Semi-leptonic W decay to B meson with lepton pairs in HQET factorization upto O

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, q2, at the lowest order in 1/mb up to O(α 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 αs. 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 mW ∼ mb ≫ ΛQCD. 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 λB.