 Solution

Initial-state radiation of gluons gives the W boson nonzero transverse momentum. Its transverse Lorentz boost then changes the charged-lepton $p_T$, washing out the sharp $M_W/2$ edge and permitting events above it. The recoil must be modelled with Quantum chromodynamics and constrained by measured hadronic activity. Independently, the finite W boson decay width spreads its actual invariant mass, also smearing the fixed-mass endpoint. Either is a theoretical broadening mechanism; neither is a detector-resolution effect.