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Measurement of the Total Cross Section for Hadronic Production by e+e- Annihilation at Ener

a r X i v :h e p -e x /9908046v 1 11 A u g 1999

MEASUREMENT OF THE TOTAL CROSS SECTION FOR HADRONIC

PRODUCTION BY e +e ?ANNIHILATION AT ENERGIES BETWEEN 2.6-5GEV §

J.Z.Bai,1Y.Ban,4J.G.Bian,1G.P.Chen,1H.F.Chen,9J.Chen,2J.C.Chen,1Y.Chen,1Y.B.Chen,1Y.Q.Chen,1B.S.Cheng,1X.Z.Cui,1H.L.Ding,1L.Y.Dong,1Z.Z.Du,1W.Dunwoodie,7C.S.Gao,1

M.L.Gao,1S.Q.Gao,1J.H.Gu,1S.D.Gu,1W.X.Gu,1Y.F.Gu,1Y.N.Guo,1Z.J.Guo,1S.W.Han,1Y.Han,1F.A.Harris,8J.He,1J.T.He,1K.L.He,1M.He,5Y.K.Heng,1G.Y.Hu,1H.M.Hu,1J.L.Hu,1Q.H.Hu,1T.Hu,1X.Q.Hu,1G.S.Huang,1Y.Z.Huang,1J.M.Izen,10C.H.Jiang,1Y.Jin,1B.D.Jones,10X.Ju,1Z.J.Ke,1D.Kong,http://www.wendangku.net/doc/be81a7c45fbfc77da269b176.htmli,http://www.wendangku.net/doc/be81a7c45fbfc77da269b176.htmlng,1C.G.Li,1D.Li,1H.B.Li,1J.Li,1J.C.Li,1P.Q.Li,1R.B.Li,1W.Li,1W.G.Li,1X.H.Li,1X.N.Li,1H.M.Liu,1J.Liu,1R.G.Liu,1Y.Liu,1X.C.Lou,10F.Lu,1J.G.Lu,1X.L.Luo,1E.C.Ma,1J.M.Ma,1R.Malchow,2H.S.Mao,1Z.P.Mao,1X.C.Meng,1J.Nie,1S.L.Olsen,8D.Paluselli,8L.J.Pan,8N.D.Qi,1X.R.Qi,1C.D.Qian,6J.F.Qiu,1Y.H.Qu,1Y.K.Que,1G.Rong,1Y.Y.Shao,1B.W.Shen,1D.L.Shen,1H.Shen,1X.Y.Shen,1H.Y.Sheng,1H.Z.Shi,1X.F.Song,1F.Sun,1H.S.Sun,1Y.Sun,1Y.Z.Sun,1S.Q.Tang,1W.Toki,2G.L.Tong,1G.S.Varner,8F.Wang,1L.S.Wang,1L.Z.Wang,1M.Wang,1P.Wang,1P.L.Wang,1S.M.Wang,1T.J.Wang,1?Y.Y.Wang,1C.L.Wei,1N.Wu,1Y.G.Wu,1D.M.Xi,1X.M.Xia,1P.P.Xie,1Y.Xie,1Y.H.Xie,1G.F.Xu,1S.T.Xue,1J.Yan,1W.G.Yan,1C.M.Yang,1C.Y.Yang,1H.X.Yang,1J.Yang,1W.Yang,2X.F.Yang,1M.H.Ye,1S.W.Ye,9Y.X.Ye,9C.S.Yu,1C.X.Yu,1G.W.Yu,1Y.H.Yu,3Z.Q.Yu,1C.Z.Yuan,1Y.Yuan,1B.Y.Zhang,1C.Zhang,1C.C.Zhang,1D.H.Zhang,1Dehong Zhang,1H.L.Zhang,1J.Zhang,1J.W.Zhang,1L.Zhang,1L.S.Zhang,1P.Zhang,1Q.J.Zhang,1S.Q.Zhang,1X.Y.Zhang,5Y.Y.Zhang,1D.X.Zhao,1H.W.Zhao,1Jiawei Zhao,9J.W.Zhao,1M.Zhao,1W.R.Zhao,1Z.G.Zhao,1J.P.Zheng,1L.S.Zheng,1Z.P.Zheng,1B.Q.Zhou,1

