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Register a new userTesting the standard model with $D_{(s)} to K_1 (to Kpipi) gamma$ decays
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The photon polarization in $D_{(s)} to K_1 (to Kpipi) gamma$ decays can be extracted from an up-down asymmetry in the $K pi pi$ system, along the lines of the method known to $B to K_1 (to Kpipi) gamma$ decays. Charm physics is advantageous as partner decays exist: $D^+ to K_1^+ (to Kpipi) gamma$, which is standard model-like, and $D_s to K_1^+ (to Kpipi) gamma$, which is sensitive to physics beyond the standard model in $|Delta c| =|Delta u|=1$ transitions. The standard model predicts their photon polarizations to be equal up to U-spin breaking corrections, while new physics in the dipole operators can split them apart at order one level. We estimate the proportionality factor in the asymmetry multiplying the polarization parameter from axial vectors $K_1(1270)$ and $K_1(1400)$ to be sizable, up to the few ${cal{O}}(10)%$ range. The actual value of the hadronic factor matters for the experimental sensitivity, but is not needed as an input to perform the null test.
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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 ${cal{O}}(10^{-4}-10^{-3})$-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.
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