Abstract
We compute 10 radiative three-body decays of charged charmed mesons {D}^{+}to {P}_1^{+}{P}_2^0gamma and {D}_sto {P}_1^{+}{P}_2^0gamma , P1,2 = π, K, in leading order QCDF, HHχPT 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 HHχPT. These studies can be performed with Cabibbo-favored modes Ds → π+π0γ, {D}^{+}to {pi}^{+}{overline{K}}^0gamma and {D}_sto {K}^{+}{overline{K}}^0gamma with mathcal{O}left({10}^{-4}-{10}^{-3}right)hbox{-} mathrm{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+ → π+π0γ, Ds → π+K0γ, Ds → K+π0γ with branching ratios within ∼ 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 D0→ P1P2γ decays.
Highlights
Insights into the resonance dynamics and new physics simultaneously, as shown for instance for radiative decays in [8, 9]
Cabibbo-suppressed modes such as D+ → π+π0γ, Ds → π+K0γ, Ds → K+π0γ with branching ratios within ∼ 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 and in single differential distributions
As in [10] we work out decay amplitudes in different QCD frameworks: leading order QCD factorization (QCDF), heavy hadron chiral perturbation theory (HHχPT) and the soft photon approximation, each of which is expected to hold in specific regions of phase space
Summary
The double differential decay rate of the radiative three-body decay D(+s)(P ) → P1+(p1) P20(p2)γ(k, ∗) can be written as [10]. Low’s theorem [19] relates the bremsstrahlungsamplitude of the radiative three-body decays to the amplitudes of the hadronic two-body decays This approach is valid for soft photons with an energy below m2P1+/EP1+ [20] and describes the opposite part of the phase space compared to QCDF. We extract the corresponding amplitudes for the remaining decays from data for final states with KS and KL. This procedure leads to huge uncertainties for the DCS decays. All upper limits refer to a 90% confidence level As it is sizable we explicitly take the uncertainty of the Ds → K+π0 amplitude in our numerical analysis into account, but neglect the uncertainties in (2.11) from the other decay channels. For the diagrams A6,1, the contributions of longitudinal polarization of the D(+s) → V +V 0 subdiagram have to be removed in order to obtain a gauge invariant amplitude [26]
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