A Simple, Yet Subtle Invariance of Two-body Decay Kinematics and its Applications
I will discuss the 2-body decay of a mother particle into a massless daughter with the assumption that the mother particle is unpolarized and has a generic boost distribution in the laboratory frame. In this case, I show analytically that the laboratory frame energy distribution of the massless decay product has a peak, whose location is identical to the (fixed) energy of that particle in the rest frame of the corresponding mother particle.
Given its simplicity and "invariance" under changes in the boost distribution of the mother particle, this observation should be useful for the determination of masses of mother particles. I make a proposal for extracting the peak position by fitting the data to a well-motivated analytic function describing the shape of such an energy distribution. This fitting function is then tested on the theoretical prediction for top quark pair production and its decay, and it is found to be quite successful in this regard. I apply this technique for measuring the masses of the supersymmetric particles in the decay of gluino into 2 bottom quarks and a lightest neutralino via on-shell bottom squark.