Radiation Problem in Transplanckian Scattering

TL;DR

This paper develops a quantum field theory approach to analyze hard radiation in transplanckian scattering, revealing a suppression of high transverse momentum gluons and proposing a method to measure extra dimensions.

Contribution

It introduces a novel formalism for calculating radiation in transplanckian collisions, incorporating shock wave effects and impact parameter representation, with applications to QCD radiation and extra dimension measurement.

Findings

Suppression of high transverse momentum gluons due to rescattering.

Dependence of suppression factor on the number of extra dimensions.

Absorption of leading-log corrections into parton distribution functions.

Abstract

We investigate hard radiation emission in small-angle transplanckian scattering. We show how to reduce this problem to a quantum field theory computation in a classical background (gravitational shock wave). In momentum space, the formalism is similar to the flat-space light cone perturbation theory, with shock wave crossing vertices added. In the impact parameter representation, the radiating particle splits into a multi-particle virtual state, whose wavefunction is then multiplied by individual eikonal factors. As a phenomenological application, we study QCD radiation in transplanckian collisions of TeV-scale gravity models. We derive the distribution of initial state radiation gluons, and find a suppression at large transverse momenta with respect to the standard QCD result. This is due to rescattering events, in which the quark and the emitted gluon scatter coherently. Interestingly, the suppression factor depends on the number of extra dimensions and provides a new experimental handle to measure this number. We evaluate the leading-log corrections to partonic cross-sections due to the initial state radiation, and prove that they can be absorbed into the hadronic PDF. The factorization scale should then be chosen in agreement with an earlier proposal of Emparan, Masip, and Rattazzi. In the future, our methods can be applied to the gravitational radiation in transplanckian scattering, where they can go beyond the existing approaches limited to the soft radiation case.