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:: 2016-08-03

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 (United States)

OSTI Identifier:: 1360101

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 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.

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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         = {2016},

  month        = {8}

}

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Abstract

Citation Formats

Unitarity and the BFKL pomeron journal, March 1995

Operator expansion for high-energy scattering journal, March 1996

Small- x F 2 structure function of a nucleus including multiple Pomeron exchanges journal, June 1999

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

Nonlinear gluon evolution in the color glass condensate: I journal, September 2001

On near forward high energy scattering in QCD journal, April 1994

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

Evolution equation for gluon Regge trajectory journal, October 1996

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

Small-x physics in perturbative QCD journal, July 1997

Factorization and high-energy effective action journal, June 1999

When does the gluon reggeize? journal, May 2015

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

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

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

Soft gluons and factorization journal, October 1988

Factorization Of Hard Processes In QCD book, July 1989

Fragmentation, nonrelativistic QCD, and NNLO factorization analysis in heavy quarkonium production journal, December 2005

Cancellation of Glauber gluon exchange in the double Drell-Yan process journal, January 2016

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

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

Invariant operators in collinear effective theory journal, September 2001

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

Hard scattering factorization from effective field theory journal, July 2002

Asymptotic expansion of Feynman integrals near threshold journal, June 1998

Foundation and generalization of the expansion by regions journal, December 2011

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

Medium-induced splitting kernels from SCETG journal, May 2013

Gauge invariant definition of the jet quenching parameter journal, February 2013

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

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

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

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

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

The high energy limit of QCD at two loops journal, October 2001

High-energy QCD amplitudes at two loops and beyond journal, May 2014

Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy journal, February 2015

Rapidity Renormalization Group journal, April 2012

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

The zero-bin and mode factorization in quantum field theory journal, October 2007

The soft-gluon current at one-loop order journal, December 2000

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

Renormalization group scaling in nonrelativistic QCD journal, March 2000

Power corrections to event shapes and factorization journal, August 1999

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

Designing gapped soft functions for jet production journal, March 2008

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

N Jettiness: An Inclusive Event Shape to Veto Jets journal, August 2010

The Higgs transverse momentum distribution at NNLL and its theoretical errors journal, December 2015

PYTHIA 6.4 physics and manual journal, May 2006

Herwig++ physics and manual journal, November 2008

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

Singularities in the physical region journal, July 1965

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

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

QCD heavy-quark potential to order v 2 : One loop matching conditions journal, September 2000

Running of the heavy quark production current and 1 / | k | potential in QCD journal, January 2001

Logarithms of α in QED Bound States from the Renormalization Group journal, September 2000

Ultrasoft renormalization in nonrelativistic QCD journal, June 2003

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

Effective-field theories for heavy quarkonium journal, December 2005

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

Reparameterization invariance for collinear operators journal, July 2002

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

Effective field theory and matching in nonrelativistic gauge theories journal, January 1998

On the equivalence of soft and zero-bin subtractions journal, June 2007

Power counting in the soft-collinear effective theory journal, September 2002

Mass divergences in annihilation processes. II. Cancellation of divergences in cut vacuum polarization diagrams journal, May 1978

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

Glauber gluons and multiple parton interactions journal, July 2014

Drell-Yan process with jet vetoes: breaking of generalized factorization journal, October 2015

Soft gluons and superleading logarithms in QCD journal, June 2009

Graviton dominance in ultra-high-energy scattering journal, November 1987

Dynamics at Infinite Momentum journal, October 1966

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

Soft Wilson lines in the soft-collinear effective theory journal, March 2005

Eikonal Approximation in Quantum Field Theory journal, October 1969

Unitarity and the BFKL pomeron
journal, March 1995

Operator expansion for high-energy scattering
journal, March 1996

Small- x $F_{2}$ structure function of a nucleus including multiple Pomeron exchanges
journal, June 1999

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

Nonlinear gluon evolution in the color glass condensate: I
journal, September 2001

On near forward high energy scattering in QCD
journal, April 1994

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

Evolution equation for gluon Regge trajectory
journal, October 1996

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

Small-x physics in perturbative QCD
journal, July 1997

Factorization and high-energy effective action
journal, June 1999

When does the gluon reggeize?
journal, May 2015

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

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

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

Soft gluons and factorization
journal, October 1988

Factorization Of Hard Processes In QCD
book, July 1989

Fragmentation, nonrelativistic QCD, and NNLO factorization analysis in heavy quarkonium production
journal, December 2005

Cancellation of Glauber gluon exchange in the double Drell-Yan process
journal, January 2016

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

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

Invariant operators in collinear effective theory
journal, September 2001

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

Hard scattering factorization from effective field theory
journal, July 2002

Asymptotic expansion of Feynman integrals near threshold
journal, June 1998

Foundation and generalization of the expansion by regions
journal, December 2011

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

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journal, May 2013

Gauge invariant definition of the jet quenching parameter
journal, February 2013

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

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journal, July 2014

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journal, July 2012

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

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journal, August 2006

The high energy limit of QCD at two loops
journal, October 2001

High-energy QCD amplitudes at two loops and beyond
journal, May 2014

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journal, February 2015

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journal, April 2012

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journal, May 2012

The zero-bin and mode factorization in quantum field theory
journal, October 2007

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journal, December 2000

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

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journal, March 2000

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journal, August 1999

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

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journal, March 2008

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journal, April 2011

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journal, August 2010

The Higgs transverse momentum distribution at NNLL and its theoretical errors
journal, December 2015

PYTHIA 6.4 physics and manual
journal, May 2006

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journal, November 2008

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

Singularities in the physical region
journal, July 1965

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

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

QCD heavy-quark potential to order $v^{2} :$ One loop matching conditions
journal, September 2000

Running of the heavy quark production current and $1 / | k |$ potential in QCD
journal, January 2001

Logarithms of $α$ in QED Bound States from the Renormalization Group
journal, September 2000

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

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journal, December 2005

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journal, January 2011

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journal, July 2002

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journal, June 2002

Effective field theory and matching in nonrelativistic gauge theories
journal, January 1998

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journal, June 2007

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journal, September 2002

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journal, May 1978

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

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journal, July 2014

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journal, October 2015

Soft gluons and superleading logarithms in QCD
journal, June 2009

Graviton dominance in ultra-high-energy scattering
journal, November 1987

Dynamics at Infinite Momentum
journal, October 1966

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

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journal, March 2005

Eikonal Approximation in Quantum Field Theory
journal, October 1969

Eikonal quantum gravity and planckian scattering
journal, December 1992

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

Constraint equations for heavy-to-light currents in soft-collinear effective theory
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