Title: NbTi: a nontrivial puzzle for the conventional theory of superconductivity

Abstract: We present the first $ab$-$initio$ study of superconductivity in NbTi, the workhorse for many applications. Despite its apparent simplicity, NbTi turns out to be a major challenge for computational superconductivity. In fact, anharmonic effects are crucial to obtain dynamically stable phonons for the ordered bcc phase, unstable at the harmonic level, and beyond-Morel Anderson effects in the Coulomb interaction reduce the Tc by more than 20%. Lattice disorder causes an additional large discrepancy in $T_c$ compared to experiment. Our results imply that a quantitative description of technologically-relevant superconductors requires methodological developments beyond the current standards.