More visualisation of decay-time-dependent asymmetries in multibody B-meson decays

TL;DR

The paper tackles the challenge that integrating over the phase space in neutral B decays to multibody final states washes out CP-violating and CP-conserving oscillation effects. It introduces phase-space weighting functions $w^{\mathcal{I}m}_f$, $w^{\mathcal{R}e}_f$, and $w^{\rm fs}_f$ to produce weighted decay-time asymmetries of the form $A^{w-\rm fs}_{C P}(t)=S^{w-\rm fs}\sin(\Delta m t)-C^{w-\rm fs}\cos(\Delta m t)$, thereby visualizing both CP-violating and CP-conserving components. The method is developed for both B0 and Bs0 transitions, with Bs -> J/\psi phi treated in the transversity amplitude formalism and B0 -> D_CP pi+ pi- analyzed via an isobar model; simulations demonstrate that the weighting accentuates oscillatory structures and provides quantitative access to the CP phase $\phi_s$ and the oscillation frequency $\Delta m_s$. The approach is general, can accompany existing analyses, and offers intuitive visual diagnostics to validate flavor tagging and amplitude models, albeit with attention to experimental effects such as backgrounds and tagging performance.

Abstract

Methods have been proposed recently to weight data in order to allow visualisation of CP-violation effects in transitions of neutral B mesons to multibody final states that are not CP-eigenstates. These are useful since integration of the unweighted data over the phase space would otherwise wash out the effects of interest. A similar method, elaborated upon here, with a different weighting function can also be used to visualise CP-conserving $B_{(s)}^0$--$\overline{B}{}_{(s)}^0$ oscillations, rather than the CP-violating asymmetries. Together with the other weighting functions, this new method could be useful, for example, to demonstrate the accuracy of the calibration of the flavour tagging algorithms that are crucial for analyses such as the measurement of the CP-violating phase in $B_s^0 \to J/\!ψφ$ decays. Their application to the formalism in common use for such decays is explicitly demonstrated.

Figures (3)

• Figure 1: Distributions of time-dependent asymmetry in simulated ${{\mathrm{B}\xspace}\xspace^0}\xspace \rightarrow\xspace D_{{C\!P}\xspace}{{\uppi\xspace}\xspace^+}\xspace{{\uppi\xspace}\xspace^-}\xspace$ decays, with the time-dependent decay rates in the numerator (left) unweighted, (right) weighted by $w^{\rm fs}_f$. The statistical uncertainties are evaluated with a bootstrap method efron:1979. Results of the fits described in the text are also shown. The left plot is identical to Fig. 4 (top) from Ref. Gershon:2024xkk.
• Figure 2: Asymmetry between the ${\overline{ \mathrm{B}\xspace}}\xspace{}^0_{\mathrm{s}\xspace}\xspace$- and ${\mathrm{B}\xspace}\xspace^0_{\mathrm{s}\xspace}\xspace$-tagged decay-time distributions, for ${{\mathrm{B}\xspace}\xspace^0_{\mathrm{s}\xspace}\xspace}\xspace \rightarrow\xspace {{\mathrm{J}\xspace / \uppsi\xspace}}\xspace \phi$ decays after integrating over the decay angles: (top left) without any weighting, (top right) weighted by $w^{\mathcal{I}m}$, (bottom left) weighted by $w^{\mathcal{R}e}$ and (bottom right) weighted by $w^{\rm fs}$. Curves described in the text are superimposed. Only the range $0 < t < 4\text{\,ps}\xspace$ is shown to allow the oscillations to be seen.
• Figure 3: Distributions of untagged decay-rate distributions (top left) without weighting, and (top right) with $w^{\mathcal{R}e}$, (bottom left) $w^{\mathcal{I}m}$ weights applied, and (bottom right) $w^{\rm fs}$ weights applied, for the pseudoexperiments for ${{\mathrm{B}\xspace}\xspace^0_{\mathrm{s}\xspace}\xspace}\xspace \rightarrow\xspace {{\mathrm{J}\xspace / \uppsi\xspace}}\xspace \phi$ decays. Curves corresponding to the expected distributions as given in Eqs. \ref{['eq:Bs-untagged-Jpsiphi']}--\ref{['eq:Bs-wIm-untagged-Jpsiphi']} are also shown.