τ , m µ , m τ , B ( τ → eν ¯ ν ) and B ( µ → eν ¯ ν ) from the PDG (4) and using the values of F W (-0.0003) and F γ (0.0001)) calculated fromreference (11), the ratio of squared coupling constants is determined to be: (cid:18) g τ g µ (cid:19) = 1 . ± . , (4)which is consistent with unity. α ( M Z ), has the largest experimental uncertainty. While its value at low energy, α (0), is known precisely, the correction necessary to determine its value at highenergy, α ( M Z ), cannot be reliably calculated theoretically. Instead, experimentallymeasured R values are used with the application of dispersion relations (18).Uncertainties in the values of R limit the precision of α ( M Z ), which in turnlimits the precision of the determination of the Higgs mass (19, 20, 21). Before themeasurement by BESII, the uncertainty in α ( M Z ) was dominated by the errors ofthe values of R in the CM energy range below 5 GeV. These were measured about20 years earlier with a precision of about 15 ∼
20% and accounted for about 50%of the uncertainty in α ( M Z ) (22). With these R values, the best fit value for theHiggs’ mass was M H = 62 +53 − GeV/ c (22), which was about one standard deviationbelow the lower limit of M H >
114 GeV/ c coming from experiments at the CERNLarge Electron Positron (LEP) collider (23). However, the calculated result was verysensitive to the value used for α ( M Z ). Clearly, a more precise determination α ( M Z )was very important.In 1998 and 1999, R value measurements were made at 91 energy points (24, 25)between 2 and 5 GeV by BESII. The BESII R values are displayed in Fig. 1 alongwith those from other experiments. BESII systematic uncertainties are between 6and 10 % with an average uncertainty of 6.6 % and are a factor of two to threeimprovement in precision in the 2 to 5 GeV energy region. Ref. (25) is the secondmost highly cited BES paper with 289 citations through the end of 2015.The importance of these results has been emphasized by Burkhardt andPietryzk (26). With the new BES R -values, they obtained a value for α − ( M Z ) =128 . ± . • Physics Accomplishments of the BES Experiments 9 roweak Group found that this result shifted the central value for the Higgs massupward to M H = 98 GeV/ c , which was in better agreement with the LEP lowerlimits. The measured mass from the LHC of the Higgs boson is 125 GeV/ c (4).In 2004, large-statistics data samples were accumulated by BESII at CM ener-gies of 2.60, 3.07 and 3.65 GeV; the total integrated luminosity was 10.0 pb − (2).Improvements in the event selection, luminosity measurement, and the use of aGEANT3-based (27, 28) simulation were made in order to decrease the systematicerrors. With these improvements, the errors on the new measured R values werereduced to about 3 . R -values are also shown in Fig. 1.BESIII has also made R scans. In 2014, a fine scan of 104 energy points throughthe resonance region above 3.8 GeV was done. The total data accumulated was 0.8fb − , which will be used to determine R , study XY Z particles, study the Λ c , etc.In 2015, 20 points were scanned in the continuum region from 2.0 GeV to 3.1 GeV.These data will be used to determine R , determine baryon form factors, and studybaryon threshold behavior. Stay tuned for the results.
6. LIGHT QUARK PHYSICS
The study of light quark mesons and baryons (mesons and baryons composed ofup, down, and strange quarks) has been a major aspect of each incarnation of theBES experiment. Charmonium states, such as the
J/ψ , decay to hundreds of differentcombinations of light quark hadrons, like π + π − π , K + K − π + π − , and γπ π , to namejust a few. This provides many opportunities to identify intermediate “resonances”in the decay sequences. For example, in the decay J/ψ → γπ π , one can search forthe intermediate process J/ψ → γf (1710), with the f (1710) subsequently decayingto π π , and thereby learn about the f (1710) isoscalar state (discussed below).Furthermore, since the quantum numbers of the initial charmonium state are known,conservation rules can be used to derive amplitudes describing the behavior of thedecay products under different assumptions about their quantum numbers. Thesequantum mechanical amplitudes can be added coherently and then squared, leadingto distributions that can be fit to data. Comparing fits, and comparing the strengthsof different amplitudes within the fits, one can then distinguish between differenthypotheses about the quantum numbers of the final state. This process, referred toas partial wave analysis (PWA), is an important aspect of the light quark physicsprogram at BES. ISOSPIN:
Aquantum numberdescribing theconfiguration of upand down quarkswithin a hadron.
ISOSCALAR:
Ahadron with zerounits of isospin.
Since the e + e − → J/ψ cross section is so large, and since the
J/ψ decays predom-inantly to light quark states, the
J/ψ is the charmonium state most often used byBES to study light quark mesons and baryons. Thus, within the collaboration, “lightquark physics” is almost synonymous with “
J/ψ physics.” From BESI to BESIII, thesize of the
J/ψ data set has grown over two orders of magnitude. BESI collected asample of 8.6 million
J/ψ decays; BESII collected 58 million; and BESIII took aninitial sample of 225 million (in 2009), and subsequently increased it to 1.3 billion
J/ψ decays (in 2012).The following sections include a few high-profile examples of how light quarkmesons and baryons have been studied in
J/ψ decays at BES. But it should be notedthat there are other interesting physics topics not discussed here, such as the physicsof η and η (cid:48) decays (which can be produced cleanly in J/ψ decays).
10 R. A. Briere, F. A. Harris and R. E. Mitchell esons and Baryons
Hadrons, or particles that interact via the strong force, are broadly classified by their total spin. Mesons haveintegral spin; baryons have fractional spin. The majority of mesons that have been discovered can be neatlydescribed using a model in which they are composed of a quark and an antiquark. Similarly, most baryonscan be successfully described as composites of three quarks. The exceptions are particularly interesting sincethey could represent novel configurations of matter, such as four-quark mesons (tetraquarks), or five-quarkbaryons (pentaquarks). Configurations such as these are allowed in QCD, but their properties are a subjectof intense experimental investigation.
One of the most high-profile aspects of light quark spectroscopy at BES is the searchfor glueballs in radiative
J/ψ decays. Glueballs are states composed of gluons (con-taining no valence quarks) and their existence is a prominent prediction of QCD (29).Their identification requires comparing their rate of production in different environ-ments (30). They should not be heavily produced in γγ collisions, for example, sincethere is no coupling between photons and gluons. On the other hand, the productionof glueballs is expected to be enhanced in radiative J/ψ decays. In this process, thecharm or anti-charm quark of the
J/ψ first radiates a photon, leaving the charmand anti-charm quark pair to subsequently annihilate into two gluons, which thenhadronize. Such a “glue-rich” environment is expected to be favorable for glueballproduction.A lot of attention was garnered at BESI (31) (and other contemporaneous ex-periments) for the apparent confirmation of a spin-2 glueball candidate, the ξ (2230),first reported by MARKIII (32). It was seen to appear in many J/ψ radiative decays,including γπ + π − (4.6 σ evidence), γK + K − (4.1 σ evidence), γK S K S (4.0 σ evidence),and γp ¯ p (3.8 σ evidence). It had several properties that made it an ideal glueballcandidate: its mass was consistent with the mass expected for the tensor glueball; itdecayed in a “flavor-symmetric” pattern; it was anomalously narrow. Unfortunately,this state was not subsequently confirmed by the BESII or BESIII collaborations, andit appears to have been an extremely unlucky fluctuation. Since that time, there hasbeen no observed state whose properties have made it such an appealing candidatefor a glueball state.The most promising place to look for glueballs is currently in the isoscalar spec-trum, where there is an overpopulation of reported states. If all mesons were com-posed of a quark and anti-quark, there would be two isoscalar states, one a mixtureof up and down quarks (the n ¯ n state) and one composed of strange quarks (the s ¯ s state). Instead, three states are seen, namely the f (1370), f (1500), and f (1710).This could indicate that one of these states is a glueball. Unfortunately, mixing isalso allowed among these states, complicating this picture (33). Thus, the f (1500),say, could be partly n ¯ n and partly glueball, and so on. BES has added a tremendousamount of information related to this problem, a sampling of which is included below.Even so, a final solution has yet to be found and work continues.The first major contribution of BES to the isoscalar problem was in the clarifica- • Physics Accomplishments of the BES Experiments 11 ion of the spin of the f (1710). This state, discovered by the Crystal Ball experimentin 1982 (34), was initially thought to be spin-2. BESI observed the f (1710) producedprominently in the reaction J/ψ → γK + K − (35). Analyzing its decay to K + K − ,BESI reported that, instead of being purely spin-2, it was actually a mixture of spin-0and spin-2. Later, with the increase of J/ψ decays between BESI and BESII, BESIIwas able to do a reanalysis of the
J/ψ → γK + K − reaction, also adding the related J/ψ → γK S K S process (36). With the much increased statistics, the f (1710) wasconclusively identified as spin-0, agreeing with other contemporaneous experiments,and now the accepted value. The results of this analysis are shown in the left panelof Figure 4. The J/ψ → γK ¯ K channel is still being analyzed at BESIII.Another major contribution from BES was the analysis of J/ψ → γππ . This wasfirst performed at BESI with low statistics (37), but later studied more conclusivelyat BESII, using both π π and π + π − (38). Here, both the f (1500) and f (1710)were seen (see the middle panel of Figure 4). This allowed a number of conclusionsto be drawn. First, since the f (1500) was not seen in J/ψ → γK ¯ K its decay to K ¯ K must be significantly smaller than its decay to ππ . Second, the rate of production ofthe f (1710) could also be compared to the previous K ¯ K analyses. From this, theratio B ( f (1710) → ππ ) /B ( f (1710) → K ¯ K ) could be derived to be 0 . +0 . − . . Thisremains the best measurement of this branching ratio. Since the f (1500) decaysmore often to ππ than K ¯ K it is more likely to be the n ¯ n state than the s ¯ s state.And conversely, the f (1710) is more likely to be the s ¯ s state.In principle, these isoscalar states could also be studied by looking at how theyare produced alongside the ω and φ in the four reactions J/ψ → ωK + K − , ωπ + π − , φK + K − , and φπ + π − . Since the φ is an s ¯ s state, it is expected, for example, thatthe f (1710) is more likely to be produced alongside it than the ω , which is an n ¯ n isovector. All four reactions were studied at BESII (39, 40, 41), but surprisingly,the opposite was found. While B ( J/ψ → φf (1710)) × B ( f (1710) → K + K − ) wasmeasured to be (2 . ± . × − , B ( J/ψ → ωf (1710)) × B ( f (1710) → K + K − )was measured to be (6 . ± . × − , about three times larger. The explanation forthis is still unknown. Furthermore, comparing B ( J/ψ → ωf (1710)) × B ( f (1710) → K + K − ) with B ( J/ψ → ωf (1710)) × B ( f (1710) → π + π − ) led to an upper limit on B ( f (1710) → ππ ) /B ( f (1710) → K ¯ K ) of 0 .
