r measurement at charm resonant region
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R Measurement at charm resonant region. Haiming HU BES Collaboration. Charm 2007 Cornell University Ithaca, NY. US. What is R value. Definition. - PowerPoint PPT PresentationTRANSCRIPT
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
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