Measurements of R Value and Hadronic Form Factors at BES Haiming Hu Institute of High Energy Physics, CAS, Beijing Novosibirsk, Russian Feb. 27 – Mar. 2, 2006

Outline  R value measurement  e + e - →2(  +  - ) cross section & form factor  e + e - →pp cross section & form factor  Summary

R measurement Part 1

Introduction The status of R value for E cm < 5 GeV before 2000 R E cm (GeV) The central values of R exp between 2 – 3.6 GeV are systematically above the band of the QCD permitted, but R QCD band is covered by the experimental errors within 1  R.

Introduction The status of R value for E cm < 5 GeV after 2000 The error of the R value measured by BES decreased by a factor of than previous experiments. The issue is now: ☻ Central values deviate 1  in energy region GeV. ☺ Central values coincide at 2.0 and in GeV. R E cm (GeV)

Influence of R on ( g-2 ) In Standard Model ， (Michel Davier, Pisa, Oct. 8-10, 2003) Conclusion: e + e - and  experiments are incompatible SM predictions differ from experiments by 1.9  [e + e - ] and 0.7  [  ]

Influence of R on  ( s ) The QED running electromagnetic coupling constant changes with s Contribution from the vacuum polarization Where S. Eidelman (1995 ) H.Burkhardt & B.Pietrzyk (2001) ± ± ± ± BES’s R no used used

Influence of R on Higgs mass fitting Before 2000After 2000 New results from BES and other’s were used The results of M H from the global fit of the Standard Model using all data

Determination of  s In perturbative QCD, R value can be expanded as a series of  s In principle, one may get  s by  solve the equation at each energy point: R QCD ( s ) =R exp ( s )   s (s)  s (3) ( 3GeV ) = ( )-( ) J.H.Kuln, hep-ph/ but no physical 2.5 GeV for central value R exp = 2.39±0.08±0.15 R QCD (s) changes with  s like following curves: ss ss ss R RR  Fit     s =  s (s;  ) 3-loop4-loop 4-loop, not full hep-ph/ Phys.Lett. B559(2003) 245 hep-ph/

Charmonium resonant structure BABAR-PUP-05/029 hep-ex/ BABAR studed initial state radiation event in e + e -  γ  +  - , observed an accumulation of event near 4.26 GeV in the invariant mass spectrum of the  +  - , which is named as Y(4260). BES scanned  (nS) structure in 1999 BES ! hep-ex/ CLEOc reports the Y(4260) in three channels :

New data sets for R value Ecm (GeV) L BSC (nb -1 ) L MDC (nb -1 ) ΔL/L (%) In 2004, BES took data samples at three energy points Preliminary values Two methods are used to calculate the integral luminosity : ① by Barrel Shower Counter (BSC) information ② by Main Drift Counter (MDC) information

Improvement in new measurement Comparing with the methods used in papers Phys. Rev. Lett. 84, 954 (2000) & 88, (2002) the five main improvements are adopted now: 1. O nly good track being accounted 2. Beam-gas samples are separated from the raw data, and are used in LUARLW tuning (new) 3. Select hadronic events: N good  2  N good  good-tracks are requested in the measurement of luminosity (new) 5. Change the cut values to estimate error  compare the difference between data & MC for all cuts These measures are effective to reduce the systematic error further

Hadronic event criteria For 2-prong and more - prong events Hadronic events may be classified as 0-prong, 1-prong, and 2 or more prongs

Hadronic event criteria In the present measurement, 1-prong hadronic events are included with the following criteria:  1 - prong good charged track is requested  and which with at least one  0 in the final states by 1-C fit to reconstruct the decay channel  0  In the previous measurement, only the events with 2 or more-prongs were selected, therefore, the lost 0-prong and 1-prong events will cause the error of the hadronic efficiency.

Systematic error due to 0-prong events The criteria for the 0-prong hadronic events:  no charged track is requested  and which with at least one  0 in the final states by 1-C fit to reconstruct the decay channel  0  The error of the efficiency due to the lost 0-prong events is estimated to be about 0.5 %. Even in the present measurement, the 0-prong events are also lost in the selection of hadronic events, but number of the 0-prong events must be estimated and used to the analysis of the error of the hadronic efficiency.

