skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: An effective field theory for forward scattering and factorization violation

Abstract

Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, and act as a kernel for forward scattering where |t| << s. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs involving soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with ≥ 2 soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to both SCET II and SCET I. The one-loop amplitude’s rapidity renormalization involves mixing of color octet operators andmore » yields gluon Reggeization at the amplitude level. The rapidity renormalization group equation for the leading soft and collinear functions in the forward scattering cross section are each given by the BFKL equation. Various properties of Glauber gluon exchange in the context of both forward scattering and hard scattering factorization are described. For example, we derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to the directions for soft and collinear Wilson lines. Conversely, certain Glauber interactions can be absorbed into these soft and collinear Wilson lines by taking them to be in specific directions. Finally, we also discuss criteria for factorization violation.« less

Authors:
 [1];  [2]
  1. Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Physics
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Carnegie Mellon Univ., Pittsburgh, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); Simons Foundation (United States)
OSTI Identifier:
1360101
Grant/Contract Number:
SC0011090; FG02-04ER41338; FG02-06ER41449; 327942
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Effective Field Theories; Renormalization Group; Scattering Amplitudes

Citation Formats

Rothstein, Ira Z., and Stewart, Iain W. An effective field theory for forward scattering and factorization violation. United States: N. p., 2016. Web. doi:10.1007/JHEP08(2016)025.
Rothstein, Ira Z., & Stewart, Iain W. An effective field theory for forward scattering and factorization violation. United States. doi:10.1007/JHEP08(2016)025.
Rothstein, Ira Z., and Stewart, Iain W. Wed . "An effective field theory for forward scattering and factorization violation". United States. doi:10.1007/JHEP08(2016)025. https://www.osti.gov/servlets/purl/1360101.
@article{osti_1360101,
title = {An effective field theory for forward scattering and factorization violation},
author = {Rothstein, Ira Z. and Stewart, Iain W.},
abstractNote = {Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, and act as a kernel for forward scattering where |t| << s. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs involving soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with ≥ 2 soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to both SCETII and SCETI. The one-loop amplitude’s rapidity renormalization involves mixing of color octet operators and yields gluon Reggeization at the amplitude level. The rapidity renormalization group equation for the leading soft and collinear functions in the forward scattering cross section are each given by the BFKL equation. Various properties of Glauber gluon exchange in the context of both forward scattering and hard scattering factorization are described. For example, we derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to the directions for soft and collinear Wilson lines. Conversely, certain Glauber interactions can be absorbed into these soft and collinear Wilson lines by taking them to be in specific directions. Finally, we also discuss criteria for factorization violation.},
doi = {10.1007/JHEP08(2016)025},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2016,
place = {United States},
year = {Wed Aug 03 00:00:00 EDT 2016},
month = {Wed Aug 03 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 21works
Citation information provided by
Web of Science

Save / Share:
  • The nonleptonic heavy meson decays B{r_arrow}D{sup ({asterisk})}{pi}({rho}), J/{psi}K{sup ({asterisk})}, and D{r_arrow}K{sup ({asterisk})}{pi} are studied based on the three-scale perturbative QCD factorization theorem developed recently. In this formalism the Bauer-Stech-Wirbel parameters a{sub 1} and a{sub 2} are treated as the Wilson coefficients, whose evolution from the W boson mass down to the characteristic scale of the decay processes is determined by effective field theory. The evolution from the characteristic scale to a lower hadronic scale is formulated by the Sudakov resummation. The scale-setting ambiguity, which exists in the conventional approach to nonleptonic heavy meson decays, is removed. Nonfactorizable and nonspectator contributionsmore » are taken into account as part of the hard decay subamplitudes. Our formalism is applicable to both bottom and charm decays, and predictions, including those for the ratios R and R{sub L} associated with the B{r_arrow}J/{psi}K{sup ({asterisk})} decays, are consistent with experimental data. {copyright} {ital 1997} {ital The American Physical Society}« less
  • We develop a perturbative QCD factorization theorem which is compatible with effective field theory. The factorization involves three scales: an infrared cutoff of order {Lambda}{sub QCD}, a hard scale of the order of the B meson mass, and an ultraviolet cutoff of the order of the W boson mass. Our approach is renormalization-group invariant and moderates the scale-dependent problem in effective field theory. Employing this formalism with nonfactorizable contributions included, we clarify the controversy over the BSW parameters a{sub 2}/a{sub 1} for charm and bottom decays. {copyright} {ital 1997} {ital The American Physical Society}
  • We reformulate the analysis of nuclear parity-violation (PV) within the framework of effective field theory (EFT). To order Q, the PV nucleon-nucleon (NN) interaction depends on five a priori unknown constants that parameterize the leading-order, short-range four-nucleon operators. When pions are included as explicit degrees of freedom, the potential contains additional medium- and long-range components parameterized by PV piNN couplings. We derive the form of the corresponding one- and two-pion-exchange potentials. We apply these considerations to a set of existing and prospective PV few-body measurements that may be used to determine the five independent low-energy constants relevant to the pionlessmore » EFT and the additional constants associated with dynamical pions. We also discuss the relationship between the conventional meson-exchange framework and the EFT formulation, and argue that the latter provides a more general and systematic basis for analyzing nuclear PV.« less