How is the 4-momentum, especially the transverse momentum, in a detector calorimeter measured?

assuming a jet is produced in the detector at a hadron collider. Some of the jet particles are uncharged and will only interact with the hadronic calorimeter and therefore there is no information about their momentum from their trajectory in a magnetic field. The calorimeter measures the jet’s kinetic energy by absorbing it, and its direction of flight can be inferred from the azimuthal and polar angle/pseudorapidity. But how do I get the jet’s transverse momentum from it? I understand that I can get the transverse energy by looking at the projection of the energy onto the transverse plane, but to get the transverse momentum I still need information about the particles mass, which I don’t have, do I?