Probing New Physics with $b\to u\mathrm{\ell }{\nu }_{\mathrm{\ell }}$ induced decays

We analyze $B^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }$, ${\bar{B}}^0\to {\pi }^{+}{\mu }^{-}{\bar{\nu }}_{\mu }$, and $B^{-}\to {\rho }^0{\mu }^{-}{\bar{\nu }}_{\mu }$ decays using the data on binned branching fractions recently measured by Belle II Collaboration for the semileptonic modes. We extend the low-energy Hamiltonian governing $b\to u\mathrm{\ell }{\bar{\nu }}_{\mathrm{\ell }}$ transitions to include the full set of dimension-six, Lorentz-invariant operators with left-handed neutrinos, consistent with the Standard Model Effective Field Theory (SMEFT) framework. The Wilson coefficients are treated as complex, lepton-flavor-dependent effective couplings. Since the three selected channels are sensitive to different non-standard structures, we perform a combined analysis using Monte Carlo methods to constrain the New Physics couplings for three benchmark values of $\mathrm{\mid }{V}_{ub}\mathrm{\mid }$. We find that, while the Standard Model remains broadly compatible with the data, some of the couplings show a mild preference for non-zero values.