Probing QCD dynamics and the standard model with $D_{(s)}\to P^{+}{P}^0\gamma$ decays

Abstract

We compute 10 radiative three-body decays of charged charmed mesons $D^{+}\to P^{+}{P}^0\gamma$ and $D_s\to P^{+}{P}^0\gamma$, $P=\pi ,K$, in leading order QCDF, HH$\chi$PT and the soft photon approximation. We work out decay distributions and asymmetries in the standard model and with new physics in the electromagnetic dipole operators. The forward-backward asymmetry is suitable to probe the QCD frameworks, in particular the $s$-channel dependent weak annihilation contributions in QCDF against the markedly different resonance structure in HH$\chi$PT. These studies can be performed with Cabibbo-favored modes $D_s\to {\pi }^{+}{\pi }^0\gamma$, $D^{+}\to {\pi }^{+}{\overline{K}}^0\gamma$ and $D_s\to K^{+}{\overline{K}}^0\gamma$ with $\mathcal{O}(10^{-4}-10^{-3})$-level branching ratio, which are standard model-like and induced by different hadronic dynamics. Understanding of the latter can therefore be improved in a data-driven way and sharpens the interpretation of standard model tests. Singly Cabibbo-suppressed modes such as $D^{+}\to {\pi }^{+}{\pi }^0\gamma$, $D_s\to {\pi }^{+}{K}^0\gamma$, $D_s\to K^{+}{\pi }^0\gamma$ with branching ratios within $\sim 10^{-5}-10^{-4}$ are sensitive to new physics that can be signalled in the forward-backward asymmetry and in the CP-asymmetry of the rate, ideally in the Dalitz region but also in single differential distributions. Results complement those with neutral $D^0\to PP\gamma$ decays.

arXiv comment22 pages + appendix, 20 Figures

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