Calculation of Certain Phase-Space Integrals

Abstract

We give the result of an approximate calculation of the phase‐space integral $${\Omega }_n\mathrm{(Q)=}{\displaystyle \int }{\delta }_4{\mathrm{(Q-\Sigma }}_i{k}_i{\mathrm{)\hspace{0.17em}\Pi }}_i{\mathrm{\hspace{0.17em}\delta (k}}_i^2{\mathrm{-\mu }}_i^2{\mathrm{)\vartheta (k}}_{\text{i0}}{\mathrm{)f}}_i{\mathrm{(k}}_{i\mathbf{T}}{\mathrm{)\hspace{0.17em}d}}_4{k}_i$$ , which appears when one takes into account the fact that only a part of the kinematically allowed phase‐space is accessible to particles produced in high‐energy collisions, because of the observed smallness of their transverse momenta.