Measurement of the Moments of the Hadronic Invariant Mass Distribution in Semileptonic B Decays

Using 180 pb^-1 of data collected with the CDF II detector at the Tevatron, we measure the first two moments of the hadronic invariant mass-squared distribution in charmed semileptonic B decays. From these we determine the non-perturbative Heavy Quark Effective Theory parameters Lambda and lambda_1, used to relate the B meson semileptonic branching ratio to the CKM matrix element |V_cb|. For a minimum lepton momentum of 0.7 GeV/c in the B rest frame me measure the first two moments of the D** --> D(*) pi component to be <m^2_D**> = (5.83 +/- 0.16(stat) +/- 0.08(syst)) GeV^2, <(m^2_D** - <m^2_D**>)^2> = (1.30 +/- 0.69(stat) +/- 0.22(syst)) GeV^4. Combining these with the discrete mass terms from the D and D* mesons, we find the total moments to be <M^2_Xc> - mbar_D^2 = (0.467 +/- 0.038_(stat) +/- 0.068(syst)) GeV^2, <(M^2_Xc - <M^2_Xc>)^2> = (1.05 +/- 0.26(stat) +/- 0.13(syst)) GeV^4, where mbar_D is the spin-averaged D mass. The systematic error is dominated by the uncertainties in the world-average branching ratios used to combine the D, D* and D** contributions. The analysis makes no assumptions about the shape or resonant structure of the D** --> D(*) pi invariant mass distribution.