2017 # Lorentz invariant relative velocity and relativistic binary collisions

**Abstract:** This article reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross section without recurring to non-physical velocities or any assumption about the reference frame. Applications such as the luminosity of a collider, the use as kinematic variable, and the statistical theory of collisions in a relativistic classical gas are reviewed. It is emphasiz…

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“…In this case, it is a good approximation to perform a nonrelativistic expansion of σv r keeping only the leading terms in the expansion in powers of v r << 1. This expansion requires the calculation of the flux for dark matter particles in the thermal bath, which can be written as [27,28]…”

confidence: 99%

“…In this case, it is a good approximation to perform a nonrelativistic expansion of σv r keeping only the leading terms in the expansion in powers of v r << 1. This expansion requires the calculation of the flux for dark matter particles in the thermal bath, which can be written as [27,28]…”

confidence: 99%

“…is the Moller velocity [114,115], with p µ and k µ respectively being the four-momentum of the dark matter particle and the nucleus in the composite rest frame. The latter is determined from Eq.…”

confidence: 99%

“…( 5) is evaluated in the CM frame and accounts for nuclear recoil. To work around this discrepancy, MARLEY uses the relative speed β rel of the two final-state particles [116]…”

confidence: 99%