Resonance enhancement of Charm CP

Abstract

It is suggested that a nearby $0^{++}$ resonance, $f_0$(1710) of mass $m_f=1723MeV$ 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 $\gamma \varphi$ are best suited for sizeable asymmetries as well as providing precise tests of the SM.

9 pages, 2 figures

References in corpus (7)

• Measurement of the branching ratio of ${\bar{B}}^0\to D^{\ast +}{\tau }^{-}{\bar{\nu }}_{\tau }$ relative to ${\bar{B}}^0\to D^{\ast +}{\ell }^{-}{\bar{\nu }}_{\ell }$ decays with a semileptonic tagging method
• Observation of $CP$ violation in charm decays
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• On $SU(3{)}_F$ Breaking through Final State Interactions and CP Asymmetries in $D\to PP$ Decays
• Shedding light on CP violation in the charm system via D to V gamma decays
• Neutral $D\to K{K}^{\ast }$ decays as discovery channels for charm CP violation
• Implications on the first observation of charm CPV at LHCb

Cited by in corpus (8)

• Revisiting CP violation in $D\to PP$ and $VP$ decays
• Direct CP violation in beauty and charm hadron decays
• Search for time-dependent $CP$ violation in $D^0\to K^{+}{K}^{-}$ and $D^0\to {\pi }^{+}{\pi }^{-}$ decays
• Updated measurement of decay-time-dependent CP asymmetries in $D^0\to K^{+}{K}^{-}$ and $D^0\to {\pi }^{+}{\pi }^{-}$ decays
• A Review of $CP$ Violation Measurements in Charm at LHCb
• Search for $\text{CP}$ violation in the phase space of $D^0\to K_S^0{K}^{\pm }{\pi }^{\mp }$ decays with the energy test
• QCD-based estimate of direct $CP$ asymmetry in charm decays
• CP violation in quasi-two-body $D\to VP$ decays and three-body $D$ decays mediated by vector resonances