Toward accurate form factors for $B$-to-light meson decay from lattice QCD

Abstract

We present the results of a lattice QCD calculation of the scalar and vector form factors for the unphysical $B_s\to {\eta }_s$ decay, over the full physical range of $q^2$. This is a useful testing ground both for lattice QCD and for our wider understanding of the behaviour of form factors. Calculations were performed using the highly improved staggered quark (HISQ) action on $N_f=2+1+1$ gluon ensembles generated by the MILC Collaboration with an improved gluon action and HISQ sea quarks. We use three lattice spacings and a range of heavy quark masses from that of charm to bottom, all in the HISQ formalism. This permits an extrapolation in the heavy quark mass and lattice spacing to the physical point and nonperturbative renormalisation of the vector matrix element on the lattice. We find results in good agreement with previous work using nonrelativistic QCD $b$ quarks and with reduced errors at low $q^2$, supporting the effectiveness of our heavy HISQ technique as a method for calculating form factors involving heavy quarks. A comparison with results for other decays related by SU(3) flavour symmetry shows that the impact of changing the light daughter quark is substantial but changing the spectator quark has very little effect. We also map out form factor shape parameters as a function of heavy quark mass and compare to heavy quark effective theory expectations for mass scaling at low and high recoil. This work represents an important step in the progression from previous work on heavy-to-heavy decays ($b\to c$) to the numerically more challenging heavy-to-light decays.

arXiv commentpublished version; 18 pages, 14 figures

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• $B\to K$ and $D\to K$ form factors from fully relativistic lattice QCD
• Exotic Tetraquark states with two $\bar{b}$-quarks and $J^P=0^{+}$ and $1^{+}$ $B_s$ states in a nonperturbatively-tuned Lattice NRQCD setup
• Improved $V_{cs}$ determination using precise lattice QCD form factors for $D\to K\ell \nu$
• D-meson semileptonic decays to pseudoscalars from four-flavor lattice QCD
• Form factors for the processes $B_c^{+}\to D^0{\ell }^{+}{\nu }_{\ell }$ and $B_c^{+}\to D_s^{+}{\ell }^{+}{\ell }^{-}(\nu \overline{\nu })$ from lattice QCD
• Probing the inverse moment of $B_s$-meson distribution amplitude via $B_s\to {\eta }_s$ form factors
• Self-consistent optimization of the $z$-Expansion for $B$ meson decays
• Transition form factors for $D/B$ to $a_0(980)$ from light-cone QCD sum rules