11, apparently in contradiction with thefinding from radiative decays.These inconsistencies possibly point towards the need for more global analyseswith higher statistics. At BESIII, with 1.3 billion
J/ψ decays, this effort has justbegun. The
J/ψ → γπ π channel, for example, was recently reanalyzed with thefull J/ψ data set (42). As a first step, rather than impose a resonant interpretationon the data, the π π mass spectrum was divided, bin-by-bin, into spin-0 and spin-2components. The spin-0 components are shown in the right panel of Figure 4, andthe shape is seen to be consistent with the BESII results. It is hoped that presentingthe data in this way will encourage new ideas on how to parameterize the data. Theseparameterizations can later be used to refit the data directly. KK , ππ and Kπ scattering The details of S-wave KK , ππ and Kπ scattering are beyond the scope of thisreview, but it should be mentioned that BESII has performed definitive work in thisimportant area. This has led to a more thorough understanding of the f (980), the
12 R. A. Briere, F. A. Harris and R. E. Mitchell
B. Global fit analysis
We now turn to the global fit to the J / ! → " K ! K " and J / ! → " K S K S data. Each sample is analyzed independently,and the fit results shown below are for their averaged values.This fit has the merit of constraining phase variations as afunction of mass to simple Breit-Wigner forms. It also per-forms the optimum averaging of helicity amplitudes andtheir phases over resonances. Partial waves are fitted to thedata for the same components described in the bin-by-bin fit.The broad 0 !! component improves the fit significantly;removing it causes the log likelihood value to become worseby 221. For the f (1270) and f (1500), we use PDG valuesof masses and widths, but allow the amplitudes to vary in thefit. For the f ! (1525), relative phases are consistent with zerowithin experimental errors. It is expected theoretically thatrelative phases should be very small, on order of ! J / ! → " ! ! . In view ofthe agreement with expectation, these relative phases are setto zero in the final fit, so as to constrain intensities further.A free fit to f ! (1525) gives a fitted mass of 1519 f (1710) are M $ $ $ " ! MeV, re-spectively. The fitted intensities are illustrated in Fig. 4. Forthe f ! (1525), we find the ratios of helicity amplitudes x $ y $ ! contribution under the f ! (1525) peak, while previousanalyses by DM2 and Mark III % & ignored the small 0 ! contributions. The branching fractions of the f ! (1525) andthe f (1710) determined by the global fit are B % J / ! → " f ! (1525) → " KK¯ & $ (3.42 % " and B % J / ! → " f (1710) → " KK¯ & $ (9.62 % " respectively.The errors shown here are also statistical. An alternative fit to f J (1710) with J P $ ! is worse by 258 in log likelihoodrelative to 0 ! for " K ! K " data and by 67 for " K S K S . Re-membering that three helicity amplitudes are fitted for spin 2but only one for spin 0, the fit with J P $ ! is preferred by & ’ after considering the two data samples together.The separation between spin 0 and 2 is illustrated in Fig.5, taking the J / ! → " K ! K " data as the example. Let usdenote the polar angle of the kaon in the KK¯ rest frame by ( K , and the polar angle of the photon in the J / ! rest frameby ( " . The data are fitted simultaneously including impor-tant correlations between ( K and ( " . The left panels showresulting fits to cos ( K for J $ ! , but the interference with the tail of f ! (1525) hasa large effect. The right panels show the fits to cos ( " ; theoptimum fit is visibly better for J $ J $ ) If onefits only the cos ( " distribution, it is possible to fit equallywell with J $ ( K gets muchworse. * If the f (1500) is removed from the fit, the log likelihoodis worse by 1.65 ) * for K ! K " ( K S K S ), corresponding toabout 1.3 ’ (2.2 ’ ). If the f (1270) is removed, the likeli-hood is worse by 57.5 ) * for K ! K " ( K S K S ), corre-sponding to & ’ (3.8 ’ ). V. SYSTEMATIC ERROR
The systematic error for the global fit is estimated byadding or removing small components used in the fit, replac- E V E N T S / . G e V ++ M(K + K - ) (GeV) ++ E V E N T S / . G e V ++ M(K S K S ) (GeV) ++ FIG. 4. The
KK¯ invariant mass distributions from J / ! → " K ! K " and J / ! → " K S K S . The points are the data and the fullhistograms in the top panels show the maximum likelihood fit. His-tograms on subsequent panels show the complete 0 ! and 2 ! con-tributions including all interferences. ++ . G e V / c < M ( K + K - ) < . G e V / c ++ cos θ Κ ++ cos θ γ ++ FIG. 5. Projections in cos ( K and cos ( " for 0 !! and 2 !! as-sumptions. The points are the data ( J / ! → " K ! K " sample * , and thehistograms are the global fit results.PARTIAL WAVE ANALYSES OF J / ! → " K ! K " AND " K S K S PHYSICAL REVIEW D , 052003 ) * M ( K + K ) GeV /c O b s e r v e d E v e n t s / M e V / c BES Collaboration / Physics Letters B 642 (2006) 441–448
J / ψ → π + π − . The crosses are data. The complete 0 ++ and 2 ++ contributions are also shown,including all interferences. with the masses and widths fixed to those in the PDG, to de-scribe the contribution of the high mass states in the mass rangebelow 2.0 GeV /c .For the 2 ++ states, relative phases between different helicityamplitudes for a single resonance are theoretically expected tobe very small [16]. Therefore, these relative phases are set tozero in the final fit so as to constrain the intensities further.After the mass and width optimization, the resulting fittedintensities are illustrated in Figs. 3 and 4. Angular distributionsin the whole mass range are shown in Fig. 5. Here, θ γ is thepolar angle of the photon in the J / ψ rest frame, and θ π is thepolar angle of the pion in the π + π − rest frame.From Figs. 3 and 5, we see that the fit agrees well with data.Fig. 4 shows the distributions of the individual componentsand full 0 ++ and 2 ++ contributions including interferences.A free fit to f ( ) gives a fitted mass of 1262 + − MeV /c and a width of 175 + − MeV /c . The fitted masses and widths ofthe f ( ) and f ( ) are M f ( ) = ± /c , Γ f ( ) = + − MeV /c and M f ( ) = + − MeV /c , Γ f ( ) = ± /c , respectively. The branchingfractions of f ( ) , f ( ) , and f ( ) determinedby the partial wave analysis fit are B (J / ψ → γ f ( ) → γ π + π − ) = ( . ± . ) × − , B (J / ψ → γ f ( ) → γ π + π − ) = ( . ± . ) × − , and B (J / ψ → γ f ( ) → γ π + π − ) = ( . ± . ) × − , respectively. For the f ( ) , we find the ratios of helicity amplitudes x = . ± .
02 and y = . ± .
02 with correlation factor ρ = . x = A /A , y = A /A , A , , correspond to the threeindependent production amplitudes with helicity 0, 1 and 2.The errors here are statistical errors. An alternative fit is triedby replacing f ( ) with a 2 ++ resonance. There are threehelicity amplitudes fitted for spin 2, while only one amplitude Fig. 5. Projections in cos θ γ and cos θ π for the whole mass range. The crossesare data ( J / ψ → γ π + π − sample), and the histograms are the fit results. for spin 0, which means the number of degrees of freedom is in-creased by 2 in the J P = + case. However, the log likelihoodis worse by 108. This indicates that f ( ) with J P = + isstrongly favored. If the f ( ) is removed from the fit, thelog likelihood is worse by 379, which corresponds to a signalsignificance much larger than 5 σ . M ( ⇡ + ⇡ ) GeV /c O b s e r v e d E v e n t s / M e V / c but have a degenerate ambiguous pair. A study of theseambiguities (Appendix B) shows consistency between themathematically predicted and experimentally determinedambiguities. Both ambiguous solutions are presented,because it is impossible to know which represent thephysical solutions without making some additional model dependent assumptions. If more than two solutions arefound in a given bin, all solutions within 1 unit of loglikelihood from the best solution are compared to thepredicted value derived from the best solution and only thatwhich matches the prediction is accepted as the ambiguouspartner. E v en t s / M e V / c ] ) [GeV/c π π Mass( E v en t s / M e V / c ] ) [GeV/c π π Mass( E v en t s / M e V / c ] ) [GeV/c π π Mass( E v en t s / M e V / c ] ) [GeV/c π π Mass( (a) 0 ++ (b) 2 ++ E1(c) 2 ++ M2(d) 2 ++ E3 FIG. 2 (color online). The intensities for the (a) þþ , (b) þþ E1, (c) þþ M2, and (d) þþ E3 amplitudes as a function of M π π for thenominal results. The solid black markers show the intensity calculated from one set of solutions, while the open red markers represent itsambiguous partner. Note that the intensity of the þþ E3 amplitude is redundant for the two ambiguous solutions (see Appendix B).Only statistical errors are presented.AMPLITUDE ANALYSIS OF THE π π SYSTEM … PHYSICAL REVIEW D M ( ⇡ ⇡ ) GeV /c C o rr ec t e d E v e n t s / M e V / c J/ ψ → γ K + K − at BESII J/ ψ → γπ + π − at BESII J/ ψ → γπ π at BESIII Figure 4
A few representative analyses of
J/ψ radiative decays at BES. (left) Analysis of
J/ψ → γK + K − at BESII (36). The points are data and the histogram shows the spin-0components of the fit to data. The peak around 1.7 GeV/ c is from the f (1710).(middle) Analysis of J/ψ → γπ + π − at BESII (38). The points are data and the histogramshows the spin-0 components of the fit to data. The peak just under 1.5 GeV/ c is due tothe f (1500), while the peak around 1.7 GeV/ c is from the f (1710). (right) Analysis of J/ψ → γπ π at BESIII (42). The points show the spin-0 components of the fits done ineach mass bin. The fits make no assumption about the mass-dependence of the amplitudes,but new complications are thereby introduced. The solid (black) and hollow (red) pointsare mathematically ambiguous solutions. Modified from References (36, 38, 42) withpermission. σ and the κ .The f (980) was seen prominently in the reaction J/ψ → φf (980), with the f (980) decaying to both π + π − and K + K − (39). Since the mass of the f (980) isclose to the K + K − threshold, its shape is distorted. This fact can be used to studythe coupling between the ππ and K ¯ K channels. A simultaneous fit to the f (980) inboth decay modes was performed; the resulting coupling parameters are often stillused today in experimental efforts to describe the f (980).The σ was studied in the channel J/ψ → ωπ + π − , where the σ is seen in the π + π − mass spectrum (40). Again, the shape used to describe the σ has had a majorinfluence on many subsequent analyses.Finally, the κ was studied in a very similar manner to the σ (41). It is seenprominently in the J/ψ → K ∗ ¯ Kπ + c.c. reaction, in the ¯ Kπ + c.c mass spectrum.The cleanliness of this channel allowed a definitive study of the κ . X (1835) The nature of the X (1835) state (or states) remains one of the biggest mysteriesin light quark physics at the BES experiments. The first observation was at BE-SII in J/ψ → γp ¯ p , where a large enhancement of events was seen around the p ¯ p threshold (43). The enhancement was unexpected and was the source of muchspeculation. This discovery paper remains the third most cited paper at BES.The enhancement was confirmed at BESIII, first using J/ψ decays coming from ψ (2 S ) → π + π − J/ψ (44), and then using 225 million directly-produced
J/ψ (45).This latter analysis also measured the spin-parity of the enhancement to be 0 − .In parallel to the p ¯ p analyses, another peak at around the same mass and with • Physics Accomplishments of the BES Experiments 13 with a Breit-Wigner (BW) function convolved with aGaussian mass resolution function (with ! !
13 MeV =c ) to represent the X " signal plus a smooth poly-nomial background function. The mass and width obtainedfrom the fit (shown in the bottom panel in Fig. 3) are M ! : $ : =c and ! ! : $ : = c . Thesignal yield from the fit is $ events with a con-fidence level 45.5% ( " = d : o : f : ! : = ) and % L ! : . A fit to the mass spectrum without a BW signalfunction returns % L ! : . The change in % L with " " d : o : f : corresponds to a statistical significanceof : ! for the signal.Using MC-determined selection efficiencies of 3.72%and 4.85% for the ! $ & $ % and ! %& modes,respectively, we determine a product BF of B ! J= ! % X " " ’ B ! X " ! $ & $ % " ! " : $ : % : The consistency between the two decay modes ischecked by fitting the distributions in Figs. 1(c) and 2(c)separately with the method described above. The fit toFig. 1(c) gives M ! : $ : =c and ! ! : $ : = c with a statistical significance of : ! . From the $ signal events obtained from thefit, the product BF is B ! J= ! % X " " ’ B ! X " ! $ & $ % " ! " : $ : % . Similar results are ob- tained if we apply only a 4C kinematic fit in this analysis.For the fit to Fig. 2(c), the mass and width are determinedto be M ! : $ : =c and ! ! : $ : = c with a statistical significance of 6.0 ! .For this mode alone, the signal yield of $ sig-nal events corresponds to B ! J= ! % X " " ’ B ! X " ! $ & $ % " ! " : $ : % . The X " mass, width, and product BF values determinedfrom the two decay modes separately are in goodagreement with each other.The systematic uncertainties on the mass and width aredetermined by varying the functional form used to repre-sent the background, the fitting range of the mass spectrum,the mass calibration, and possible biases due to the fittingprocedure. The latter are estimated from differences be-tween the input and output mass and width values from MCstudies. The total systematic errors on the mass and widthare : and : =c , respectively. The systematic erroron the branching fraction measurement comes mainly fromthe uncertainties of MDC simulation (including systematicuncertainties of the tracking efficiency and the kinematicfits), the photon detection efficiency, the particle identifi-cation efficiency, the decay branching fractions to $ & $ % and %& , the background function parametrization,the fitting range of the mass spectrum, the requirements onnumbers of photons, the invariant-mass distributions of %% pairs in the two analyses, the $ & $ % invariant-mass distri-bution in ! %$ & $ % decays, MC statistics, the totalnumber of J= events [15], and the unknown spin-parity ofthe X " . For the latter, we use the difference betweenphase space and a J PC ! %& hypothesis for the X " .The total relative systematic error on the product branchingfraction is 20.2%.In summary, the decay channel J= ! %$ & $ % isanalyzed using two decay modes, ! $ & $ % and ! %& . A resonance, the X " , is observed with ahigh statistical significance of : ! in the $ & $ % invariant-mass spectrum. From a fit with a Breit-Wignerfunction, the mass is determined to be M ! : $ : " stat : " syst MeV =c , the width is ! ! : $ : " stat : " syst MeV =c , and the product branch-ing fraction is B " J= ! % X B " X ! $ & $ % : $ : " stat : " syst % . The mass and widthof the X " are not compatible with any known mesonresonance [16]. In Ref. [16], the candidate closest in massto the X " is the (unconfirmed) %& " with M ! $ =c . The width of this state, ! ! $
14 MeV = c , is considerably larger than that of the X " (see also [17], where the %& component in the mode of J= radiative decay has a mass $
15 MeV =c and a width $
