R Measurement at charm resonant region

Haiming HUBES Collaboration

Charm 2007Cornell UniversityIthaca, NY. US

What is R value

Definition

i.e. R value is the inclusive hadronic cross section in e+e collision and through single photon annihilation, and normalized by Born cross section of +

The measured R value, Rexp, contains the contributions from the continuous and resonant states. In theory, they may be written as:

R value in experiment

In which, each quantity is obtained by Data analysis Theoretical calculations Monte Carlo simulations

R value is measured by

: observed number of hadronic events;

: number of background events; : integrated luminosity;

: trigger efficiency; : acceptance for hadronic events;

: initial state radiative correction factor.

The original R value from BESIn 1998 & 1999, scan data were taken between 2-5 GeV with BESthe energy steps in 3.7– 4.6 GeV are 10 20 MeVthe statistic errors are about 2~3 %the systematic errors are about 5~8 % the results published in Phys. Rev. Lett. 84 (2000)594, and 88 (2002)101802

In the calculation of ISR factor (1+), the values of resonant parameters in PDG2000 were used

Higher charmonia

The 4 heavy charmonia with J PC = 1ˉˉare

Their properties of production and decays are characterized by the Breit-Wigner amplitude and resonant parameters:

Nominal mass M total width tot

electronic width ee

phase angle According to Eichten’s model, there are following decay channels

K.K.Seth’s results

Conclusion:CB and BES measurements are in excellent agreement

K.K.Seth fit the resonant parameters of (4040), (4160) and (4415) based on the R values measured by CB and BES (hep-ex/0405007)

Summary of the previous fitting

Fit the published R values

Did not consider the phase angle of the Breit-Wigner amplitude

Neglected the interference effects

Assumed the total width is energy independent

Fitting

Resonant parameters

Experimental quantity Theoretical quantity

Some works have measured the resonant parameters of the higher chamonia. The methods of these works may be summarized as:

Problems in Fitting

PhysicalBreit-Wigner amplitude with or not?energy dependence of total width ?form of the continuous charm BG ?interference among the 4 ?

Definition of 2 in fittingtarget function A: fitting true R valuetarget function B: fitting R-like value

All of these physical problems and fitting schemes will influence the values of the resonant parameters

If we inspect the previous fittings, the following questions should be reviewed

Problem in physics

Breit-Winger amplitude

or

Interference

the interferential summation of the amplitude for same decay channel

the non-interferential summation for the different decay channels

resonant cross section expressed by the form of R value

Without phase-angle : with phase-angle:

Problem in model

Non-resonant charm backgrounds near threshold

① Polynomial of degree 2 (experiential)

② DASP form (phenomenological)

The continuous background

C0 , C1, C2 are free parameters

Ak (k=1,…,6) are free parameters. Inclusive data can not give enough information to determine the correct ratios among Ak

Problem in modelEnergy dependence of hadronic width

① Potential well model in quantum mechanics

② Effective interaction theory (EIT)

Hadronic width: Total width:

,

Inclusive data can not give enough information to determine the correct ratios among GPP, GVP,GVV.

Hamiltonian

Fitting proceduresThe values of the resonant parameters will influence (1+) and then Rexp value, so the measurement of R value and the determination of the resonant parameters should be done in iterative way and in same procedure with the MINUIT. But no one did so before.

Initialization

raw data, parameters

2 (Rexp , Rthe)

convergence ?No

Yes

Output

Rexp , M , tot , ee ,

Follow chart for fitting:

Fitting schemesTwo experimental quantities: R value or R-like value

Scheme A: fitting true R value Scheme B: fitting R-like value

Errors are not constant in iterative fitting, but they can not correctly update in fitting

Errors are independent of fitting, and they keep constant in iterative fitting

It is noticed that the errors of the experimental quantities will affect the convergence condition and then the fitting results. Therefore the correct input of the error is important. Errors in scheme B are correct.

Uncertainty in fitting We have some different models and experiential expressions, but none of them is “correct”, they are only approximations.

For this reason, we have tried all possible combinations, and the results are not the same, but they are consistent considering the errors.

We will show the results which is obtained based on the original data taken in 1999 and a reasonable combination of models and target function of fitting.

The reasonable combination isBreit-Wigner : relativistic form with phase angleenergy-dependence of had : potential model in quantum mechanicscontinuous charm background: polynomial of degree 2interference: consideredtarget function of 2: scheme B

The new results

Fig.1

The new results

The comparison of the updated R value and the old results in

Phys. Rev. Lett. 88 (2002)101802

The differences of R values are due to the updated resonant parameters and initial state radiative correction factor (1+obs)

Resonant parameters

scheme dependencePhase angle and =0 scheme A and scheme Btotal width energy dependence in QM and polynomial of degree 2 for charm BG

Interference

are different for or

It is noticed that the peak of (4040) in scheme A is clearer than in scheme B.

But scheme A is incorrect !!!

Fig.1

Scheme BScheme A

Fig.2

Fig.3

Scheme A

model dependenceEnergy dependence for total width: QM and EIT

• Breit-Wigner with non-zero phase angle

• Polynomial of degree 2 for the charmed continuous BG

• target function B for 2

Energy dependence of total width in

quantum mechanicsEnergy-dependence of total width in

effective interaction theory

Fig.1 Fig.4

Summary

The R values and the resonant parameters are related closely, they

should be measured in the same program in the iterative method;

The interferential effect is important in the determination of the

shape of the resonant structure;

The extracted values of the resonant parameters are theory and

model dependent;

The values of the resonant parameters are also fitting function

or scheme dependent.

Prospects

Theorists should make more reliable calculations on the energy-dependence of the total width and the continuous charm background.

It is hopeful to make more detailed scan and collect large sample between 3.7 4.6 GeV with the future BESIII, so that one may determine the fine shape of the resonant structure and hadronic widths of the 4 higher charmonia.

PDG may set up a standard fitting procedure in order to avoid the uncertainty of the fitting among the different experiments.

Thank you

Appendix: MINUIT’s report for EIT

Appendix: MINUIT’s report for DASP

ComparisonsT.Barnes’s paper

Phys. Rev. D72, (2005)504026, hep-ph/0505002v3

studied the experimental and theoretical (nonrelativistic potential model

and Godfrey-Isgur relativistic potential model) status of higher chamonia, the values about hadronic and total widths are listed below

BES new value 25.6±6.3

BES new value 88.9±12.4

Comparison

BES new value 78.8±16.1

BES new fitting: (4159) (4195)

Comparison

BES new value 80.4±24.7

Upper limit of electronic width of Y(4260)Scanned resonant structure of the higher charmonia by BES

BABAR discovered Y(4260)

Based on the published R value measured at BES, the upper limit of the electronic width of Y(4260) was estimated:

　　　 ee < 580 eV/c2 at 90% CL

See the detail descriptions in Phys. Lett. B640, (2006)182-187

!