G.P.Zhou,1H.S.Zhou,1L.Zhou,1K.J.Zhu,1Q.M.Zhu,1Y.C.Zhu,1Y.S.Zhu,1B.A.Zhuang 1

(BES Collaboration)

1

Institute of High Energy Physics,Beijing 100039,People’s Republic of China

2

Colorado State University,Fort Collins,Colorado 80523

3

Hangzhou University,Hangzhou 310028,People’s Republic of China 4

Peking University,Beijing 100871,People’s Republic of China 5

Shandong University,Jinan 250100,People’s Republic of China

6

Shanghai Jiaotong University,Shanghai 200030,People’s Republic of China

7

Stanford Linear Accelerator Center,Stanford,California 94309

8

University of Hawaii,Honolulu,Hawaii 96822

9

University of Science and Technology of China,Hefei 230026,People’s Republic of China

10

University of Texas at Dallas,Richardson,Texas 75083-0688

(February 7,2008)Using the upgraded Beijing Spectrometer (BESII),we have measured the total cross section for e +e ?

annihilation into hadronic ?nal states at center-of-mass energies of 2.6,3.2,3.4,3.55,4.6and 5.0GeV.Values of R ,σ(e +e ?→hadrons)/σ(e +e ?→μ+μ?),are determined.

The lowest order cross section for e +e ?→γ?→hadrons is usually parameterized in terms of the ratio R ,which is de?ned as R =σ(e +e ?→hadrons)/σ(e +e ?→μ+μ?),where the denominator is the lowest-order QED cross section,

σ(e +e ?→μ+μ?)=σ0

μμ=4πα2/3s .This ratio has been measured by many experiments over the center-of-mass (cm)energy range from the hadron production threshold to the Z pole [1].The measured R values are,in general,consistent with theoretical predictions,and provide an impressive con?rmation of the hypothesis of three color degrees of freedom for quarks.

However,the existing R measurements for cm energies below 5GeV were performed 17to 25years ago [2–8]and have average experimental uncertainties of about 15%[9].Uncertainties in the values of R in this energy region limit

the precision of the QED running coupling constant evaluated at the mass of the Z boson,α(M 2

Z

),which in turn limits the precision of the determination of the Higgs mass from radiative corrections in the Standard Model [9–15].Measurements of R ,particularly for cm energies below the J/ψmass,are also required for the interpretation of the

muon (g ?2)measurement at Brookhaven [9–15].About 50%and 20%of the error in α(M 2

Z

)and a μ=(g ?2)/2,respectively,are due to the uncertainty of the values of R in the 2-5GeV cm energy region [15].

In this letter,we report measurements of R at cm energies of 2.6,3.2,3.4,3.55,4.6and 5.0GeV.The measurements were carried out with the BESII,which is a conventional solenoidal detector that is described in detail in Ref.[16].Upgrades include the replacement of the central drift chamber with a vertex chamber (VC)composed of 12tracking layers organized around a beryllium beam pipe.This chamber provides a spatial resolution of about 90μm.The barrel time-of-?ight counter (BTOF)was replaced with a new array of 48plastic scintillators that are read out by ?ne

1

mesh photomultiplier tubes situated in the0.40T magnetic?eld volume,providing180ps resolution.A new main drift chamber(MDC)has10superlayers,each with four sublayers of sense wires.It provides dE/dx information for particle identi?cation and has a momentum resolution ofσp/p=1.8%

E(E in GeV)and a spatial resolution of7.9mrad inφand3.6cm in z.The outermost component of BESII is aμidenti?cation system consisting of three double layers of proportional tubes interspersed in the iron?ux return of the magnet.These measure coordinates along the muon trajectories with resolutions of3cm and5.5cm in rφand z,respectively.

