MMeasurement of Hadronic Cross Sections at BESIII
Christoph Florian Redmer for the BESIII Collaboration
Institute for Nuclear PhysicsJohannes Gutenberg-University Mainz, 55128 Mainz, GERMANY
The uncertainties of the Standard Model prediction of the anomalousmagnetic moment of the muon are currently completely dominated byhadronic contributions. The largest contribution is due to the hadronicvacuum polarization. Hadronic cross sections measured at e + e − colliderscan be exploited as experimental input to improve the calculations, mak-ing use of the optical theorem. At the BESIII experiment in Beijing thesecross sections are determined using different methods. At center-of-massenergies above 2 GeV exclusive and inclusive cross sections can be mea-sured in an energy scan. Additionally, cross sections can be determinedstarting from the π + π − mass threshold using the method of Initial StateRadiation. An overview of the recent results and the status of the analysesis provided. PRESENTED AT Thirteenth International Conference on the Intersections ofParticle and Nuclear Physics (CIPANP2018)Palm Springs, California, May 28–June 3, 2018 a r X i v : . [ h e p - e x ] O c t Anomalous magnetic moment of the muon
The muon anomaly a µ = g µ − describes the relative deviation of the muon’s gyro-magnetic factor from the value expected in Dirac theory, which is g µ = 2. It is one ofthe most precisely determined parameters in the Standard Model (SM). The theoryprediction as well as the direct measurement have achieved an accuracy on the levelof 0.5 ppm. However, there is a long standing discrepancy between experiment andtheory, which differ by more than three standard deviations [1]. This difference givesrise to numerous activities in experiment as well as theory in order to understand ifit should be considered as a hint for New Physics.The most recent direct measurement of a µ was performed by E821 at BNL [2].Two new and systematically independent direct measurements of a µ are planned.Both aim at a fourfold improvement of the Brookhaven result. The E989 experimentat Fermilab reuses the BNL storage ring [3]. Higher beam intensities and an improvedapparatus are used to bring down the errors. It is expected to reproduce the accuracyof the BNL result by spring 2019. The second experiment is under construction at J-PARC [4]. A new and independent approach is applied by using a beam of ultra-coldmuons, which allows to avoid the use of focusing electric fields.The SM prediction of a µ takes into account contributions from electromagnetic,weak and strong interactions. While the first two are well understood and known withgood accuracy, the latter completely dominates the uncertainty of the SM prediction.Due to the running of the strong coupling constant, the contribution cannot be treatedin perturbation theory at the relevant energies. The contribution of strong interactionis separated into two parts. On the one hand there is the contributions due to thehadronic vacuum polarization a hV Pµ , and on the other hand there is the contributiondue to the hadronic light-by-light scattering a hLbLµ . Recently, there have been a lot ofactivities to calculate these contributions in lattice QCD [5]. Another approach is touse experimental data as input to the calculations for the SM prediction. Especiallythe leading order contribution of a hV Pµ can be systematically improved in this way.Here, the optical theorem relates the vacuum polarization to hadronic cross sections,which can be measured in e + e − annihilation. By increasing the accuracy of thecross section measurements, the uncertainty of a hV Pµ is reduced. The measured crosssections are evaluated in a dispersion integral, which also contains a kernel function.Both the kernel function as well as the cross sections show an energy dependence,which decreases with the square of the center-of-mass energy. Thus, the knowledgeof hadronic cross sections at √ s < ρ resonance, which predominantly decay into π + π − pairs.The cross section σ ( e + e − → π + π − ) makes up for more than 70% of the value of a hV Pµ . It is also the dominating contribution to the uncertainty of a hV Pµ , however,here also higher pion multiplicities, and final states with kaons play a significant role.In order to contribute to the efforts to improve the SM prediction of a µ , the BESIII1ollaboration has started a program to measure hadronic cross sections with highaccuracy. The BESIII detector is a magnetic spectrometer [6] located at the Beijing ElectronPositron Collider (BEPCII) [7]. The cylindrical core of the BESIII detector consistsof a helium-based multilayer drift chamber (MDC), a plastic scintillator time-of-flightsystem (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all en-closed in a superconducting solenoidal magnet providing a 1.0 T magnetic field. Thesolenoid is supported by an octagonal flux-return yoke with resistive plate countermuon identifier modules interleaved with steel. The acceptance of charged particlesand photons is 93% over 4 π solid angle. The charged-particle momentum resolutionat 1 GeV /c is 0 . dE/dx resolution is 6% for the electrons from Bhabhascattering. The EMC measures photon energies with a resolution of 2 .
