Measurement of J/psi leptonic width with the KEDR detector
V.V.Anashin, V.M.Aulchenko, E.M.Baldin, A.K.Barladyan, A.Yu.Barnyakov, M.Yu.Barnyakov, S.E.Baru, I.Yu.Basok, O.L.Beloborodova, A.E.Blinov, V.E.Blinov, A.V.Bobrov, V.S.Bobrovnikov, A.V.Bogomyagkov, A.E.Bondar, A.R.Buzykaev, S.I.Eidelman, D.N.Grigoriev, Yu.M.Glukhovchenko, V.V.Gulevich, D.V.Gusev, S.E.Karnaev, G.V.Karpov, S.V.Karpov, T.A.Kharlamova, V.A.Kiselev, V.V.Kolmogorov, S.A.Kononov, K.Yu.Kotov, E.A.Kravchenko, V.N.Kudryavtsev, V.F.Kulikov, G.Ya.Kurkin, E.A.Kuper, E.B.Levichev, D.A.Maksimov, V.M.Malyshev, A.L.Maslennikov, A.S.Medvedko, O.I.Meshkov, S.I.Mishnev, I.I.Morozov, N.Yu.Muchnoi, V.V.Neufeld, S.A.Nikitin, I.B.Nikolaev, I.N.Okunev, A.P.Onuchin, S.B.Oreshkin, I.O.Orlov, A.A.Osipov, S.V.Peleganchuk, S.G.Pivovarov, P.A.Piminov, V.V.Petrov, A.O.Poluektov, V.G.Prisekin, A.A.Ruban, V.K.Sandyrev, G.A.Savinov, A.G.Shamov, D.N.Shatilov, B.A.Shwartz, E.A.Simonov, S.V.Sinyatkin, A.N.Skrinsky, V.V.Smaluk, A.V.Sokolov, A.M.Sukharev, E.V.Starostina, A.A.Talyshev, V.A.Tayursky, V.I.Telnov, Yu.A.Tikhonov, K.Yu.Todyshev, G.M.Tumaikin, Yu.V.Usov, A.I.Vorobiov, A.N.Yushkov, V.N.Zhilich, V.V.Zhulanov, A.N.Zhuravlev
aa r X i v : . [ h e p - e x ] O c t CPC(HEP & NP), 2009, (6): 836—841 Chinese Physics C
Vol. 34, No. 6, Jun, 2009
Measurement of
J/ψ leptonic width with the KEDRdetector * A. G. Shamov , [KEDR collaboration] Abstract
We report a new precise determination of the leptonic widths of the J/psi meson performed withthe KEDR detector at the VEPP-4M e + e − collider. The measured values of the J/psi parameters are:Γ ee × Γ ee / Γ = 0 . ± . ± . , Γ ee × Γ µµ / Γ = 0 . ± . ± . . Assuming eµ universality and using the table value of the branching ratios the leptonic Γ ℓℓ = 5 . ± .
12 keVwidth and the total Γ = 94 . ± . Key words
J/ψ meson, lepton width, full width
PACS
The
J/ψ meson is frequently referred to as a hy-drogen atom for QCD. The electron widths Γ ee ofcharmonium states are rather well predicted by po-tential models [1, 2]. The uncertainty in the QCD lat-tice calculations of Γ ee gradually approaches the ex-perimental errors [3]. The full and dileptonic widthsof a hadronic resonance, Γ and Γ ℓℓ , describe funda-mental properties of the strong potential [4].In this report we discuss the results of the J/ψ meson observation in leptonic decay channels. Studyof the e + e − → J/ψ → ℓ + ℓ − cross section as functionof energy allows one to determine the leptonic widthΓ ℓℓ and its product to the decay ratio Γ ee × Γ ℓℓ / Γ thusthe total width Γ can be also found. The productΓ ee × Γ ℓℓ / Γ determines the peak cross section whilethe leptonic width Γ ℓℓ is contained in the interferencewave magnitude. Due to smallness of the interferenceeffect the experimental accuracy of the Γ ℓℓ determina-tion is rather poor. However, the branching ratio B ℓℓ is known with the accuracy of 0.7% from the cascadedecay ψ (2 S ) → J/ψ π + π − thus we report the highprecision results on Γ ee × Γ ee / Γ and Γ ee × Γ µµ / Γ anduse the Γ ℓℓ value to check the analysis consistencyonly. The extraction of resonance parameters from themeasured cross section requires the accurate account-ing of radiative corrections. The Sec. 8.2.4 of thehighly cited report [4] treats the radiative correctionsto e + e − → J/ψ → ℓ + ℓ − cross section in the way con-tradicting to that used in the experiments [5, 6] andour work [7] therefore me start with the discussion ofthis issue. J/ψ pro-duction and decays