Triggers are formed from signals derived from the BTOF,VC,MDC,and BSC,and referenced in time to signals from a beam pickup electrode located upstream of the detector[16].Event categories are classi?ed according to numbers of charged and neutral tracks seen at the trigger level.For beam crossings with charged tracks,two trigger topologies are utilized:in the?rst,we require at least one hit in the48BTOF counter array,one track in the VC and MDC,and at least100MeV of energy deposited in the BSC;in the second,we require back-to-back hits in the BTOF counter with one track in the VC and two tracks in the MDC.For the neutral track trigger,we require that the sum of the deposited energy of the tracks in two adjacent towers of the BSC is greater than80MeV in the?rst level trigger and that the total energy deposited in BSC from all sources is greater than800MeV in the second level trigger.A tower in the BSC is one tube inφ(11mrad)by24layers radially.

The value of R is determined from the number of observed hadronic events(N obs

had

)by the relation

R=N obs

had?N bg?

l

N ll?Nγγ

?The two tracks must not be back-to-back;

?There must be at least two isolated neutral tracks that have more than 100MeV of energy and are at least 15?from the closest charged track in azimuthal angle.

There are three major types of background to be considered.One type,consisting of cosmic rays,Bhabha,dimuon events and some two-photon process events,is directly removed by the event selection.The second,consisting of tau-pair production events and residual lepton-pair events from two-photon processes,is subtracted out statistically.The most serious sources of background in the hadronic event sample are beam-gas and beam-wall interactions.To understand these,separated beam data were taken at each energy point,and single beam data were accumulated at 3.55GeV.Most of the beam associated background events are rejected by a vertex cut.The salient features of the beam associated background are that their tracks are very much along the beam pipe direction,the energy deposited in BSC is small,and most of the tracks are protons.The same hadronic event selection criteria are applied to the separated-beam data,and the number of separated-beam events N sep surviving these criteria are obtained.The number of the beam associated background events N bg in the corresponding hadronic event sample is given by N bg =f ×N sep ,where f is the ratio of the product of the pressure at the collision region times the integrated beam currents for colliding beam runs and that for the separated beam runs.

The integrated luminosity is determined using large-angle Bhabha events with the following selection criteria,using only BSC information:

?Two clusters in the BSC with largest deposited energy in the polar angle |cos θ|≤0.55;?Each cluster with energy >1.0GeV (for 3.55GeV data,scaled for other energy points);

?2?<||φ1?φ2|?180?|<16?,where φ1and φ2are the azimuthal angles of the clusters.The 2?cut removes e +e ?→γγevents.

A cross check using only dE/dx information from the MDC to identify electrons was generally consistent with the BSC measurement;the di?erence was taken into account in the overall systematic error of 2.1-2.8%.

The

detection e?ciency for hadronic events is determined via a Monte Carlo simulation using the JETSET7.4event generator [18].Parameters in the generator are tuned [19]using a 40k hadronic event sample collected near 3.55GeV for the tau mass measurement done by the previous experiment at BESI [20].The parameters of the generator are adjusted to reproduce distributions of kinematic variables such as multiplicity,sphericity,transverse momentum,etc.Fig.1shows these distributions for the real and simulated event samples.The parameters have also been obtained using the 2.6GeV data (≈5k events).The di?erence between the two parameter sets and between the data and the Monte Carlo data based on these parameter sets is used to determine a systematic error of 1.9-3.2%in the hadronic e?ciency.

Measurement of the Total Cross Section for Hadronic Production by e+e- Annihilation at Ener

Measurement of the Total Cross Section for Hadronic Production by e+e- Annihilation at Ener

00.10.20.30.4N ch

N e v t

00.511.52Sphericity

1/N e v d N /d (S p h )

Measurement of the Total Cross Section for Hadronic Production by e+e- Annihilation at Ener

Measurement of the Total Cross Section for Hadronic Production by e+e- Annihilation at Ener

0.511.5η=0.5ln(p+p //)/(p-p //)

1/σd σ/d η

10

10110

>(GeV/c)

21/N e v d N c h /d P T 2(G e V /c )-2

http://www.wendangku.net/doc/be81a7c45fbfc77da269b176.htmlparison of hadronic event shapes between data (shaded region)and Monte Carlo (histogram).(a)Multiplicity;

(b)Sphericity;(c)Rapidity;(d)Transverse momentum.