5% (5%) at1 GeV in the barrel (end cap) region. The time resolution of the TOF barrel part is68 ps, while that of the end cap part is 110 ps.The accelerator BEPCII provides e + e − collisions at center-of-mass energies be-tween √ s = 2 . GeV and 4.6 GeV. The performance in terms of peak luminosityis optimized for data taking at √ s = 3 .
773 GeV, which corresponds to the peak ofthe ψ (3770) resonance. The design luminosity of 10 cm − s − is reached. Over thepast years large data samples have been collected, which are used to pursue the BE-SIII physics program, focusing on charm physics, charmonium and charmoniumlikespectroscopy, light hadron physics, QCD tests, and precise τ mass measurements.Hadronic cross section are measured at BESIII using different techniques. In theenergy range covered by BEPCII the energy dependence of cross sections can bestudied in a conventional energy scan. It is used to investigate exclusive as well asinclusive cross section, like the R-ratio, which relates the total inclusive hadronic crosssection to the cross section of muon pair production.Recently, also the method of initial state radiation (ISR) is used to extend theaccessible energy range. The emission of a photon from the initial state lowers theeffective center-of-mass energy √ s (cid:48) = (cid:113) s − √ sE γ , where E γ is the energy of theISR photon. The method allows to study hadronic cross sections down to √ s = 2 m π .However, cross sections measured through ISR events are radiative cross sections.The cross section of the non-radiative process can be calculated, taking into accountthe radiator function H ( s, E γ , θ γ ), which describes the probability at a specific √ s toemit an ISR photon of the energy E γ at the polar angle θ γ . The relation of radiativeand non-radiative cross sections is given by dσ had+ γ dm γ = m had s H ( s, E γ , θ γ ) σ had .The ISR photons are emitted with a characteristic angular distribution, where theemission along the initial lepton beam direction is strongly preferred. Due to momen-2um conservation, a hadronic system produced at √ s (cid:48) is boosted to the opposite direc-tion. Depending on the possibility to register the ISR photon in the BESIII detector,two different analysis strategies are defined for ISR events. When the hadronic sys-tem as well as the ISR photon are detected the measurement is referred to as “taggedISR measurement”. In this case, cross sections can be measured from √ s (cid:48) = 2 m π inprinciple up to √ s . However, the larger the mass of the produced hadronic system,i.e. √ s (cid:48) becomes, the higher is the background contamination. Random signals inthe EMC, e.g. from noise or machine background, can easily be mistaken the lowenergetic ISR photon. This is much less of a problem when the ISR photon escapesdetection by being emitted along the beam pipe and only the hadronic system ismeasured. This type of measurement is referred to as “untagged ISR measurement”.The four-momentum of the unmeasured photon can be reconstructed using energyand momentum conservation. By rejecting event candidates, where the momentumdoes not point along the beam axis, background is rejected efficiently. At the sametime this analysis strategy selects the peaking part of the differential cross section ofthe ISR process, allowing for a high statistics measurement. A slight restriction inthe applicability of the method comes from the boost of the hadronic system. Thehigher the energy of the emitted photon, the more the hadrons are boosted towardsthe beam axis, where the detector acceptance is limited due to the accelerator. Thus,there is a lower limit for the mass of hadronic systems to be measured in the un-tagged ISR method. The acceptance of the BESIII detector imposes a threshold ofapproximately 1 GeV/c .The radiation of a photon from the initial state is a higher order effect. Radiativeprocesses are suppressed by a factor απ . Precision studies performed using either ofthe ISR methods require large data samples. The BESIII collaboration has acquireddata sets of more than 10 fb − at √ s ≥ .