40 MeV =c ).We examined the possibility that the X " is respon-sible for the p p mass threshold enhancement observed inradiative J= ! % p p decays [1]. It has been pointed outthat the S -wave BW function used for the fit in Ref. [1] M( π + π - η ´) (GeV/c ) EVE N T S / ( M e V / c ) M( π + π - η ´) (GeV/c ) EVE N T S / ( M e V / c ) FIG. 3. The $ & $ % invariant-mass distribution for selectedevents from both the J= ! %$ & $ % " ! $ & $ % ; ! %% and J= ! %$ & $ % " ! %& analyses. The bottompanel shows the fit (solid curve) to the data (points with errorbars); the dashed curve indicates the background function. PRL week ending31 DECEMBER 2005 M( π + π − η ʹ ) (GeV/c ) efficiency-corrected Breit-Wigner functions convolvedwith a Gaussian mass resolution plus a nonresonant ! þ ! " " contribution and background representations,where the efficiency for the combined channels is obtainedfrom the branching-ratio-weighted average of the efficien-cies for the two " modes. The contribution from non-resonant þ ! " " production is described byreconstructed Monte Carlo (MC)-generated J= c ! þ ! " " phase space decays, and it is treated as anincoherent process. The background contribution can bedivided into two different components: the contributionfrom non- " events estimated from " mass sideband,and the contribution from J= c ! ! ! þ ! " " . For thesecond background, we obtain the background ! þ ! " " mass spectrum from data by selecting J= c ! ! ! þ ! " " events and reweighting their mass spectrum with a weightequal to the MC efficiency ratio of the þ ! " " and ! ! þ ! " " selections for J= c ! ! ! þ ! " " . Themasses, widths, and number of events of the f ð Þ ,the X ð Þ and the resonances near 2.1 and : =c , the X ð Þ and X ð Þ , are listed inTable I. The statistical significance is determined fromthe change in " L in the fits to mass spectra with andwithout signal assumption while considering the change ofdegree of freedom of the fits. With the systematicuncertainties in the fit taken into account, the statistical significance of the X ð Þ is larger than $ , while thosefor the f ð Þ , the X ð Þ , and the X ð Þ are largerthan : $ , : $ , and : $ , respectively. The mass andwidth from the fit of the f ð Þ are consistent withPDG values [17]. With MC-determined selection efficien-cies of 16.0% and 11.3% for the " ! and " ! ! þ ! " " decay modes, respectively, the branching fractionfor the X ð Þ is measured to be B ð J= c ! X ð Þ Þ B ð X ð Þ ! ! þ ! " " Þ ¼ ð : & : Þ’ " . The con-sistency between the two " decay modes is checked byfitting their ! þ ! " " mass distribution separately with theprocedure described above.For radiative J= c decays to a pseudoscalar meson, thepolar angle of the photon in the J= c center of mass system, & , should be distributed according to þ cos & . Wedivide the j cos & j distribution into 10 bins in the regionof [0, 1, 0]. With the same procedure as described above,the number of the X ð Þ events in each bin can beobtained by fitting the mass spectrum in this bin, andthen the background-subtracted, acceptance-corrected j cos & j distribution for the X ð Þ is obtained as shownin Fig. 3, where the errors are statistical only. It agrees with þ cos & , which is expected for a pseudoscalar, with ’ = d : o : f ¼ : = .The systematic uncertainties on the mass and width aremainly from the uncertainty of background representation,the mass range included in the fit, different shapes forbackground contributions, and the nonresonant processand contributions of possible additional resonances in the : =c and : =c mass regions. The total sys-tematic errors on the mass and width are þ : " : and ) ’)(GeV/c η - π + π M(1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 ) E v e n t s / ( . G e V / c ’)(GeV/c η - π + π M(1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 ) E v e n t s / ( . G e V / c (a) ) ’)(GeV/c η - π + π M(1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 ) E v e n t s / ( . G e V / c ’)(GeV/c η - π + π M(1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 ) E v e n t s / ( . G e V / c (b) FIG. 2 (color online). (a) The ! þ ! " " invariant-mass distri-bution for the selected events from the two " decay modes.(b) Mass spectrum fitting with four resonances; here, the dash-dotted line is contributions of non- " events and the ! ! þ ! " " background for two " decay modes, and the dashed line iscontributions of the total background and nonresonant ! þ ! " " process. TABLE I. Fit results with four resonances for the combinedtwo " decay modesResonance M ð MeV =c Þ ! ð MeV =c Þ N event f ð Þ : & : &
11 230 & X ð Þ : & : : & : & X ð Þ : & : &
16 647 & X ð Þ : & : &
17 565 & | γ θ |cos | γ θ d N / d | c o s FIG. 3. The background-subtracted, acceptance-corrected j cos & j distribution of the X ð Þ for two " decay modesfor J= c ! þ ! " " . PRL week ending18 FEBRUARY 2011 M( π + π − η ʹ ) (GeV/c ) E v e n t s / M e V / c E v e n t s / M e V / c J/ ψ → γπ + π − η ʹ J/ ψ → γπ + π − η ʹ BESII BESIII
Figure 5
Observation of the X (1835) in J/ψ → γX (1835); X (1835) → π + π − η (cid:48) at BESII (46) (left)and BESIII (45) (right). Additional states were discovered in the BESIII analysis.Modified from References (46, 45) with permission. about the same width was seen in J/ψ → γπ + π − η (cid:48) decays. This was first seen byBESII (46) (see the left panel of Figure 5). BESIII was able to confirm the existenceof this peak with increased statistics, but, surprisingly, also observed clear peaks athigher mass (47) (see the right panel of Figure 5). These high mass peaks are equallyas mysterious as the X (1835). In addition, another enhancement of events around1.8 GeV/ c was seen in the related channel J/ψ → γK S K S η at BESIII (48). In thisreaction, the enhancement was shown to have J P = 0 − , the same as that for the p ¯ p enhancement. It seems likely that the structures around 1.8 GeV/ c in π + π − η (cid:48) , K S K S η , and pp correspond to the same X (1835), but there is as yet no definitiveproof.A series of searches was also performed in other channels including a p ¯ p pair, suchas J/ψ → ωp ¯ p (49). The lack of evidence for a pp threshold enhancement in thesetypes of decays appears to disfavor a final-state interaction interpretation. Otherinterpretations have been proposed, from a glueball state to a radial excitation of the η to a baryonium state, but no definitive conclusion has yet been reached (see thereferences in (48)). FINAL STATEINTERACTIONS:
Interactions amongparticles in the finalstate that cansometimes lead tomisleading peaks notassociated withresonances.
BARYONIUM:
Abound stateconsisting of twobaryons.
J/ψ and ψ (2 S ) decays In addition to the meson analyses described above, BES has also had a significantinfluence in light baryon spectroscopy. Just as in the case of mesons, the well-definedinitial state can be used to constrain properties of the final state. For example, inthe reaction
J/ψ → p + X , the X baryon must have isospin-1/2 (in the absence ofisospin violation), since the J/ψ has isospin-0 and the proton has isospin-1/2. It isthus a useful way to filter N ∗ states from ∆ states. This type of filter is not availablein fixed-target π + N reactions, for example.Studies of the N ∗ states have been particularly fruitful, as can be seen in thefollowing chain of analyses from BESI through BESIII. In BESI, the J/ψ → p ¯ pη channel was analyzed as a relatively simple one with which to begin (50). The well-established J P = 1 / + states N (1535) and N (1650) were clearly observed and their
14 R. A. Briere, F. A. Harris and R. E. Mitchell P assignments were confirmed. At BESII, this analysis was extended to the channel J/ψ → pπ − ¯ n + c.c. (51). The same two states were observed, but in addition the1 / + N (1440) was observed more clearly than other experiments (since it is usuallyeclipsed by the ∆, which was absent in the BESII analysis). And a new high-massresonance, the 1 / + or 3 / + N (2040) was found. Finally, in BESIII, an analysis of ψ (2 S ) → p ¯ pπ was performed using 106 million ψ (2 S ) decays (52). Using the ψ (2 S )instead of the J/ψ allowed an analysis of higher mass baryons and yet two more newones were discovered, the 1 / + N (2300) and the 5 / − N (2570). Both of these stateswere observed with a significance of greater than 10 σ . These efforts from BES havebeen greatly influential in filling out the spectrum of N ∗ states. N*’S AND ∆ ’S: Excited states of theproton and neutron.
The ability of BES to produce baryon resonances in
J/ψ and ψ (2 S ) decays hasmade it a meaningful place to search for exotic baryons. Such was the case in 2004,when there was much excitement about the pentaquark candidate Θ + (1540). BE-SII performed a search for this state in the K S pK − ¯ n and K S ¯ pK + n decays of the J/ψ and ψ (2 S ) (53). The idea was that the pentaquark might be produced in pairs(to conserve flavor and other quantum numbers). No evidence was found for thepentaquark decaying to K S p or K + n and tight upper limits were placed on its pro-duction. Eventually, the initial evidence for the pentaquark was overturned. TheBESII search was among the earliest of the negative searches.
7. CHARMONIUM PHYSICS
While the study of light quark physics is generally associated with the
J/ψ data setsat BES, the study of charmonium is most often pursued through data taken at the ψ (2 S ). From the ψ (2 S ), all charmonium states below D ¯ D threshold can be reached,making the ψ (2 S ) data ideal for charmonium studies. The χ cJ (1 P ) can be accessedthrough E1 radiative transitions; the η c (1 S, S ) through M1 radiative transitions;and the J/ψ and h c (1 P ) states through hadronic transitions. BESI, BESII, andBESIII have all collected increasingly large samples of ψ (2 S ) decays, and there havebeen important results from each. BESI collected 3.8 million ψ (2 S ) decays; BESIIcollected 14 million; and BESIII took an initial sample of 106 million in 2009 andincreased it to 448 million in 2012.One of the most interesting features of the states below D ¯ D threshold is thatthey can be successfully described by treating the c ¯ c pair as being bound in a poten-tial. Studying the masses and radiative transitions of the charmonium states givesvaluable insight into the shape of the potential. On the other hand, the shape of thepotential and its spin-dependence can be derived from QCD (lattice QCD) or phe-nomenologically. Furthermore, masses and radiative transitions can now be directlycalculated in lattice QCD. The properties of charmonium thus provide a convenientpoint of contact between experiment and QCD. See Ref. (54) for a review of issuesin charmonium. Lattice QCD(LQCD):
A methodfor calculatingstrong interactionquantities oncomputers, withspace-timerepresented by adiscrete lattice.
The following two sections will cover a selection of BES results on masses andradiative transitions of charmonium states below D ¯ D threshold. The final sectionwill discuss some anomalies in J/ψ and ψ (2 S ) decays. • Physics Accomplishments of the BES Experiments 15 harmonium
A charmonium state is made of a charm quark and an anti-charm quark with a given set of internalquantum numbers, such as spin ( S ), orbital angular momentum ( L ), and principal quantum number ( n ).The charmonium system is the set of all possible charmonium states. It is thus similar to the Hydrogenatom or the positronium system in Quantum Electrodynamics. Unlike Hydrogen or positronium, however,each state of charmonium has a different name. The η c (1 S ) is the ground state, with n = 1, L = 0, and S = 0. The h c (1 P ), as another example, has n = 1, L = 1, and S = 0. As mentioned above, masses of charmonium states provide key information aboutthe form of the potential binding the c ¯ c pair. The η c (1 S ) plays a special role sinceit is the ground state of charmonium. Furthermore, since the η c (1 S ) and J/ψ onlydiffer in their spin (the η c (1 S ) has S = 0 while the J/ψ has S = 1), their massdifference, also known as the hyperfine splitting, is sensitive to the spin-spin part ofthe potential. The calculation of the hyperfine splitting is a key prediction of manymodels. The mass splitting between the h c (1 P ) and the χ cJ (1 P ) states (combinedin the form of a spin-weighted average) plays a similar role. These states also differonly in their spin (the h c (1 P ) has S = 0, while the χ cJ (1 P ) has S = 1), but theirinternal orbital angular momentum ( L ) is one. In this case it is expected that themass splitting vanishes to lowest order. Thus a measurement of the mass splitting issensitive to higher order effects.BES has made important and unique contributions to the measurement of themasses of the η c (1 S ), h c (1 P ), and χ cJ (1 P ). The measurement of each is summarizedbelow.
1. Measurement of the mass of the η c (1 S ). BES has a long history of η c (1 S )mass measurements using the M1 transitions J/ψ → γη c (1 S ) and ψ (2 S ) → γη c (1 S ).BESI, combining results from 7.8 million J/ψ and 3.8 million ψ (2 S ) decays foundthe mass to be 2976 . ± . ± . c (55, 56) (see the left panel of Figure 6);and BESII, using 58 million J/ψ decays, found 2977 . ± . ± . c (57) (seethe middle panel of Figure 6). These measurements were consistent with other mea-surements from radiative decays, but systematically lower than measurements fromother production mechanisms, such as γγ collisions, B decays, or p ¯ p annihilation.This represented a serious problem. At BESIII, using 106 million ψ (2 S ) decays, theline-shape of the η c (1 S ) was found to be clearly distorted (see the right panel ofFigure 6). Taking into account the expected E energy-dependence of the radiatedphoton (58), and including interference with the non- η c (1 S ) background, the masswas found to be 2984 . ± . ± . c (59), more in line with other measure-ments, and resolving the previous discrepancy. The lower statistics of the previousmeasurements apparently hid these important effects. A subsequent measurementusing h c (1 P ) → γη c (1 S ) confirmed this higher mass (60).
2. Measurement of the mass of the χ cJ (1 P ). BESII measured the massesof the χ cJ (1 P ) states using the process ψ (2 S ) → γχ cJ (1 P ) (61). The χ cJ (1 P ) wereallowed to decay inclusively. Rather than detect the energy of the photon directly,
16 R. A. Briere, F. A. Harris and R. E. Mitchell ! ! " are allowed to float, the resulting mass value and numberof events are m c ! " " m c deter-mination arise from the mass-scale calibration, the detectionefficiency, and the uncertainties associated with the selection of the cut values. In the case of the $ (2 S ) measurement % & ,the level of the systematic error on the overall mass scale ofBES was estimated as 0.8 MeV by comparing the masses ofthe ’ c and ’ c charmonium states, detected in the samedecay channels, with their PDG values. These masses havebeen measured in a number of experiments, and the reportedvalues have good internal consistency. Because the energy FIG. 1. The ( a ) m K K $ * * $ , ( b ) m * * $ * * $ , ( c ) m K " K S * % , ( d ) m ++ and ( e ) m K K $ * distributionin the c region; ( f ) is the com-bined four-charged-track massdistribution of ( a ) , ( b ) , ( c ) and ( d ) .TABLE I. The number of fitted events and the mass for individual channels. The errors are statistical. " is the full width of the c fixed at the PDG value. ! is the mass resolution given by the Monte Carlosimulation.Channel No. of events mass ( MeV ) "(
MeV ) !(
MeV ) K K $ * * $ " " * * $ * * $ " " K " K S * % → K " * % * * $ " " ++ → K K $ K K $ " " K K $ * " " M ( K ± K S ⇡ ⌥ ) GeV/c E v e n t s / M e V / c BESI
BES Collaboration / Physics Letters B 555 (2003) 174–180
Fig. 1. The invariant mass distributions in the η c region for channels (a) m K + K − π + π − , (b) m π + π − π + π − , (c) m K ± K S π ∓ , (d) m φφ and(e) m p ¯ p .Table 3Comparison of K s , φ and Λ mass peak positions K s ( MeV /c ) φ ( MeV /c ) Λ ( MeV /c )Our measurements 496 . ± . . ± . . ± . . ± .
