Angular analyses of exclusive $\text{Bbar}\to X{\ell }_1{\ell }_2$ with complex helicity amplitudes

Abstract

We present the differential rates for exclusive $\text{Bbar}\to X{\ell }_1{\ell }_2$, 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) $\text{Bbar}\to \text{xcu}\text{ellm}\text{barnuell}$ decays, and $\text{Bbar}\to X_s\text{ellm}\text{ellp}$ 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 $\text{babar}$ and LHCb.