An effective field theory for forward scattering and factorization violation

Rothstein, Ira Z.; Stewart, Iain W.

doi:10.1007/JHEP08(2016)025

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 and yields gluonmore »« less

Authors:

Rothstein, Ira Z. ^[1]; Stewart, Iain W. ^[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:: Wed Aug 03 00:00:00 EDT 2016

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); Simons Foundation

OSTI Identifier:: 1360101

Alternate Identifier(s):: OSTI ID: 1253892

Report Number(s):: DOE-MIT4655-11090
Journal ID: ISSN 1029-8479; PII: 4436

Grant/Contract Number:: SC0011090; FG02-04ER41338; FG02-06ER41449; 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: 2016; Journal Issue: 8; Journal ID: ISSN 1029-8479

Publisher:: Springer Nature

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Effective Field Theories; Renormalization Group; Scattering Amplitudes; 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.

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                    Rothstein, Ira Z., & Stewart, Iain W. An effective field theory for forward scattering and factorization violation.  United States.  https://doi.org/10.1007/JHEP08(2016)025

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                    Rothstein, Ira Z., and Stewart, Iain W. Wed .  
"An effective field theory for forward scattering and factorization violation".  United States.  https://doi.org/10.1007/JHEP08(2016)025.  https://www.osti.gov/servlets/purl/1360101.

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@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}

}

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

Abstract

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Renormalization group analysis of the QCD quark potential to order v 2 journal, June 2000

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Effective Field Theory for Ultrasoft Momenta in NRQCD and NRQED text, January 1997

Transverse momentum distribution in Drell-Yan pair and W and Z boson production journal, January 1985

A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory journal, May 2012

Soft gluons and superleading logarithms in QCD text, January 2009

Asymptotic expansion of Feynman integrals near threshold journal, June 1998

Resummation of transverse energy in vector boson and Higgs boson production at hadron colliders text, January 2010

Classical space–times from the S-matrix journal, December 2013

Singularities in the physical region journal, July 1965

Effective-field theories for heavy quarkonium journal, December 2005

PYTHIA 6.4 physics and manual journal, May 2006

Factorization of the Drell-Yan cross section in perturbation theory journal, May 1985

The quark beam function at NNLL journal, September 2010

Operator expansion for high-energy scattering journal, March 1996

An effective theory for jet propagation in dense QCD matter: jet broadening and medium-induced bremsstrahlung journal, June 2011

A general algorithm for calculating jet cross sections in NLO QCD journal, February 1997

On the breaking of collinear factorization in QCD journal, November 2012

Beam Thrust Cross Section for Drell-Yan Production at Next-to-Next-to-Leading-Logarithmic Order journal, January 2011

Electromagnetic fields of a massless particle and the eikonal journal, February 1992

Super-leading logarithms in non-global observables in QCD? text, January 2006

Unitarity and the BFKL pomeron journal, March 1995

Factorization and N3LLp+NNLO predictions for the Higgs cross section with a jet veto journal, October 2013

The BFKL equation from the Wilson renormalization group journal, October 1997

Mass divergences in annihilation processes. I. Origin and nature of divergences in cut vacuum polarization diagrams journal, May 1978

Phenomenology of event shapes at hadron colliders journal, June 2010

Deep inelastic scattering as x → 1 using soft-collinear effective theory journal, December 2003

Summing Sudakov logarithms in B → X s γ in effective field theory journal, December 2000

Gauge invariant effective action for high-energy processes in QCD text, January 1995

Gauge invariant effective action for high energy processes in QCD journal, October 1995

Renormalization group scaling in nonrelativistic QCD journal, March 2000

Eikonal quantum gravity and planckian scattering journal, December 1992

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journal, November 1987

The BFKL Equation from the Wilson Renormalization Group
text, January 1997

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text, January 1992

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text, January 2014

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journal, July 1997

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journal, October 2015

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journal, December 2011

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text, January 2000

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journal, August 2010

Higgs production with a central jet veto at NNLL+NNLO
journal, April 2011

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journal, January 2001

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journal, December 2015

On power corrections to the event shape distributions in QCD
journal, October 2000