In virtually all experimental analyses it is assumedthat the resonant contribution to the cross section of e + e − → J/ψ → ℓ + ℓ − is proportional to the productΓ ee × Γ ℓℓ / Γ where Γ ee and Γ ℓℓ are so called experi-mental partial widths [8] recommended to use by theParticle Data Group since 1990:Γ ℓℓ ≡ B ll ( nγ ) × Γ = Γ (0) ℓℓ | − Π | , (1)where B ll ( nγ ) is the branching ratio as it is measuringexperimentally, Γ ee is the lowest order QED partialwidth and Π is the vacuum polarization operator ex-cluding J/ψ contribution. In contrast, the Sec. 8.2.4of Ref. [4] proposes that the resonant contribution is ∗ Partially supported by the Russian Foundation for Basic Research, Grants 08-02-00258, 09-02-08537 and RF PresidentialGrant for Sc. Sch. NSh-5655.2008.21) E-mail: [email protected] c (cid:13) J/ψ leptonic width with the KEDR detector 837 proportional to Γ ee × Γ (0) ℓℓ / Γ = Γ ee × Γ ℓℓ / Γ.According to Ref. [9] the cross section of thesingle–photon annihilation e + e − → ℓ + ℓ − can be writ-ten in the form σ = Z dx σ ((1 − x ) s ) | − Π((1 − x ) s ) | f ( s, x ) , (2)where the f ( s, x ) is calculated with a high accuracy,the Π( s ) represents the vacuum polarization opera-tor and σ ( s ) in the Born level cross section of theprocess.Assuming the Breit-Wigner shape for σ σ ( s ) = 12 π Γ ee Γ ℓℓ ( s − M ) + M Γ (3)and replacing Π( s ) with Π mentioned above, one re-produces the result of the Sec. 8.2.4 of Ref. [4].However, the Born level cross section of the e + e − → ℓ + ℓ − process is the smooth function of s therefore the resonance behavior of the cross section(2) is due to energy dependence of the full vacuumpolarization operator Π containing the resonant con-tribution ∗ . One has Π = Π + Π R with nonresonantΠ = Π ee +Π µµ +Π ττ +Π q ¯ q andΠ R ( s ) = 3Γ ee α sM s − M + iM Γ , (4)where M , Γ and Γ (0) ee are the “bare” resonance massand widths.The formula (2) gives the cross section withoutseparation to the continuum, resonant and interfer-ence parts. To obtain the contribution of the reso-nance, the continuum one must be subtracted fromthe amplitude. It can be done with the equality11 − Π − Π R ( s ) ≡ − Π + 1(1 − Π ) ee α sM s − ˜ M + i ˜ M ˜Γ (5)in which both ˜ M and ˜Γ depend on s :˜ M = M + 3Γ ee α sM Re 11 − Π , ˜ M ˜Γ = M Γ − ee α sM Im 11 − Π . (6)In a vicinity of a narrow resonance this dependence isnegligible thus the resonant contribution can be de-scribed with the Breit-Wigner amplitude containing“dressed” parameters M ≈ ˜ M ( M ), Γ ≈ ˜Γ( M ). Dueto the extra power of the vacuum polarization factor1 / | − Π | in the second term of (5) the resonant part of the e + e − → ℓ + ℓ − cross section is proportional toΓ ee × Γ ℓℓ / Γ and does not depend on Γ (0) ee explicitly.The analytical expressions for the e + e − → ℓ + ℓ − cross section in the soft photon approximation werefirst derived by Ya. A. Azimov et al. in 1975 [10].With some up-today modifications one obtains in thevicinity of a narrow resonance (cid:18) dσd Ω (cid:19) ee → µµ ≈ (cid:18) dσd Ω (cid:19) ee → µµ QED + 34 M (1 + δ sf ) (1 + cos θ ) × ( ee Γ µµ Γ M Im F − α p Γ ee Γ µµ M Re F − Π ) , (7)where a correction δ sf follows from the structure func-tion approach of [9]: δ sf = 34 β + απ (cid:18) π − (cid:19) + β (cid:18) − π −
136 ln Wm e (cid:19) (8)and F = πβ sin πβ (cid:18) M/ − W + M − i Γ / (cid:19) − β (9)with β = 4 απ (cid:18) ln Wm e − (cid:19) . (10)The terms proportional to Im F and Re F describethe contribution of the resonance and the interferenceeffect, respectively.Originally in Ref. [10] the electron loops only weretaken into account in Π while the terms . β wereomitted including the πβ/ sin πβ factor [11] in (9).For the e + e − final state one has (cid:18) dσd Ω (cid:19) ee → ee ≈ (cid:18) dσd Ω (cid:19) ee → ee QED +1 M (cid:26)
