Standard Model prediction and new physics tests for $ {D^0}\to h_1^{+}h_2^{-}{\ell^{+}}{\ell^{-}}\left( {h=\pi, K;\ell =e,\mu } \right) $

Abstract

Motivated by the recent evidence for direct CP-violation in D 0 → h + h − decays, we provide an exhaustive study of both Cabibbo-favored and Cabibbo-suppressed (singly and doubly)In particular, we study the Dalitz plot for the long-distance contributions in the (m 2 ll , m 2 hh ) parameter space. We find that near-resonant effects, i.e., D 0 → V (hwith V = ρ, K * , φ, are sizeable and even dominant (over Bremsstrahlung) for the µ + µ − decay modes, bringing the branching ratios close to the LHCb reach. We also provide a detailed study of the angular asymmetries for such decays and identify signatures for new physics detection. In particular, new physics signals can be neatly isolated in asymmetries involving the semileptonic operator Q10, where for typical new physics scenarios the effects can be as sizeable as O(1%) for the doubly Cabibbo-suppressed modes.

D → ρℓ + ℓ − decays in the QCD factorization approach

“…The various contributions that appear to order α s , again, can be adapted from [19,24] with the appropriate modifications for c → u transitions. 9 We find…”

“…Nevertheless, there have been a number of phenomenological studies on the new-physics (NP) sensitivities of rare charm decays, including radiative and rare semileptonic D-meson decays induced by c → uγ and c → u + − transitions, see e.g. [4][5][6][7][8][9][10][11][12][13][14][15][16].…”

“…and 9) where the function h(s, m) can be found, for instance, in [45], and -with our normalization convention 5 -is given in (B.15) in the appendix. Notice that the contribution of the function Y (b) (s) to the decay amplitudes is strongly CKM suppressed.…”

“…A straightforward approach, which has already been extensively used in the past [7,9,12,13,15], assumes that the long-distance hadronic effects are completely dominated by the lowest-lying narrow vector states (ρ, ω, φ etc.) which are then modelled by Breit-Wigner resonances.…”

Searches for rare charm decays at LHCb

“…The branching fraction of these decays is dominated by Long Distance (LD) contributions, with the two muons originating from a vector resonance such as ρ/ω and φ , and usually yield branching fractions of O(10 −6 ). On the other hand Short Distance (SD) contributions, accessible in the regions away from resonances, are expected to be O(10 −9 ) or below [1] in the Standard Model(SM). The SD contribution is accessible in regions free from dimuon resonances and is potentially extremely sensitive to contributions from physics beyond the SM (BSM).…”