Midrapidity

Midrapidity is a term used in high-energy collider and heavy-ion physics to denote the region of phase space around zero rapidity (y ≈ 0) in the center-of-mass frame. Rapidity y is defined as y = 0.5 ln[(E + pz)/(E − pz)], where E is energy and pz is the momentum along the beam axis. Because boosts along the beam axis translate to shifts in y, the region near y = 0 is singled out as midrapidity.

In symmetric collisions, such as proton–proton or nucleus–nucleus at equal and opposite beam energies, the center-of-mass frame coincides with the laboratory frame, making y ≈ 0 the natural midrapidity. For asymmetric collisions, midrapidity refers to the y value in the center-of-mass frame and may appear at a nonzero rapidity in the laboratory frame. This region is often approximately boost-invariant over a finite range, an expectation from the Bjorken model for the early-time evolution of a hot, dense medium formed in heavy-ion collisions.

Experimentally, rapidity is related to, but not identical to, pseudorapidity η, defined from the polar angle θ by η = −ln[tan(θ/2)]. Midrapidity studies typically focus on y near zero or on η near zero, where particle production is highest and detector acceptance is greatest.

Observables measured at midrapidity include particle yields dN/dy, transverse momentum spectra, identified-particle ratios, and anisotropic flow coefficients. The midrapidity region is central to probing the properties of quark–gluon plasma, such as temperature, chemical composition, and collective expansion, as well as to characterizing baryon transport and stopping.