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Measurement of the $D^*$ longitudinal polarization in $B^0 \to D^{* -}\tau^+\nu_{\tau}$ decays  

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Abstract

The longitudinal polarization fraction of the $D^{*}$ meson is measured in $B^0\to D^{*-}\tau^{+}\nu_{\tau}$ decays, where the $\tau$ lepton decays to three charged pions and a neutrino, using proton-proton collision data collected by the LHCb experiment at center-of-mass energies of 7, 8 and 13 TeV and corresponding to an integrated luminosity of 5 fb$^{-1}$. The $D^{*}$ polarization fraction $F_{L}^{D^{*}}$ is measured in two $q^{2}$ regions, below and above 7 GeV$^{2}/c^{4}$, where $q^{2}$ is defined as the squared invariant mass of the $\tau\nu_{\tau}$ system. The $F_{L}^{D^{*}}$ values are measured to be $0.51 \pm 0.07 \pm 0.03$ and $0.35 \pm 0.08 \pm 0.02$ for the lower and higher $q^{2}$ regions, respectively. The first uncertainties are statistical and the second systematic. The average value over the whole $q^{2}$ range is: $$F_{L}^{D^{*}} = 0.43 \pm 0.06 \pm 0.03.$$ These results are compatible with the Standard Model predictions.

Figures and captions

Signal distributions of the $\cos\theta_{D}$ variable in the two $ q^2$ regions for the unpolarized and polarized components. The template for the unpolarized component is distorted by the effect of the reconstruction and the signal selection.

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Simulated (left) $ q^2$ and (right) $\cos\theta_{D}$ distributions for the $ B \rightarrow D ^{*-} D ^0 (X)$ control sample before and after the correction for the data-simulation differences in the Run 2 weighted data sample. The $ B \rightarrow D ^{*-} D ^0 (X)$ sample is selected using the isolation algorithm to search for an extra kaon around the $3\pi$ vertex.

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Distribution of the key analysis variables obtained in the $ B \rightarrow D ^{*-} D ^+_ s (X)$ enhanced Run 2 data sample with the result of the fit superimposed: (top left) $m( D ^* 3\pi)$, (top right) anti- $ D ^+_ s $ BDT output, (middle left) $t_{\tau}$, (middle right) $ q^2$ and (bottom) $\cos\theta_{D}$ .

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Distributions of the fit variables in the (left) Run 1 and (right) Run 2 datasets with the fit results superimposed.

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Animated gif made out of all figures.

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Tables and captions

List of all the requirements included in the signal selection.

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Decay fractions for the $ B \rightarrow D ^{*-} D ^+_ s (X)$ decays, normalized for the $ B ^0 \rightarrow D ^{*-} D ^{*+}_ s $ yield, obtained from the Run 1 and Run 2 control samples.

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Fit results for the Run 1 and Run 2 datasets.

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Values of $ a_{\theta_D}(q^2)$ , $ c_{\theta_D}(q^2)$ and $ F_L^{ D ^* }$ from the fit.

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Summary of the systematic uncertainties related to the $ D ^{*-}$ polarization measurement.

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Created on 27 April 2024.