Radiative three-body D-meson decays in and beyond the standard model

Abstract

We study radiative charm decays $$D \rightarrow P_1 P_2 \gamma $$ D → P 1 P 2 γ , $$P_{1,2}=\pi ,K$$ P 1 , 2 = π , K in QCD factorization at leading order and within heavy hadron chiral perturbation theory. Branching ratios including resonance contributions are around $$\sim 10^{-3}$$ ∼ 10 - 3 for the Cabibbo-favored modes into $$K \pi \gamma $$ K π γ and $$\sim 10^{-5}$$ ∼ 10 - 5 for the singly Cabibbo-suppressed modes into $$\pi ^+ \pi ^- \gamma , K^+ K^- \gamma $$ π + π - γ , K + K - γ , and thus in reach of the flavor factories BES III and Belle II. Dalitz plots and forward–backward asymmetries reveal significant differences between the two QCD frameworks; such observables are therefore ideally suited for a data-driven identification of relevant decay mechanisms in the standard-model dominated $$D \rightarrow K \pi \gamma $$ D → K π γ decays. This increases the potential to probe new physics with the $$D \rightarrow \pi ^+ \pi ^- \gamma $$ D → π + π - γ and $$D \rightarrow K^+ K^- \gamma $$ D → K + K - γ decays, which are sensitive to enhanced dipole operators. CP asymmetries are useful to test the SM and look for new physics in neutral $$|\Delta C|=1$$ | Δ C | = 1 transitions. Cuts in the Dalitz plot enhance the sensitivity to new physics due to the presence of both s- and t, u-channel intermediate resonances.

Disentangling QCD and new physics in D → πℓ+ℓ−

“…Note however that weak annihilation effects for D → V γ and three-body hadronic D decays have been studied in the QCDf framework in refs. [15,16]. Our results are further ameliorated by the recent advances on the form factors from the Lattice [17,18] and Wilson coefficients from ref.…”

Probing QCD dynamics and the standard model with $$ {D}_{(s)}^{+}\to {P}_1^{+}{P}_2^0\gamma $$ decays

“…The double differential decay rate of the radiative three-body decay D + (s) (P ) → P + 1 (p 1 ) P 0 2 (p 2 )γ(k, * ) can be written as [10]…”

“…Instead, we refer to the literature cited below, as well as ref. [10], where further information on kinematics, the models and our notation is provided.…”

“…The D 0 decays given in parentheses are covered in [10]. The modes D + → K + K 0 γ and D s → π + K 0 γ are |∆s| = 2 processes and are not induced by dimension 6 operators, and not considered in this works.…”

“…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. We show that the forward-backward asymmetry efficiently disentangles different resonance contributions and therefore probes the QCD frameworks.…”