The trigger e?ciencies are measured by comparing the responses to di?erent trigger requirements in special runs taken at the J/ψresonance.From the trigger measurements,the e?ciencies for Bhabha,dimuon and hadronic events

3

are determined to be99.96%,99.33%and99.76%,respectively.As a cross check,the trigger information from the 2.6and3.55GeV data samples are used to provide independent measurements of the trigger e?ciencies.These are consistent with the e?ciencies determined from the J/ψdata.The errors in the trigger e?ciencies for Bhabha and hadronic events are less than±0.5%.

Radiative corrections determined using four di?erent schemes[21–24]agreed with each other to within1%below charm threshold.Above charm threshold,where resonances are important,the agreement is within1~3%.The major uncertainties common to all models are due to errors in previously measured R-values and in the choice of values for the resonance parameters.For the measurements reported here,we use the formalism of Ref.[23]and include the di?erences with the other schemes in the systematic error of2.2-4.1%.

The R values obtained at the six energy points are shown in Table I and graphically displayed in Fig.2.A breakdown of contributions to the systematic errors is given in Table II.The largest systematic error is due to the hadronic event selection and is determined to be3.8-6.0%by varying the selection criteria.The systematic errors on the measurements below4.0GeV are similar and are a measure of the amount of error common to all points.We have also done the analysis including only events with greater than two charged tracks;although the statistics are smaller,the results obtained agree well with the results shown here.The R values for E cm below4GeV are in good agreement with results fromγγ2[6]and Pluto[8]but are below those from Mark I[7].Above4GeV,our values are consistent with previous measurements.

TABLE I.Summary of R data and values.

N bg L?had(1+δ)R Stat.Sys.

E cm N obs

had

(GeV)(nb?1)(%)error error

2.60 5.10.06 2.120.000.04 4.100.50 2.6

3.20 3.80.15 2.830.000.04 1.900.50 2.2 3.40

4.60.27 2.830.000.04 2.900.50 3.0

3.55 5.50.27 2.320.000.04 2.300.50 2.4

4.60

5.70.75 2.160.320.00 3.600.50 4.1

5.00

6.0 1.26 2.810.320.00 3.200.50 3.8

We would like to thank the sta?of the BEPC accelerator and IHEP Computing Center for their e?orts.We also wish to acknowledge useful discussions with B.Andersson,H.Burkhardt,M.Davier,B.Pietrzyk,T.Sj¨o strand,M.L. Swartz,J.M.Wu,C.X.Zhang,X.M.Zhang,and G.D.Zhao.We especially thank M.Tigner for major contributions not only to BES but also to the operation of the BEPC.

1.5

22.533.544.555.56

Measurement of the Total Cross Section for Hadronic Production by e+e- Annihilation at Ener

R V a l u e

Ecm (GeV)

FIG.2.Plot of R values vs E cm .

[2]F.Ceradini et al.,Phys.Lett.B 47,80(1973);B.Bartoli et al.,Phys.Rev.D 6,2374(1972);M.Bernardini et al.,Phys.

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[16]J.Z.Bai et al.,(BES Collab.),Nucl.Instrum.Methods A 344,319(1994);“The Upgraded BES Detector (BESII)”talk by

J.Li at Workshop on Relativistic Heavy Ion Collisions and Quark Matter Physics,Wuhan,China,April 5-8,1999.

[17]“Measurement of R Between 2-5GeV”a talk presented by D.Kong,DPF99at Los Angeles,California,Jan.5-9,1999;

hep-ph/9903521.[18]Torbj¨o rn Sj¨o strand,Computer Physics Commun 82,74(1994).

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