Combined analysis of the singly-Cabbibo-suppressed decays of $D^{0} \to VP$

TL;DR

This study probes six singly Cabibbo-suppressed $D^{0}\to VP$ decays to disentangle direct emission (DE) and internal conversion (IC) contributions. DE amplitudes are computed in a non-relativistic constituent quark model (NRCQM), while IC is treated as a complex, data-constrained term linked across channels by $SU(3)$ flavor symmetry; the total amplitude is $G^{total}=G^{DE}+G^{IC}$ with CKM factors. The fits to experimental BRs show DE and IC are of comparable magnitude, but enter with a destructive phase, and the IC component is essential to reproduce the data, especially in IC-dominated channels $D^{0}\to K^{(*)0}\bar{K}^{(*)0}$. Tests varying harmonic-oscillator parameters indicate the DE prediction is robust, while IC remains tightly constrained by the data, highlighting the importance of non-perturbative mechanisms in charm hadronic decays. Overall, the work demonstrates the IC mechanism plays a crucial, measurable role in $D^{0}$ hadronic decays and provides quantitative constraints on non-perturbative charm dynamics and SU(3) flavor relations.

Abstract

We investigate six singly Cabibbo-suppressed decay channels in $D^0\to VP$ ( $V$ and $P$ stand for the ground state vector and pseudoscalar mesons, respectively), i.e. $D^{0}\to ρ^{+}π^{-}$, $ρ^{-}π^{+}$, $K^{*+}K^{-}$, $K^{*-}K^{+}$, $K^{*0}\bar{K}^{0}$, and $\bar{K}^{*0}K^{0}$. These decay channels share the similar transition mechanisms involving only the direct emission (DE) and internal conversion (IC) processes. We show that a combined analysis of these channels can explicitly highlight the role played by the IC processes which contribute to the amplitudes at the same order of magnitude as the DE processes.

Figures (1)

• Figure 1: Schematic diagrams for $D^{0}\to VP$ processes considered in this work.