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

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