"Verify Mandelstam variables for W pair production" p = sqrt(E^2 - m^2) -- m is mass of electron rho = sqrt(E^2 - M^2) -- M is mass of W p1 = (E, 0, 0, p) p2 = (E, 0, 0, -p) p3 = (E, rho sin(theta) cos(phi), rho sin(theta) sin(phi), rho cos(theta)) p4 = (E, -rho sin(theta) cos(phi), -rho sin(theta) sin(phi), -rho cos(theta)) gmunu = ((1,0,0,0),(0,-1,0,0),(0,0,-1,0),(0,0,0,-1)) s = dot(p1 + p2, gmunu, p1 + p2) t = dot(p1 - p3, gmunu, p1 - p3) u = dot(p1 - p4, gmunu, p1 - p4) check(s == 4 E^2) check(t == -2 E^2 + M^2 + m^2 + 2 p rho cos(theta)) check(u == -2 E^2 + M^2 + m^2 - 2 p rho cos(theta)) m = 0 check(t == -2 E^2 + M^2 + 2 E rho cos(theta)) check(u == -2 E^2 + M^2 - 2 E rho cos(theta)) beta = rho / E check(t == -E^2 (1 + beta^2 - 2 beta cos(theta))) check(u == -E^2 (1 + beta^2 + 2 beta cos(theta))) "ok" Run