Data sample: 130 pb-1 (2001) + 250 pb-1 (2002)
• Spectra of 2001 and 2002 data
• Evaluation of luminosity and number of events
• Fit of the 2001+2002 spectrum
• Branching Ratio of f0
f0 C. Bini S. Ventura
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Invariant Mass MSpectra
2001 2002
Evaluation of luminosity
A run is included in the evaluation of the total luminosity ifR is compatible with the average.
N is the number of events after selection.
The mean value of R is 1.75 events per nb-1 for 2001 and 2002 data.
We have the ratio between number of events and integrated luminosityfor every run: L N R/
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Nrun 2001 Nrun 2002
year Number of events Luminosity (nb-1) Rejected luminosity (nb-1)
2001 189424 108026 14600
2002 409364 233656 5900
Using the values of luminosity found we can compare the spectra of 2001 and 2002.
20012002
Fit of the spectra 2001+2002
The function for the fit has 4 terms:
• Initial State Radiation Achasov• Final State Radiation Achasov f0 Giovannella-
Miscetti• Interference with Final Achasov-Giovannella-Miscetti State Radiation
We have a fit for each possible sign of the interference term.
The function for the fit depends on 9 parameters:
(d/dM)= fisr(x, m ,,m ,, , ) + ffsr(x, m ,,m ,, , ) +
ff0(x, g2f0KK/4, g2
f0KK/gf0
mf ) +
fint(x, g2f0KK/4, g2
f0KK/gf0
mf , m ,,m ,, , )
The function is multiplied by the efficiency and the luminosity:
f(x) = (d/dM) × × T × L × × C
TT is a factor that takes into account the cut on the polar angle of the pionsis the bin sizeC an overall factor : 0.8
In the f0-term we replace (f0 ) with:
(f0 ) = 2 × (f0 )
Destructive Interference
ALL ISR FSR f0 INT
fisr + ffsr + ff0 fint
No Interference
ALL ISR FSR f0 INT
fisr + ffsr + ff0
Constructive Interference
ALL ISR FSR f0 INT
fisr + ffsr + ff0 + fint
Results of the fit
Interference Destructive No int. Constructive PDG
g2f0KK/4(GeV2) 0.39 ± 0.02 0.29 ± 0.02 0.23 ± 0.01
g2f0KK/g
f0 3.06 ± 0.12 3.49 ± 0.15 3.75 ± 0.18
mf0 (MeV) 975.10 ± 0.62 980.16 ± 0.57 984.17 ± 0.48 980 ± 10
m(MeV) 774.27 ± 0.19 774.18 ± 0.19 774.15 ± 0.47 771.1 ± 0.9
(MeV) 140.60 ± 0.29 140.98 ± 0.30 141.41 ± 0.31 149.2 ± 0.7
m(MeV) 782.09 ± 0.17 782.11 ± 0.16 782.10 ± 0.17 782.57 ± 0.12
(MeV) 8.41 ± 0.43 8.48 ± 0.53 8.57 ± 0.54 8.44 ± 0.09
(0.162 ± 0.007) (0.163 ± 0.009) (0.1627±0.009)
-0.145 ± 0.001 -0.146 ± 0.001 -0.147 ± 0.001
ndf 452 / 342 479 / 342
537 / 342
For the case of destructive interference we show the variable:
spe
speteo
N
NN
Estimate of BR( f0 )
)(
)()( 0exp
0
L
fNfBR
Nexp( f0) is the number of f0 events calculated integrating thecontribution of the f0 to the total function without the efficiency.
=bL = 342 pb-1
Interference Nexp( f0) BR( f0 )
Destructive 100338 8.79 × 10-5
Zero 64974 5.69 × 10-5
Constructive 44728 3.92 × 10-5
Comparison with the Giovannella-Miscetti results:
Giovannella-Miscetti
g2f0KK/4GeV2 2.79 ± 0.12 0.39 ± 0.02
g2f0KK/g2
f0 4.00 ± 0.14 3.06 ± 0.12
mf0 (MeV) 973 ± 1 975.10 ± 0.62
Giovannella – Miscetti found this value:
BR( f0 ) = (1.49 ± 0.07) ×10-4
We expect BR( f0 ) ~ 2 ×BR( f0 )
Instead we find:
BR( f0 ) ~ 0.58 × BR( f0 )
Using the parameters of Giovannella-Miscetti in the function for the fitthere is not agreementwith data.
Constructive int.Zero int.Destructive int.
= 25º
= 45º
= 65º
Spectrum of the data and function for different values of the photon polar angle range:
The function describes quite well how the spectrum changes varying the photon polar angle range.
Fit with contribution of the The parameterization of (f0+ is taken from Giovannella-Miscetti
We include the term of interference between and the Final State Radiation.
The mass and width of the arefixed at: m= 480 MeV = 324 MeV
We have only a new free parameter for the fit: g
Without With g2
f0KK/4(GeV2)
0.39 ± 0.02 0.56 ± 0.02
g2f0KK/g
f0 3.06 ± 0.12 3.38 ± 0.05
mf0 (MeV) 975.10 ± 0.62 976.54 ± 0.44
gMeV 6.99 ± 0.05
m(MeV) 774.27 ± 0.19 773.93 ± 0.19
(MeV) 140.60 ± 0.29 138.13 ± 0.51
m(MeV) 782.09 ± 0.17 782.01 ± 0.16
(MeV) 8.41 ± 0.43 8.17± 0.50
(0.162 ± 0.007) 0.159 ± 0.005
-0.145 ± 0.001 -0.161 ± 0.008
ndf 452 / 342 476/342
Results of the fit with the contribution
In the case of destructive interference
Conclusions
• the spectrum is well described by the function in the case of destructive interference
• in the case of destructive interference we have: without the contribution we find: BR( f0 ) = 8.79 × 10-5 ~ 0.58 × BR( f0 )
