Semileptonic $W$ Decay to the $B$ Meson with Lepton Pairs in Heavy Quark Effective Theory Factorization upto $\mathcal{O}$$({\alpha }_s)$

Abstract

Motivated by the study of heavy-light meson production within the framework of heavy quark effective theory (HQET) factorization, we extend the factorization formalism for a rather complicated process $W^{+}\to B^{+}{\ell }^{+}{\ell }^{-}$ in the limit of a non-zero invariant squared-mass of dilepton, $q^2$, at the lowest order in $1/m_b$ up to $\mathcal{O}({\alpha }_s)$. The purpose of the current study is to extend the HQET factorization formula for the $W^{+}\to B^{+}{\ell }^{+}{\ell }^{-}$ process and subsequently compute the form factors for this channel up to next-to-leading-order corrections in ${\alpha }_s$. We explicitly show the amplitude of the $W^{+}\to B^{+}{\ell }^{+}{\ell }^{-}$ process can also be factorized into a convolution between the perturbatively calculable hard-scattering kernel and the non-perturbative yet universal light-cone distribution amplitude (LCDA) defined in HQET. The validity of HQET factorization depends on the assumed scale hierarchy $m_W\sim m_b\gg {\Lambda }_{\mathrm{QCD}}$. Within the HQET framework, we evaluate the form factors associated with the $W^{+}\to B^{+}{\ell }^{+}{\ell }^{-}$ process, providing insights into its phenomenology. In addition, we also perform an exploratory phenomenological study on $W^{+}\to B^{+}{\ell }^{+}{\ell }^{-}$ by employing an exponential model for the LCDAs for $B^{+}$ meson. Our findings reveal that the branching ratio for $W^{+}\to B^{+}{\ell }^{+}{\ell }^{-}$ is below $10^{-10}$. Although the branching ratios are small, this channel in high luminosity LHC experiments may serve to further constraints the value of ${\lambda }_B$.

Comments: 6 figures, 20 pages