94 Γ ee Γ M (1 + cos θ ) (1 + δ sf ) Im F− α ee M (cid:20) (1 + cos θ ) − (1 + cos θ ) (1 − cos θ ) (cid:21) Re F (cid:27) , (11)where the relative accuracy of the interference termis about β (7.6% for J/ψ ). That is sufficient for theanalysis reported.For the nonresonant contribution σ QED the calcu-lations of [12, 13] can be used implemented in theevent generators BHWIDE [14] and MCGPJ [15].In order to compare the theoretical cross sec-tions (7) and (11) with experimental data, it is neces-sary to perform their convolution with a distributionof the total collision energy which is assumed to beGaussian with an energy spread σ W : ρ ( W ) = 1 √ π σ W exp (cid:18) − ( W − W ) σ W (cid:19) , ∗ We are grateful to V. S. Fadin for clarification of this issue.o. 6 A.G. Shamov [KEDR collaboration]: Measurement of
J/ψ leptonic width with the KEDR detector 838 where W is an average c.m. collision energy. The VEPP-4M collider [16] can operate in thewide range of beam energy from 1 to 6 GeV. Thepeak luminosity in the
J/ψ energy region is about 2 × cm − s − . e - e + HPGe detector
VEPP-4M VEPP-3
B-4
RFRF KEDR s.c.s.c. s.c.s.c. depolarizerplates
Fig. 1. VEPP-4M/KEDR complex with theresonant depolarization and the infrared lightCompton backscattering facilities.
One of the main features of the VEPP-4M is apossibility of precise energy determination. The reso-nant depolarization method [17, 18] was implementedat VEPP-4 from the beginning of experiments in earlyeighties for the measurements of the
J/ψ and ψ (2 S )mass with the OLYA [19] detector and Υ family masswith the MD-1 [19] detector.At VEPP-4M the accuracy of the energy calibra-tion with the resonant depolarization is improved toabout 10 − . The interpolation of energy between cal-ibrations [20] in the J/ψ region has the accuracy of6 · − ( ≃
10 keV).In 2005 a new technique developed at the BESSY-I and BESSY-II synchrotron radiation sources [21, 22]was adopted for VEPP-4M. It employs the infraredlight Compton backscattering and has a worse preci-sion (50 ÷
70 keV in the
J/ψ region) but, unlike theresonant depolarization, can be used during data tak-ing.The KEDR detector [23] includes the vertex de-tector, the drift chamber, the scintillation time-of-flight counters, the aerogel Cherenkov counters, thebarrel liquid krypton calorimeter, the endcap CsIcalorimeter, and the muon system built in the yokeof a superconducting coil generating a field of 0.65T. The detector also includes the scattered electrontagging system for studying of the two-photon pro- cesses. The on-line luminosity is measured by twoindependent single bremsstrahlung monitors.
In April 2005, the 11-point scan of the
J/ψ hasbeen performed with the integral luminosity of 230nb − . This corresponds approximately to 15000 J/ψ → e + e − decays. During this time, 26 calibrationsof the beam energy were done using the resonance-depolarization method.Single bremsstrahlung and Bhabha scattering tothe endcap calorimeter were used in the relative mea-surement of luminosity. The absolute calibration ofthe luminosity was performed using the large angleBhabha scattering in the Γ ee × Γ ee / Γ analysis. E W ( MeV ) σ obs ( nb ) Fig. 2. Observed e + e − → hadrons cross sectionaccording to the results of the J/ψ scan.
