Weak Annihilation Contribution to Angular Observables in $B_{c}^+\to D^{\ast+}\ell^{+}\ell^{-}$ Decays

TL;DR

This paper investigates the impact of weak annihilation contributions on angular observables in rare $B_c^+ o D^{*+} \, \ell^+\ell^-$ decays, emphasizing their significance at low momentum transfer for precise Standard Model predictions.

Contribution

It provides the first detailed analysis of weak annihilation effects on angular observables in $B_c^+$ decays using covariant quark model form factors.

Findings

Weak annihilation significantly affects observables at low $q^2$.

Weak annihilation shifts zero-crossings of angular coefficients.

Resonance effects dominate at high $q^2$, limiting analysis regions.

Abstract

We analyze the rare semileptonic decays $B_{c}^+ \to D^{\ast+}(\to P_1 P_2)\ell^{+}\ell^{-}$, with $P_1 P_2 = D^+ \pi^0$ or $D^0 \pi^+$, and $\ell=\mu, \tau$. We focus on the impact of weak annihilation contributions alongside penguin, box, and long-distance effects. Using the effective Hamiltonian for $b \to d \ell^+ \ell^-$ transitions and $B_c \to D^{*}$ form factors from covariant confined quark model inputs, we compute the differential branching ratios, forward-backward asymmetry, longitudinal helicity fraction of the $D^{\ast}$, and various normalized angular coefficients. The results of the observables show that weak annihilation effects are sizable, particularly at low $q^2$, significantly modifying several observables and shifting zero-crossings. Resonance effects dominate at high $q^2$, restricting reliable analysis windows. We conclude that the inclusion of weak annihilation is essential for precise Standard Model predictions and for isolating possible New Physics effects in $B_c^+ \to D^{*+} \ell^+ \ell^-$ decays.