Inclusive Processes at Large Mass

The combined assumptions of strongly convergent operator-product expansions near the light cone (LC) and pure multi-Regge theory are used to study the inclusive process $\sigma \mathrm{}\left(p\right)+\sigma \left(p^{\prime }\right)\to \gamma \mathrm{}\left(q\right)+\mathrm{anything}$, where $\sigma$ and $\gamma$ are scalar particles, in the limit of large $s={(p+p^{\prime })}^2$, $\nu =p·q$, ${\nu }^{\prime }=p^{\prime }·q$, and $\kappa =q^2$. The leading LC singularity is used to obtain the behavior for $\kappa \to \infty$, with $\frac{s}{\kappa }$, $\frac{\nu }{\kappa }$, and $\frac{{\nu }^{\prime }}{\kappa }$ fixed. The results are not changed by including nonleading LC contributions. The result for large $\frac{s}{\kappa }$, $\frac{\nu }{\kappa }$, $\frac{{\nu }^{\prime }}{\kappa }$ with fixed ratio $\eta =\frac{\nu {\nu }^{\prime }}{s\kappa }$ is made to agree with the large-$\kappa$ fixed-$\eta$ behavior of the Regge (pionization) limit of large $s$, $\nu$, ${\nu }^{\prime }$ and fixed $\eta$ and $\kappa$. We find that the cross section $\frac{d\sigma }{d\kappa }$ is a sum of two different exponentially falling terms, one being the pionization contribution and the other being the fragmentation contribution.