Null tests from angular distributions in $D\to P_1{P}_2{l}^{+}{l}^{-}$, $l=e,\mu$ decays on and off peak

Abstract

We systematically analyze the full angular distribution in $D\to P_1{P}_2{l}^{+}{l}^{-}$ decays, where $P_{1,2}=\pi ,K$, $l=e,\mu$. We identify several null tests of the standard model (SM). Notably, the angular coefficients $I_{5,6,7}$, driven by the leptons' axial-vector coupling $C_{10}^{(\prime )}$, vanish by means of a superior GIM-cancellation and are protected by parity invariance below the weak scale. CP-odd observables related to the angular coefficients $I_{5,6,8,9}$ allow to measure CP-asymmetries without $D$-tagging. The corresponding observables $A_{5,6,8,9}$ constitute null tests of the SM. Lepton universality in $|\Delta c|=|\Delta u|=1$ transitions can be tested by comparing $D\to P_1{P}_2{\mu }^{+}{\mu }^{-}$ to $D\to P_1{P}_2{e}^{+}{e}^{-}$ decays. Data for $P_1{P}_2={\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ on muon modes are available from LHCb and on electron modes from BESIII. Corresponding ratios of dimuon to dielectron branching fractions are at least about an order of magnitude away from probing the SM. In the future electron and muon measurements should be made available for the same cuts as corresponding ratios $R_{P_1{P}_2}^D$ provide null tests of $e$-$\mu$-universality. We work out beyond-SM signals model-independently and in SM extensions with leptoquarks.

arXiv comment18 pages plus references and appendix, 7 figures

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