Proof of a new colour decomposition for QCD amplitudes

Melia, Tom

doi:10.1007/JHEP12(2015)107

Title: Proof of a new colour decomposition for QCD amplitudes

Abstract

Recently, Johansson and Ochirov conjectured the form of a new colour decom-position for QCD tree-level amplitudes. This note provides a proof of that conjecture. The proof is based on ‘Mario World’ Feynman diagrams, which exhibit the hierarchical Dyck structure previously found to be very useful when dealing with multi-quark amplitudes.

Authors:

Melia, Tom ^[1]

Univ. of California, Berkeley, CA (United States). Department of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group

Publication Date:: Wed Dec 16 00:00:00 EST 2015

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1378664

Grant/Contract Number:: AC02-05CH11231

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: 2015; Journal Issue: 12; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Phenomenology; NLO Computations

Citation Formats


                    Melia, Tom. Proof of a new colour decomposition for QCD amplitudes.  United States: N. p., 2015. 
Web.  doi:10.1007/JHEP12(2015)107.

Copy to clipboard


                    Melia, Tom. Proof of a new colour decomposition for QCD amplitudes.  United States.  https://doi.org/10.1007/JHEP12(2015)107

Copy to clipboard


                    Melia, Tom. Wed .  
"Proof of a new colour decomposition for QCD amplitudes".  United States.  https://doi.org/10.1007/JHEP12(2015)107.  https://www.osti.gov/servlets/purl/1378664.

Copy to clipboard


                    
@article{osti_1378664,

  title        = {Proof of a new colour decomposition for QCD amplitudes},

  author       = {Melia, Tom},

  abstractNote = {Recently, Johansson and Ochirov conjectured the form of a new colour decom-position for QCD tree-level amplitudes. This note provides a proof of that conjecture. The proof is based on ‘Mario World’ Feynman diagrams, which exhibit the hierarchical Dyck structure previously found to be very useful when dealing with multi-quark amplitudes.},

  doi          = {10.1007/JHEP12(2015)107},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 12,

  volume       = 2015,

  place        = {United States},

  year         = {Wed Dec 16 00:00:00 EST 2015},

  month        = {Wed Dec 16 00:00:00 EST 2015}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/JHEP12(2015)107

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 18 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Pure gravities via color-kinematics duality for fundamental matter
journal, November 2015

Johansson, Henrik; Ochirov, Alexander
Journal of High Energy Physics, Vol. 2015, Issue 11
DOI: 10.1007/JHEP11(2015)046

Multigluon cross sections and 5-jet production at hadron colliders
journal, January 1989

Kleiss, Ronald; Kuijf, Hans
Nuclear Physics B, Vol. 312, Issue 3
DOI: 10.1016/0550-3213(89)90574-9

Numerical evaluation of virtual corrections to multi-jet production in massless QCD
journal, August 2013

Badger, Simon; Biedermann, Benedikt; Uwer, Peter
Computer Physics Communications, Vol. 184, Issue 8
DOI: 10.1016/j.cpc.2013.03.018

The six-gluon process as an example of Weyl-van der Waerden spinor calculus
journal, January 1987

Berends, F. A.; Giele, W.
Nuclear Physics B, Vol. 294
DOI: 10.1016/0550-3213(87)90604-3

The color structure of gluon emission
journal, November 1988

Mangano, Michelangelo
Nuclear Physics B, Vol. 309, Issue 3
DOI: 10.1016/0550-3213(88)90453-1

Colour decompositions of multi-quark one-loop QCD amplitudes
journal, February 2012

Ita, Harald; Ozeren, Kemal
Journal of High Energy Physics, Vol. 2012, Issue 2
DOI: 10.1007/JHEP02(2012)118

New color decompositions for gauge amplitudes at tree and loop level
journal, April 2000

Del Duca, Vittorio; Dixon, Lance; Maltoni, Fabio
Nuclear Physics B, Vol. 571, Issue 1-2
DOI: 10.1016/S0550-3213(99)00809-3

One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts
journal, September 2012

Ellis, R. Keith; Kunszt, Zoltan; Melnikov, Kirill
Physics Reports, Vol. 518, Issue 4-5
DOI: 10.1016/j.physrep.2012.01.008

One-loop corrections to two-quark three-gluon amplitudes
journal, March 1995

Bern, Zvi; Dixon, Lance; Kosower, David A.
Nuclear Physics B, Vol. 437, Issue 2
DOI: 10.1016/0550-3213(94)00542-M

Duality and multi-gluon scattering
journal, March 1988

Mangano, Michelangelo; Parke, Stephen; Xu, Zhan
Nuclear Physics B, Vol. 298, Issue 4
DOI: 10.1016/0550-3213(88)90001-6

Dyck words and multiquark primitive amplitudes
journal, July 2013

Melia, Tom
Physical Review D, Vol. 88, Issue 1
DOI: 10.1103/PhysRevD.88.014020

Proof of the fundamental BCJ relations for QCD amplitudes
journal, September 2015

de la Cruz, Leonardo; Kniss, Alexander; Weinzierl, Stefan
Journal of High Energy Physics, Vol. 2015, Issue 9
DOI: 10.1007/JHEP09(2015)197

Works referencing / citing this record:

