A Phenomenological Model of Mesons for Charged Current Weak Decays

Abstract

We propose a phenomenological model of pseudo scalar mesons to describe charged-current weak decays of heavy-light mesons. The approach combines chiral symmetry in the light sector with heavy-quark flavor symmetry, while Cabibbo--Kobayashi--Maskawa (CKM) matrix elements are incorporated as spurions that encode explicit symmetry breaking. Restricting to charged-current interactions, we systematically organize the leading-order current-current operators at dimension six and identify the relevant operator structures governing fully-leptonic, semi-leptonic, and hadronic decays. This framework reproduces known heavy-quark scaling relations for decay constants and form factors in agreement with expectations from heavy quark effective theory, providing nontrivial consistency checks. Operators responsible for hadronic transitions are further classified into double-trace operators and single-trace operators. These single traces, interestingly, often capture several higher order corrections, non-factorizable effects etc. We check for consistencies for both single-trace and double-trace operators demanding that the resulting amplitudes should satisfy established isospin sum rules. As an application, we analyze the decay modes $B\to K + η_{c} / η^{\prime}/ η$. We find that these processes receive contributions from a host of non-trivial processes such as mixing between various states, non-perturbative QCD parameters such as the heavy quark condensates, non-factorizable effects, etc, apart from the straightforward perturbative $W$ exchange diagrams in the quark picture. Our set-up neatly captures all of these effects. The phenomenological model we provide here is a symmetry-guided, hadron-level description of charged-current processes and offers a complementary perspective to conventional quark-level approaches, with a natural avenue for incorporating non-factorizable effects.