Solutions of the Ortvay Rudolf International Competition in Physics: Mass of a Force Carrier Particle (2014/24 Problem)

This paper is the fourth in a series of published solutions discussing problems of the Ortvay Rudolf international competition. The problem treated below is an exercise in special relativity, applied to classical description of particle-exchange during scattering. As it is known, introducing rapidity can radically simplify the calculations in special relativity, as well as offer a simple geometric intuition. However, students often prefer doing calculations directly through formulas involving velocities, resulting in lengthy calculations, often increasing the chance of errors. It is our belief that giving the students simple, but not trivial problems before demonstrating the short and elegant solution presented below can help students to appreciate and understand the geometrical formulation of special relativity. Our calculation does not use mathematical techniques beyond those expected of high-school students, and the first half of this work may be used in special high-school classes.