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journal, September 2000

Resummed event shapes at hadron-hadron colliders
text, January 2004

Soft-Collinear Factorization in Effective Field Theory
text, January 2001

On Glauber modes in soft-collinear effective theory
journal, July 2011

Soft-gluon cancellation, phases and factorization with initial-state partons
text, January 2009

Renormalization group analysis of the QCD quark potential to order $v^{2}$
journal, June 2000

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journal, January 2009

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text, January 1997

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journal, January 1985

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journal, May 2012

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text, January 2009

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journal, June 1998

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text, January 2010

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journal, December 2013

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journal, July 1965

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journal, December 2005

PYTHIA 6.4 physics and manual
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journal, May 1985

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journal, March 1996

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A general algorithm for calculating jet cross sections in NLO QCD
journal, February 1997

On the breaking of collinear factorization in QCD
journal, November 2012

Beam Thrust Cross Section for Drell-Yan Production at Next-to-Next-to-Leading-Logarithmic Order
journal, January 2011

Electromagnetic fields of a massless particle and the eikonal
journal, February 1992

Super-leading logarithms in non-global observables in QCD?
text, January 2006

Unitarity and the BFKL pomeron
journal, March 1995

Factorization and N3LLp+NNLO predictions for the Higgs cross section with a jet veto
journal, October 2013

The BFKL equation from the Wilson renormalization group
journal, October 1997

Mass divergences in annihilation processes. I. Origin and nature of divergences in cut vacuum polarization diagrams
journal, May 1978

Phenomenology of event shapes at hadron colliders
journal, June 2010

Deep inelastic scattering as $\vec{x} 1$ using soft-collinear effective theory
journal, December 2003

Summing Sudakov logarithms in $\vec{B} X_{s} γ$ in effective field theory
journal, December 2000

Gauge invariant effective action for high-energy processes in QCD
text, January 1995

Gauge invariant effective action for high energy processes in QCD
journal, October 1995

Renormalization group scaling in nonrelativistic QCD
journal, March 2000

Eikonal quantum gravity and planckian scattering
journal, December 1992

Strong phases and factorization for color suppressed decays
journal, December 2003

The role of Glauber exchange in soft collinear effective theory and the Balitsky–Fadin–Kuraev–Lipatov Equation
journal, July 2014

Designing gapped soft functions for jet production
journal, March 2008

On near forward high energy scattering in QCD
text, January 1993

Initial-State Interactions and the Drell-Yan Process
journal, December 1981

Collinear effective theory at subleading order and its application to heavy-light currents
journal, June 2002

The soft-gluon current at one-loop order
text, January 2000

Factorization and end point singularities in heavy-to-light decays
journal, April 2003

Factorization and high-energy effective action
journal, June 1999

Cancellation of Glauber gluon exchange in the double Drell-Yan process
text, January 2015

Resummed event shapes at hadron-hadron colliders
journal, August 2004

Soft-collinear factorization in effective field theory
journal, February 2002

Medium-induced splitting kernels from SCETG
journal, May 2013

Power corrections to event shapes and factorization
journal, August 1999

Invariant Operators in Collinear Effective Theory
text, January 2001

Space-like (vs. time-like) collinear limits in QCD: is factorization violated?
journal, July 2012

Factorization and N3LLp+NNLO predictions for the Higgs cross section with a jet veto
text, January 2013

Logarithms of alpha in QED bound states from the renormalization group
text, January 2000

Universality of Soft and Collinear Factors in Hard-Scattering Factorization
journal, December 2004

Enhanced nonperturbative effects in Z decays to hadrons
journal, August 2004

Effective field theory for ultrasoft momenta in NRQCD and NRQED
journal, May 1998

Singular and regular gauges in soft–collinear effective theory: The introduction of the new Wilson line T
journal, January 2011

Higgs- and Z-boson Production with a Jet Veto
text, January 2012

Invariant operators in collinear effective theory
journal, September 2001

The infrared structure of gauge theory amplitudes in the high-energy limit
journal, December 2011

Quantum Chromodynamics at High Energy
book, September 2012

Soft gluons and factorization
journal, October 1988

Super-leading logarithms in non-global observables in QCD?
journal, August 2006

High-energy scattering in QCD and cross singularities of Wilson loops
journal, March 1995