# Global Fit to Moments Measurements from b->clv and b->sg decays

(A comprehensive explanation of the fit and its results can be found in hep-ph/0507253.)

The fit uses all public moment measurements of the hadronic mass and lepton energy distribution in b->clv decays and photon energy distribution of b-> s gamma decays where correlation matrices are available. It follows closely the approach of hep-ex/0404017

It is based on calculations in Refs. hep-ph/0401063 and hep-ph/0410080 . Theoretical errors concerning the accuracy in the expression for a given moment have been assigned following the recipes given by the authors of the above publications.

## Fit Input

The table below lists the moment measurements that form the basis for the combined fit. 'n' indicated the order of the (central) moment while 'c' indicates the value of the minimum lepton or photon energy for which the moments is measured.

Experiment Hadron Moments Lepton Moments Photon Moments References
BABAR n=2 c=0.9,1.0,1.1,1.2,1.3,1.4,1.5 n=0 c=0.6,1.2,1.5 n=1 c=1.9,2.0 hep-ex/0403031 , hep-ex/0403030
BABAR n=4 c=0.9,1.0,1.1,1.2,1.3,1.4,1.5 n=1 c=0.6,0.8,1.0,1.2,1.5 n=2 c=1.9 Measurement of the B->Xs gamma Branching Fraction and Spectral Shape from a Sum of Exclusive Final States, presented at Moriond 2005
BABAR . n=2 c=0.6,1.0,1.5 . Results from the BaBar Fully Inclusive Measurement of B->Xs gamma, contributed to Lepton-Photon 2005
BABAR . n=3 c=0.8,1.2 . .
Belle . . n=1 c=1.8 hep-ex/0403004
CDF n=2 c=0.7 . . hep-ex/0502003
CDF n=4 c=0.7 . . .
CLEO n=2 c=1.0,1.5 . n=1 c=2.0 hep-ex/0403052
CLEO n=4 c=1.0,1.5 . . hep-ex/0108032
DELPHI n=2 c=0.0 n=1 c=0.0 . DELPHI 2004-021 CON 696 - ICHEP04
DELPHI n=4 c=0.0 n=2 c=0.0 . .
DELPHI n=6 c=0.0 n=3 c=0.0 . .
HFAG . n=0 c=0.6 . HFAG SUMMER 04 update

### Fit Results in Kinetic Scheme

We considered two separate scenarios. The fit was carried out using:

- only hadron and lepton moments from b->clv decays as input

- using all moment measurements listed in the above table (b->clv and b->sgamma)

Fit Input mb mu_pi^2 Correlation Chi^2/Ndof
All moments mb = 4.591 +- 0.040GeV mu_pi^2 = 0.406 +- 0.041 GeV^2 rho = -0.318 chi2/Ndof = 17.6/41
clv moments mb = 4.644 +- 0.074 GeV mu_pi^2 = 0.392 +- 0.043 GeV^2 rho = -0.393 chi2/Ndof = 15.3/33

A figure of the Delta chi^2 ellipse in the (mb,mu_pi^2) plane can be found here: mb vs mupi2 in kinetic scheme

### Translation to Kagan-Neubert and the Shape Function Scheme

The fit results obtained in the kinetic scheme have been translated to the parameters used in Kagan-Neubert scheme hep-ex/9805303 and the more recent Shape Function scheme hep-ph/0402094. This was done by 'predicting' values for the first and second moment of the photon spectrum above Egamma = 1.6 GeV using the results for the Heavy Quark parameters from the fit in the kinetic scheme. The errors on all the parameters were propagated into errors on the photon moments and a chi2 was calculated with respect to the photon energy moments obtained in the other schemes.
Scheme Fit Input mb mu_pi^2
Kagan-Neubert All moments Lambda = 0.628 - 0.038 + 0.041 GeV lambda_1 = -0.499 - 0.081 + 0.067 GeV^2
Kagan-Neubert clv moments Lambda = 0.569 - 0.074 + 0.079 GeV lambda_1 = -0.494 - 0.091 + 0.072 GeV^2
Shape Function scheme All moments mb = 4.603 - 0.038 + 0.040 GeV mupi^2 = 0.203 - 0.039 + 0.038 GeV^2
Shape Function Scheme clv moments mb = 4.662 - 0.078 + 0.079 GeV mupi^2 = 0.188 - 0.043 + 0.042 GeV^2

A figure of the Delta chi^2 ellipse in the (Lambda,lambda_1) plane for Kagan-Neubert can be found here: Lambda vs lambda_1 in Kagan-Neubert scheme

A figure of the Delta chi^2 ellipse in the (mb,mu_pi^2) plane for the Shape Function scheme can be found here: mb vs mupi2 in shape function scheme

Last update: 2005/06/27 Henning Flaecher