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

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 ⁺ → B ⁺ℓ⁺ℓ⁻ in the limit of a nonzero invariant squared mass of the 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 ⁺ → B ⁺ℓ⁺ℓ⁻ process and subsequently compute the form factors for this channel up to next-to-leading-order corrections in α _s . We explicitly show that the amplitude of the W ⁺ → B ⁺ℓ⁺ℓ⁻ process can also be factorized into a convolution between the perturbatively calculable hard-scattering kernel and the nonperturbative yet universal light-cone distribution amplitude (LCDA) defined in HQET. The validity of the HQET factorization depends on the assumed scale hierarchy m_W ∼ m_b ≫ Λ_QCD. Within the HQET framework, we evaluate the form factors associated with the W ⁺ → B ⁺ℓ⁺ℓ⁻ process, providing insights into its phenomenology. In addition, we also perform an exploratory phenomenological study on W ⁺ → B ⁺ℓ⁺ℓ⁻ by employing an exponential model for the LCDAs for the B ⁺ meson. Our findings reveal that the branching ratio for W ⁺ → B ⁺ℓ⁺ℓ⁻ is below 10⁻¹⁰. Although the branching ratios are small, this channel in high-luminosity LHC experiments may serve to further constrain the value of λ _B . [ABSTRACT FROM AUTHOR]