Lund area law generator hep-ph/

Tuning of LUARLW parameters BES data Method: compare all distributions related to the hadronic criteria between data & MC in the detector level. Tune LUARLW parameters It is required that a set of parameters of JESTSET & LUARLW agree with data well in 2.0–3.65 GeV region There are some free parameters in JETSET and LUARLW, which are needed to be tuned at low energies by comparing with data. typesstatistics Good simulation of hadron production by LUARLW will reduce the systematic error of R measurement. compare Monte Carlo

Distributions related to hadronic criteria Top : charged track ; Bottom : good charged track GeV 2.600GeV GeV GeV

Top:  ; Bottom: cos  of charged track in MDC GeV 2.600GeV GeV GeV Distributions related to hadronic criteria

Top : momentum p ; Bottom : deposit energy in BSC GeV 2.600GeV GeV GeV Distributions related to hadronic criteria

Top : Px ; Middle :Py Bottom: Pz GeV 2.600GeV GeV GeV Distributions related to hadronic criteria

Top : time of flight; Bottom : velocity  GeV 2.600GeV GeV GeV Distributions related to hadronic criteria

Error of hadronic event criteria &  had The systematic errors for selecting 1-prong and more-prong events are estimated by the difference of the number of events between data and MC for using or no using the every cuts

Systematic error of R value R value formula: Where Estimated by using two sets of different but reasonable parameters in LUARLW The good agreement between data and LUARLW will reduce the error of the number of hadronic events. Relative error:

Comparison of main systematic errors The main relative systematic errors (in %) between the previous and present R 3 GeV itemsN had L  had  trg 1+  total previous ~ 5 Present (preliminary) ~ 3 The systematic errors for the present measurements are significantly improved than the previous results

e + e - →  +  -  +  - cross section Part 2

Introduction At low energies, e + e -  +  -  +  - (  ) is important to the calculation of (g-2) for it has large production cross section. BABAR used the data with hard photon radiated from the initial state (ISR events), the effective center of mass energies are between ▬ GeV. CMD2, SND, OLYA, GG2, ND, DM1, DM2, M3N used the data with the fixed colliding energies below 2 GeV.

The measurement of the  4  (s) cross section may also give the information about hadronic form factor. In the mixed vector meson dominant model Theoretical model Born cross section: Final state factor : Form factor:

Data analysis e + e -   +  -  +  - cross section was measured by following expression 4  event number back-ground number luminositytrigger efficiency 4  efficiency effective ISR factor Procedures for data analysis  Event pre -selection  4-C fit 1. error-matrix correction 2. selection criterion  QED backgrounds subtraction 1. particle identification 2. collinear-angle cut Event pre-selection criteria ( Good track helix fit ) ( 4-momentum conservation)

2 (  +  - ) cross cection Estimation of systematic 3.07GeV The preliminary results E cm L L            2.1 Luminosity (nb -1 ) Born cross section for 4-  by BES and BABAR Preliminary

Form factor fitting Fitted parameters with MIUNIT The measured cross section of 4  by CMD2, DM1 and BES and the fitted curve with the formula given by N.N. Achasov & A.A.Kozhennikov in Phys. Rev. D55, 2663 (1997) Curve by fitting the theory

Form factor fitting Fitted parameters with MIUNIT The measured cross section of 4  by BABAR and the fitted curve with the formula given by N.N. Achasov & A.A.Kozhennikov in Phys. Rev. D55, 2663 (1997) Data and theory coincide excellently

Comparison between two fittings

Form factor of 2(  +  - ) Extracted from the BABAR’s measurement Extracted from the CMD2, DM1 and BES’s measurements

Part 3 The Proton Form Factor

Cross section E.A.Kureav V.S.Fadin The total cross section of e + e - → p p is measured by The Born level cross section may be obtained by performing the various corrections: number of pp event Luminositypp efficiencyTrigger efficiency ISR correction factorCoulomb factor Final state correction Sov. Nucl. Phys. 41, 1985, J.Schwinger Particle, Source and Field Landau:,

Results % Relative systematic error

Form factor fitting Due to the limited statistics, the existed BES data can not measure the electric G E and magnetic G M at same time. Under the assumption of |G E | = |G M |≡|G|, the Born cross section is simplified as: pQCD predicts pp form factor ~[α s (s)] 2, one often uses Λ = 0.3 GeV is the QCD scale parameter C is the free parameter in fitting PLB630,(2005)14-20

Summary  New R value data at 2.6, 3.07 and 3.65 GeV are being analyzed.  The statistic error is smaller than 1%, and the systematic error is expected to be about 3%.  The cross sections and the form factors of e + e -  2(  +  - ) and pp have been measured with BESII data.  Prospect: more precise R values and the cross sections and form factors for the important exclusive channels will be obtained at BESIII.