Global analysis of inclusive B decays

TL;DR

This work refines the inclusive B decay analysis to extract |V_{cb}| and the b-quark mass by performing a global fit to a broad set of shape observables, incorporating higher-order perturbative and nonperturbative corrections within multiple heavy-quark mass schemes. It demonstrates that short-distance mass schemes (notably 1S_EXP and kin_EXP) provide better convergence and smaller theoretical uncertainties than pole or MSbar schemes, while showing robust agreement with experimental data and a consistent picture across observables. The study also tests potential duality violations and quantifies theoretical uncertainties, yielding a precise, cross-validated determination of |V_{cb}| and m_b^{1S} with implications for CKM phenomenology and CP-violation constraints. Overall, the analysis strengthens the reliability of inclusive determinations of |V_{cb}|, complements exclusive determinations, and informs future precision tests of the Standard Model in B physics.

Abstract

In light of the large amount of new experimental data, we revisit the determination of V_{cb} and m_b from inclusive semileptonic and radiative B decays. We study shape variables to order lqcd^3/m_b^3 and alpha_s^2β_0, and include the order alpha_s, lqcd/m_b correction to the hadron mass spectrum in semileptonic decay, which improves the agreement with the data. We focus on the 1S and kinetic mass schemes for the b quark, with and without expanding m_b-m_c in HQET. We perform fits to all available data from BABAR, BELLE, CDF, CLEO, and DELPHI, discuss the theoretical uncertainties, and compare with earlier results. We find V_{cb} = (41.4 +- 0.6 +- 0.1) x 10^{-3} and m_b^{1S} = 4.68 +- 0.03 GeV, including our estimate of the theoretical uncertainty in the fit.

Figures (6)

• Figure 1: Fit results for $|V_{cb}|$ and $m_b$ in the $1S_{\text{EXP}}$, $1S_{\text{NO}}$, $\hbox{kin}_{\text{EXP}}$, $\hbox{kin}_{\text{NO}}$, and $\hbox{kin}_{\text{UG}}$ schemes defined in Eq. (\ref{['schemedef']}) and in the traditional pole scheme. The red doted, blue dashed, and black solid ellipses denote the results at tree level, order $\alpha_s$, and $\alpha_s^2\beta_0$, respectively, corresponding to $\Delta\chi^2 = 1$.
• Figure 2: Measurements (blue squares: BABAR Aubert:2004teAubert:2004td, green triangles: CLEO Csorna:2004kpMahmood:2004kq, black dots: BELLE Abe:2004ksAbe:2004zv) and fit results for the hadron invariant mass (left) and the lepton energy moments (right) as functions of the lepton energy cut, $E_{\rm cut}$. For the hadron moments $m_X^n$ denotes $\langle m_X^{n}\rangle$, while for the lepton moments BR is branching ratio, M1 is first moment, and M2 and M3 are the second and third central moments, respectively. The red (dark) shaded regions show the fit error, while the yellow (light) shaded regions are our estimates of the theoretical uncertainties from the $A$ terms in Eq. (\ref{['adef']}). The $A$ term for $\langle m_X^{}\rangle$ and $\langle m_X^{3}\rangle$ is three times larger than for $\langle m_X^{2}\rangle$ and $\langle m_X^{4}\rangle$, because of the worse expansion for the non-integer moments.
• Figure 3: Measurements and fit results for the hadron invariant mass and the lepton energy moments, setting all theory errors to zero in the fit. (See the caption for Fig. \ref{['fig:hadlepcompare']}.) The yellow (light) shaded band gives the estimated theoretical uncertainty, as in Fig \ref{['fig:hadlepcompare']}. It is not included in the fit, but it can help to decide the significance of any differences between theory and experiment.
• Figure 4: Fit results for $|V_{cb}|$ and $m_b$ in the $\hbox{kin}_{\text{EXP}}$ and $\hbox{kin}_{\text{UG}}$ schemes using $\mu_b=1$ GeV (blue and black) and using $\mu_b=1.5\,$ GeV (green and yellow). $\mu_c$ for the $\hbox{kin}_{\text{UG}}$ scheme has been kept fixed at 1 GeV. The regions correspond to $\Delta\chi^2 = 1$ (black and yellow) and 4 (blue and green). The upper plots includes theory errors in the fit, and the lower plot does not.
• Figure 5: Fit results for $|V_{cb}|$ and $m_b$ in the PS scheme using $\mu = 2\,$ GeV (blue and black) and using $\mu = 1.5\,$ GeV (green and yellow) The regions correspond to $\Delta\chi^2 = 1$ (black and yellow) and 4 (blue and green). The upper plots includes theory errors in the fit, and the lower plot does not.