Quasi-two-body decays in perturbative QCD
Zi-Yu Zhang, Zhi-Qing Zhang, Si-Yang Wang, Zhi-Jie Sun, and You-Ya Yang
Phys. Rev. D 108, 076009 (2023) - Published 17 October, 2023
In this work, we study the quasi-two-body decays in the perturbative QCD (PQCD) approach. The two-meson distribution amplitudes are introduced to describe the final-state interactions of the pair, which involve the timelike form factors parametrized by the relativistic Breit-Wigner function and the Gegenbauer polynomials. We calculate the branching ratios for these quasi-two-body decays, from which one can obtain the branching ratios for the corresponding two-body decays under the narrow width approximation relation. We find that and have the largest branching ratios, which can reach up to , while the branching ratios for other two-body decays are very small and only about . As we expected, the branching ratios of the pure annihilation decays are usually small, while in our considered such type of decays, the channel has the largest branching ratio, which is near . These results are consistent with the previously PQCD calculations obtained in the two-body framework, which can be tested by future LHCb experiments. For the decays , , and , we also calculate their direct violations and find that is the largest one, which is possible measured by the present LHCb experiments. For the pure annihilation type decays, there is no violation, because only the tree operators are involved. Furthermore, we give the differential distributions of the branching ratios and the direct violations in the invariant mass for the decays .