Transverse mass

The transverse mass is a useful quantity to define for use in particle physics as it is invariant under Lorentz boost along the z direction. In natural units it is: The transverse mass is a useful quantity to define for use in particle physics as it is invariant under Lorentz boost along the z direction. In natural units it is: This definition of the transverse mass is used in conjunction with the definition of the (directed) transverse energy with the transverse momentum vector p → T = ( p x , p y ) {displaystyle {vec {p}}_{T}=(p_{x},p_{y})} . It is easy to see that for vanishing mass ( m = 0 {displaystyle m=0} ) the three quantities are the same: E T = p T = m T {displaystyle E_{T}=p_{T}=m_{T}} .The transverse mass is used together with the rapidity, transverse momentum and polar angle in the parameterization of the four-momentum of a single particle: Using these definitions (in particular for E T {displaystyle E_{T}} ) gives for the mass of a two particle system: Looking at the transverse projection of this system (by setting p a , z = p b , z = 0 {displaystyle p_{a,z}=p_{b,z}=0} ) gives: