Null tests from angular distributions in $D \to P_1 P_2 l^+l^-$, $l=e,\mu$ decays on and off peak

TL;DR

This paper analyzes angular distributions in $D o P_1 P_2 l^+ l^-$ decays to identify null tests of the Standard Model and explore CP asymmetries and lepton universality, providing a framework for future experimental tests and beyond-SM signals.

Contribution

It systematically identifies null tests and CP asymmetries in $D$ decays using angular distributions, and explores beyond-SM signals in a model-independent way.

Findings

Angular coefficients $I_{5,6,7}$ vanish due to GIM cancellation.

CP-odd observables $A_{5,6,8,9}$ serve as null tests of the SM.

Current data are far from probing SM predictions for lepton universality.

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.