An effective field theory for forward scattering and factorization violation
Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the softcollinear 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 lightcone 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 1gluon 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 oneloop matching calculations from full QCD to both SCET _{II} and SCET _{I}. The oneloop amplitude’s rapidity renormalization involves mixing of color octet operators andmore »
 Authors:

^{[1]};
^{[2]}
 Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Physics
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics
 Publication Date:
 Grant/Contract Number:
 SC0011090; FG0204ER41338; FG0206ER41449; 327942
 Type:
 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 10298479
 Publisher:
 Springer Berlin
 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) (SC26); Simons Foundation (United States)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Effective Field Theories; Renormalization Group; Scattering Amplitudes
 OSTI Identifier:
 1360101
Rothstein, Ira Z., and Stewart, Iain W.. An effective field theory for forward scattering and factorization violation. United States: N. p.,
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.. 2016.
"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 softcollinear 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 lightcone 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 1gluon 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 oneloop matching calculations from full QCD to both SCETII and SCETI. The oneloop 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 = {2016},
month = {8}
}