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 (directed) transverse energy
with the transverse momentum vector formula_6. It is easy to see that for vanishing mass (formula_7) the three quantities are the same: formula_8.
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 formula_10) gives for the mass of a two particle system:
Looking at the transverse projection of this system (by setting formula_14) 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 (and transverse energy), 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 formula_10 is the transverse energy of each daughter, a positive quantity defined using its true invariant mass formula_4 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 formula_22, we again have formula_23, and the transverse mass of the two particle system becomes:
where formula_25 is the angle between the daughters in the transverse plane.
The distribution of formula_26 has an end-point at the invariant mass formula_27 of the system with formula_28. This has been used to determine the formula_29 mass at the Tevatron.