Rare $Λ_b \rightarrow Λl^+ l^- $ decay in the Bethe-Salpeter equation approach

Abstract

We study the rare decays Λ b → Λl + l − (l = e, µ, τ ) in the Bethe-Salpeter equation approach. We find that depending on the values of parameters in our model the branching ratio Br(Λ b → Λµ + µ − )×10 6 varies from 0.812 to 1.445 when κ = 0.050 ∼ 0.060 GeV 3 and the binding energy E 0 = −0.14 GeV while Br(Λ b → Λµ + µ − ) × 10 6 varies from 1.051 to 1.098 when κ = 0.055 Gev 3 and the binding energy E 0 changes from −0.19 to −0.09 GeV. These results agree with the experimental data. In the same parameter regions, we find that the branching ratio Br(Λ b → Λe + e − (τ + τ − )) × 10 6 varies in the range 0.660− 1.028 (0.252− 0.392) and 0.749− 1.098 (0.286− 0.489), respectively.

FCNC transitions of $$\Lambda _b$$ to neutron in Bethe–Salpeter equation approach

“…Following our previous work, in order more precisely calculate the FFs of Λ b → n, we can take E 0 = −0.14 GeV (where E 0 = M − m − m D is the binding energy) and κ to be about 0.05 ± 0.005 GeV 3 for Λ b → n [43]. Defining f1(2) = dp l 2π f 1(2) , and using the covariant instantaneous approximation, p l = q l , the scalar BS wave functions satisfy the following coupled integral equation:…”