Full Colour for Loop Amplitudes in Yang-Mills Theory
text, January 2016

Ochirov, Alexander; Page, Ben
arXiv
DOI: 10.48550/arxiv.1612.04366

Similar Records in DOE PAGES and OSTI.GOV collections:

Constructing QCD one-loop amplitudes

Conference Forde, Darren ; /SLAC /UCLA - Proceedings of Science

In the context of constructing one-loop amplitudes using a unitarity bootstrap approach we discuss a general systematic procedure for obtaining the coefficients of the scalar bubble and triangle integral functions of one-loop amplitudes. Coefficients are extracted after examining the behavior of the cut integrand as the unconstrained parameters of a specifically chosen parameterization of the cut loop momentum approach infinity. Measurements of new physics at the forthcoming experimental program at CERN's Large Hadron Collider (LHC) will require a precise understanding of processes at next-to-leading order (NLO). This places increased demands for the computation of new one-loop amplitudes. This in turnmore »« less
Full Text Available
Consistency of the Baryon-Multimeson Amplitudes for Large-{ital N}{sub {ital c}} QCD Feynman Diagrams

Journal Article Lam, C S ; Liu, K F - Physical Review Letters

We study the pion-baryon scattering process {pi}+B{r_arrow}(n{minus}1){pi}+B in a QCD theory with a large number (N{sub c} ) of colors. It is known that this scattering amplitude decreases with N{sub c} like N{sup 1{minus}n/2}{sub c} , and that its individual tree diagrams grow like N{sup n/2}{sub c} . The only way these two can be consistent is for n{minus}1 powers of N{sub c} to be canceled when the Feynman diagrams are summed. We prove this to be true in tree order for any n . {copyright} {ital 1997} {ital The American Physical Society}
https://doi.org/10.1103/PhysRevLett.79.597
Iteration of Planar Amplitudes inMaximally Supersymmetric Yang-Mills Theoryat Three Loops

Journal Article Bern, Zvi ; /UCLA ; Dixon, Lance J ; ... - Phys.Rev.D72:085001,2005

We compute the leading-color (planar) three-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 - 2{epsilon} dimensions, as a Laurent expansion about {epsilon} = 0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planarmore »« less
https://doi.org/10.1103/PhysRevD.72.085001

Full Text Available
Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond

Journal Article Bern, Zvi ; Dixon, Lance J ; Smirnov, Vladimir A ; ... - Physical Review. D, Particles Fields

We compute the leading-color (planar) three-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4-2{epsilon} dimensions, as a Laurent expansion about {epsilon}=0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N=4 amplitudes have an iterative structure.more »« less
https://doi.org/10.1103/PhysRevD.72.085001
All Tree-level Amplitudes in Massless QCD

Journal Article Dixon, Lance J. ; /CERN /SLAC ; Henn, Johannes M. ; ... - JHEP 1101:035,2011

We derive compact analytical formulae for all tree-level color-ordered gauge theory amplitudes involving any number of external gluons and up to three massless quark-anti-quark pairs. A general formula is presented based on the combinatorics of paths along a rooted tree and associated determinants. Explicit expressions are displayed for the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (NNMHV) gauge theory amplitudes. Our results are obtained by projecting the previously-found expressions for the super-amplitudes of the maximally supersymmetric Yang-Mills theory (N = 4 SYM) onto the relevant components yielding all gluon-gluino tree amplitudes in N = 4 SYM. We show howmore »« less
Full Text Available

Similar Records

Title: Proof of a new colour decomposition for QCD amplitudes

Abstract

Citation Formats

Pure gravities via color-kinematics duality for fundamental matter journal, November 2015

Multigluon cross sections and 5-jet production at hadron colliders journal, January 1989

Numerical evaluation of virtual corrections to multi-jet production in massless QCD journal, August 2013

The six-gluon process as an example of Weyl-van der Waerden spinor calculus journal, January 1987

The color structure of gluon emission journal, November 1988

Colour decompositions of multi-quark one-loop QCD amplitudes journal, February 2012

New color decompositions for gauge amplitudes at tree and loop level journal, April 2000

One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts journal, September 2012

One-loop corrections to two-quark three-gluon amplitudes journal, March 1995

Duality and multi-gluon scattering journal, March 1988

Dyck words and multiquark primitive amplitudes journal, July 2013

Proof of the fundamental BCJ relations for QCD amplitudes journal, September 2015

Full Colour for Loop Amplitudes in Yang-Mills Theory text, January 2016

Pure gravities via color-kinematics duality for fundamental matter
journal, November 2015

Multigluon cross sections and 5-jet production at hadron colliders
journal, January 1989

Numerical evaluation of virtual corrections to multi-jet production in massless QCD
journal, August 2013

The six-gluon process as an example of Weyl-van der Waerden spinor calculus
journal, January 1987

The color structure of gluon emission
journal, November 1988

Colour decompositions of multi-quark one-loop QCD amplitudes
journal, February 2012

New color decompositions for gauge amplitudes at tree and loop level
journal, April 2000

One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts
journal, September 2012

One-loop corrections to two-quark three-gluon amplitudes
journal, March 1995

Duality and multi-gluon scattering
journal, March 1988

Dyck words and multiquark primitive amplitudes
journal, July 2013

Proof of the fundamental BCJ relations for QCD amplitudes
journal, September 2015

Full Colour for Loop Amplitudes in Yang-Mills Theory
text, January 2016