$\bar B\to Dτ\bar ν_τ$ vs. $\bar B\to Dμ\bar ν_μ$

Recent experimental results for the ratio of the branching fractions of $\bar B\to D^{(*)}τ\bar ν_τ$ and $\bar B\to D^{(*)}μ\bar ν_μ$ decays came as a surprise and lead to a discussion of possibility to constraining New Physics through these modes. Here we focus on ${\cal B}(\bar B\to Dτ\bar ν_τ)/{\cal B}(\bar B\to Dμ\bar ν_μ)$ and argue that the result is consistent with the Standard Model within $2σ$, and that the test of compatibility of this ratio with the Standard Model can be done experimentally with a minimal theory input. We also show that these two decay channels can provide us with quite good constraints of the New Physics couplings.

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