Fit to Moments of Inclusive B->Xc lv and B-> Xs gamma Decay Distributions using Heavy Quark Expansions in the Kinetic Scheme

TL;DR

The paper performs a global χ^2 fit of Heavy Quark Expansion predictions in the kinetic scheme to moments from inclusive B -> X_c l nu and B -> X_s gamma decays, extracting |V_cb|, m_b, m_c, and six HQE parameters. By combining hadronic-mass, lepton-energy, and photon-energy moments with published correlations and conservative theoretical uncertainties, the authors achieve a precise determination of |V_cb| and heavy-quark masses and translate these results into Kagan-Neubert and Shape-Function schemes to support |V_ub| determinations. The analysis demonstrates internal consistency across decay channels, quantifies theoretical error contributions, and provides extrapolation factors for comparing B -> X_s gamma branching fractions across photon-energy cuts. The resulting HQE parameters enable improved OPE expressions for |V_ub| and cross-scheme inputs, contributing to precision flavor physics and tests of the CKM paradigm.

Abstract

We present a fit to measured moments of inclusive distributions in B->Xc lv and B-> Xs gamma decays to extract values for the CKM matrix element |Vcb|, the b- and c-quark masses, and higher order parameters that appear in the Heavy Quark Expansion. The fit is carried out using theoretical calculations in the kinetic scheme and includes moment measurements of the Babar, Belle, CDF, CLEO and DELPHI collaborations for which correlation matrices have been published. We find |Vcb| = (41.96 +- 0.23(exp) +- 0.35(HQE) +- 0.59(Gamma_SL)) 10^-3 and m_b = 4.590 +- 0.025(exp) +- 0.30(HQE) GeV where errors are experimental and theoretical respectively. We also derive values for the heavy quark distribution function parameters m_b and μ_π^2 in different theoretical schemes that can be used as input for the determination of |Vub|.

Figures (6)

• Figure 1: Comparison of fit predictions and the hadron moment measurements: (a) $\langle M_X\rangle$, (b) $\langle M_X^2\rangle$, (c) $\langle M_X^3\rangle$, (d) $\langle (M_X^2-\langle M_X^2\rangle )^2\rangle$ and (e) $\langle (M_X^2-\langle M_X^2\rangle )^3\rangle$. The yellow bands represent the total experimental and theoretical fit uncertainty as obtained by converting the fit errors of each individual HQE parameter into an error for the individual moment. The green band indicates the experimental uncertainty only. Solid markers are included in the fit while open markers are only overlaid for comparison. Moment measurements at different $E_{cut}$ are highly correlated.
• Figure 2: Comparison of fit predictions and measurements for the lepton moments: (a) $BR$, (b) $\langle E_L\rangle$, (c) $\langle (E_L-\langle E_L\rangle )^2\rangle$ and (d) $\langle (E_L-\langle E_L\rangle )^3\rangle$. The yellow bands represent the total experimental and theoretical fit uncertainty while the green band indicates the experimental uncertainty only. Solid markers are included in the fit while open markers are only overlaid for comparison. Moment measurements at different $E_{cut}$ are highly correlated.
• Figure 3: Comparison of fit predictions and measurements for the photon moments: (a) $\langle E_{\gamma} \rangle$ and (b) $\langle (E_{\gamma} -\langle E_{\gamma} \rangle)^2 \rangle$. The bands in the figures on the left show the fit prediction for the pure OPE calculation neglecting effects of the minimal photon energy cut on the OPE part (biases). The bands in figures (c) and (d) include those bias corrections of Ref. Benson:2004sg. The yellow bands represent the total experimental and theoretical fit uncertainty while the green band indicates the experimental uncertainty only. Solid markers are included in the fit while open markers are only overlaid for comparison. Moment measurements at different $E_{cut}$ are highly correlated.
• Figure 4: Comparison of the different fit scenarios. Figure (a) shows the $\Delta \chi^2$ = 1 contour in the ($m_b$,$\mu_{\pi}^2$) plane for the combined fit to all moments (solid red), the fit to hadron and lepton moments only (dashed blue) and the fit to photon moments only (dotted green). Figure (b) shows the results for the combined fit (solid red) and the fit to hadron and lepton moments only (dashed blue) in the ($m_b$,$|V_{cb}|$) plane.
• Figure 5: Translation of fit results in the kinetic scheme to Kagan-Neubert (a) and the Shape Function scheme (b) via predicted photon moments. Figure (a) shows the results for the shape function parameters in the ($\bar{\Lambda},\lambda_1$) plane from the combined fit to all moments (solid red) and the fit to hadron and lepton moments only (dashed blue). Figure (b) shows the corresponding fit results in the ($m_{b~SF},\mu_{\pi~SF}^2$) plane.