Probing New Physics with $b \to u \ell ν_{\ell}$ induced decays
We analyze $B^- \to μ^- \barν_μ$, $\bar{B}^0 \to π^+ μ^-\barν_μ$, and $B^- \to ρ^0 μ^- \barν_μ$ 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 $b \to u \ell \barν_\ell$ 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 $|V_{ub}|$. 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.