03 1019 . ± .
014 1115 . ± . % M − . ± . . ± . − . ± . M ( K ± K S ⇡ ⌥ ) GeV/c E v e n t s / M e V / c BESII background processes, but do find dozens of decay modesthat each make small additional contributions to the back-ground. These decays typically have additional or fewerphotons in their final states. The sum of these backgroundevents is used to estimate the contribution from other c ð Þ decays. Backgrounds from the e þ e $ ! q ! q con-tinuum process are studied using a data sample taken at ffiffiffi s p ¼ :
65 GeV . Continuum backgrounds are found to besmall and uniformly distributed in M ð X i Þ . There is also anirreducible nonresonant background, c ð Þ ! ! X i , thathas the same final state as signal events. A nonresonantcomponent is included in the fit to the " c invariant mass.Figure 1 shows the " c invariant mass distributions forselected " c candidates, together with the estimated X i backgrounds, the continuum backgrounds normalized byluminosity, and other c ð Þ decay backgrounds esti-mated from the inclusive MC sample. A clear " c signalis evident in every decay mode. We note that all of the " c signals have an obviously asymmetric shape: there is along tail on the low-mass side; while on the high-mass side,the signal drops rapidly and the data dips below the ex-pected level of the smooth background. This behavior ofthe signal suggests possible interference with the nonreso-nant ! X i amplitude. In this analysis, we assume 100% ofthe nonresonant amplitude interferes with the " c .The solid curves in Fig. 1 show the results of an un-binned simultaneous maximum likelihood fit in the rangefrom 2.7 to : =c with three components: signal,nonresonant background, and a combined background consisting of X i decays, continuum, and other c ð Þ decays. The signal is described by a Breit-Wigner function convolved with a resolution function.The nonresonant amplitude is real, and is described by anexpansion to second order in Chebyshev polynomials de-fined and normalized over the fitting range. The combinedbackground is fixed at its expected intensity, as describedearlier. The fitting probability density function as a func-tion of mass ( m ) reads F ð m Þ ¼ $ & ½ % ð m Þ j e i & E = ! S ð m Þ þ ’ N ð m Þ j ( þ B ð m Þ ; where S ð m Þ , N ð m Þ , and B ð m Þ are the signal, the non-resonant ! X i component, and the combined background,respectively; E ! is the photon energy, $ is the experimentalresolution, and % ð m Þ is the mass-dependent efficiency. The E ! multiplying j S ð m Þ j reflects the expected energy depen-dence of the hindered- M transition [16], which partiallycontributes to the " c low-mass tail as well as the interfer-ence effect. The interference phase & and the strength ofthe nonresonant component ’ are allowed to vary in the fit.The mass-dependent efficiencies are determined fromphase space distributed MC simulations of the " c decays.Efficiencies obtained from MC samples that include inter-mediate states change the resulting mass and width bynegligible amounts. MC studies indicate that the resolutionis almost constant over the fitting range. Thus, a mass-independent resolution is used in the fit. The detectorresolution is primarily determined by MC simulation for ) GeV/c π M(KsK E v en t s / M e V / c ) GeV/c π M(KsK E v en t s / M e V / c ) GeV/c π M(KsK E v en t s / M e V / c ) GeV/c π M(KsK E v en t s / M e V / c data ’ decays ψ other i X π contsignon-resoint ) GeV/c π M(KK E v en t s / M e V / c ) GeV/c π M(KK E v en t s / M e V / c ) GeV/c π M(KK E v en t s / M e V / c ) GeV/c π M(KK E v en t s / M e V / c data ’ decays ψ other i X π contsignon-resoint ) GeV/c ηππ M( E v en t s / M e V / c -20020406080100120140160 ) GeV/c ηππ M( E v en t s / M e V / c -20020406080100120140160 ) GeV/c ηππ M( E v en t s / M e V / c -20020406080100120140160 ) GeV/c ηππ M( E v en t s / M e V / c -20020406080100120140160 data ’ decays ψ other i X π contsignon-resoint ) GeV/c π M(KsK3 E v en t s / M e V / c ) GeV/c π M(KsK3 E v en t s / M e V / c ) GeV/c π M(KsK3 E v en t s / M e V / c ) GeV/c π M(KsK3 E v en t s / M e V / c data ’ decays ψ other i X π contsignon-resoint ) GeV/c ππ M(2K2 E v en t s / M e V c ) GeV/c ππ M(2K2 E v en t s / M e V c ) GeV/c ππ M(2K2 E v en t s / M e V c data ’ decays ψ other i X π contsignon-resoint ) GeV/c π M(6 E v en t s / M e V / c ) GeV/c π M(6 E v en t s / M e V / c ) GeV/c π M(6 E v en t s / M e V / c data ’ decays ψ other i X π contsignon-resoint FIG. 1 (color). The M ð X i Þ invariant mass distributions for the decays K S K þ $ , K þ K $ , " þ $ , K S K þ þ $ $ , K þ K $ þ $ , and ð þ $ Þ , respectively, with the fit results (for the constructive solution) superimposed. Points are data andthe various curves are the total fit results. Signals are shown as short-dashed lines, the nonresonant components as long-dashed lines,and the interference between them as dotted lines. Shaded histograms are (in red, yellow, green) for [continuum, X i , other c ð Þ decays] backgrounds. The continuum backgrounds for K S K þ $ and " þ $ decays are negligible. PRL week ending1 JUNE 2012 M ( K ± K S ⇡ ⌥ ) GeV/c E v e n t s / M e V / c BESIII
Figure 6
Evolution of measurements of the η c (1 S ) mass. (left) Measurement of the η c (1 S ) mass atBESI (56) in the process J/ψ → γη c (1 S ); η c (1 S ) → K ± K S π ∓ using 7.8 million J/ψ decays. (middle) Measurement of the η c (1 S ) mass at BESII (57) in the same process using58 million J/ψ decays. (right) Measurement of the η c (1 S ) mass at BESIII (59) in the sameprocess except from ψ (2 S ) using 106 million ψ (2 S ) decays. In each case the K ± K S π ∓ decay mode of the η c (1 S ) is shown as an example – each analysis used a combination of anumber of different η c (1 S ) decays. In both BESI and BESII (the left two plots), the η c (1 S )peak was fit with a symmetric Breit-Wigner distribution. In BESIII (the right plot), an E γ term was added, and interference with the non- η c (1 S ) background was allowed. Notice theobvious distortion in the lineshape at BESIII and hints of the same distortion at BESII.Modified from References (56, 57, 59) with permission. events in which the photon converted in the detector to an e + e − pair were used. Thisallowed a much better determination of the photon energy, with resolutions on theorder of 2-4 MeV. The spin-weighted average mass of the χ cJ (1 P ) was determined tobe 3524 . ± . ± .
30 MeV/ c . Despite being over a decade old, this measurementstill represents a major component of the world average. It is surpassed in precisiononly by measurements in p ¯ p annihilation (62).
3. Measurement of the mass of the h c (1 P ). BESIII has made two mea-surements of the h c (1 P ) mass, both using the transition ψ (2 S ) → π h c (1 P ). Inthe first, the h c (1 P ) was reconstructed both inclusively and by tagging the pho-ton in the transition h c (1 P ) → γη c (1 S ) (63). Even though the inclusive processhas a large background, the measurement of the mass had a total error (statisti-cal and systematic combined) of around 200 keV. This analysis will be discussedfurther below in the context of the measurement of B ( h c (1 P ) → γη c (1 S )). Thesecond measurement, however, was even more precise. In this analysis, the process ψ (2 S ) → π h c (1 P ); h c (1 P ) → γη c (1 S ) was reconstructed exclusively using 16 decaymodes of the η c (1 S ) (60) . This allowed an extremely clean sample of over 800 h c (1 P )events. The mass was determined to be 3525 . ± . ± .
14 MeV/ c and the widthwas measured as 0 . ± . ± .
22 MeV/ c . Both are the most precise measurementsto date. BES has also made a number of influential measurements of radiative transitionsamong charmonium states. A few of its unique contributions are highlighted below.
1. Measurement of B ( h c (1 P ) → γη c (1 S )). Using its initial sample of106 million ψ (2 S ) decays, BESIII was able to make the first measurement of theE1 transition rate B ( h c (1 P ) → γη c (1 S )) (63). This was measured by fitting the • Physics Accomplishments of the BES Experiments 17 ! ! " þ " " " ( ). For the K S K " $ channel, thesebackground contributions are suppressed by requiring thatthe recoil mass of all " þ " " pairs be less than :
05 GeV =c .For the K þ K " " channel, this type of contamination isremoved by requiring that the invariant mass of the twocharged tracks, assuming they are muons, be less than : =c . The remaining dominant background sourcesare (1) c ð Þ ! K S K " $ ( K þ K " " ) events with a fakephoton candidate; (2) events with the same final statesincluding K S K " $ ISR = FSR ( K þ K " " ISR = FSR ) with thephoton from initial- or final-state radiation (ISR, FSR) and c ð Þ ! !K þ K " with ! ! ; and (3) events withan extra photon, primarily from c ð Þ ! " K S K " $ ( " K þ K " " ) with " ! . MC studies demonstrate thatcontributions from all other known processes are negligible.The events in the first category, with a fake photonincorporated into the kinematic fit, produce a peak in the K S K " $ ( K þ K " " ) mass spectrum close to the expected ! c ð S Þ mass, with a sharp cutoff due to the 25-MeVphoton-energy threshold.Because the fake photon adds no information to the fit,its inclusion distorts the mass measurement. We thereforedetermine the mass from a modified kinematic fit in whichthe magnitude of the photon momentum is allowed tofreely float (3C for K S K " $ and 4C for K þ K " " ).In the case of a fake photon, the momentum tends to zero,which improves the background separation with minimaldistortion of the signal line shape [16].Background contributions from c ð Þ ! K S K " $ ( K þ K " " ) and c ð Þ ! K S K " $ FSR ( K þ K " " FSR ) are estimated with MC distributions for thoseprocesses normalized according to a previous measure-ment of the branching ratios [21]. FSR is simulated inour MC generations with
PHOTOS [22], and the FSR con-tribution is scaled by the ratio of the FSR fractions in dataand MC generations for a control sample of c ð Þ ! cJ ( J ¼ or 1) events. For this study the $ cJ isselected in three final states with or without an extra FSRphoton, namely K S K " $ ð FSR Þ , " þ " " " þ " " ð FSR Þ , and " þ " " K þ K " ð FSR Þ , as described in Ref. [16]. Background contributions from the continuum process e þ e " ! ( ! K S K " $ ð FSR Þ ( K þ K " " ð FSR Þ ) and the ISRprocess e þ e " ! ( ISR ! K S K " $ ISR ð K þ K " " ISR Þ are estimated with data collected at ffiffiffi s p ¼ :
65 GeV corrected for differences in the integrated luminosity andthe cross section, and with particle momenta andenergies scaled to account for the beam-energy dif-ference. MC simulations show that the K S K " $ ( K þ K " " ) mass spectra are similar for FSR and ISR events.Events without radiation have the same mass distributionindependently of originating from a resonant c ð Þ decayor from the nonresonant continuum production. Thus,the background shapes from K S K " $ ð K þ K " " Þ and K S K " $ ISR = FSR ð K þ K " " ISR = FSR Þ are described by thesum of the MC-simulated K S K " $ ð K þ K " " Þ and K S K " $ FSR ð K þ K " " FSR Þ invariant-mass shapes, withthe proportions fixed according to the procedure describedabove. The shapes of background mass distributions from c ð Þ ! !K þ K " with ! ! are parameterizedwith a double-Gaussian function, and its level is measuredwith the same data sample and fixed in the final fit.The third type of background, that with an extra photon, " K S K " $ ð " K þ K " " Þ , is measured with data and nor-malized according to the simulated contamination rate. Itcontributes a smooth component around the $ cJ ( J ¼ , 2)mass region with a small tail in the ! c ð S Þ signal regionthat is described by a Novosibirsk function [23] (Gaussianfunction) for the " K S K " $ ( " K þ K " " ) background.The shape and size of this background is fixed in the fit.The mass spectra for the K S K " $ and K þ K " " chan-nels are fitted simultaneously to extract the yield, mass, andwidth of ! c ð S Þ . To better determine the background andmass resolution from the data, the mass spectra are fittedover a range ( : – :
71 GeV =c ) that includes the $ c and $ c resonances as well as the ! c ð S Þ signal. The final massspectra and the likelihood fit results are shown in Fig. 1.Each fitting function includes four components, namely, ! c ð S Þ , $ c , $ c , and the summed background describedabove. Line shapes for $ c and $ c are obtained from MCsimulations and convolved with Gaussian functions to ) (GeV/c π ± K K m ) E v e n t s / ( . G e V / c ) (GeV/c ± π ± K K m ) E v e n t s / ( . G e V / c ) ± π ± K data (Kfit result cJ χ (2S) c η background ± π ± K K ISR/FSR γ ± π ± K K ± π ± K K π ) (GeV/c π - K + K m ) E v e n t s / ( . G e V / c ) (GeV/c π - K + K m ) E v e n t s / ( . G e V / c ) π - K + data (Kfit result cJ χ (2S) c η background π - K + K ISR/FSR γ π - K + K - K + K ω π - K + K π FIG. 1 (color online). The invariant-mass spectrum for K S K " $ (left panel), K þ K " " (right panel), and the simultaneouslikelihood fit to the three resonances and combined background sources as described in the text. PRL week ending27 JULY 2012
The cylindrical core of the BESIII detector consists of ahelium-gas-based drift chamber (MDC), a plastic scintilla-tor time-of-flight system, and a CsI(Tl) electromagneticcalorimeter (EMC), all enclosed in a superconducting so-lenoidal magnet providing a 1.0-T magnetic field. Thesolenoid is supported by an octagonal flux-return yokewith resistive plate counter muon identifier modules inter-leaved with steel. The charged particle and photon accep-tance is 93% of ! , and the charged-particle momentumand photon-energy resolutions at 1 GeVare 0.5% and 2.5%,respectively.We perform the analysis on a data sample consisting of ð : " : Þ $ c decays [14]. An independent sam-ple of : % at 3.65 GeV is used to determine contin-uum ( e þ e % ! q ! q ) background. We measure h c productionby selecting events consistent with c ! ! h c [momen-tum p ð ! Þ ’
84 MeV =c ] and fitting the distribution ofmasses recoiling against the ! . The yield of c ! ! h c , h c ! " c is determined with the same techniqueon events containing a ’
500 MeV photon.We model BESIII with a Monte Carlo (MC) simulationbased on
GEANT4 [15,16].
