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Test of lepton flavour universality using $B^0 \to D^{*-}\tau^+\nu_{\tau}$ decays with hadronic $\tau$ channels

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Abstract

The branching fraction $\mathcal{B}(B^0 \to D^{*-}\tau^+\nu_{\tau})$ is measured relative to that of the normalisation mode $B^0 \to D^{*-}\pi^+\pi^-\pi^+$ using hadronic $\tau^+ \to \pi^+\pi^-\pi^+(\pi^0)\bar{\nu}_{\tau}$ decays in proton-proton collision data at a centre-of-mass energy of 13 TeV collected by the LHCb experiment, corresponding to an integrated luminosity of 2 fb$^{-1}$. The measured ratio is $\mathcal{B}(B^0 \to D^{*-}\tau^+\nu_{\tau})/\mathcal{B}(B^0 \to D^{*-}\pi^+\pi^-\pi^+)= 1.70 \pm 0.10^{+0.11}_{-0.10}$, where the first uncertainty is statistical and the second is related to systematic effects. Using established branching fractions for the $B^0 \to D^{*-}\pi^+\pi^-\pi^+$ and $B^0 \to D^{*-} \mu^+\nu_\mu$ modes, the lepton universality test, $\mathcal{R}(D^{*-}) \equiv \mathcal{B}(B^0 \to D^{*-}\tau^+\nu_{\tau})/\mathcal{B}(B^0 \to D^{*-} \mu^+\nu_\mu)$ is calculated, $$ \mathcal{R}(D^{*-}) = 0.247 \pm 0.015 \pm 0.015 \pm 0.012 , $$ where the third uncertainty is due to the uncertainties on the external branching fractions. This result is consistent with the Standard Model prediction and with previous measurements.

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Projections of the $ D ^+_ s \rightarrow 3\pi X $ components for the variables: min[$m(\pi ^+ \pi ^- )$], max[$m(\pi ^+ \pi ^- )$], $m(\pi ^+ \pi ^+ )$ and $m(3\pi)$ in the fit to the control data samples.

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Distributions of $\Delta M _{D^*D_s}$, $q^2$, $t_{\tau}$ and anti- $ D ^+_ s $ BDT output for the $ B \rightarrow D ^{*-} D ^+_ s (X)$ components. The results of the fit are overlaid.

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Simulated $q^2$ distributions for $B \rightarrow D^{*-}D^0(X)$ before and after weighting based on the data control samples.

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Distributions of the fit variables in the $ B ^0 \rightarrow D ^{*-} \tau ^+ \nu _\tau $ data sample with the fit result overlaid.

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Invariant-mass distribution of the (left) $ D ^{*-} 3\pi$ and (right) $3\pi$ system for $ B ^0 \rightarrow D ^{*-} 3\pi $ candidates in data with corresponding fit models superimposed.

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Tables and captions

Relative fractions of various $ D ^+_ s \rightarrow 3\pi X $ decays obtained from the fit to the $ D ^+_ s $ control sample (see \cref{fig:dspfit}) before applying any bias correction to the mean value of its uncertainty.

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Decay fractions for $ B \rightarrow D ^{*-} D ^+_ s (X) $ decays obtained from data control samples. The fractions are normalised relative to that of the $ B ^0 \rightarrow D ^{*-} D ^{*+}_ s $ decay.

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List of components in the signal yield extraction fit and their normalisation.

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Fit results from the three-dimensional signal-extraction fit to $q^2$, $t_{\tau}$ and anti- $ D ^+_ s $ BDT output in the data.

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Summary of relative systematic uncertainties on the ratio $\mathcal{K}( D ^{*-} )$ .

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Created on 27 April 2024.