${\mathrm{\Lambda }}_c\to \mathrm{\Lambda }{l}^{+}{\nu }_l$ Form Factors and Decay Rates from Lattice QCD with Physical Quark Masses

The first lattice QCD calculation of the form factors governing ${\mathrm{\Lambda }}_c\to \mathrm{\Lambda }{\ell }^{+}{\nu }_{\ell }$ decays is reported. The calculation was performed with two different lattice spacings and includes one ensemble with a pion mass of 139(2) MeV. The resulting predictions for the ${\mathrm{\Lambda }}_c\to \mathrm{\Lambda }{e}^{+}{\nu }_e$ and ${\mathrm{\Lambda }}_c\to \mathrm{\Lambda }{\mu }^{+}{\nu }_{\mu }$ decay rates divided by $|V_{cs}{|}^2$ are 0.2007(71)(74) and $0.1945(69)(72){\mathrm{ps}}^{-1}$, respectively, where the two uncertainties are statistical and systematic. Taking the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{cs}|$ from a global fit and the ${\mathrm{\Lambda }}_c$ lifetime from experiments, this translates to branching fractions of $\mathcal{B}({\mathrm{\Lambda }}_c\to \mathrm{\Lambda }{e}^{+}{\nu }_e)=0.0380(19{)}_{\mathrm{LQCD}}(11{)}_{{\tau }_{{\mathrm{\Lambda }}_c}}$ and $\mathcal{B}({\mathrm{\Lambda }}_c\to \mathrm{\Lambda }{\mu }^{+}{\nu }_{\mu })=0.0369(19{)}_{\mathrm{LQCD}}(11{)}_{{\tau }_{{\mathrm{\Lambda }}_c}}$. These results are consistent with, and two times more precise than, the measurements performed recently by the BESIII Collaboration. Using instead the measured branching fractions together with the lattice calculation to determine the CKM matrix element gives $|V_{cs}|=0.949(24{)}_{\mathrm{LQCD}}(14{)}_{{\tau }_{{\mathrm{\Lambda }}_c}}(49{)}_{\mathcal{B}}$.

Figure 1

Lattice results from the CP ensemble for the ratios $R_f(|{\mathbf{p}}^{\prime }|,t)$, defined as in Eqs. (52)–(54) and (58)–(60) of Ref. [3], at $|{\mathbf{p}}^{\prime }{|}^2=4(2\pi /L{)}^2$. These ratios are equal to the ground-state form factors $f(|{\mathbf{p}}^{\prime }|)$ up to contamination from excited states that decays exponentially with $t$. The curves shown are correlated fits of the form $R_f(|{\mathbf{p}}^{\prime }|,t)=f(|{\mathbf{p}}^{\prime }|)+A_f(|{\mathbf{p}}^{\prime }|)e^{-{\delta }_f(|{\mathbf{p}}^{\prime }|)t}$, which includes the leading excited-state contributions. Data points at the smallest separations that are plotted with open symbols are excluded from the fits to suppress contamination from higher excited states; the values of $t_{\min }$ were chosen such that ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.\le 1$. The remaining systematic uncertainties due to higher excited states were estimated as the shifts in the fitted $f(|{\mathbf{p}}^{\prime }|)$ when further increasing $t_{\min }$ by one unit everywhere; these uncertainties were added in quadrature to the statistical uncertainties.

Figure 2

Lattice QCD results for the ${\mathrm{\Lambda }}_c\to \mathrm{\Lambda }$ form factors, along with the modified $z$-expansion fits evaluated at the lattice parameters (dashed and dotted lines) and in the physical limit (solid lines, with statistical and total uncertainties indicated by the inner and outer bands).

Figure 3

Predictions for the ${\mathrm{\Lambda }}_c\to \mathrm{\Lambda }{\ell }^{+}{\nu }_{\ell }$ differential decay rates (divided by $|V_{cs}{|}^2$) in the standard model. For clarity, the uncertainties are shown only for $\ell =e$; the inner and outer bands correspond to the statistical and total uncertainties.