EVTGEN [17] is used to generate c ! ! h c events with an h c mass of :
28 MeV =c [11] and a width equal to that of the $ c (0.9 MeV). The E transition h c ! " c (assumed branching ratio 50%) ismodeled with EVTGEN , with an angular distribution in the h c frame of þ cos % . Other h c decays are simulated by PYTHIA [17]. The c decay parameters are set to ParticleData Group values [6], with known modes simulated by EVTGEN and the remainder by
PYTHIA . Backgrounds arestudied with a sample of c generated by KKMC calcula-tions [18] with known decays modeled by
EVTGEN andother modes generated with
LUNDCHARM [17].Charged tracks in BESIII are reconstructed from MDChits. To optimize the momentum measurement, we selecttracks in the polar angle range j cos % j < : and requirethat they pass within "
10 cm of the interaction point in thebeam direction and within " in the plane perpendicu-lar to the beam. Electromagnetic showers are reconstructedby clustering EMC crystal energies. Efficiency and energyresolution are improved by including energy deposits innearby time-of-flight counters. Showers used in selecting E -transition photons and in ! reconstruction must sat-isfy fiducial and shower-quality requirements. Showers inthe barrel region ( j cos % j < : ) must have a minimumenergy of 25 MeV, while those in the end caps ( : < j cos % j < : ) must have at least 50 MeV. Showers in theregion between the barrel and end cap are poorly recon-structed and are excluded. To eliminate showers fromcharged particles, a photon must be separated by at least10 ( from any charged track. EMC cluster timing require-ments suppress electronic noise and energy deposits unre-lated to the event. Diphoton pairs are accepted as ! candidates if their reconstructed mass satisfies 145 MeV =c , approximately equivalent to 1.5 (2.0) standard deviations on the low-mass (high-mass)side of the mass distribution. A 1-C kinematic fit withthe ! mass constrained to its nominal value is used toimprove the energy resolution.Candidate events must have at least two charged tracks,with at least one passing the fiducial and vertex cuts. Forselection of inclusive ! events we demand at least twophotons passing the above requirements, with at least threephotons for E -tagged candidate events. To suppress con-tinuum background, the total energy deposition in theEMC must be greater than 0.6 GeV. Background eventsfrom c ! ! þ ! % J= c and ! ! J= c are suppressed byrequiring that the ! þ ! % ( ! ! ) recoil mass be outside therange " =c ( " 15 MeV =c ).To improve the signal-to-noise ratio, photons used insignal ! candidates must be in the barrel and have ener-gies greater than 40 MeV. For the inclusive analysis, ! candidates are excluded if either daughter photon can makea ! with another photon in the event. Figure 1 shows theinclusive ! recoil-mass spectra after applying the aboveselection criteria. For the E -tagged selection [Fig. 1(a)],we require one photon in the energy range 465–535 MeV,demanding that it not form a ! with any other photon inthe event. Because E -tagged events have reduced back-ground, we keep them even if daughter photons can be usedin more than one ! combination, choosing the candidatewith the minimum 1-C fit $ . Events with more than one ! in the : – : 555 GeV =c recoil-mass region areexcluded.The ! recoil-mass spectra (Fig. 1) are fitted by anunbinned maximum likelihood method. Because of its (a)(b) FIG. 1 (color online). (a) The ! recoil-mass spectrum and fitfor the E -tagged analysis of c ! ! h c , h c ! " c . (b) The ! recoil-mass spectrum and fit for the inclusive analysis of c ! ! h c . Fits are shown as solid lines, background as dashed lines.The insets show the background-subtracted spectra. PRL week ending2 APRIL 2010 M ( K ± K S ⇡ ⌥ ) GeV/c E v e n t s / M e V / c Figure 7 Measurements of radiative transitions at BESIII. (left) The top plot shows a fit to the h c (1 P ) mass in the process ψ (2 S ) → π h c (1 P ); h c (1 P ) → γη c (1 S ). The energy of theradiated photon is used to tag this process. The bottom plot is a fit to the h c (1 P ) mass inthe process ψ (2 S ) → π h c (1 P ). The ratio of the two fits gives B ( h c (1 P ) → γη c (1 S )) (63).(right) The measurement of B ( ψ (2 S ) → γη c (2 S )) (64). The η c (2 S ) is the peak between3.60 and 3.65 GeV/ c , surrounded by prominent backgrounds on either side. Modified fromReferences (63, 64) with permission. h c (1 P ) peak in the inclusive π recoil mass spectrum with and without taggingthe photon from h c (1 P ) → γη c (1 S ). When the photon is tagged, the fit gives theproduct B ( ψ (2 S ) → π h c (1 P )) × B ( h c (1 P ) → γη c (1 S )) (see the top histogram inthe left panel of Figure 7). When the photon is not tagged, the fit gives B ( ψ (2 S ) → π h c (1 P )) (see the bottom histogram in the left panel of Figure 7). Dividing thesetwo results gives a measurement of B ( h c (1 P ) → γη c (1 S )) = (54 . ± . ± . 2. Measurement of B ( ψ (2 S ) → γη c (2 S )). Unsuccessful searches for thetransition ψ (2 S ) → γη c (2 S ) have been carried out since the early 1980’s. BESIIIwas finally able to make the first observation of this process using its initial sampleof 106 million ψ (2 S ) decays (64). The low energy of the transition photon and theprominent background peaks due to ψ (2 S ) → γχ cJ (1 P ) make this an especiallydifficult measurement. To reduce background, the η c (2 S ) was reconstructed in theexclusive channels K S K ± π ∓ and K + K − π . The resulting K S K ± π ∓ mass spectrumis shown in the right panel of Figure 7 (the K + K − π mass spectrum is similar, but notshown). The signal appears as the peak between 3 . 60 and 3 . 65 GeV/ c . The peaks tothe left of the signal are from the χ cJ ; the peak to the right is from spurious showersin the calorimeter. Normalizing to a BaBar measurement of B ( η c (2 S ) → K ¯ Kπ ) (65)gives a branching fraction of B ( ψ (2 S ) → γη c (2 S )) = (6 . ± . ± . × − . Thisremains the only observation of this process. MULTIPOLES: Terms in anexpansion of theradiative transitionamplitude.Higher-order termsare suppressed, butare sensitive todetails of thetransition. 3. Measurement of multipoles in ψ (2 S ) → γχ c . The high statisticsand cleanliness of the process ψ (2 S ) → γχ c ; χ c → π + π − and K + K − have alloweddetailed studies of multipoles beyond the dominant E1 transition. These higher mul- 18 R. A. Briere, F. A. Harris and R. E. Mitchell ipoles are important for a number of reasons: they could serve as an explanationfor some apparent deviations from theoretical E1 rates; the M2 amplitude is sensi-tive to the anomalous magnetic moment of the charm quark; and the E3 amplitudeis sensitive to the orbital angular momentum of the quarks in the ψ (2 S ). An ini-tial measurement from BESII (66), using 14 million ψ (2 S ) decays, found M2 andE3 contributions consistent with zero. The measurement from BESIII (67), using106 million ψ (2 S ), gave the first evidence of a non-zero M2 component. It is incon-sistent with zero with a significance of 4 . σ . It is consistent with predictions when theanomalous magnetic moment of the charm quark is assumed to be zero. An improvedresult from BESIII, using the full 448 million ψ (2 S ) decays dataset, is forthcoming. J/ψ and ψ (2 S ) Another interesting feature of charmonium physics is the surprising differences be-tween J/ψ and ψ (2 S ) decays to light quark states. It is reasonable to think thatonce the charm and anti-charm quarks of the initial J/ψ or ψ (2 S ) annihilate, pre-dominantly going through a single virtual photon or three gluons, the subsequenthadronization of the photon or gluons should be independent of their origin. Fromthis reasoning, one would expect that the ratio of rates for the ψ (2 S ) and J/ψ todecay to any specific combination of light quark hadrons would be roughly constant(after adjusting for the mass difference of the J/ψ and ψ (2 S ) in a straightforwardway). Since the rate for the dilepton decay of ψ (2 S ) is roughly 12% that of the J/ψ ,it is thought that this constant ratio should be around 12%. This is the “12% rule.”The 12% rule does, in fact, hold for many decays of the J/ψ and ψ (2 S ). Forexample, BESII made the best measurement of the branching fraction B ( J/ψ → p ¯ pπ ) (68), while BESIII made the best measurement of B ( ψ (2 S ) → p ¯ pπ ) (52).Taking the ratio of the world average values (dominated by the BES measurements)one finds B ( ψ (2 S ) → p ¯ pπ ) /B ( J/ψ → p ¯ pπ ) = (12 . ± . J/ψ and ψ (2 S ) decays to ρπ , where the ρπ decays to the π + π − π final state (69). Using a combination of 58 million directly produced J/ψ and J/ψ produced using 14 million ψ (2 S ), BESII determined B ( J/ψ → ρπ ) = (2 . ± . × − (70). In contrast, BESII performed a PWA of the ψ (2 S ) → π + π − π channel to determine B ( ψ (2 S ) → ρπ ) = (5 . ± . × − (71). The ratio of ψ (2 S )to J/ψ is only (0 . ± . ρπ puzzle; a definitive solution is yet to be found. In addition to the vastlydifferent rates of ρπ production in ψ (2 S ) and J/ψ decays, there is also a strikingdifference between their π + π − π Dalitz plots. BESIII published a stark comparisonin Ref. (72).Two other interesting decays where the 12% rule fails are γη and γη (cid:48) . BESIdid an early analysis of the ψ (2 S ) decays (73); and BESII did an early analysis of J/ψ decays (74). BESIII made a definitive measurement of the ψ (2 S ) decays (75),the most precise measurements to date. The ratio of branching fractions to γη (cid:48) is(2 . ± . γη channel,where the ratio of ψ (2 S ) to J/ψ decays is only (0 . ± . ρπ ratio. In addition to violating the 12% rule, it is also surprising that the ratiosfor γη and γη (cid:48) are so different from one another. • Physics Accomplishments of the BES Experiments 19 . XYZ PHYSICS Apart from a few anomalies, such as the ρπ puzzle, discussed above, the charmoniumsystem below D ¯ D threshold is fairly well understood. The same is not true for thestates above D ¯ D threshold. Starting with the discoveries of the X (3872) in 2003 atBelle (76) and the Y (4260) in 2005 at BaBar (77), there has been a flood of newstates that cannot be accommodated within the c ¯ c picture of charmonium. Theseanomalous states, referred to as the “ XY Z ” states (reflecting their still-mysteriousnature), could be pointing towards the existence of exotic compositions of quarks andgluons (54).For example, the Y (4260) could be a “hybrid meson,” a meson made of a quarkand an anti-quark (as in a “conventional meson”), but with the gluonic field in anexcited state. The X (3872), on the other hand, could be a “meson molecule,” ameson composed of a bound state of two conventional mesons. Other possibilitiesfor the XY Z are “tetraquarks” (composites of two quarks and two anti-quarks),or “hadrocharomium” (conventional mesons surrounded by a field of light quarkmesons), among others (54).The existence of non- q ¯ q states would help clarify our understanding of QCD,which, according to the latest calculations, predicts them. It is also possible that afew of these observed phenomena may not actually be “states” at all, but instead arisefrom rescattering effects, or the opening of thresholds, etc. If this turns out to be thecase, then the XY Z region would provide a prime testing ground for understandingsuch phenomena. In any case, studies of the XY Z are continually breaking newground, and the issues that have arisen have not yet been resolved.The “Y” family of states is especially relevant for the BESIII studies that will bediscussed below. They are produced in the process e + e − → Y , where the center-of-mass collision energy of the e + e − matches the mass of the produced Y . But beforeBESIII, they were studied primarily at Belle and BaBar, where the center-of-massenergies of the e + e − collisions are typically in the 10 GeV region, far above the massesof the Y states, which are in the region of 4 − c . To produce them, Belleand BaBar relied on initial state radiation (ISR), a relatively rare process wherebythe initial e + or e − first radiates a high-energy photon before annihilating, reducingthe center-of-mass collision energy to the required region.The breakthrough at BESIII was to produce these states directly, taking ad-vantage of the more propitious energy range of BEPC. Thus, the Y (4260) could beproduced by tuning the e + e − center-of-mass energy to 4.26 GeV, the Y (4360) couldbe produced at 4.36 GeV, and so on. This has at least two advantages. The rates arehigher, because the process does not depend on the emission of a high-energy ISRphoton. Also, the Y is produced at rest in the laboratory, as opposed to boostedalong the beam direction as in the ISR process, making the detection of the finaldecay products more efficient.The initial idea at BESIII was to collect 500 pb − of data at both 4.26 and4.36 GeV in 2013 in order to study decays of the Y (4260) and Y (4360), respectively.However, after many discoveries, such as the discoveries of the charged Z c states,to be discussed below, the program was extended. After an extended running pe-riod in 2013 and another year of running in 2014, BESIII now has large samplesof events at 4.23 GeV (1092 pb − ), 4.26 GeV (826 pb − ), 4.36 GeV (540 pb − ),4.42 GeV (1074 pb − ), and 4.60 GeV (567 pb − ), as well as smaller samples at many 20 R. A. Briere, F. A. Harris and R. E. Mitchell nergy points between (78). This is in addition to the 482 pb − of data collected at4.01 GeV in 2011. Z c states The initial samples of 500 pb − of e + e − collision data at 4.26 and 4.36 GeV werecollected between mid-December of 2012 and February