Soft fragmentation on the celestial sphere

A bstract We develop two approaches to the problem of soft fragmentation of hadrons in a gauge theory for high energy processes. The first approach directly adapts the standard resummation of the parton distribution function’s anomalous dimension (that of twist-two local operators) in the forward sc...

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Bibliographic Details
Published in:The journal of high energy physics 2020-06, Vol.2020 (6), p.1-41, Article 86
Main Authors: Neill, Duff, Ringer, Felix
Format: Article
Language:English
Subjects:
ATOMIC AND MOLECULAR PHYSICS
Atomic, Nuclear and Particle Physics
Celestial sphere
Classical and Quantum Gravitation
Distribution functions
Elementary Particles
Evolution
Forward scattering
Fragmentation
Gauge theory
Hadrons
High energy physics
Mapping
NUCLEAR PHYSICS AND RADIATION PHYSICS
Partons
Perturbative QCD
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Regularization
Relativity Theory
Resummation
String Theory
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Summary:A bstract We develop two approaches to the problem of soft fragmentation of hadrons in a gauge theory for high energy processes. The first approach directly adapts the standard resummation of the parton distribution function’s anomalous dimension (that of twist-two local operators) in the forward scattering regime, using k T -factorization and BFKL theory, to the case of the fragmentation function by exploiting the mapping between the dynamics of eikonal lines on transverse-plane to the celestial-sphere. Critically, to correctly resum the anomalous dimension of the fragmentation function under this mapping, one must pay careful attention to the role of regularization, despite the manifest collinear or infra- red finiteness of the BFKL equation. The anomalous dependence on energy in the celestial case, arising due to the mismatch of dimensionality between positions and angles, drives the differences between the space-like and time-like anomalous dimension of parton densities, even in a conformal theory. The second approach adapts an angular-ordered evolution equation, but working in 4 − 2 ϵ dimensions at all angles. The two approaches are united by demanding that the anomalous dimension in 4 − 2 ϵ dimensions for the parton distribution function determines the kernel for the angular-ordered evolution to all orders.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP06(2020)086