Measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast })$ with a semileptonic tagging method

Abstract

The experimental results on the ratios of branching fractions $\mathcal{R}(D)=\mathcal{B}(\bar{B}\to D{\tau }^{-}{\bar{\nu }}_{\tau })/\mathcal{B}(\bar{B}\to D{\ell }^{-}{\bar{\nu }}_{\ell })$ and $\mathcal{R}(D^{\ast })=\mathcal{B}(\bar{B}\to D^{\ast }{\tau }^{-}{\bar{\nu }}_{\tau })/\mathcal{B}(\bar{B}\to D^{\ast }{\ell }^{-}{\bar{\nu }}_{\ell })$, where $\ell$ denotes an electron or a muon, show a long-standing discrepancy with the Standard Model predictions, and might hint to a violation of lepton flavor universality. We report a new simultaneous measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast })$, based on a data sample containing $772\times 10^6$ $B\bar{B}$ events recorded at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. In this analysis the tag-side $B$ meson is reconstructed in a semileptonic decay mode and the signal-side $\tau$ is reconstructed in a purely leptonic decay. The measured values are $\mathcal{R}(D)=0.307\pm 0.037\pm 0.016$ and $\mathcal{R}(D^{\ast })=0.283\pm 0.018\pm 0.014$, where the first uncertainties are statistical and the second are systematic. These results are in agreement with the Standard Model predictions within $0.2$, $1.1$ and $0.8$ standard deviations for $\mathcal{R}(D)$, $\mathcal{R}(D^{\ast })$ and their combination, respectively. This work constitutes the most precise measurements of $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast })$ performed to date as well as the first result for $\mathcal{R}(D)$ based on a semileptonic tagging method.

8 pages, 1 figure, submitted to Physical Review Letters