Measurements of R Valueand

Hadronic Form Factors at BES

Haiming HuInstitute 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 1Part 1

Introduction

The status of R value for Ecm < 5 GeV before 2000R

Ecm (GeV)

The central values of Rexp between 2 – 3.6 GeV are systematically above the band of the QCD permitted, but RQCD band is covered by the experimental errors within 1R .

IntroductionThe status of R value for Ecm < 5 GeV after 2000

The error of the R value measured by BES decreased by a factor of 2-3 than previous experiments. The issue is now:

☻ Central values deviate 1 in energy region 2.2-2.7GeV.

☺ Central values coincide at 2.0 and in 2.8-3.73GeV.

R

Ecm (GeV)

Influence of R on (g-2)

QED had weak2

2g

a a a a

2

2had

2

4

( ) ( )

3m

K sa ds R s

s

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)

)( 2)5(Zhad M

)M( 2Z

1

0.0280 ± 0.0007 0.0276 ± 0.00036

128.90 ± 0.09 128.936 ± 0.0046

BES’s R no used used

Influence of R on Higgs mass fitting

Before 2000 After 2000

New results fromBES and other’swere used

GeVm

GeVm

H

H

170

62 5330

GeVm

GeVm

H

H

212

98 5838

The results of MH from the global fit of the Standard Model using all data

Determination of sIn perturbative QCD, R value can be expanded as a series of s

...)()()( )3(2)2(2)1()0(QCD Q

sQ

sQ

s

QQ RRRRsR

In principle, one may get s by

solve the equation at each energy point: RQCD(s) =Rexp (s) s (s)

s(3)(3GeV) = 0.369+(0.047+0.123)-(0.046+0.130) J.H.Kuln, hep-ph/0109084

but no physical solution @ 2.5 GeV for central value Rexp = 2.39±0.08±0.15

RQCD(s) changes with s like following curves:

ss s

RR R

Fit s = s (s;)

n

i

QCDRR

12

i

2iiexp2

)(

)]s()s([

3-loop 4-loop 4-loop, not full

hep-ph/0109084 Phys.Lett. B559(2003) 245 hep-ph/0212294

Charmonium resonant structure

BABAR-PUP-05/029 hep-ex/0506081

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/0602034 CLEOc reports the Y(4260) in three channels :

New data sets for R value

Ecm

(GeV)

LBSC

(nb-1)

LMDC

(nb-1)

ΔL/L

(%)

2.60 1231 1229 0.15

3.07 2273 2257 0.75

3.65 6450 6446 0.10

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, 101802 (2002)

the five main improvements are adopted now:

1. Only 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: Ngood 2 Ngood 1

4. 2 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/9910285

Tuning of LUARLW parameters

BES data

LUARLWLhadrons

LBhabha

L

BGgasbeam

MC

had

ee

:

:

:

: *

Method: compare all distributions related to the hadronic criteria between data & MC in the detector level.

Tune LUARLWparameters

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.

types statistics

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

2.200 GeV 2.600GeV 3.070 GeV 3.650 GeV

Top: ; Bottom: cos of charged track in MDC

2.200 GeV 2.600GeV 3.070 GeV 3.650 GeV

Distributions related to hadronic criteria

Top : momentum p ; Bottom : deposit energy in BSC

2.200 GeV 2.600GeV 3.070 GeV 3.650 GeV

Distributions related to hadronic criteria

Top : Px ; Middle :Py Bottom: Pz

2.200 GeV 2.600GeV 3.070 GeV 3.650 GeV

Distributions related to hadronic criteria

Top : time of flight; Bottom : velocity

2.200 GeV 2.600GeV 3.070 GeV 3.650 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

)1(L

N~

)1(L

NR

trg

had

hadtrg

had

R value formula:

WhereMCobs

hadMCgenMC

genMCobs

had

had

hadhad N

NN

N/N

NNN~

22

had

had

22

had

had

2

sys 1

]1[

L

L

N~N~

R

R

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 measurements @ 3 GeV

items Nhad L had trg 1+ total

previous 3.30 2.30 2.66 0.5 1.32 ~ 5

Present(preliminary

)

1.5 1.5 1.7 0.5 1 ~ 3

The systematic errors for the present measurements are significantly improved than the previous results

e+ e - → + -+ - cross section

Part 2Part 2

IntroductionAt 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 0.6125 ▬ 4.4500 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:

(4 )4

4 (0)(1 )

cbg

trg obs

N N

L

Data analysise+ e- + - + - cross section was measured by following expression

4 event number back-ground number

luminosity trigger 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 error @ 3.07GeV

The preliminary results

Ecm L Ecm L2.00 45.81.4 2.80 89.0 1.8

2.20 59.4 3.7 2.90 94.0 2.6

2.40 61.0 1.6 3.00 947 22

2.50 47.0 1.0 3.07 2272.8 36.4

2.60 1231.0 14.8 3.65 6450.4 90.3

2.70 71.6 2.1

Luminosity (nb-1)

Born cross section for 4- by BES and BABAR

Preliminary

Form factor fittingFitted 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 fittingFitted parameters with MIUNITThe measured cross section of 4 b

y 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 3Part 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

Luminosity pp efficiency Trigger efficiency

ISR correction factor Coulomb factor

Final state correction

Sov. Nucl. Phys. 41, 1985, 466 - 472

/1

/

e

Fc

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 GE and magnetic GM at same time.

Under the assumption of |GE| = |GM|≡|G|, the Born cross section is simplified as:

pQCD predicts pp form factor ~[αs(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

SummaryNew R value data at 2.6, 3.07 and 3.65 GeV ar

e 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.