def get_t_prime(collection: vectors.ParticlePool) -> npy.ndarray:
# Get initial values
proton = collection.get_particles_by_name("Proton")[0]
s_value = get_s(collection)
sqrt_s = npy.sqrt(s_value)
mx2 = get_event_mass(collection)**2
# Calculate for Px and Ex
ex = (s_value * mx2 * _PROTON_GEV**2) / 2 * sqrt_s
px = npy.sqrt((ex**2) - mx2)
# Calculate t0
t0_left = (mx2 / (2 * sqrt_s))**2
t0_right = (((proton.e * _PROTON_GEV) / sqrt_s) - px)**2
t0 = t0_left - t0_right
return get_t(collection) - t0
def get_s(collection: vectors.ParticlePool) -> npy.ndarray:
proton = collection.get_particles_by_name("Proton")[0]
momenta = proton.x**2 + proton.y**2 + proton.z**2
energy = (proton.e + _PROTON_GEV)**2
return energy - momenta