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

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.