Unitarity Constraints on Semi-hard Jet Production in Impact Parameter Space

TL;DR

This paper establishes unitarity-based bounds on the minimum transverse momentum for semi-hard jet production in impact parameter space, highlighting the importance of saturation effects at high energies like the LHC.

Contribution

It provides new bounds on the minimum p_T for minijet production based on unitarity, and discusses the role of saturation effects at high energies.

Findings

Minimum p_T > 2.5 GeV at LHC energies

Minimum p_T > 3.5 GeV at cosmic ray energies

Saturation effects are significant but not sufficient for unitarity restoration

Abstract

The perturbative QCD formula for minijet production consitutes an important ingredient in models describing the total cross section and multiparticle production in hadron-hadron scattering at high energies. Using arguments based on s-channel unitarity we set bounds on the minimum value of p_T for which the leading twist minijet formula can be used. For large impact parameters where correlations between partons appear to be small we find that the minimum value of p_T should be greater than 2.5 GeV for LHC energies and greater than 3.5 GeV for cosmic ray energies of about 50 TeV. We also argue that for collisions with values of impact parameters typical for heavy particle production the values of minimum p_T are likely to be considerably larger. We also analyze and quantify the potential role of saturation effects in the gluon density. We find that although saturation effects alone are not sufficient to restore unitarity, they are likely to play an important role at LHC energies.