Measuring $D^0-\bar D^0$ mixing in $D^0(\bar D^0)\to f_0(980) K^{*}$ and more

TL;DR

This paper proposes a method to measure $D^0-ar D^0$ mixing parameters using specific decay channels involving $f_0(980)$ and $K^*$ mesons, which are experimentally accessible despite small branching ratios.

Contribution

It introduces a novel approach to extract all mixing parameters from time-dependent decay widths without dependence on strong phase differences.

Findings

Method is valid across all mixing parameter regions.

Allows extraction of mass and decay width differences.

Applicable with various meson final states.

Abstract

We investigate the $D^0-\bar D^0$ mixing through the doubly Cabibbo suppressed (DCS) channel $D^0\to f_0(980)K^{*0}$ and its charge conjugate channel, in which the $K^{*0}$ meson is reconstructed in both $K^+\pi^-$ and $K_S\pi^0$ final state. Although the decay $D^0\to f_0(980)K^{*}$ has a small branching ratio, the final state mesons are relatively easy to identify. The $f_0(980)$ meson can be replaced by $\pi^+\pi^-$ in which $\pi^+\pi^-$ form an $S$-wave state, or a longitudinally polarized vector meson $\rho^0,\omega$. All mixing parameters, including the mass difference and decay width difference, can be extracted by studying the time-dependent decay width of these channels. We show that the method is valid in all regions for mixing parameters and it does not depend on the strong phase difference.