Transcript R Measurement at resonant region

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, Rexp, contains the contributions from the
continuous and resonant states. In theory, they may be written as:
R value in experiment
R value is measured by
: observed number of hadronic events;
: number of background events;
: trigger efficiency;
: integrated luminosity;
: acceptance for hadronic events;
: initial state radiative correction factor.
In which, each quantity is obtained by
 Data analysis
 Theoretical calculations
 Monte Carlo simulations
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)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
 total width
M
tot
 electronic width ee
 phase angle

According to Eichten’s model, there are following decay channels
K.K.Seth’s results
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)
Conclusion:
CB and BES measurements are in excellent agreement
Summary of the previous fitting
Some works have measured the resonant parameters of the higher
chamonia. The methods of these works may be summarized as:
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
Experimental quantity
Theoretical quantity
Resonant parameters
Problems in Fitting
If we inspect the previous fittings, the following questions
should be reviewed
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
Problem in physics
 Breit-Winger amplitude
Without phase-angle :
with phase-angle:
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
Problem in model
The continuous background
Non-resonant charm backgrounds near threshold
① Polynomial of degree 2 (experiential)
C0 , C1, C2 are free parameters
② DASP form (phenomenological)
Ak (k=1,…,6) are free parameters. Inclusive data can not give
enough information to determine the correct ratios among Ak
Problem in model
Energy dependence of hadronic width
① Potential well model in quantum mechanics
,
② Effective interaction theory (EIT)
Hamiltonian
Inclusive data can not give enough
information to determine the correct
ratios among GPP, GVP,GVV.
Hadronic width:
Total width:
Fitting procedures
The 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.
Follow chart for fitting:
Initialization
raw data, parameters
2 (Rexp , Rthe)
convergence ?
Yes
Output
Rexp , M , tot ,  ee , 
No
Fitting schemes
Two experimental quantities: R value or R-like value
Scheme A: fitting true R value
Errors are not constant in iterative fitting,
but they can not correctly update in fitting
Scheme B: fitting R-like value
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)101802
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  
Fig.2
Scheme A
It is noticed that the peak of (4040) in
scheme A is clearer than in scheme B.
But scheme A is incorrect !!!

Fig.3

Scheme A
Fig.1

Scheme B
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
Fig.1
Fig.4
Energy dependence of total width in
Energy-dependence of total width in
quantum mechanics
effective interaction theory
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/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
BES new fitting:
 (4159)   (4195)
78.8±16.1
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