of 2013. One of the first chan-nels to be checked, even before data-taking had finished, was e + e − → π + π − J/ψ at4.26 GeV, since this is near the peak of the Y (4260), and the Y (4260) is known todecay to π + π − J/ψ . Initial checks of the cross section agreed with what was expectedbased on the Belle and BaBar measurements of the same channel using the ISR pro-cess. But it was also quickly noticed that there was a large peak around 3900 MeV/ c in the π ± J/ψ subsystem. Such a peak, subsequently named the Z c (3900), points to-wards the existence of a particle that is manifestly exotic. Decaying to the J/ψ , itmost likely contains a c ¯ c pair. But being charged, it must include more than that c ¯ c pair. The simplest interpretation is that its electric charge comes from an additionallight quark and anti-quark pair, making it a strong candidate for a tetraquark or ameson molecule, among other possibilities.The analysis of the e + e − → π + π − J/ψ process at 4.26 GeV, and the observedcharged Z c (3900) in the π ± J/ψ subsystem, was performed quickly, but with manycross-checks. The result was made public in March of 2013 and was published inJune (79), only four months after the data was taken. A simultaneous observationof the Z c (3900), but with fewer events, was published by Belle (80). In fact, a fewof the primary authors on the BESIII paper were also among the primary authorsof the Belle paper. The Z c (3900), as seen by BESIII, is shown in the left panelof Figure 8. Its mass and width were found to be 3899 . ± . ± . c and46 ± ± 20 GeV/ c , respectively. Although only published in 2013, the observationof the Z c (3900) is already the highest cited paper at BESIII, having received over300 citations.In February of 2013, shortly after the end of the initial round of data-taking,there was a BESIII collaboration meeting at Tsinghua University. Many surprisingresults from the new data sets were shown (some of which are discussed below), andit was decided to extend the data-taking time until June of 2013.The first of these additional surprises was the discovery of the charged Z c (4020)that appears in the π ± h c (1 P ) subsystem of the process e + e − → π + π − h c (1 P ) (81).The discovery is shown in the right panel of Figure 8. Its mass and width weredetermined to be 4022 . ± . ± . c and 7 . ± . ± . c , respectively.The reasons that this state is interesting are the same as those for the Z c (3900): itdecays to charmonium and it is charged. It is therefore an additional tetraquark (ormeson molecule) candidate.One clue about the nature of the Z c (3900) and the Z c (4020) may come from theirmasses. The Z c (3900) has a mass just above D ∗ ¯ D threshold and the Z c (4020) has amass just above D ∗ ¯ D ∗ threshold. Thus, along with the closed charm channels, analy-ses were simultaneously performed in the open charm reactions e + e − → ( D ¯ D ∗ ) ± π ∓ and ( D ∗ ¯ D ∗ ) ± π ∓ . In each case, a peak was found just above the charged D ∗ ¯ D ( ∗ ) threshold. In the case of the ( D ¯ D ∗ ) ± π ∓ channel, the peak was measured to havea mass and width of 3883 . ± . ± . c and 24 . ± . ± . c , re-spectively (82) . By looking at the angular distribution of its decay, this peak was • Physics Accomplishments of the BES Experiments 21 a mass difference of : =c , a width difference of3.7 MeV, and production ratio difference of 2.6% absolute.Assuming the Z c ð Þ couples strongly with D ! D resultsin an energy dependence of the total width [22], and the fityields a difference of : =c for mass, 15.4 MeV forwidth, and no change for the production ratio. We estimatethe uncertainty due to the background shape by changing toa third-order polynomial or a phase space shape, varyingthe fit range, and varying the requirements on the ! of thekinematic fit. We find differences of : =c for mass,12.1 MeV for width, and 7.1% absolute for the productionratio. Uncertainties due to the mass resolution are esti-mated by increasing the resolution determined by MCsimulations by 16%, which is the difference between theMC simulated and measured mass resolutions of the J= c and D signals. We find the difference is 1.0 MeV in thewidth, and 0.2% absolute in the production ratio, which aretaken as the systematic errors. Assuming all the sources ofsystematic uncertainty are independent, the total system-atic error is : =c for mass, 20 MeV for width and7.5% for the production ratio.In Summary, we have studied e þ e % ! " þ " % J= c at ac.m. energy of 4.26 GeV. The cross section is measured tobe ð : & : & : Þ pb , which agrees with the existingresults from the BABAR [5], Belle [3], and CLEO [4]experiments. In addition, a structure with a mass of ð : & : & : Þ MeV =c and a width of ð & & Þ MeV is observed in the " & J= c mass spectrum. Thisstructure couples to charmonium and has an electriccharge, which is suggestive of a state containing morequarks than just a charm and anticharm quark. Similarstudies were performed in B decays, with unconfirmedstructures reported in the " & c ð Þ and " & ! c systems[23–26]. It is also noted that model-dependent calculationsexist that attempt to explain the charged bottomonium-like structures which may also apply to the charmonium-like structures, and there were model predictions of charmoniumlike structures near the D ! D and D ! D thresholds [27].The BESIII collaboration thanks the staff of BEPCII andthe computing center for their hard efforts. This work issupported in part by the Ministry of Science andTechnology of China under Contract No. 2009CB825200;National Natural Science Foundation of China (NSFC)under Contracts No. 10625524, No. 10821063,No. 10825524, No. 10835001, No. 10935007,No. 11125525, and No. 11235011; Joint Funds of theNational Natural Science Foundation of China underContracts No. 11079008, and No. 11179007; the ChineseAcademy of Sciences (CAS) Large-Scale Scientific FacilityProgram; CAS under Contracts No. KJCX2-YW-N29, andNo. KJCX2-YW-N45; 100 Talents Program of CAS;German Research Foundation DFG under ContractNo. Collaborative Research Center CRC-1044; IstitutoNazionale di Fisica Nucleare, Italy; Ministry ofDevelopment of Turkey under Contract No. DPT2006K-120470; U. S. Department of Energy under ContractsNo. DE-FG02-04ER41291, No. DE-FG02-05ER41374,and No. DE-FG02-94ER40823; U.S. National ScienceFoundation; University of Groningen (RuG) and theHelmholtzzentrum fuer Schwerionenforschung GmbH(GSI), Darmstadt; National Research Foundation of KoreaGrant No. 2011-0029457 and WCU Grant No. R32-10155. *Also at the Moscow Institute of Physics and Technology,Moscow 141700, Russia. † On leave from the Bogolyubov Institute for TheoreticalPhysics, Kiev 03680, Ukraine. ‡ Also at University of Texas at Dallas, Richardson, Texas75083, USA. § Also at the PNPI, Gatchina 188300, Russia. ∥ Present address: Nagoya University, Nagoya 464-8601,Japan.[1] B. Aubert et al. ( BABAR Collaboration), Phys. Rev. Lett. , 142001 (2005).[2] Q. He et al. (CLEO Collaboration), Phys. Rev. D ,091104(R) (2006).[3] C. Z. Yuan et al. (Belle Collaboration), Phys. Rev. Lett. ,182004 (2007).[4] T. E. Coan et al. (CLEO Collaboration), Phys. Rev. Lett. , 162003 (2006).[5] J. P. Lees et al. ( BABAR Collaboration), Phys. Rev. D ,051102(R) (2012).[6] T. Barnes, S. Godfrey, and E. S. Swanson, Phys. Rev. D ,054026 (2005).[7] X. H. Mo, G. Li, C. Z. Yuan, K. L. He, H. M. Hu, J. H.Hu, P. Wang, and Z. Y. Wang, Phys. Lett. B , 182(2006).[8] D. Cronin-Hennessy et al. (CLEO Collaboration), Phys.Rev. D , 072001 (2009).[9] G. Pakhlova et al. (Belle Collaboration), Phys. Rev. Lett. , 092001 (2007). ) ) (GeV/c J / ± π ( max M E v en t s / . G e V / c ) ) (GeV/c ψ ± ( max E v en t s / . G e V / c ) ± ( max E v en t s / . G e V / c DataTotal fitBackground fitPHSP MCSideband FIG. 4 (color online). Fit to the M max ð " & J= c Þ distribution asdescribed in the text. Dots with error bars are data; the red solidcurve shows the total fit, and the blue dotted curve the back-ground from the fit; the red dotted-dashed histogram shows theresult of a phase space (PHSP) MC simulation; and the greenshaded histogram shows the normalized J= c sideband events. PRL week ending21 JUNE 2013 Gaussian with a mass resolution determined from the datadirectly. Assuming the spin parity of the Z c ð Þ J P ¼ þ , a phase space factor pq is considered in the partialwidth, where p is the Z c ð Þ momentum in the e þ e % c.m. frame and q is the h c momentum in the Z c ð Þ c.m.frame. The background shape is parametrized as anARGUS function [18]. The efficiency curve is consideredin the fit, but possible interferences between the signal andbackground are neglected. Figure 4 shows the fit results;the fit yields a mass of ð : & : Þ MeV =c and a widthof ð : & : Þ MeV . The goodness of fit is found to be ! = n : d : f : ¼ : = ¼ : by projecting the events into a histogram with 46 bins. The statistical significance of the Z c ð Þ signal is calculated by comparing the fit like-lihoods with and without the signal. Besides the nominalfit, the fit is also performed by changing the fit range, thesignal shape, or the background shape. In all cases, thesignificance is found to be greater than : " .The numbers of Z c ð Þ events are determined to be N ½ Z c ð Þ & ( ¼ & , & , and & at 4.23,4.26, and 4.36 GeV, respectively. The cross sections arecalculated to be " ½ e þ e % ! & Z c ð Þ ) ! þ % h c ( ¼ð : & : & : & : Þ pb at 4.23 GeV, ð : & : & : & : Þ pb at 4.26 GeV, and ð : & : & : & : Þ pb at4.36 GeV, where the first errors are statistical, the secondones systematic (described in detail below), and the thirdones from the uncertainty in B ð h c ! $% c Þ [14]. The Z c ð Þ production rate is uniform at these three energypoints.Adding a Z c ð Þ with the mass and width fixed to theBESIII measurement [1] in the fit results in a statisticalsignificance of : " (see the inset in Fig. 4). We set upperlimits on the production cross sections as " ½ e þ e % ! & Z c ð Þ ) ! þ % h c ( < 13 pb at 4.23 GeV and < 11 pb at 4.26 GeV, at the 90% confidence level (C.L.).The probability density function from the fit is smeared bya Gaussian function with a standard deviation of " sys toinclude the systematic error effect, where " sys is the rela-tive systematic error in the cross section measurementdescribed below. We do not fit the 4.36 GeV data, as the Z c ð Þ signal overlaps with the reflection of the Z c ð Þ signal.The systematic errors for the resonance parameters ofthe Z c ð Þ come from the mass calibration, parametri-zation of the signal and background shapes, possible exis-tence of the Z c ð Þ and interference with it, fitting range,efficiency curve, and mass resolution. The uncertaintyfrom the mass calibration is estimated by using the differ-ence between the measured and known h c masses and D masses (reconstructed from K % þ ). The differences are( : & : ) and %ð : & : Þ MeV =c , respectively. Sinceour signal topology has one low momentum pion and manytracks from the h c decay, we assume these differencesadded in quadrature, : =c , is the systematic errordue to the mass calibration. Spin parity conservation for-bids a zero spin for the Z c ð Þ , and, assuming thatcontributions from D wave or higher are negligible, theonly alternative is J P ¼ % for the Z c ð Þ . A fit underthis scenario yields a mass difference of : =c and awidth difference of 0.8 MeV. The uncertainty due to thebackground shape is determined by changing to a second-order polynomial and by varying the fit range. A differenceof : =c for the mass is found from the former, anddifferences of : =c for mass and 1.1 MeV for widthare found from the latter. Uncertainties due to the massresolution are estimated by varying the resolution differ-ence between the data and MC simulation by one standard ) (GeV/c c h ± π M ) E v e n t s / ( . G e V / c FIG. 3 (color online). M & h c distribution of e þ e % ! þ % h c candidate events in the h c signal region (dots with error bars) andthe normalized h c sideband region (shaded histogram), summedover data at all energy points. ) (GeV/c c h ± π M ) E v e n t s / ( . G e V / c ) (GeV/c c h + π M ) E v e n t s / ( . G e V / c FIG. 4 (color online). Sum of the simultaneous fits to the M & h c distributions at 4.23, 4.26, and 4.36 GeV as described inthe text; the inset shows the sum of the simultaneous fit to the M þ h c distributions at 4.23 and 4.26 GeV with Z c ð Þ and Z c ð Þ . Dots with error bars are data; shaded histograms arethe normalized sideband background; the solid curves show thetotal fit, and the dotted curves the backgrounds from the fit. PRL week ending13 DECEMBER 2013 E v e n t s / M e V / c E v e n t s / M e V / c M max ( ⇡ ± J/ ) (GeV/c ) M ( ⇡ ± h c (1 P )) (GeV/c ) Figure 8 Discoveries of the Z c (3900) and Z c (4020) at BESIII. (left) Discovery of the Z c (3900) in the π ± J/ψ substructure of the e + e − → π + π − J/ψ reaction (79). (right) Discovery of the Z c (4020) in the π ± h c (1 P ) substructure of e + e − → π + π − h c (1 P ) (81). The points are dataand the solid (green) histogram shows the background estimate from the J/ψ (left) and h c (1 P ) (right) sidebands. The inset in the right plot shows a search for the Z c (3900)decaying to π ± h c (1 P ). Modified from References (79, 81) with permission. conclusively found to have J P = 1 + . This result was also confirmed using a moreexclusive method of reconstruction (83). And in the case of the ( D ∗ ¯ D ∗ ) ± π ∓ chan-nel, the peak occurred at a mass of 4026 . ± . ± . c and had a width of24 . ± . ± . c . (84). While the masses and widths of the open and closedcharm peaks are slightly different, it is