Figure 2 shows the observed e + e − → hadrons crosssection at the J/ψ energy region. These data wereused to fix the resonance peak position and to de-termine the beam energy spread. The value of the
J/ψ mass agrees with the earlier VEPP-4M/KEDRexperiments [20].
In our analysis we employed the simplest selectioncriteria that ensured a sufficient suppression of multi-hadron events and the cosmic-ray background, pleasesee Ref. [24] for details.In order to measure the resonance parameters inthe e + e − channel, the set of events was divided intoten equal angular intervals from 40 ◦ to 140 ◦ . At the i -th point in energy E i and the j -th angular interval θ j , the expected number of events was parameterized o. 6 A.G. Shamov [KEDR collaboration]: Measurement of J/ψ leptonic width with the KEDR detector 839 as N exp ( E i , θ j ) = R L × L ( E i ) × (cid:16) σ theorres ( E i , θ j ) · ε simres ( E i , θ j )+ σ theorinter ( E i , θ j ) · ε siminter ( E i , θ j )+ σ simBhabha ( E i , θ j ) · ε simBhabha ( E i , θ j ) (cid:17) . (12)where L ( E i ) is the integrated luminosity measuredby luminosity monitor at the i -th point; σ theorres , σ theorinter and σ theorBhabha are the theoretical cross sections respec-tively for resonance, interference and Bhabha contri-butions; ε simres , ε siminter and ε simBhabha are detector efficien-cies obtained from simulated data.In this formula the following free parameters wereused:1. the product Γ ee × Γ ee / Γ, which determines themagnitude of the resonance signal;2. the electron width Γ ee , which specifies the am-plitude of the interference wave;3. the coefficient R L , which provides the absolutecalibration of the luminosity monitor. ◦ θ < ◦ ◦ θ < ◦ ◦ θ < ◦ ◦ θ ◦ E W , MeV E W , MeV E W , MeV E W , MeV σ obs , nb σ obs , nb σ obs , nb σ obs , nb Fig. 3. Fits to experimental data for e + e − → e + e − process at J/ψ energy region for fourangular ranges.
We note that the coefficient R L partially accountsthe possible difference between the actual detectionefficiency and simulation in the case where these dif-ference do not depend on the scattering angle or thebeam energy (or the data taking time) thus the sub-stantial cancellation of errors occurs.Figure 3 shows our fit to the data for four angularintervals. The joined fit in ten equal intervals from40 ◦ to 140 ◦ produce the following basic result:Γ ee × Γ ee / Γ = 0 . ± . , R L = 93 . ± . , Γ ee = 5 . ± . . (13)Due to different angular distributions for Bhabhascattering and resonance events, subdivision of the data into several angular bins decreases a statisticalerror for Γ ee × Γ ee / Γ by 40 ÷
50 %. The electron widthobtained by the fit has a statistical error of about 10%and agrees with the world-average value. W, MeV σ obs , nb χ /ndf = 11 / Fig. 4. Fit to experimental data for e + e − → µ + µ − process at J/ψ energy region.
Similarly to (12), the expected number of e + e − → µ + µ − events was parameterized in the form: N exp ( E i ) = R L × L ( E i ) × (cid:16) σ theorres ( E i ) · ε simres ( E i )+ σ theorinter ( E i ) · ε siminter ( E i )+ σ theorbg ( E i ) · ε simbg ( E i ) (cid:17) + F cosmic × T i , (14)with the same meaning of R L and L ( E i ) as in (12). L ( E i ) is multiplied by the sum of the products oftheoretical cross sections for resonance, interferenceand QED background and detection efficiencies asobtained from simulated data. R L was fixed by re-sult (13). T i is the live data taking time. Unlike (12)there is only one angular interval from 40 ◦ to 140 ◦ .The following free parameters were used:1. the product Γ ee × Γ µµ / Γ, which determines themagnitude of the resonance signal;2. the square root of electron and muon widths p Γ ee Γ µµ , which specifies the amplitude of theinterference wave;3. the cosmic events rate F cosmic passed the selec-tion criteria for the e + e − → µ + µ − events.Due to variations of luminosity during the experimentit is possible to separate cosmic events contribution( F cosmic · T i ) from nonresonant background contribu-tion ( σ theorbg ( E i ) · ε simbg ( E i ) · L i ).Figure 4 shows our fit to the e + e − → µ + µ − data.It yields the following result:Γ ee × Γ µµ / Γ = 0 . ± . , p Γ ee × Γ µµ = 5 . ± . . (15) o. 6 A.G. Shamov [KEDR collaboration]: Measurement of J/ψ leptonic width with the KEDR detector 840
As can be seen from (15) the statistical error ofΓ ee × Γ µµ / Γ is about 1.6%.
