Rare Semileptonic $B_s$ Decays to $\eta$ and ${\eta }^{\prime }$ mesons in QCD

Abstract

We analyze the rare semileptonic $B_s\to (\eta ,{\eta }^{\prime })l^{+}{l}^{-}$, $(l=e,\mu ,\tau )$ and $B_s\to (\eta ,{\eta }^{\prime })\nu \bar{\nu }$ transitions probing the $\bar{s}s$ content of the $\eta$ and ${\eta }^{\prime }$ mesons via three--point QCD sum rules. We calculate responsible form factors for these transitions in full theory. Using the obtained form factors, we also estimate the related branching fractions and longitudinal lepton polarization asymmetries. Our results are in a good consistency with the predictions of the other existing nonperturbative approaches.

Comments: 28 Pages, 15 Figures and 5 Tables