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Title: Collinear factorization violation and effective field theory

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Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
SC0013607; SC0011090
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 96; Journal Issue: 5; Related Information: CHORUS Timestamp: 2017-09-12 11:58:40; Journal ID: ISSN 2470-0010
American Physical Society
Country of Publication:
United States

Citation Formats

Schwartz, Matthew D., Yan, Kai, and Zhu, Hua Xing. Collinear factorization violation and effective field theory. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.96.056005.
Schwartz, Matthew D., Yan, Kai, & Zhu, Hua Xing. Collinear factorization violation and effective field theory. United States. doi:10.1103/PhysRevD.96.056005.
Schwartz, Matthew D., Yan, Kai, and Zhu, Hua Xing. 2017. "Collinear factorization violation and effective field theory". United States. doi:10.1103/PhysRevD.96.056005.
title = {Collinear factorization violation and effective field theory},
author = {Schwartz, Matthew D. and Yan, Kai and Zhu, Hua Xing},
abstractNote = {},
doi = {10.1103/PhysRevD.96.056005},
journal = {Physical Review D},
number = 5,
volume = 96,
place = {United States},
year = 2017,
month = 9

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on September 12, 2018
Publisher's Accepted Manuscript

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  • 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 whichmore » 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 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.« less
  • We give a detailed description of the differences between the factorization and results derived from SCET and QCDF for decays B{yields}M{sub 1}M{sub 2}. This serves as a reply to the preceding Comment. We disagree with their criticisms.
  • We present a new analysis of two-jet event shape distributions in soft collinear effective theory. Extending previous results, we observe that a large class of such distributions can be expressed in terms of vacuum matrix elements of operators in the effective theory. We match these matrix elements to the full theory in the two-jet limit without assuming factorization of the complete set of hadronic final states into independent sums over partonic collinear and soft states. We also briefly discuss the relationship of this approach to diagrammatic factorization in the full theory.
  • We derive a factorization theorem for the Higgs boson transverse momentum (p{sub T}) and rapidity (Y) distributions at hadron colliders, using the soft-collinear effective theory (SCET), for m{sub h}>>p{sub T}>>{Lambda}{sub QCD}, where m{sub h} denotes the Higgs mass. In addition to the factorization of the various scales involved, the perturbative physics at the p{sub T} scale is further factorized into two collinear impact-parameter beam functions (IBFs) and an inverse soft function (ISF). These newly defined functions are of a universal nature for the study of differential distributions at hadron colliders. The additional factorization of the p{sub T}-scale physics simplifies themore » implementation of higher order radiative corrections in {alpha}{sub s}(p{sub T}). We derive formulas for factorization in both momentum and impact parameter space and discuss the relationship between them. Large logarithms of the relevant scales in the problem are summed using the renormalization group equations of the effective theories. Power corrections to the factorization theorem in p{sub T}/m{sub h} and {Lambda}{sub QCD}/p{sub T} can be systematically derived. We perform multiple consistency checks on our factorization theorem including a comparison with known fixed-order QCD results. We compare the SCET factorization theorem with the Collins-Soper-Sterman approach to low-p{sub T} resummation.« less
  • Proof of factorization of soft and collinear divergences in non-equilibrium QCD may be necessary to study hadronic signatures of quark-gluon plasma at RHIC and LHC. In this paper we prove factorization of soft and collinear divergences in non-equilibrium QED by using Schwinger-Keldysh closed-time path integral formalism in the background field method in pure gauge.