Extracting $B_s\to D_s^*\ellν_\ell$ form factors

Abstract

Semileptonic $B_{(s)}$ decays are of great phenomenological interest because they allow to determine e.g. CKM matrix elements or test lepton flavor universality. Taking advantage of already existing lattice data, we demonstrate the analysis steps to extract the four form factors describing exclusive semileptonic $B_s\to D_s^*\ellν_\ell$ decays using the narrow width approximation. Our data are based on RBC/UKQCD's set of 2+1 flavor gauge field ensembles with Shamir domain-wall fermion and Iwasaki gauge field action featuring inverse lattice spacings of $a^{-1}=$1.785, 2.383, and 2.785 GeV as well as pion masses between 268 and 433 MeV. Light, strange and charm quarks are simulated using domain-wall fermions, whereas bottom quarks are generated with the relativistic heavy quark (RHQ) action.

Figures (6)

• Figure 1: In the left panel we show the $D_s^*$ effective energies on C1, $am_c=0.300$ against the $D_s^*$ momentum in lattice units $n^2$. Green circles show the fitted values, red triangles are obtained using the lattice dispersion relation and blue squares using the continuum dispersion relation. In the right panel we plot the squared ratio of the fitted $D_s^*$ effective energies over the effective energies obtained using dispersion relations vs. $k^2 = (2\pi n/L)^2$. The dashed lines indicate the leading order discretization error.
• Figure 2: Comparison of extracting the signal for the $\widetilde{A}_0$ form factor on the F1S ensemble by performing a simple ground state fit (left) vs. accounting for excited states (right).
• Figure 3: Extracting form factors $\widetilde{V}$ and $\widetilde{A}_1$ for F1S, $am_c=0.259$ projecting the $D_s^*$ hadronic final states to different momenta $\vec{k}^{\,2} = (2\pi \vec{n}/L)^2$ and performing a combined fit for all momenta parametrizing excited state contributions.
• Figure 4: Blinded renormalized form factors $V, A_0$ and $A_1$ as a function of $q^2$. The different colors indicate the different ensembles and corresponding charm masses.
• Figure 5: 3-dimensional plots for the $V$ form factor on F1S (left) and C1 (right) with the $D_s^*$ momentum in lattice units $(2\pi \vec{n}/L)^2$ on the $x$-axis, the $D_s^*$ meson masses using the dispersion relation on the $y$-axis and the $V$ form factor fits on the $z$-axis. The central plane of the curved fit function defined in Eq. \ref{['eq:curved']} in terms of $(2\pi \vec{n}/L)^2$ and $E_{\rm eff}^{D_s^*}$ is given by the green plane, while the $\pm 1\sigma$ planes are shown in red and blue. The values of the form factors corresponding to physical charm quark masses are shown by the black data points.