Abstract

We present results of the first lattice QCD calculations of $B_c \to B_s$ and $B_c \to B_d$ weak matrix elements. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the physical-continuum limit before combining with CKM matrix elements to predict the semileptonic decay rates $\Gamma(B_c^+ \to B_s^0 \overline{\ell} \nu_{\ell}) = 26.2(1.2) \times 10^9 \,\text{s}^{-1}$ and $\Gamma(B_c^+ \to B^0 \overline{\ell} \nu_{\ell}) = 1.65(10) \times 10^9 \,\text{s}^{-1}$. The lattice QCD uncertainty is comparable to the CKM uncertainty here. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with a range of lattice spacings including 2+1+1 flavours of dynamical sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for the propagators of the valence light, strange, and charm quarks. Two different formalisms are employed for the bottom quark: non-relativistic QCD (NRQCD) and heavy-HISQ. Checking agreement between these two approaches is an important test of our strategies for heavy quarks on the lattice. From chained fits of NRQCD and heavy-HISQ data, we obtain the differential decay rates $d\Gamma/ d q^2$ as well as integrated values for comparison to future experimental results.

Highlights

  • The semileptonic weak decays Bþc → B0slνl and Bþc → B0lνl proceed via tree-level flavor changing processes c → sWþ and c → dWþ parametrized by the CabbiboKobayashi-Maskawa (CKM) matrix of the Standard Model

  • Results are derived from correlation functions computed on MILC Collaboration gauge configurations with a range of lattice spacings including 2 þ 1 þ 1 flavors of dynamical sea quarks in the highly improved staggered quark (HISQ) formalism

  • Two different formalisms are employed for the bottom quark: nonrelativistic QCD (NRQCD) and heavy-HISQ

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Summary

INTRODUCTION

The semileptonic weak decays Bþc → B0slνl and Bþc → B0lνl proceed via tree-level flavor changing processes c → sWþ and c → dWþ parametrized by the CabbiboKobayashi-Maskawa (CKM) matrix of the Standard Model. Precise determination of the normalization and the q2 dependence of these form factors from lattice QCD will allow a novel comparison with future experiment to deduce the CKM parameters Vcs and Vcd. Lattice studies of other semileptonic meson decays that involve tree-level weak decays of a constituent charm quark include [1,2,3,4,5,6]. Lattice studies of other semileptonic meson decays that involve tree-level weak decays of a constituent charm quark include [1,2,3,4,5,6] Precise determination of these CKM matrix elements is critical for examining the second row unitary constraint. By calculating correlators at a range of transfer momenta on lattices with different spacings and quark masses, continuum form factors at physical quark masses are obtained and appropriately integrated to offer a direct comparison with decay rates that could be measured in experiment.

Parameters and setup
NRQCD spectator case
HISQ spectator case
Fitting the correlators
Extracting the form factors
Bs ðdÞ ðEsBimc ðjaqj
Correlators
Form factors
DISCUSSION
NRQCD form factor fits
Heavy-HISQ form factor fits
Chained fit
Dependence of the form factors on the spectator quark mass
Decay rate
CONCLUSIONS

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