The most significant systematic uncertainties inthe Γ ee × Γ ee / Γ and Γ ee × Γ µµ / Γ measurements arelisted in Tables 1 and 2, respectively.
Table 1. Systematic uncertainties in Γ ee × Γ ee / Γ. Systematic uncertainty source Error %Luminosity monitor instability 0.8Offline event selection 0.7Trigger efficiency 0.5Energy spread accuracy 0.2Beam energy measurement (10–30 keV) 0.3Fiducial volume cut 0.2Calculation of radiative correction 0.2Cross section for Bhabha (MC generators) 0.4Uncertainty in the final state radiation (PHOTOS) 0.4Background from
J/ψ decays 0.2Fitting procedure 0.2
Quadratic sum 1.4
Table 2. Systematic uncertainties in Γ ee × Γ µµ / Γ. Systematic uncertainty source Error %Luminosity monitor instability 0.8Absolute luminosity calibration by e + e − data 1.2Trigger efficiency 0.5Energy spread accuracy 0.4Beam energy measurement (10–30 keV) 0.5Fiducial volume cut 0.2Calculation of radiative correction 0.1Uncertainty in the final state radiation (PHOTOS) 0.5Nonresonant background 0.1Background from J/ψ decays 0.6
Quadratic sum 1.8
A rather large uncertainty of 0.8% common for theelectron and muon channels is due to the luminositymonitor instability. It was estimated from compar-ing the results obtained using the on-line luminosityof the single bremsstrahlung monitor and the off-lineluminosity measured by the e + e − scattering in theendcap calorimeter.The essential source of uncertainty is an imper-fection of the detector response simulation resultingin the errors in the trigger and offline event selectionefficiencies. It was studied using collected data andthe correction of 0 . ± .
7% was applied. The dominant uncertainty of the Γ ee × Γ µµ / Γ re-sult is associated with the absolute luminosity cal-ibration done in e + e − -channel. It includes the ac-curacy of the Bhabha event generators, the statisticerror of R L parameter (13) and the residual (aftercorrection using simulated data) efficiency differencefor e + e − and µ + µ − events. The additional correctionapplied to this difference is − . ± . The new measurement of the Γ ee × Γ ee / Γ andΓ ee × Γ µµ / Γ has been performed at the VEPP-4M col-lider using the KEDR detector. The following resultshave been obtained (in keV):Γ ee × Γ ee / Γ = 0 . ± . ± . ee × Γ µµ / Γ = 0 . ± . ± . Γ ee × Γ ee / Γ SPEC 1975FRAM 1975FRAG 1975DASP 1979KEDR 2009 Γ ee × Γ µµ / Γ FRAM 1975DASP 1975
BaBar
Fig. 5. Comparison of Γ ee × Γ ee / Γ and Γ ee × Γ µµ / Γ measured at different experimentsmentioned in [25] with KEDR 2009 results.The vertical strip is for the world averageΓ ee × Γ µµ / Γ value.
Figure 5 shows the comparison of our results withthose of the previous experiments. The grey lineshows PDG average and the error for the Γ ee × Γ µµ / Γproduct measurement. The new KEDR results arethe most precise. Results are in good agreementwith each other and with the world average value ofΓ ee × Γ µµ / Γ. o. 6 A.G. Shamov [KEDR collaboration]: Measurement of J/ψ leptonic width with the KEDR detector 841
Accounting the correlations in the Γ ee × Γ ee / Γ andΓ ee × Γ µµ / Γ errors the mean value isΓ ee × Γ ℓℓ / Γ = 0 . ± . ± . B ( J/ψ → e + e − ) = (5 . ± .
06) % [25] leptonic and full widths of
J/ψ meson were determined:Γ ℓℓ = 5 . ± .
12 keVΓ = 94 . ± . BaBar [5] andCLEO-c [6] experiments.
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