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:
This definition of the transverse mass is used in conjunction with the definition of the transverse energy
with the transverse momentum vector. It is easy to see that for vanishing mass the three quantities are the same:.
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 gives for the mass of a two particle system:
Looking at the transverse projection of this system gives:
These are also the definitions that are used by the software package ROOT, which is commonly used in high energy physics.

Transverse mass in two-particle systems

Hadron collider physicists use another definition of transverse mass, in the case of a decay into two particles. This is often used when one particle cannot be detected directly but is only indicated by missing transverse energy. In that case, the total energy is unknown and the above definition cannot be used.
where is the transverse energy of each daughter, a positive quantity defined using its true invariant mass as:
which is coincidentally the definition of the transverse mass for a single particle given above.
Using these two definitions, one also gets the form:
For massless daughters, where, we again have, and the transverse mass of the two particle system becomes:
where is the angle between the daughters in the transverse plane.
The distribution of has an end-point at the invariant mass of the system with. This has been used to determine the mass at the Tevatron.