$|V_{ub}|$ determination and testing of lepton flavour universality in semileptonic $B_c\to D^{(\ast )}$ decays

Abstract

In light of prospects for measurements of $B_c\to D^{(\ast )}l\nu$ decays in the upcoming Upgrade II of the LHC, we show that by using calculated $B_c\to D^{(\ast )}$ form factors competitive extraction of the $|V_{ub}|$ CKM matrix element from the $B_c\to D\mu {\bar{\nu }}_{\mu }$ decay might be possible. To minimize experimental and theoretical uncertainties we provide the ratio $|V_{ub}|/|V_{cb}|$ by normalizing the $B_c\to D^{(\ast )}\mu {\bar{\nu }}_{\mu }$ to $B_c\to J/\psi \mu {\bar{\nu }}_{\mu }$ decay. We also briefly examine the suggestion to extract $|V_{ub}|/|V_{cs}|$ from the theoretically interesting ratio of $B_c\to D^{0}e{\bar{\nu }}_e$ and $B_c\to B_{s}e{\bar{\nu }}_e$ decay rates in the zero-recoil limit. With the present average value of $|V_{ub}|$, the predicted branching ratios are estimated to be $BR(B_c\to D^0\mu {\bar{\nu }}_{\mu })=(2.4\pm 0.4)\cdot 10^{-5}$ and $BR(B_c\to D^{\ast }\mu {\bar{\nu }}_{\mu })=(7\pm 3)\cdot 10^{-5}$, and the semileptonic ratios for testing the lepton flavour universality in these $B_c$ decays are $R_c(D^0)=0.64\pm 0.05$ and $R_c(D^{\ast })=0.55\pm 0.05$. We also provide $q^2$ distributions and various angular observables of $B_c\to D^{(\ast )}l\nu$ decays.

Comments: 46 pages, 13 figures, published version. Some clarifications of the method are given. New subsection 2.2 on the discussion of correlations between the pseudo-data points and on the error budget of the results is inserted. Additional references added