Exploring

\nMotivated by the interplay between the LEFT and SMEFT operators at the electroweak scale, we study the interrelation among the B decays mediated by b → cℓνℓ, b → sνℓνℓ and b → sℓℓ (ℓ = e, µ, τ) quark level transitions in the context of six-dimensional SMEFT operators such as $${Q_{\\ell q}^{(3)},\\,{Q_{\\ell edq}},\\,Q_{\\ell equ}^{(1)},\\,Q_{\\ell equ}^{(3)},\\,{\\rm{and}}\\,Q_{\\phi q}^{(3)}} $$. We constrain the new physics parameter space through a com-ℓequ ϕq prehensive global fit incorporating the observables RD, RD∗, Pτ(D∗), FL(D∗), RΛ, B(B0 → K∗νν), B(B → K+νν), B(B → K+τ+τ−) and B(Bs → τ+τ−). We then investigate the sensitivity of new physics in the semi-leptonic decay modes of b-baryons, specifically Ξb → Ξcτ− ν¯τ. We further explore the impact of the new physics couplings on several observables such as the differential branching ratio (DBR), forward-backward asymmetry ($${A_{FB}^\\tau} $$) the lepton flavor non-universality ($${R_{{\\Xi _b}}} $$) for this processes.\n