PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment
Symmetry and Flavour, Ch Four-vectors at work: boosts, invariants and the shape of a final state
Problem
A sample of W→eν decays (mW=80.4GeV, electron and neutrino massless) differs from the idealised one in a single respect: each W carries transverse momentum pTW=15.0GeV. Take every W on its mass shell, meν=mW, neglect the W width and all detector smearing, and let each decay be isotropic in the W rest frame.
((a)) Estimate, to first order in pTW, the range of electron transverse momentum pTe over which the Jacobian peak (sharp at mW/2 for a W at rest) is now smeared.
((b)) Show that the endpoint of the mT distribution stays at mW, and that the transverse motion changes mT only at second order in pTW. Estimate the scale of that change for this sample.
((c)) State which of pTe or mT is the more reliable variable for reading off mW, and why.