Parton momentum fraction ($x$)

In the collinear approximation, a parton carries a fraction $0<x<1$ of its parent hadron's longitudinal momentum. A parton distribution function $f_i(x,Q^2)$ gives its distribution at the specified factorization scale. For production of one on-shell particle with no transverse recoil, $x_{+}{x}_{-}s=M^2$ and $x_{\pm }=(M/\sqrt{s})e^{\pm y}$, where $y$ is its rapidity.