Soft fragmentation on the celestial sphere
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Springer
Received: March 26, 2020 Accepted: May 12, 2020 Published: June 12, 2020
Soft fragmentation on the celestial sphere
a
Theoretical Division, MS B283, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A. b Physics Department, University of California, Berkeley, CA 94720, U.S.A. c Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A.
E-mail: [email protected], [email protected] Abstract: 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 kT -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 infrared 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 dimensions at all angles. The two approaches are united by demanding that the anomalous dimension in 4 − 2 dimensions for the parton distribution function determines the kernel for the angular-ordered evolution to all orders. Keywords: Perturbative QCD, Resummation ArXiv ePrint: 2003.02275
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)086
JHEP06(2020)086
Duff Neilla and Felix Ringerb,c
Contents 1 Introduction
1
2 Review of factorization with PDFs and FFs 2.1 Factorization in dimensional regularization 2.2 Structure of anomalous dimensions and resummed perturbation theory
5 7 9
3 BFKL in 4 − 2 dimensions
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5 Angular regularization of the soft region of fragmentation and reciprocity 5.1 Angular evolution 5.2 Structure of the angular-ordered evolution kernel 5.3 Solution 5.4 Comparison to literature 5.4.1 The anomalous dimension 5.4.2 Coefficient function for φ → h + X
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6 Comparing celestial BFKL to angular-ordered DGLAP
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7 Towards full flavor QCD
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8 Discussion
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9 Conclusions
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A Constants
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B Stereographic mapping and BFKL
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C Reciprocity equations
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D Derivation of celestial BFKL
34
1
Introduction
A basic problem in high-energy scattering is that of fragmentation: how is the total energy of the scattering process divided amongst the final-state remnants? Fragmentation is a critical concern since it probes the dynamical properties of the theory. Not only must one know the bound states or res
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