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

• where the z-direction is along the beam pipe and so

• are the momentum perpendicular to the beam pipe and

• is the (invariant) mass.

This definition of the transverse mass is used in conjunction with the definition of the (directed) transverse energy. The transverse mass is used together with the rapidity, transverse momentum and polar angle in the parameterization of the four-momentum

) gives for the mass of a two particle 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 (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.

is the transverse energy of each daughter, a positive quantity defined using its true invariant mass as:

1. ,

which is coincidentally the definition of the transverse mass for a single particle given above. Using these two definitions, one also gets the form:

!)

, and the transverse mass of the two particle system becomes:

mass at the Tevatron.

References

• ) for definitions of transverse mass.

• ) for definitions of transverse mass.