Anomalous dimensions from soft Regge constants
Abstract
Using an effective field theory (EFT) formalism for forward scattering, we reconsider the factorization of 2 → 2 scattering amplitudes in the Regge limit. Expanding the amplitude in gauge invariant operators labelled by the number of Glauber exchanges, allows us to further factorize the standard impact factors into separate collinear and soft functions. The soft functions are universal, and describe radiative corrections to the Reggeized gluon states exchanged by the collinear projectiles. Remarkably, we find that the one-loop soft function for the single Reggeized gluon state is given to O(ϵ) in terms of the two-loop cusp and two-loop rapidity anomalous dimensions. We argue that this iterative structure follows from the simple action of crossing symmetry in the forward scattering limit, which in the EFT allows us to replace the divergent part of a soft loop by a much simpler Glauber loop. We use this correspondence to provide a simple calculation of the two-loop Regge trajectory using the EFT. We then explore its implications at higher perturbative orders, and derive the maximally matter dependent contributions to the Regge trajectory to all loop orders, i.e. the terms ~ α$$^{k+1}_{s}$$n$$^{k}_{f}$$ for any k, where nf is the number of massless flavors. These simplifications suggests that the EFT approach to the Regge limit will be helpful to explore and further understand the structure of the Regge limit.
- Authors:
-
- Yale University, New Haven, CT (United States)
- Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); Simons Foundation
- OSTI Identifier:
- 1991324
- Grant/Contract Number:
- SC0011090; 327942
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2023; Journal Issue: 5; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories of QCD; Scattering Amplitudes; Factorization; Renormalization Group
Citation Formats
Moult, Ian, Raman, Sanjay, Ridgway, Gregory, and Stewart, Iain W. Anomalous dimensions from soft Regge constants. United States: N. p., 2023.
Web. doi:10.1007/jhep05(2023)025.
Moult, Ian, Raman, Sanjay, Ridgway, Gregory, & Stewart, Iain W. Anomalous dimensions from soft Regge constants. United States. https://doi.org/10.1007/jhep05(2023)025
Moult, Ian, Raman, Sanjay, Ridgway, Gregory, and Stewart, Iain W. Wed .
"Anomalous dimensions from soft Regge constants". United States. https://doi.org/10.1007/jhep05(2023)025. https://www.osti.gov/servlets/purl/1991324.
@article{osti_1991324,
title = {Anomalous dimensions from soft Regge constants},
author = {Moult, Ian and Raman, Sanjay and Ridgway, Gregory and Stewart, Iain W.},
abstractNote = {Using an effective field theory (EFT) formalism for forward scattering, we reconsider the factorization of 2 → 2 scattering amplitudes in the Regge limit. Expanding the amplitude in gauge invariant operators labelled by the number of Glauber exchanges, allows us to further factorize the standard impact factors into separate collinear and soft functions. The soft functions are universal, and describe radiative corrections to the Reggeized gluon states exchanged by the collinear projectiles. Remarkably, we find that the one-loop soft function for the single Reggeized gluon state is given to O(ϵ) in terms of the two-loop cusp and two-loop rapidity anomalous dimensions. We argue that this iterative structure follows from the simple action of crossing symmetry in the forward scattering limit, which in the EFT allows us to replace the divergent part of a soft loop by a much simpler Glauber loop. We use this correspondence to provide a simple calculation of the two-loop Regge trajectory using the EFT. We then explore its implications at higher perturbative orders, and derive the maximally matter dependent contributions to the Regge trajectory to all loop orders, i.e. the terms ~ α$^{k+1}_{s}$n$^{k}_{f}$ for any k, where nf is the number of massless flavors. These simplifications suggests that the EFT approach to the Regge limit will be helpful to explore and further understand the structure of the Regge limit.},
doi = {10.1007/jhep05(2023)025},
journal = {Journal of High Energy Physics (Online)},
number = 5,
volume = 2023,
place = {United States},
year = {Wed May 03 00:00:00 EDT 2023},
month = {Wed May 03 00:00:00 EDT 2023}
}
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Works referenced in this record:
Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
journal, March 2022
- Falcioni, Giulio; Gardi, Einan; Maher, Niamh
- Journal of High Energy Physics, Vol. 2022, Issue 3
The gluon Regge trajectory at three loops from planar Yang-Mills theory
journal, January 2022
- Del Duca, Vittorio; Marzucca, Robin; Verbeek, Bram
- Journal of High Energy Physics, Vol. 2022, Issue 1
Conformal properties of four-gluon planar amplitudes and Wilson loops
journal, May 2008
- Drummond, J. M.; Korchemsky, G. P.; Sokatchev, E.
