The Jet/CGC correspondence: a conformal perspective

Bohra, Jibranhusain

The Jet/CGC correspondence: a conformal perspective

Thesis / Dissertation

2023

Abstract

This study aims to bridge, with the use of conformal transformations, two distinct applications of QCD which are encapsulated by evolution equations for associated observables. Superficially, the interjet energy flow multiplicity and the cross section of Deep Inelastic Scattering (DIS) at small-xbj describe, as observables, entirely different phenomena. Jet evolution equations describe how soft gluons enter the final state of e +e − annihilation events and, accordingly, drive the energy dependence of s-channel multiplicities. On the other hand, Color Glass Condensate (CGC) evolution equations describe the change of dynamic gluon saturation effects (characteristic of DIS events at small-xbj) in terms of the change in kinematic rapidity – and, accordingly, characterize the t-channel exchange between probe and target. Despite differences in phenomenological applications, independently derived 't Hooft large Nc limit Jet and CGC evolution equations (namely: BMS and BK, respectively) demonstrate remarkable structural similarities. These have triggered a search for tools to understand the origin and limitations of this relationship. The correspondence of Jet/CGC evolution at large Nc was key in the derivation of the BMS-W equation – which, along with JIMWLK equation, establishes an analogous correspondence at finite Nc. In parallel, a surge of N = 4 SYM interest in relating small-xbj DIS and interjet energy flow – based on the AdS/CFT Correspondence – provided new perspectives on associated QCD descriptions. Foundationally, the structural similarities showcased by BMS-W/JIMWLK equations are geometric in origin: Wilson lines and the product of integration kernels and measures are tagged by transverse coordinates in the CGC case and by a sphere of directions on the Jet side. The product measures and kernels are known to be related explicitly through a Euclidean stereographic projection. Moreover, a Minkowskian conformal transformation posited by Hofman and Maldacena (HM) has been used to relate Wilson line geometry in other applications. It is this transformation (called the HM map), properly adapted to the present purpose, that is used to study the relationship of virtually all ingredients of BMS-W/JIMWLK. In particular, re-parametrization of independently established mathematical objects encountered in both Jet and CGC evolution is used to furnish a four dimensional relationship of Wilson line geometry, logarithm structure, and integration kernels.

Keywords

Physics

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