reasonable to assume these phenomena arerelated. One of the goals of the BESIII XY Z physics program is to establish patterns amongthe multitude of new states. For example, it seems possible the interpretation ofthe Y (4260) is somehow related to the interpretation of the Z c (3900) and Z c (4020),since the latter are possibly produced in the decays of the former. To establishthis hypothesis, though, the e + e − → Z c (3900 , ± π ∓ cross sections need to bemapped as a function of e + e − center-of-mass energy to see if they follow the shapeof the Y (4260).Another connection between the XY Z states was also possibly found throughthe observation of the process e + e − → γX (3872) (85). Mapping the cross sectionas a function of e + e − center-of-mass energy does appear to trace out the Y (4260).However, more data is needed to show this conclusively. It is hoped that connectionssuch as these among established XY Z states will aid in their interpretation.Another satisfying set of results was the observation of neutral partners to thecharged Z c (3900) and Z c (4020). In this series of analyses, the neutral partner tothe Z c (3900) was seen in the π J/ψ subsystem of e + e − → π π J/ψ (86); theneutral partner to the Z c (4020) was seen in the π h c (1 P ) subsystem of e + e − → π π h c (1 P ) (87); the neutral partner to the charged D ¯ D ∗ state (presumably relatedto the Z c (3900)) was found in the neutral D ¯ D ∗ subsystem of e + e − → π ( D ¯ D ∗ ) (88);and the neutral partner to the charged D ∗ ¯ D ∗ state (presumably related to the 22 R. A. Briere, F. A. Harris and R. E. Mitchell c (4020)) was found in the neutral D ∗ ¯ D ∗ subsystem of e + e − → π ( D ∗ ¯ D ∗ ) (89).Finally, connections are also possibly emerging between the charmonium andstrangeonium systems. BESII observed a state called the Y (2175) (originally ob-served by BaBar using ISR (90)) in the decay J/ψ → ηY (2175) with Y (2175) → f (980) φ and f (980) → π + π − (91). It was confirmed with higher statistics atBESIII (92). This state is thought to possibly be the strangeonium analog of the Y (4260).But alongside the emergence of these patterns have come new problems. The mostprominent of these is the behavior of exclusive e + e − cross sections as a functionof center-of-mass energy, where there currently appears to be little order. It waspreviously known that the Y (4260) appears in the e + e − → π + π − J/ψ cross section,but does not appear in the e + e − → π + π − ψ (2 S ) cross section. Instead, e + e − → π + π − ψ (2 S ) shows two clear structures, one called the Y (4360) and one called the Y (4660). BESIII has already added to this mystery by measuring a number of otherchannels. The e + e − → π + π − h c (1 P ) cross section (81) shows no evidence for the Y (4260), the Y (4360), or the Y (4660), only a very broad hump and possibly a narrowpeak around 4.23 GeV/ c . The ηJ/ψ cross section (93, 94) is also inconsistent with π + π − J/ψ , but a finer scan is needed to determine the energy-dependence. Finally,the ωχ c cross section (95) was seen to peak near threshold, then quickly fade away.What are the mechanisms that cause the cross sections to behave so differently?And why, in general, is so much closed charm being produced so far above opencharm thresholds? With more data in the coming years, BESIII will be capable ofadding valuable information concerning these issues. And there will likely be moresurprises. 9. CHARM PHYSICS At colliders operating near charm threshold, studies of the physics of D and D + mesons are performed primarily via data taken at the ψ (3770) resonance. This isthird-lowest J PC = 1 −− state (the quantum numbers directly accessible in e + e − collisions) and the first with a mass above the D ¯ D threshold. The ψ (3770) decaysprimarily to D + D − and D ¯ D pairs; it lacks sufficient energy to produce even oneadditional pion, which is the lightest hadron. It is common to reconstruct one D meson in a well-understood hadronic final state (the “tag” side), and then study thedecay of the other meson (the “signal” side) to some final state of interest. Thistagging technique removes non-resonant collision events and also reduces combina-torics, i.e., the number of ways of forming the desired final state from the detectedparticles. MARKIII pioneered the use of D tagging to measure absolute D mesonbranching fractions (96, 97); constrained kinematics also permit studies of final stateswith neutrinos. ψ (3770) Properties of the ψ (3770) resonance itself have long been of interest and BESII wasan important contributor in this area. Using a sample of 27.7 pb − taken near3773 MeV, BESII provided the first evidence for a specific non- D ¯ D decay of thisstate: ψ (3770) → J/ψπ + π − (98). A signal of about 12 events with a significanceof more than three standard deviations indicated a branching ratio of order 0.3%. • Physics Accomplishments of the BES Experiments 23 y now, several more exclusive non- D ¯ D modes are known (4), but their sum is stillonly 0.5%. One can investigate instead the inclusive, or total, non- D ¯ D branchingfraction; two subsequent BESII papers addressed this issue. One measured the D ¯ D , D + D − , and total hadronic cross sections vs. CM energy across the ψ (3770) peakregion (99). By subtracting the D ¯ D sum from the total, one obtains B ( ψ (3770) → non − D ¯ D ) = (16 . ± . ± . − of data taken near the ψ (3770) peak. Combinedwith previous determinations of D ¯ D and D + D − peak cross sections (101), BESIIobtained B ( ψ (3770) → non − D ¯ D = (14 . ± . ± . B ( ψ (3770) → non − D ¯ D ) < 9% at 90% confidence level (102), a limit extracted from a result with a centralvalue quite close to zero. More precise determinations are desirable, but controllingsystematic uncertainties is challenging. D Decays BESII also performed a measurement of the semileptonic D decays D → K − e + ν e and D → π − e + ν e (103). These measurements are of great interest as a middle-ground between all-hadronic final states (easy to measure, theoretically difficult) andall-leptonic decays (hard to measure, theoretically clean). Hadronic uncertaintiesare summarized as functions of q = m eν , known as form-factors (FF). Theory canprovide a controlled series expansion of the form-factor shape (104), but the normal-ization has only been addressed by Lattice QCD (LQCD). One can use LQCD as aninput, and directly extract the CKM matrix quark-couplings, | V cd | and | V cs | . This CKM MATRIX V qq (cid:48) : Measures therelative amplitude ofweak interactiontransitions betweenquark types q and q (cid:48) . provides a valuable alternative to other CKM element determinations, which oftenassume there are no quarks beyond the six types currently known. One can alsotest LQCD FF shapes and, using external | V cq | values, also the FF normalizations(in particular, the “intercepts,” or values at q = 0). The BESII work was the firstthreshold semileptonic measurement in fifteen years, since MARKII’s initial workwith 9.56 pb − (105). Modest statistics meant that only estimates of the form-factorintercepts, f + K (0) and f + π (0), were obtained, by assuming naive FF shapes (from so-called “pole models”). But this analysis was a bridge to the modern era: it was soonfollowed by higher-statistics CLEO-c results, which were then surpassed by BESIII.BESIII has accumulated 2.9 fb − of data at the ψ (3770) (106), which is 3.5 timesthe previous largest sample, obtained by CLEO-c. With this, BESIII obtained themost precise semileptonic form factors obtained to date (107). In Figure 9, we displayboth the main signal plot for the more difficult (Cabibbo-suppressed) π − e + ν e mode,as well as the extracted form factor compared to a LQCD result. The key signal Cabibbo Suppression: Reduction of decayrates due to CKMmatrix elementsmuch smaller thanone. variable is U miss = E miss − p miss , where “miss” refers to the missing neutrino four-vector inferred via energy-momentum conservation. As with the following D + → µν analysis, it is impressive how clean a signal is obtained for suppressed decays involvingundetectable neutrinos!The purely leptonic decay D + → µ + ν µ is important since all hadronic uncer-tainties are summarized in one number, the pseudoscalar decay constant, f D + (108).This is related to the square of the wave-function of the quarks forming the D + me-son. It is experimentally challenging, due to Cabibbo-suppression of the rate and thepresence of only one detectable decay product. The analysis reconstructs a hadronic D tag opposite the signal decay, which here consists of only a single muon track. The 24 R. A. Briere, F. A. Harris and R. E. Mitchell nal signal plot makes use of the missing-mass-squared, MM , calculated from theinferred neutrino four-vector, which should peak at MM = m ν = 0. The BESIIIresult is shown in Figure 10. A well-known theoretical expression relates the branch-ing ratio to the decay constant, and BESIII obtains f D + = (203 . ± . ± . 8) MeV(109). This is the most precise determination to date, and it compares well to LQCDcalculations (108). Quantum Correlations The pair of D mesons produced in ψ (3770) decays are correlated: the state of one influences the state of theother. In particular, if one is detected decaying to an odd eigenstate of CP , then the other one must be even,and vice-versa. This involves the same basic quantum mechanics as the famous Einstein-Podolsky-Rosencorrelations of photon pairs. CP Tagging of D ¯ D Pairs from the ψ (3770) Due to quantum correlations, charm threshold data allows for CP -tagging of neutral D mesons: reconstructing one D in a CP eigenstate projects the other into theopposite CP eigenstate. These eigenstates are linear superpositions of the form( D ± ¯ D ) / √ 2. Interference in the decays of such states allows the extraction ofrelative phase information between D and ¯ D decays. A measurement of the D → K − π + “strong phase” difference has been performed in this manner (110) . Thisphase arises from strong-interaction scattering of the final-state particles. BESIII CP : An operationwherein particlesand antiparticles areinterchanged ( C ),and left and rightare inverted ( P ). directly measures the difference between the CP − and CP + eigenstates decayingto K − π + divided by their sum, obtaining the asymmetry A CP = (12 . ± . ± . δ Kπ = 1 . ± . ± . ± . 01 (errors are statistical, systematic, and external),indicating a small phase δ Kπ . This result is useful in the interpretation of D − ¯ D oscillation results obtained using the Kπ final state (111). Other quantum-correlationanalyses are underway; many of these are useful inputs to studies of the CKM matrixperformed with B meson decays. D + and D BESIII continues to broaden its impact on charm physics with analyses using datafrom energies above the ψ (3770). A recent measurement of B (Λ c → Λ e + ν e ) (112),utilizes similar tagging techniques, but with Λ c ¯Λ c pairs produced at 4.6 GeV. Thistechnique has also been applied to hadronic final states, such as Λ c → pKπ (113),the “golden mode” which anchors most Λ c branching fractions. Another example isa recent precise measurement of the D ∗ branching fractions to D π and D γ (114).Using 482 pb − of data taken at √ s = 4009 MeV, BESIII obtains the ratio of decaywidths Γ( D ∗ → D π ) / Γ(( D ∗ → D γ ) = 1 . ± . ± . 05, which is both moreprecise and noticeably higher than previous results.In the near future, BESIII anticipates dedicated running at 4170 MeV, where D ∗± s D ∓ s pairs are produced in abundance, thus adding precision D s physics to the • Physics Accomplishments of the BES Experiments 25 ESIII charm portfolio. In addition, significant samples exist at a variety of otheropen-charm energies, as described above in the discussion of the XY Z states. Withthis wealth of data, one may expect not only increased precision on existing resultsfrom charm threshold, but also novel uses of the large and varied datasets of BESIII. TABLE I. Summary of the single ¯ D tags and efficiencies for reconstruction of the single ¯ D tags, where ∆ E gives therequirements on the energy difference between the measured E Knπ and beam energy E beam , while the M B range defines thesignal region of the single ¯ D tags. N tag is the number of single ¯ D tags and ϵ tag is the efficiency for reconstruction of thesingle ¯ D tags.Tag mode ∆ E (GeV) M BC range (GeV /c ) N tag ϵ tag (%) K + π − ( − . , . . , . ± 848 70 . ± . K + π − π ( − . , . . , . ± . ± . K + π − π − π + ( − . , . . , . ± . ± . K + π − π − π + π ( − . , . . , . ± 749 15 . ± . K + π − π π ( − . , . . , . ± . ± . ± the single ¯ D tags. To select the D → K − e + ν e and D → π − e + ν e events, it is required that there are onlytwo oppositely charged tracks, one of which is identifiedas a positron and the other as a kaon or a pion. Thecombined confidence level CL K ( CL π ) for the K ( π )hypothesis is required to be greater than CL π ( CL K )for kaon (pion) candidates. For positron identification,the combined confidence level ( CL e ), calculated for the e hypothesis using the dE/dx , TOF and EMC measure-ments (deposited energy and shape of the electromag-netic shower), is required to be greater than 0 . CL e / ( CL e + CL π + CL K ) is required to begreater than 0 . 