- Nuclear Physics B, Vol. 795, Issue 1-2
Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond
journal, October 2005
- Bern, Zvi; Dixon, Lance J.; Smirnov, Vladimir A.
- Physical Review D, Vol. 72, Issue 8
Toward massless and massive event shapes in the large-β0 limit
journal, July 2021
- Gracia, N. G.; Mateu, V.
- Journal of High Energy Physics, Vol. 2021, Issue 7
On planar gluon amplitudes/Wilson loops duality
journal, May 2008
- Drummond, J. M.; Henn, J.; Korchemsky, G. P.
- Nuclear Physics B, Vol. 795, Issue 1-2
Gluon Regge trajectory in the two-loop approximation
journal, October 1996
- Fadin, V. S.; Fiore, R.; Kotsky, M. I.
- Physics Letters B, Vol. 387, Issue 3
Bootstrapping the QCD soft anomalous dimension
journal, September 2017
- Almelid, Øyvind; Duhr, Claude; Gardi, Einan
- Journal of High Energy Physics, Vol. 2017, Issue 9
Multi-Loop Techniques for Massless Feynman Diagram Calculations
journal, January 2019
- Kotikov, A. V.; Teber, S.
- Physics of Particles and Nuclei, Vol. 50, Issue 1
The four-loop cusp anomalous dimension from the N = 4
journal, August 2020
- Huber, Tobias; von Manteuffel, Andreas; Panzer, Erik
- Physics Letters B, Vol. 807
All two-loop MHV remainder functions in multi-Regge kinematics
journal, January 2019
- Del Duca, Vittorio; Duhr, Claude; Dulat, Falko
- Journal of High Energy Physics, Vol. 2019, Issue 1
Fermionic Glauber operators and quark reggeization
journal, February 2018
- Moult, Ian; Solon, Mikhail P.; Stewart, Iain W.
- Journal of High Energy Physics, Vol. 2018, Issue 2
Six-Gluon amplitudes in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops
journal, August 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Journal of High Energy Physics, Vol. 2019, Issue 8
An effective field theory for collinear and soft gluons: Heavy to light decays
journal, May 2001
- Bauer, Christian W.; Fleming, Sean; Pirjol, Dan
- Physical Review D, Vol. 63, Issue 11
When does the gluon reggeize?
journal, May 2015
- Caron-Huot, Simon
- Journal of High Energy Physics, Vol. 2015, Issue 5
High-energy evolution to three loops
journal, February 2018
- Caron-Huot, Simon; Herranen, Matti
- Journal of High Energy Physics, Vol. 2018, Issue 2
Gluon Reggeization in QCD in the next to leading order
journal, October 1995
- Fadin, V. S.; Fiore, R.; Kotsky, M. I.
- Physics Letters B, Vol. 359, Issue 1-2
Adjoint BFKL at finite coupling: a short-cut from the collinear limit
journal, January 2015
- Basso, Benjamin; Caron-Huot, Simon; Sever, Amit
- Journal of High Energy Physics, Vol. 2015, Issue 1
Elementary Particles of Conventional Field Theory as Regge Poles. III
journal, January 1964
- Gell-Mann, M.; Goldberger, M. L.; Low, F. E.
- Physical Review, Vol. 133, Issue 1B
Iterated amplitudes in the high-energy limit
journal, December 2008
- Duca, Vittorio Del; Duhr, Claude; Glover, E. W. N.
- Journal of High Energy Physics, Vol. 2008, Issue 12
Three-loop helicity amplitudes for quark-gluon scattering in QCD
journal, December 2022
- Caola, Fabrizio; Chakraborty, Amlan; Gambuti, Giulio
- Journal of High Energy Physics, Vol. 2022, Issue 12
Evolution equation for gluon Regge trajectory
journal, October 1996
- Korchemskaya, I. A.; Korchemsky, G. P.