773 GeV [15, 16]. Hadronic cross sectionsare measured based on these data sets making use of both the tagged and untaggedISR methods. e + e − → π + π − Since the cross section σ ( e + e − → π + π − ) make up for more than 70% of a hV Pµ , it isof utmost importance to have data with highest accuracy to improve the SM predic-tion. The pion production process has been studied by several experiments in thepast. The results with leading accuracy come from the KLOE [9] and BaBar [10]collaborations. Both claim sub-percent accuracy for their results. However, the datadiffer by more than 3%, which is also reflected in the uncertainty of the evaluation of a hV P,LOµ . In order to clarify the situation, a new high precision measurement has beenperformed at BESIII [11]. Using the tagged ISR method, a data set of 2.93 fb − takenat √ s = 3 .
773 GeV has been analyzed. The cross section of two-pion production at300 ≤ √ s [ GeV] ≤
900 is investigated selecting the final state π + π − γ . Radiative pro-duction of muon pairs in e + e − → µ + µ − γ is the dominating background contribution.The similarity of the signals of pions and muons in most detectors make it hard todistinguish them based on a single source of information. An artificial neural network(ANN) has been designed combining the information from different sub-detectors,like energy loss in the MDC, energy deposits and shower shapes in the EMC, and thepenetration depth of a particle in the MUC. Taking carefully into account system-atic differences between data and simulation, the ANN is trained with Monte Carlosamples. It allows to effectively separate muons from pions. The correct operation ofthe ANN and the validity of systematic corrections has been tested by comparing themuon event yield in data with the QED prediction as implemented in the Phokhara event generator [12], where an accuracy of 0.5% is claimed. Excellent agreement withthe selected data is found.Finally, the e + e − → π + π − γ ISR signal event yield is corrected for detection effi-ciency, and is normalized to the integrated luminosity of the data set to obtain theradiative cross section. By correcting for vacuum polarization and FSR effects, andby dividing out the radiator function, the bare cross section, relevant to determinethe contribution to a hV P,LOµ , is calculated. A total uncertainty of the cross sectionof 0.9% is achieved. The dominating systematic uncertainties are due to the lumi-nosity determination and the knowledge of the radiator function, with 0.5% each.Extracting the cross section by normalizing to the muon yield might avoid these twocontributions, however, the statistical uncertainty of the muon yield in the analyzeddata does not allow for a result with the aimed accuracy. [GeV]s' | p | F BESIII fit BESIII ] -10 (600 - 900 MeV) [10 ,LO ppm a
360 365 370 375 380 385 390 395
BaBar 09KLOE 12KLOE 10KLOE 08BESIII 1.9 – – – – – – – – – – – – – Figure 1: (From Ref. [11]) left:
Pion form factor determined at BESIII with theresult of a Gounaris-Sakurai fit. right:
Comparison of a ππ,LOµ (600 −
900 MeV) deter-mined at BESIII and by previous experiments.The BESIII result is compared with previous measurements based on a fit of thepion form factor with a Gounaris-Sakurai parameterization, which is illustrated inFig. 1. Though systematic deviations can be observed for both the KLOE results aswell as the BaBar results, the value of a hV P,LOµ obtained from the evaluation of thedispersive integral agrees nicely with the values obtained by the KLOE collaboration,4s shown in Fig. 1. The result of the BESIII measurement is a ππ,LOµ (600 −
900 MeV) =368 . ± . stat ± . syst · − . It confirms the deviation between the direct measurementand the SM prediction of a µ to be on the level of more than three standard deviations.Recent dispersive evaluations of compilations of hadronic cross sections [13, 14], whichinclude the BESIII result, were able to reduce the uncertainty of the hadronic vacuumcontribution to a µ by more than 20%. e + e − → π + π − π The same data set of 2.93 fb − taken at √ s = 3 .
