R Measurement at charm resonant region Haiming HU BES Collaboration Charm 2007 Cornell University Ithaca, 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, R exp, 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 BES  In 1998 & 1999, scan data were taken between 2-5 GeV with BES  the energy steps in 3.7– 4.6 GeV are 10  20 MeV  the 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) 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 = 1 ˉˉ are 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/ )

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 Physical  Breit-Wigner amplitude with  or not?  energy dependence of total width ?  form of the continuous charm BG ?  interference among the 4  ? Definition of  2 in fitting  target function A: fitting true R value  target 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 C 0, C 1, C 2 are free parameters A k (k=1,…,6) are free parameters. Inclusive data can not give enough information to determine the correct ratios among A k

Problem in model  Energy 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 G PP, G VP,G VV. Hamiltonian

Fitting procedures The values of the resonant parameters will influence ( 1+  ) and then R exp 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 (R exp, R the ) convergence ? No Yes Output R exp, M,  tot,  ee,  Follow chart for fitting:

Fitting schemes Two experimental quantities: R value or R-like value Scheme A: fitting true R valueScheme 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 is  Breit-Wigner : relativistic form with phase angle  energy-dependence of  had : potential model in quantum mechanics  continuous charm background: polynomial of degree 2  interference: considered  target 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) The differences of R values are due to the updated resonant parameters and initial state radiative correction factor (1+  obs )

Resonant parameters

scheme dependence Phase angle  and  =0 scheme A and scheme B total 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 B Scheme A Fig.2 Fig.3   Scheme A

model dependence Energy 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 mechanics Energy-dependence of total width in effective interaction theory Fig.1Fig.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

Comparisons T.Barnes’s paper Phys. Rev. D72, (2005)504026, hep-ph/ v3 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/c 2 at 90% CL See the detail descriptions in Phys. Lett. B640, (2006) !