Transformation properties of the transverse mass under transverse Lorentz boosts at hadron colliders

Abstract

The transverse mass of semi-invisibly decaying particles, calculated from the transverse momenta of their decay products, has been used in a broad range of searches and measurements at hadron colliders, such as the LHC. This variable is invariant by construction under Lorentz boosts purely in the longitudinal (beam) direction, thereby minimising sensitivity to fluctuations in the fractions of the proton momentum carried by the colliding partons. In this paper we examine, by contrast, the properties of the transverse mass under boosts with a component also in the transverse plane perpendicular to the beam direction. We show that this variable is invariant under such boosts in cases where the boost is purely transverse and (a) the momenta of the decay products are confined to the transverse plane in the rest frame of the parent particle and/or (b) the transverse momenta of the decay products are perpendicular to the boost direction. We discuss the transformation properties of the transverse mass in the case of combined transverse and longitudinal boosts and identify the criteria under which the transverse mass in the laboratory frame can equal the rest mass of the parent particle, irrespective of its value in the rest frame of the parent.

arXiv comment7 pages double column, 7 figures, formatted for EPJC

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