8. We include the 4-momenta of near-byphotons with the direction of the positron momentum topartially account for final-state-radiation energy losses(FSR recovery). In addition, to suppress fake photonbackground it is required that the maximum energy ofany unused photon in the recoil system, E γ, max , be lessthan 300 MeV.Since the neutrino escapes detection, the kinematicvariable U miss ≡ E miss − | ⃗p miss | (IV.6)is used to obtain the information about the missing neu-trino, where E miss and ⃗p miss are, respectively, the totalmissing energy and momentum in the event, computedfrom E miss = E beam − E h − − E e + , (IV.7)where E h − and E e + are the measured energies of thehadron and the positron, respectively. The ⃗p miss is cal-culated by ⃗p miss = ⃗p D − ⃗p h − − ⃗p e + , (IV.8)where ⃗p D , ⃗p h − and ⃗p e + are the momenta of the D me-son, the hadron and the positron, respectively. The 3-momentum ⃗p D of the D meson is computed by ⃗p D = − ˆ p tag ! E − m D , (IV.9)where ˆ p tag is the direction of the momentum of the single¯ D tag. If the daughter particles from a semileptonic (a) (b) -0.2 -0.1 0 0.1 0.20100200300400 (GeV) miss U E v en t s / ( . M e V ) FIG. 2. U miss distributions of events for (a) ¯ D tags vs. D → K − e + ν e , and for (b) ¯ D tags vs. D → π − e + ν e ,where the dots with error bars show the data, the solid linesshow the best fit to the data, and the dashed lines show thebackground shapes estimated by analyzing the “cocktail vs.cocktail D ¯ D process” Monte Carlo events and the “non- D ¯ D process” Monte Carlo events (see text for more details). decay are correctly identified, U miss is zero, since onlyone neutrino is missing.Figures 2 (a) and (b) show the U miss distributions forthe D → K − e + ν e and D → π − e + ν e candidate events,respectively. In both cases, most of the events are fromthe D → K − e + ν e and D → π − e + ν e decays. Back-grounds from D ¯ D processes include mistagged ¯ D and D decays other than the semileptonic decay in ques-tion. Other backgrounds are from “non- D ¯ D process”processes. From the simulated “cocktail vs. cocktail D ¯ D process” events, we find that the D ¯ D background eventsare mostly from D → K − π e + ν e , D → K − µ + ν µ and D → π − e + ν e selected as D → K − e + ν e , and TABLE I. Summary of the single ¯ D tags and efficiencies for reconstruction of the single ¯ D tags, where ∆ E gives therequirements on the energy difference between the measured E Knπ and beam energy E beam , while the M B range defines thesignal region of the single ¯ D tags. N tag is the number of single ¯ D tags and ϵ tag is the efficiency for reconstruction of thesingle ¯ D tags.Tag mode ∆ E (GeV) M BC range (GeV /c ) N tag ϵ tag (%) K + π − ( − . , . . , . ± 848 70 . ± . K + π − π ( − . , . . , . ± . ± . K + π − π − π + ( − . , . . , . ± . ± . K + π − π − π + π ( − . , . . , . ± 749 15 . ± . K + π − π π ( − . , . . , . ± . ± . ± the single ¯ D tags. To select the D → K − e + ν e and D → π − e + ν e events, it is required that there are onlytwo oppositely charged tracks, one of which is identifiedas a positron and the other as a kaon or a pion. Thecombined confidence level CL K ( CL π ) for the K ( π )hypothesis is required to be greater than CL π ( CL K )for kaon (pion) candidates. For positron identification,the combined confidence level ( CL e ), calculated for the e hypothesis using the dE/dx , TOF and EMC measure-ments (deposited energy and shape of the electromag-netic shower), is required to be greater than 0 . CL e / ( CL e + CL π + CL K ) is required to begreater than 0 . 8. We include the 4-momenta of near-byphotons with the direction of the positron momentum topartially account for final-state-radiation energy losses(FSR recovery). In addition, to suppress fake photonbackground it is required that the maximum energy ofany unused photon in the recoil system, E γ, max , be lessthan 300 MeV.Since the neutrino escapes detection, the kinematicvariable U miss ≡ E miss − | ⃗p miss | (IV.6)is used to obtain the information about the missing neu-trino, where E miss and ⃗p miss are, respectively, the totalmissing energy and momentum in the event, computedfrom E miss = E beam − E h − − E e + , (IV.7)where E h − and E e + are the measured energies of thehadron and the positron, respectively. The ⃗p miss is cal-culated by ⃗p miss = ⃗p D − ⃗p h − − ⃗p e + , (IV.8)where ⃗p D , ⃗p h − and ⃗p e + are the momenta of the D me-son, the hadron and the positron, respectively. The 3-momentum ⃗p D of the D meson is computed by ⃗p D = − ˆ p tag ! E − m D , (IV.9)where ˆ p tag is the direction of the momentum of the single¯ D tag. If the daughter particles from a semileptonic (a) (b) -0.2 -0.1 0 0.1 0.20100200300400 (GeV) miss U E v en t s / ( . M e V ) FIG. 2. U miss distributions of events for (a) ¯ D tags vs. D → K − e + ν e , and for (b) ¯ D tags vs. D → π − e + ν e ,where the dots with error bars show the data, the solid linesshow the best fit to the data, and the dashed lines show thebackground shapes estimated by analyzing the “cocktail vs.cocktail D ¯ D process” Monte Carlo events and the “non- D ¯ D process” Monte Carlo events (see text for more details). decay are correctly identified, U miss is zero, since onlyone neutrino is missing.Figures 2 (a) and (b) show the U miss distributions forthe D → K − e + ν e and D → π − e + ν e candidate events,respectively. In both cases, most of the events are fromthe D → K − e + ν e and D → π − e + ν e decays. Back-grounds from D ¯ D processes include mistagged ¯ D and D decays other than the semileptonic decay in ques-tion. Other backgrounds are from “non- D ¯ D process”processes. From the simulated “cocktail vs. cocktail D ¯ D process” events, we find that the D ¯ D background eventsare mostly from D → K − π e + ν e , D → K − µ + ν µ and D → π − e + ν e selected as D → K − e + ν e , and f π + (0) | V cd | f K + (0) | V cs | given inEq.(VI.27) together with the LCSR calculation of f π + (0) /f K + (0) = 0 . ± . 04 [44], we determine | V cd || V cs | = 0 . ± . ± . ± . , (VII.3)where the first error is statistical, the second one system-atic, and the third one is from LCSR normalization. B. Comparison of | V cs | and | V cd | Table XVIII and Table XIX give comparisons of ourmeasured | V cs | and | V cd | with those measured at otherexperiments. Our measurements of | V cs | and | V cd | are ofhigher precision than previous results from both D mesondecays and W boson decays. ) /c (GeV q ) ( q K + f e ν + e - K → (a) D dataLQCDLQCD stat. errorLQCD syst. error ) /c (GeV q ) ( q π + f e ν + e - π→ (b) D dataLQCDLQCD stat. errorLQCD syst. error FIG. 10. Comparisons of the measured form factors (squareswith error bars) with the LQCD calculations [14] (solid linespresent the central values, bands present the LQCD uncer-tainties). Table XX gives a comparison of our measured | V cd | / | V cs | with the one measured by CLEO-c [28] andthe world average calculated with | V cd | and | V cs | given inPDG2014 [6]. Our measurement of the ratio is in excel-lent agreement with the world average. VIII. SUMMARY In summary, by analyzing about 2.92 fb − data col-lected at 3.773 GeV with the BESIII detector operatedat the BEPCII collider, the semileptonic decays of D → K − e + ν e and D → π − e + ν e have been studied. From atotal of 2793317 ± D tags, 70727 . ± . D → K − e + ν e and 6297 . ± . D → π − e + ν e signalevents are observed in the system recoiling against thesingle ¯ D tags. These yield the decay branching frac-tions B ( D → K − e + ν e ) = (3 . ± . ± . B ( D → π − e + ν e ) = (0 . ± . ± . . Using these samples of D → K − e + ν e and D → π − e + ν e decays, we study the form factors as a functionof the squared four-momentum transfer q for these twodecays. By fitting the partial decays rates, we obtain theparameter values for several different form-factor func-tions. For the physical interpretation of the shape pa-rameters in the single pole and modified pole models,the values of the parameters obtained from our fits sig-nificantly deviate from those expected by these models.This means that the data do not support the physicalinterpretation of the shape parameter in those models.We choose the values of f K + (0) | V cs | and f π + (0) | V cd | ob-tained with the two-parameter series expansion as ourmain result. In this case, we obtain the form factors f K + (0) = 0 . ± . ± . f π + (0) = 0 . ± . ± . . Furthermore, using the form factors calculated in recentLQCD calculations [45, 46], we obtain the CKM matrixelements | V cs | = 0 . ± . ± . ± . | V cd | = 0 . ± . ± . ± . , where the errors are dominated by the theoretical un-certainties in the form factor calculations. Our measure-ment of the product f K + (0) | V cs | = 0 . ± . ± . f π + (0) | V cd | = 0 . ± . ± . | V cs | Figure 9 BESIII analysis of D → π − e + ν e . Left: U miss = E miss − p miss distribution; the bluecurve is a fit to the data points, including the red dashed background contribution Right:The extracted form factor, f π ( q ), compared to lattice QCD. Modified from Ref. (107)with permission. K L π + and D + → π + π , as well as D + → τ + ν τ , are es-timated by analyzing Monte Carlo samples that are 10times larger than the data. The input branching fractionsfor D + → K L π + and D + → π + π are from Ref. [2].For estimation of the backgrounds from D + → τ + ν τ decay, we use branching fraction B ( D + → τ + ν τ ) =2 . × B ( D + → µ + ν µ ), where B ( D + → µ + ν µ ) is quotedfrom Ref. [10] and 2.67 is expected by the SM. ] /c [GeV miss2 M-0.2 0 0.2 0.4 0.6 N u m b e r o f E v e n t s -1 10 110 Data µ ν + µ → + D + π L0 K → + D π + π → + D τ ν + τ → + DOther D decays processesDnon-D ] /c [GeV miss2 M-0.2 0 0.2 0.4 0.6 N u m b e r o f E v e n t s -1 10 110 FIG. 2: The M distribution for selected single µ + can-didates, where dots with error bars indicate the data, theopened histogram is for Monte Carlo simulated signal eventsof D + → µ + ν µ decays, and the hatched histograms are for thesimulated backgrounds from D + → K L π + (red), D + → π π + (green), D + → τ + ν τ (blue), all other D -meson decays (yel-low), and non- D ¯ D processes (pink). The backgrounds from other D decays are correctedconsidering the difference in the numbers of events fromthe data and simulated events in the range from 0 . . 60 GeV /c . Other background events are from e + e − → γ ISR ψ (3686), e + e − → γ ISR J/ψ , where γ ISR denotes the photon produced due to initial state radi-ation, e + e − → q¯q (q = u, d, or s), e + e − → τ + τ − and ψ (3770) → non- D ¯ D decays that satisfy the event-selection criteria of purely leptonic decays. The num-bers of these background events are estimated by ana-lyzing Monte Carlo samples of each of the above-listedprocesses, which are about 10 times more than the data.After normalizing these numbers of background eventsfrom the Monte Carlo samples to the data, we expectthat there are 42 . ± . . ± . ± . N netsig ) for D + → µ + ν µ remain, where the first error is statistical and the sec-ond is the systematic associated with the uncertaintyof the background estimate. The weighted overall effi-ciency for detecting D + → µ + ν µ decays is determined to be ϵ = 0 . ± . D + → µ + ν µ in each tagged D − mode;here the error is due to Monte Carlo statistics. Final stateradiation is included in the Monte Carlo simulation.Inserting N D − tag , N netsig and ϵ into B ( D + → µ + ν µ ) = N netsig N D − tag × ϵ and subtracting from the signal a 1 . 0% contribution com-ing from D + → γD ∗ + → γµ + ν µ [10, 11], in which D ∗ + is a virtual vector or axial-vector meson, yields B ( D + → µ + ν µ ) = (3 . ± . ± . × − , where the first error is statistical and the second sys-tematic. This measured branching fraction is consistentwithin errors with those measured at BES-I [12], BES-II [13], and CLEO-c [10], but with the best precision.The systematic uncertainty in the D + → µ + ν µ branch-ing fraction determination includes seven contributions:(1) the uncertainty in the number of D − tags (0 . M BC dis-tribution (0 . π ratesbetween the data and the Monte Carlo events (0 . µ tracking/identification (0 . / . µ tracking/identificationefficiencies for data and Monte Carlo events, where the µ ± samples are from the copious e + e − → γµ + µ − pro-cess; (3) the uncertainty in the E γ max selection require-ment (0 . D ¯ D hadronic decay events in the data and Monte Carlo;(4) the uncertainty associated with the choice of the M signal window (0 . . . . . G F , themass of the muon, the mass of the D + meson and thelifetime of the D + meson [2] into Eq.(1) yields f D + | V cd | = (45 . ± . ± . 39) MeV , where the first error is statistical and the second system-atic arising mainly from the uncertainties in the mea-sured branching fraction (1 . D + meson (0 . . f D + | V cd | . Figure 10 Distribution of missing-mass-squared, M miss , for the D → µν µ analysis, showing clear andclean excess at m ν = 0. The blue fit to the data points includes many backgroundprocesses shown as colored shaded regions. Modified from Ref. (109) with permission. 10. FUTURE PROSPECTS The scientific output summarized in this review is both broad in scope and acceler-ating in pace. Physics results obtained by BES inform a variety of subjects, directlyimpacting our understanding of both weak and strong interactions. Traditional ar-eas of strength have been supplemented by new topical areas, such as studies of the 26 R. A. Briere, F. A. Harris and R. E. Mitchell xotic XY Z states and searches for new particles.The current BESIII collaboration has grown, both in size and in internationalparticipation, into a leading player in particle physics today. Existing data setsare proving to be very productive and data-taking runs are anticipated to continuebeyond 2020. As discussed in the previous sections, these future physics resultspromise to be an substantial addition to the existing BES legacy. 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