New Predictions for ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c$ Semileptonic Decays and Tests of Heavy Quark Symmetry

The heavy quark effective theory makes model independent predictions for semileptonic ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c$ decays in terms of a small set of parameters. No subleading Isgur-Wise function occurs at order ${\mathrm{\Lambda }}_{\mathrm{QCD}}/m_{c,b}$, and only two subsubleading functions enter at order ${\mathrm{\Lambda }}_{\mathrm{QCD}}^2/m_c^2$. These features allow us to fit the form factors and decay rates calculated up to order ${\mathrm{\Lambda }}_{\mathrm{QCD}}^2/m_c^2$ to LHCb data and lattice QCD calculations. We derive a significantly more precise standard model prediction for the ratio $\mathcal{B}({\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\tau \overline{\nu })/\mathcal{B}({\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\mu \overline{\nu })$ than prior results, and find the expansion in ${\mathrm{\Lambda }}_{\mathrm{QCD}}/m_c$ well behaved, addressing a long-standing question. Our results allow more precise and reliable calculations of ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\ell \overline{\nu }$ rates, and are systematically improvable with better data on the $\mu$ (or $e$) modes.

Figure 1

The red band shows our fit of the HQET predictions to $d\mathrm{\Gamma }({\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\mu \overline{\nu })/d{q}^2$ measured by LHCb [15] and the LQCD form factors [16]. The heather gray band shows the LQCD prediction. The blue curve shows our prediction for $d\mathrm{\Gamma }({\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\tau \overline{\nu })/d{q}^2$.

Figure 2

Fit of the HQET predictions in Eq. (8) to the LQCD results [16] and the LHCb spectrum [15] for the six form factors (red bands). The heather gray bands and data points show the LQCD prediction; see text for details.