Angular analyses of exclusive $\Bbar\to X \ell_1 \ell_2$ with complex helicity amplitudes

TL;DR

This paper develops a comprehensive angular analysis framework for exclusive B meson decays involving complex helicity amplitudes, aiming to identify potential new sources of CP violation and assist ongoing experimental data analyses.

Contribution

It introduces a novel, model-independent technique to project out angular moments in decay rates with complex helicity amplitudes, enhancing CP violation studies.

Findings

Demonstrates the effectiveness of angular moment projection method

Provides detailed differential decay rate formulas including complex phases

Aids ongoing analyses at BaBar and LHCb

Abstract

We present the differential rates for exclusive $\Bbar\to X \ell_1 \ell_2$, where $\ell_1$ is a charged massless lepton and $\ell_2$ is a charged or neutral massless lepton, and $X$ is a mesonic system up to spin 2. The cases of interest are semileptonic (SL) $\Bbar\to \xcu\ellm \barnuell$ decays, and $\Bbar \to X_s \ellm \ellp$ where the the di-lepton can be $c \bar{c}$ resonances or non-resonant electroweak penguins (EWP). We consider helicity amplitudes having non-zero relative phases that can be potential new sources for CP-violation. Our motivations for these additional phases include a complex right-handed admixture in the hadronic weak charged current for the SL decays and complex Wilson coefficients in the effective Hamiltonians for the EWP decays. We demonstrate the efficacy of a novel technique of projecting out the individual angular moments in the full rate expression in a model-independent fashion. Our work is geared towards ongoing data analyses at $\babar$ and LHCb.