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

Abstract

We investigate the $D^0-{\bar{D}}^0$ mixing through the doubly Cabibbo suppressed (DCS) channel $D^0\to f_0(980)K^{\ast 0}$ and its charge conjugate channel, in which the $K^{\ast 0}$ meson is reconstructed in both $K^{+}{\pi }^{-}$ and $K_S{\pi }^0$ final state. Although the decay $D^0\to f_0(980)K^{\ast }$ 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.

Comments: 7 pages revtex4, no figure