Resonance enhancement of Charm CP

Abstract

It is suggested that a nearby $0^{++}$ resonance, $f_0$(1710) of mass $m_f=1723 MeV$ and width $\Gamma=139$ MeV is playing a significant role in efficiently providing the strong (CP-conserving) and weak (CP-odd) phase simultaneously in the recently observed direct CP asymmetry $\Delta A_{CP}$ by the LHCb collaboration. The direct CP arises by the well known penguin-tree interference wherein the virtual b-quark in the c-u penguin is the source of the Kobayashi-Maskawa CP-odd phase, $\gamma$, in the SM. Loop (penguin) corrections generate left-right operators enhancing coupling to the $0^{++}$ scalar resonance. The scalar resonance is likely rich in gluonic content perhaps leading to a better understanding of large breaking of flavor SU(3) that has been known for a long-time. Approximate calculations give a rough understanding of the observed size of the CP asymmetry. The mechanism leads to several interesting implications which can be experimentally studied and tested. Moreover, in an analogous fashion to $f_0$, 4-quark operators also generate $P \times P$, P being a pseudo-scalar bilinear, which may be dominated by the nearby $\eta (1760)$ of width about 250 MeV that can influence final states such as 4 $\pi$'s, $\eta^{\prime}(\eta) + \pi^+ + \pi^-$ etc which could exhibit CP violating triple correlation or energy asymmetries. We also briefly discuss CP violation in radiative charm decays and suggest that simple final states $\gamma \rho$ and $\gamma \phi$ are best suited for sizeable asymmetries as well as providing precise tests of the SM.