773 GeV is used to investigate thecross section of e + e − → π + π − π . In this analysis both the tagged and untagged ISRmethod are applied. The final result is obtained from the error weighted mean ofboth methods.For the tagged analysis, events with two oppositely charged tracks and at leastthree photons are selected. A 5 C kinematic fit, constrained by energy and momentumconservation, as well as the mass of the π for two photon candidates, is applied toreject background and to settle the photon combinatorics. An additional requirement,where the assigned ISR photon combined with another photon candidate in the eventshows an invariant mass close to the π mass, can effectively suppress remainingbackground.In the untagged analysis, events with at least two photon candidates are accepted.The kinematic fit is performed, considering the ISR photon an an unmeasured particle,with known mass but unknown momenta. Consequently, the number of constraintsof the fit reduces to 2 C . Remaining background can be efficiently suppressed byrejecting all events where the photon four-momentum resulting from the kinematicfit is not pointing along the beam axes, i.e. | cos θ γ ISR | ≤ . e + e − → π + π − π π ( γ ISR ). It is studied in aseparate analysis in order to tune MC simulations for reduced systematics due tobackground subtraction. Details of the analysis can be found in section 5.From the extracted signal event yields, the differential cross section is calculated.Figure 2 shows the preliminary results for the cross section as function of √ s . Atthe narrow resonances ω and φ the BESIII result can be compared with the resultsof the scan measurements performed at CMD-2 [18]. Good agreement is observedis both cases. The systematic uncertainty at the narrow resonances is better than2%. Above the φ (1020), the previous measurements are dominated BaBar result [19],obtained in an ISR measurement. Good agreement is observed with the BaBar result,including the structure attributed to the ω (cid:48)(cid:48) resonance, which was not observed in themeasurement by DM2 [20]. A VMD inspired fit function can only describe the BESIIIdata by including this resonance. Furthermore, the preliminary result also allows to5 (GeV/c π - π + π M C r o ss s e c t i on ( nb ) × BESIIICMD2 M ( ω ) BESIII preliminary ) (GeV/c π - π + π M C r o ss s e c t i on ( nb ) BESIIICMD2 M ( φ ) BESIII preliminary ) (GeV/c π - π + π M C r o ss s e c t i on ( nb ) BESIIIBESIII fitBABARSNDDM2
Above φ BESIII preliminary
Figure 2: Comparison of the preliminary BESIII results for the cross section of e + e − → π + π − π (solid black) and previous measurements. left/center: At the ω/φ resonances with CMD-2 results [18] (open blue). right:
Above the φ resonances withBabar [19] and DM2 [20]. The green line shows a fit to the BESIII data.determine the branching ratio of J/ψ → π + π − π . The final publication will alsocontain the resulting contribution of the three-pion channel to a hV P,LOµ . e + e − → π + π − π π The analysis of the four pion final state is performed analogously to the strategydescribed in section 4, taking into account the higher photon multiplicity for theadditional π . The tagged ISR method applies a 6 C kinematic fit, exploiting theadditionally possible constraint of another π mass. In the same manner, a 3 C fit isperformed for the untagged ISR method. The dominating background contributionis the five-pion channel with three neutral pions. It is measured in a separate analysisin order to accommodate for a reliable background subtraction. Special attention isalso paid to the systematic differences in the reconstruction efficiency of π . The totalsystematic uncertainty of the preliminary result is estimated to be on the level of 3%.Figure 3 shows the preliminary result of the cross section for e + e − → π + π − π π . TheBESIII result is in good agreement with the recently published BaBar result [21].Both results illustrate the potential of the ISR method to provide data with highaccuracy over a wide energy range. The BESIII result has also been used to calculatethe preliminary value of the contribution a π + π . π ,LOµ = 18 , ± . ± .