- Physics Letters B, Vol. 387, Issue 2
High energy QCD as a completely integrable model
journal, January 1995
- Faddeev, L. D.; Korchemsky, G. P.
- Physics Letters B, Vol. 342, Issue 1-4
The multi-Regge limit from the Wilson loop OPE
journal, May 2020
- Bargheer, Till; Chestnov, Vsevolod; Schomerus, Volker
- Journal of High Energy Physics, Vol. 2020, Issue 5
An effective field theory for forward scattering and factorization violation
journal, August 2016
- Rothstein, Ira Z.; Stewart, Iain W.
- Journal of High Energy Physics, Vol. 2016, Issue 8
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
journal, June 2018
- Del Duca, Vittorio; Druc, Stefan; Drummond, James
- Journal of High Energy Physics, Vol. 2018, Issue 6
The four-loop six-gluon NMHV ratio function
journal, January 2016
- Dixon, Lance J.; von Hippel, Matt; McLeod, Andrew J.
- Journal of High Energy Physics, Vol. 2016, Issue 1
High-energy QCD amplitudes at two loops and beyond
journal, May 2014
- Del Duca, Vittorio; Falcioni, Giulio; Magnea, Lorenzo
- Physics Letters B, Vol. 732
Relating amplitude and PDF factorisation through Wilson-line geometries
journal, November 2019
- Falcioni, Giulio; Gardi, Einan; Milloy, Calum
- Journal of High Energy Physics, Vol. 2019, Issue 11
The high energy limit of QCD at two loops
journal, October 2001
- Duca, Vittorio Del; Glover, E. W. Nigel
- Journal of High Energy Physics, Vol. 2001, Issue 10
Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory
journal, March 2010
- Drummond, J. M.; Henn, J.; Korchemsky, G. P.
- Nuclear Physics B, Vol. 828, Issue 1-2
Gauge theory webs and surfaces
journal, January 2015
- Erdoğan, Ozan; Sterman, George
- Physical Review D, Vol. 91, Issue 1
Invariant operators in collinear effective theory
journal, September 2001
- Bauer, Christian W.; Stewart, Iain W.
- Physics Letters B, Vol. 516, Issue 1-2
Many-loop calculations: The uniqueness method and functional equations
journal, January 1985
- Kazakov, D. I.
- Theoretical and Mathematical Physics, Vol. 62, Issue 1
The infrared structure of gauge theory amplitudes in the high-energy limit
journal, December 2011
- Del Duca, Vittorio; Duhr, Claude; Gardi, Einan
- Journal of High Energy Physics, Vol. 2011, Issue 12
Summing Sudakov logarithms in in effective field theory
journal, December 2000
- Bauer, Christian W.; Fleming, Sean; Luke, Michael
- Physical Review D, Vol. 63, Issue 1
Disentangling the Regge Cut and Regge Pole in Perturbative QCD
journal, March 2022
- Falcioni, Giulio; Gardi, Einan; Maher, Niamh
- Physical Review Letters, Vol. 128, Issue 13
Climbing three-Reggeon ladders: Four-loop amplitudes in the high-energy limit in full color
journal, June 2021
- Falcioni, Giulio; Gardi, Einan; Milloy, Calum
- Physical Review D, Vol. 103, Issue 11
Gauge invariant effective action for high energy processes in QCD
journal, October 1995
- Lipatov, L. N.
- Nuclear Physics B, Vol. 452, Issue 1-2
Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
journal, February 2010
- Drummond, J. M.; Henn, J.; Korchemsky, G. P.
- Nuclear Physics B, Vol. 826, Issue 1-2
High-energy scattering in QCD and cross singularities of Wilson loops
journal, March 1995
- Korchemskaya, I. A.; Korchemsky, G. P.
- Nuclear Physics B, Vol. 437, Issue 1
Iterating QCD scattering amplitudes in the high-energy limit
journal, February 2018
- Del Duca, Vittorio
- Journal of High Energy Physics, Vol. 2018, Issue 2
Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
journal, August 2016
- Del Duca, Vittorio; Druc, Stefan; Drummond, James
- Journal of High Energy Physics, Vol. 2016, Issue 8
The quark Regge trajectory at two loops
journal, March 2002
- Bogdan, Andrey V.; Fadin, Victor S.; Duca, Vittorio Del
- Journal of High Energy Physics, Vol. 2002, Issue 03
All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit
journal, April 2020
- Del Duca, V.; Druc, S.; Drummond, J. M.
