$Ξ_c \to Ξ$ form factors from lattice QCD with domain-wall quarks: A new piece in the puzzle of $Ξ_c^0$ decay rates

Abstract

We present a lattice-QCD determination of the vector and axial-vector form factors that describe the charm-baryon semileptonic decays $Ξ_c\to Ξ\ell^+ ν_\ell$. The calculation uses a domain-wall action for the up, down, and strange quarks, and an anisotropic clover action for the charm quark. We use four ensembles of gauge-field configurations generated by the RBC and UKQCD collaborations, with lattice spacings between 0.111 and 0.073 fm and pion masses ranging from 420 to 230 MeV. We present Standard-Model predictions for the decay rates and branching fractions of $Ξ_c^0\to Ξ_c^-\ell^+ ν_\ell$ and $Ξ_c^+\toΞ_c^0\ell^+ ν_\ell$ for $\ell=e,μ$. In particular, we obtain $Γ(Ξ_c^0 \to Ξ^- e^+ ν_e)/|V_{cs}|^2 = 0.2515(73)\text{ ps}^{-1}$ and $\mathcal{B}(Ξ_c^0 \to Ξ^- e^+ ν_e) = 3.58(12)\:\%$. These values are higher than those predicted by a previous lattice calculation and substantially higher than the experimentally measured values, but consistent with expectations from approximate $SU(3)$ flavor symmetry.

Figures (8)

• Figure 1: The $t'$ dependence of both the vector-current and axial-vector-current ratios for three different values of the source-sink separation, $t$. The data from the C005, C01, and F004 ensembles are shown at $|\mathbf{p}^\prime|^2=1 \cdot (\tfrac{2\pi}{L})^2$, and the data from the F1M ensemble are shown at $|\mathbf{p}^\prime|^2=2\cdot (\tfrac{2\pi}{L})^2$. The plots are in units of $\rm{GeV}^{-2}$ for the dimensionful ratios $(\mathscr{R}^V_\perp, \mathscr{R}^V_0, \mathscr{R}^A_\perp, \mathscr{R}^A_0)$; the uncertainty from the lattice spacing is not shown. Note that the results from the different ensembles are not expected to be numerically close because of mass-dependent factors and because the $q^2$ values do not match exactly.
• Figure 2: Evolution of the AIC average and uncertainty of the form factor $f_\perp$ at $|\mathbf{p}^\prime|^2=1\cdot (\tfrac{2\pi}{L})^2$ as a function of the number of sample fits, for widths of the $t_{\rm min}$ random distributions equal to $\delta=1,...,7$ (in lattice units). Values of $\delta > 4$ required larger numbers of sample fits to comprehensively explore the model space, but trended toward the same central value. The larger model space gained by increasing $\delta$ adds many models, but they have comparatively small model weights as the number of cut data points is increased without corresponding improvement in the $\chi^2$. Therefore, we use $\delta=4$ and 10,000 sample fits to obtain the final estimates.
• Figure 3: Plots showing the AIC analysis of the quantities $R_f(|\mathbf{p}^\prime|,t)$ for the $\rm{C01}$ ensemble at $|\mathbf{p}^\prime|^2=1(2\pi/L)^2$. The curves going through the data points belong to the sample fit with the highest model weight, with the bands showing only the statistical uncertainty, whereas the horizontal bands depict to the AIC average values of the extracted ground-state form factors and their total uncertainty. Data points plotted with open symbols were omitted in the highest-model-weight fit.
• Figure 4: Chiral and continuum extrapolations of the $\Xi_c \to \Xi$ vector form factors. The solid blue lines show the form factor curves in the physical limit, while the dashed lines show the modified $z$-expansion fits evaluated with the individual lattice spacings and pion masses for each ensemble. The bands include the combined statistical and systematic uncertainties.
• Figure 5: Like Fig. \ref{['fig:vector_extrap']}, but for the axial-vector form factors.