57, whichagrees well within errors with the published value from BaBar.Further investigations of the possible sub-processes in e + e − → π + π − π π havebeen carried out by studying the cross section as a function of the masses of dif-ferent final state particle combinations. The important sub-process e + e − → ωπ isstudied by determining the contribution of the ω resonance in the three-pion mass M ( π + π − π ). The preliminary result of the cross section is shown in Fig. 3, and is ingood agreement with previous measurements, while providing an improved accuracy.6 ) [GeV/c π - π + π M( ) [ nb ] π - π + π → - e + ( e σ SNDCMD2GG2ACOM3NNDMEAOLYABaBar
BESIII preliminary
BESIII ] ) [GeV/c pw M( ) [ nb ] pwfi - e + ( e s BESIIISNDSND-2000CMD2NDDM2KLOE
BESIII preliminary
Figure 3: left:
The preliminary cross section of e + e − → π + π − π π from BESIII(solid black), compared to the BaBar result [21] (solid green), and further previousscan measurements. right: The cross section of the sub-process e + e − → ωπ fromBESIII (solid black) and previous scan experiments. With the high accuracy measurement of the pion form factor, the BESIII collaborationprovided already important input to the SM calculations of a µ . The accuracy of thecurrent result is limited by systematics. An alternative approach, which normalizesthe pion cross section to the muon yield, can reduce the uncertainties, but requireshigher statistics. It is planned to extend the data set at √ s = 3 .
773 GeV to anintegrated luminosity of 20 fb − . This data set will be large enough to determine thepion form factor with an expected accuracy on the level of 0.5%.Additionally, the hadronic cross sections at higher multiplicities are studied. Theresults for e + e − → π + π − π and e + e − → π + π − π π will be published in the nearfuture and provide further important input for a µ . The cross section of e + e − → π + π − π , measured to determine the background contributions to e + e − → π + π − π π provides the first accurate measurement for the cross section in more than sixty years.So far, the channel has been taken into account in a hV Pµ by evaluating isospin relations.Apart from exclusive processes, also a measurement of the inclusive cross sectionratio R of hadron production to muon production is performed [22]. A scan over thefull energy range covered by BEPCII has been performed, providing 130 scan points.The expected number of more than 10 hadronic events at each energy allows for ameasurement of the R ratio, which is not limited by statistics. The final goal for themeasurement is an accuracy of better than 3%. It is expected that the dominatinguncertainties come from the event generator LundAreaLaw [23], which is used toestimate the reconstruction efficiencies. 7 eferences [1] T. Blum, A. Denig, I. Logashenko, E. de Rafael, B. Lee Roberts, T. Teubner andG. Venanzoni, arXiv:1311.2198 [hep-ph].[2] G. W. Bennett et al. , [Muon g-2 Collaboration], Phys. Rev. D , 072003, 2006.[3] J. Grange et al. [Muon g-2 Collaboration], arXiv:1501.06858, 2015.[4] Tsutomu Mibe [J-PARC g-2 Collaboration], Nucl. Phys. Proc. Suppl. 218, 242-246, 2011.[5] T. Blum et al. [RBC and UKQCD Collaborations], Phys. Rev. Lett. , 022003(2018).T. Blum, S. Chowdhury, M. Hayakawa and T. Izubuchi, Phys. Rev. Lett. ,012001 (2015).[6] M. Ablikim et al. [BESIII Collaboration], Nucl. Instrum. Meth. A , 345(2010).[7] C. H. Yu et al. , Proceedings of IPAC2016, Busan, Korea, 2016,doi:10.18429/JACoW-IPAC2016-TUYA01.[8] X. Li et al. , Radiat. Detect. Technol. Methods , 13 (2017);Y. X. Guo et al. , Radiat. Detect. Technol. Methods , 15 (2017).[9] A. Anastasi et al. [KLOE-2 Collaboration], JHEP , 173 (2018).[10] B. Aubert et al. [BaBar Collaboration], Phys. Rev. Lett. , 231801 (2009).[11] M. Ablikim et al. [BESIII Collaboration], Phys. Lett. B , 629 (2016).[12] G. Rodrigo, H. Czyz, J. H. Kuhn, and M. Szopa, Eur. Phys. J. C , 71 (2002).H. Czyz, J. H. Kuhn, and A. Wapienik, Phys. Rev. D , 114005 (2008).[13] M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang, Eur. Phys. J. C , 827(2017).[14] A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D , 114025 (2018).[15] M. Ablikim et al. [BESIII Collaboration], Chin. Phys. C , 123001 (2013).[16] M. Ablikim et al. [BESIII Collaboration], Chin. Phys. C , 093001 (2015).[17] M. Ablikim et al. [BESIII Collaboration], Chin. Phys. C et al. [CMD-2 Collaboration] Phys. Lett. B
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