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Angular analysis of $ {B}^0\to {D}^{\ast -}{D}_s^{\ast +} $ with $ {D}_s^{\ast +}\to {D}_s^{+}\gamma $ decays

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Abstract

The first full angular analysis of the $B^0 \to D^{*-} D_s^{*+}$ decay is performed using 6 fb$^{-1}$ of $pp$ collision data collected with the LHCb experiment at a centre-of-mass energy of 13 TeV. The $D_s^{*+} \to D_s^+ \gamma$ and $D^{*-} \to \bar{D}^0 \pi^-$ vector meson decays are used with the subsequent $D_s^+ \to K^+ K^- \pi^+$ and $\bar{D}^0 \to K^+ \pi^-$ decays. All helicity amplitudes and phases are measured, and the longitudinal polarisation fraction is determined to be $f_{\rm L} = 0.578 \pm 0.010 \pm 0.011$ with world-best precision, where the first uncertainty is statistical and the second is systematic. The pattern of helicity amplitude magnitudes is found to align with expectations from quark-helicity conservation in $B$ decays. The ratio of branching fractions $[\mathcal{B}(B^0 \to D^{*-} D_s^{*+}) \times \mathcal{B}(D_s^{*+} \to D_s^+ \gamma)]/\mathcal{B}(B^0 \to D^{*-} D_s^+)$ is measured to be $2.045 \pm 0.022 \pm 0.071$ with world-best precision. In addition, the first observation of the Cabibbo-suppressed $B_s^0 \to D^{*-} D_s^+$ decay is made with a significance of seven standard deviations. The branching fraction ratio $\mathcal{B}(B_s^0 \to D^{*-} D_s^+)/\mathcal{B}(B^0 \to D^{*-} D_s^+)$ is measured to be $0.049 \pm 0.006 \pm 0.003 \pm 0.002$, where the third uncertainty is due to limited knowledge of the ratio of fragmentation fractions.

Figures and captions

Illustration of the $ B^0 \rightarrow D^{*-} D_s^{*+}$ decay angles.

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(Top) Distribution of $m(D^{*-}D_s^+)$ for selected candidates in data, with the fit overlaid. Where indicated, $L$ ($T$) represents longitudinally (transverse) polarised decays. (Bottom) Restricted to region for candidates with $m(D^{*-}D_s^+) > 5325$ $\text{ Me V /}c^2$ , where the Cabibbo-suppressed $B_s^0 \rightarrow D^{*-} D_s^+$ contribution is visible.

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Distribution of $m(D^{*-}D_s^{*+})$ for selected candidates in data, with the fit overlaid.

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(Left) Comparison of signal-weighted data and generated (top) $\cos\theta_D$ and (bottom) $\cos\theta_X$ distributions, where the differences observed are due to the experimental acceptance and resolution. (Right) Data to generated sample ratios, with the polynomial fits overlaid.

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Comparison of reconstructed $\chi$ distribution in a fully-simulated $ B^0 \rightarrow D^{*-} D_s^{*+}$ sample and the generated $\chi$ distribution in a RapidSim sample produced with the same helicity amplitude model (left). The ratio is fitted with a second-order polynomial to determine the acceptance function for use in the data fit (right).

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Decay-angle distributions of signal-weighted $ B^0 \rightarrow D^{*-} D_s^{*+}$ candidates in data, with the one-dimensional angular fit projections overlaid.

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Relationship between $m(D^{*-}D_s^+)$ and $\cos\theta_X$ in a sample of fully reconstructed $B^0 \rightarrow D^{*-} (D_s^{*+} \rightarrow D_s^+ \gamma)$ simulated decays. The colour scale indicates the number of candidates in each bin.

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Transverse and longitudinal contributions to the one-dimensional decay rate shown as a function of $\cos\theta_X$.

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Invariant-mass distributions of (left) pure transverse and (right) longitudinal $B^0 \rightarrow D^{*-} (D_s^{*+} \rightarrow D_s^+ \gamma)$ simulated decays. Fits to the distributions are overlaid, from which shape parameters for use in the $m(D^{*-}D_s^+)$ data fit are derived.

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Animated gif made out of all figures.

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Tables and captions

Systematic uncertainties on the branching fraction ratios and $f_L$ as measured in the $m(D^{*-} D_s^+)$ fit.

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Systematic uncertainties on the helicity parameters measured in the unbinned angular fit.

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Created on 18 April 2024.