Quasi-two-body decays $B^+\to D_s^+ (R\to) K^+K^-$ in the perturbative QCD approach

TL;DR

The paper develops a perturbative QCD framework to study quasi-two-body decays $B^+ \to D_s^+(R \to K^+K^-)$, incorporating $S$-, $P$-, and $D$-wave resonances in the $K^+K^-$ system via two-meson distribution amplitudes and timelike form factors $F_{S,P,D}(\omega^2)$. It models resonance line shapes with relativistic Breit–Wigner functions for most states and uses the Flatté formula for $f_0(980)$, including mixing among scalar and tensor resonances, to compute complete LO PQCD amplitudes across emission and annihilation topologies. The results yield quasi-two-body branching fractions in the $10^{-8}$ to $10^{-6}$ range and allow extraction of two-body $B^+ \to D_s^+ R$ rates via the Narrow-Width Approximation, with consistency with prior PQCD predictions. The study also notes that direct CP asymmetries vanish in the Standard Model for these channels, making any observed nonzero CPV a potential sign of new physics, and provides a framework for interpreting future amplitude analyses at LHCb and Belle II.

Abstract

A search for the decay $B^+\to D_s^+ K^+K^-$ has been reported by the LHCb Collaboration using $pp$ collision data corresponding to an integrated luminosity of $4.8\,\mathrm{fb}^{-1}$, collected at center-of-mass energies of 7, 8, and 13~TeV, in which no amplitude analysis of the $K^+K^-$ subsystem was performed. In this work, we study the resonant contributions to the decay $B^+\to D_s^+ K^+K^-$ within the perturbative QCD (PQCD) factorization framework. Contributions from the $S$-wave resonances $f_0(980)$, $f_0(1370)$, and $f_0(1500)$, the $P$-wave resonance $φ(1020)$, and the $D$-wave resonances $f_2(1270)$ and $f_2(1525)$ are taken into account. By introducing the corresponding two-meson distribution amplitudes for the $K^+K^-$ system, we perform a complete perturbative analysis of the quasi-two-body decays $B^+\to D_s^+(R\to)K^+K^-$, where $R$ denotes an intermediate resonance, and present the first PQCD predictions for the associated branching fractions. Using the narrow-width approximation, we further extract the branching fractions of the corresponding two-body decays $B^+\to D_s^+R$. Our results are consistent with the available experimental measurements and previous theoretical studies. Finally, we find that direct CP asymmetries vanish for these quasi-two-body decays within the Standard Model, so that any experimentally observed nonzero CP asymmetry would constitute a clear signal of physics beyond the Standard Model.

Figures (2)

• Figure 1: Leading order emission type Feynman diagrams for the $B^+\to D_{s}^{+}( f_{0} /f_{2}\to ) K^{+} K^{-}$ decays.
• Figure 2: Leading order annihilation type Feynman diagrams contributing to $B^+\to D_{s}^{+}(R\to ) K^{+} K^{-}$