- Physical Review Letters, Vol. 124, Issue 16
Gluon Regge trajectory in
journal, October 1998
- Blümlein, J.; Ravindran, V.; van Neerven, W. L.
- Physical Review D, Vol. 58, Issue 9
Reggeization of Elementary Particles in Renormalizable Gauge Theories: Vectors and Spinors
journal, December 1973
- Grisaru, Marcus T.; Schnitzer, Howard J.; Tsao, Hung-Sheng
- Physical Review D, Vol. 8, Issue 12
Hard scattering factorization from effective field theory
journal, July 2002
- Bauer, Christian W.; Fleming, Sean; Pirjol, Dan
- Physical Review D, Vol. 66, Issue 1
Theory of fermion exchange in massive quantum electrodynamics at high energy. I
journal, January 1976
- McCoy, Barry M.; Wu, Tai Tsun
- Physical Review D, Vol. 13, Issue 2
Two-parton scattering in the high-energy limit
journal, June 2017
- Caron-Huot, Simon; Gardi, Einan; Vernazza, Leonardo
- Journal of High Energy Physics, Vol. 2017, Issue 6
A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory
journal, May 2012
- Chiu, Jui-Yu; Jain, Ambar; Neill, Duff
- Journal of High Energy Physics, Vol. 2012, Issue 5
Infrared approach to Reggeization
journal, April 2012
- Del Duca, Vittorio; Duhr, Claude; Gardi, Einan
- Physical Review D, Vol. 85, Issue 7
Three-loop helicity amplitudes for four-quark scattering in massless QCD
journal, October 2021
- Caola, Fabrizio; Chakraborty, Amlan; Gambuti, Giulio
- Journal of High Energy Physics, Vol. 2021, Issue 10
The analytic structure and the transcendental weight of the BFKL ladder at NLL accuracy
journal, October 2017
- Del Duca, Vittorio; Duhr, Claude; Marzucca, Robin
- Journal of High Energy Physics, Vol. 2017, Issue 10
Single-valued harmonic polylogarithms and the multi-Regge limit
journal, October 2012
- Dixon, Lance J.; Duhr, Claude; Pennington, Jeffrey
- Journal of High Energy Physics, Vol. 2012, Issue 10
Hexagon Wilson loop = six-gluon MHV amplitude
journal, July 2009
- Drummond, J. M.; Henn, J.; Korchemsky, G. P.
- Nuclear Physics B, Vol. 815, Issue 1-2
Non-Regge Terms in the Vector-Spinor Theory
journal, February 1965
- Mandelstam, S.
- Physical Review, Vol. 137, Issue 4B
On the pomeranchuk singularity in asymptotically free theories
journal, December 1975
- Fadin, V. S.; Kuraev, E. A.; Lipatov, L. N.
- Physics Letters B, Vol. 60, Issue 1
The three-loop splitting functions in QCD: the non-singlet case
journal, June 2004
- Moch, S.; Vermaseren, J. A. M.; Vogt, A.
- Nuclear Physics B, Vol. 688, Issue 1-2
The full four-loop cusp anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills and QCD
journal, April 2020
- Henn, Johannes M.; Korchemsky, Gregory P.; Mistlberger, Bernhard
- Journal of High Energy Physics, Vol. 2020, Issue 4
Reggeization of the quark-quark scattering amplitude in QCD
journal, March 1996
- Fadin, V. S.; Fiore, R.; Quartarolo, A.
- Physical Review D, Vol. 53, Issue 5
Renormalization of the Wilson loops beyond the leading order
journal, January 1987
- Korchemsky, G. P.; Radyushkin, A. V.
- Nuclear Physics B, Vol. 283
Soft-collinear factorization in effective field theory
journal, February 2002
- Bauer, Christian W.; Pirjol, Dan; Stewart, Iain W.
- Physical Review D, Vol. 65, Issue 5