The c \, l^+_ weak decay including new physics

We investigate the c ^+ _ decay with a focus on potential new physics (NP) effects in the = channel. We employ an effective Hamiltonian within the framework of the Standard Model Effective Field Theory (SMEFT) to consider generalized dimension-6 semileptonic c s operators of scalar, pseudoscalar, vector, axial-vector and tensor types. We rely on Lattice QCD (LQCD) for the hadronic transition form factors, using heavy quark spin symmetry (HQSS) to determine those that have not yet been obtained on the lattice. Uncertainties due to the truncation of the NP Hamiltonian and different implementations of HQSS are taken into account. As a result, we unravel the NP discovery potential of the c semileptonic decay in different observables. Our findings indicate high sensitivity to NP in lepton flavour universality ratios, probing multi-TeV scales in some cases. On the theoretical side, we identify LQCD uncertainties in axial and vector form factors as critical for improving NP sensitivity, alongside better SMEFT uncertainty estimations.