Abstract
It is well known that the MHV action, i.e. the action containing all the maximally helicity violating vertices, is alone not sufficient for loop computations. In order to develop loop contributions systematically and to ensure that there are no missing terms, we propose to formulate the quantum MHV action via one-loop effective action approach. The quadratic field fluctuations in the light cone Yang-Mills theory are explicitly integrated, followed by the classical canonical field transformation. We test the approach by calculating one loop (++++) and (+++) amplitudes, i.e. amplitudes that cannot be calculated from ordinary MHV action. Such an approach can be further used to unambiguously define loop corrections in other theories related to Yang-Mills theory by field transformations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.J. Parke and T.R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].
F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, On-Shell Methods in Perturbative QCD, Annals Phys. 322 (2007) 1587 [arXiv:0704.2798] [INSPIRE].
A. Brandhuber and M. Vincon, MHV One-Loop Amplitudes in Yang-Mills from Generalized Unitarity, JHEP 11 (2008) 078 [arXiv:0805.3310] [INSPIRE].
W.B. Perkins and E. Warrick, Unitarity methods for one-loop QCD amplitudes, Nucl. Phys. B Proc. Suppl. 186 (2009) 82 [INSPIRE].
Z. Bern and Y.-t. Huang, Basics of Generalized Unitarity, J. Phys. A 44 (2011) 454003 [arXiv:1103.1869] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
K. Risager, A Direct proof of the CSW rules, JHEP 12 (2005) 003 [hep-th/0508206] [INSPIRE].
N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, A.B. Goncharov, A. Postnikov and J. Trnka, Grassmannian Geometry of Scattering Amplitudes, Cambridge University Press (2016), https://doi.org/10.1017/CBO9781316091548 [arXiv:1212.5605] [INSPIRE].
W.-J. Zhang, J.-B. Wu and C.-J. Zhu, Cachazo-Svrček-Witten rules for tree-level gluonic amplitudes revisited, Sci. China Phys. Mech. Astron. 65 (2022) 240011 [arXiv:2110.04569] [INSPIRE].
P. Mansfield, The Lagrangian origin of MHV rules, JHEP 03 (2006) 037 [hep-th/0511264] [INSPIRE].
J.H. Ettle and T.R. Morris, Structure of the MHV-rules Lagrangian, JHEP 08 (2006) 003 [hep-th/0605121] [INSPIRE].
J.H. Ettle, C.-H. Fu, J.P. Fudger, P.R.W. Mansfield and T.R. Morris, S-matrix equivalence theorem evasion and dimensional regularisation with the canonical MHV Lagrangian, JHEP 05 (2007) 011 [hep-th/0703286] [INSPIRE].
A. Brandhuber, B. Spence and G. Travaglini, Amplitudes in Pure Yang-Mills and MHV Diagrams, JHEP 02 (2007) 088 [hep-th/0612007] [INSPIRE].
A. Brandhuber, B. Spence, G. Travaglini and K. Zoubos, One-loop MHV Rules and Pure Yang-Mills, JHEP 07 (2007) 002 [arXiv:0704.0245] [INSPIRE].
J.H. Ettle, T.R. Morris and Z. Xiao, The MHV QCD Lagrangian, JHEP 08 (2008) 103 [arXiv:0805.0239] [INSPIRE].
H. Feng and Y.-t. Huang, MHV Lagrangian for N = 4 super Yang-Mills, JHEP 04 (2009) 047 [hep-th/0611164] [INSPIRE].
P. Kotko and A.M. Stasto, Wilson lines in the MHV action, JHEP 09 (2017) 047 [arXiv:1706.00052] [INSPIRE].
H. Kakkad, P. Kotko and A. Stasto, Exploring straight infinite Wilson lines in the self-dual and the MHV Lagrangians, Phys. Rev. D 102 (2020) 094026 [arXiv:2006.16188] [INSPIRE].
Z. Bern and D.A. Kosower, The Computation of loop amplitudes in gauge theories, Nucl. Phys. B 379 (1992) 451 [INSPIRE].
Z. Kunszt, A. Signer and Z. Trócsányi, One loop helicity amplitudes for all 2 → 2 processes in QCD and N = 1 supersymmetric Yang-Mills theory, Nucl. Phys. B 411 (1994) 397 [hep-ph/9305239] [INSPIRE].
W. Bardeen, Self-dual Yang-Mills theory, integrability and multiparton amplitudes, Prog. Theor. Phys. Suppl. (1996) 1.
G. Chalmers and W. Siegel, The Selfdual sector of QCD amplitudes, Phys. Rev. D 54 (1996) 7628 [hep-th/9606061] [INSPIRE].
D. Cangemi, Selfdual Yang-Mills theory and one loop like - helicity QCD multi - gluon amplitudes, Nucl. Phys. B 484 (1997) 521 [hep-th/9605208] [INSPIRE].
A.A. Rosly and K.G. Selivanov, On amplitudes in selfdual sector of Yang-Mills theory, Phys. Lett. B 399 (1997) 135 [hep-th/9611101] [INSPIRE].
R. Monteiro and D. O’Connell, The Kinematic Algebra From the Self-Dual Sector, JHEP 07 (2011) 007 [arXiv:1105.2565] [INSPIRE].
H. Kakkad, P. Kotko and A. Stasto, A new Wilson line-based action for gluodynamics, JHEP 07 (2021) 187 [arXiv:2102.11371] [INSPIRE].
J. Scherk and J.H. Schwarz, Gravitation in the Light - Cone Gauge, Gen. Rel. Grav. 6 (1975) 537 [INSPIRE].
C. Schwinn and S. Weinzierl, Scalar diagrammatic rules for Born amplitudes in QCD, JHEP 05 (2005) 006 [hep-th/0503015] [INSPIRE].
F.A. Berends and W.T. Giele, Recursive Calculations for Processes with n Gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE].
J. Bedford, A. Brandhuber, B.J. Spence and G. Travaglini, Non-supersymmetric loop amplitudes and MHV vertices, Nucl. Phys. B 712 (2005) 59 [hep-th/0412108] [INSPIRE].
C.-H. Fu, J. Fudger, P.R.W. Mansfield, T.R. Morris and Z. Xiao, S-matrix equivalence restored, JHEP 06 (2009) 035 [arXiv:0902.1906] [INSPIRE].
R. Boels and C. Schwinn, Deriving CSW rules for massive scalar legs and pure Yang-Mills loops, JHEP 07 (2008) 007 [arXiv:0805.1197] [INSPIRE].
H. Elvang, D.Z. Freedman and M. Kiermaier, Integrands for QCD rational terms and N = 4 SYM from massive CSW rules, JHEP 06 (2012) 015 [arXiv:1111.0635] [INSPIRE].
Z. Bern, G. Chalmers, L.J. Dixon and D.A. Kosower, One loop N gluon amplitudes with maximal helicity violation via collinear limits, Phys. Rev. Lett. 72 (1994) 2134 [hep-ph/9312333] [INSPIRE].
D. Chakrabarti, J. Qiu and C.B. Thorn, Scattering of glue by glue on the light-cone worldsheet. I. Helicity non-conserving amplitudes, Phys. Rev. D 72 (2005) 065022 [hep-th/0507280] [INSPIRE].
D. Chakrabarti, J. Qiu and C.B. Thorn, Scattering of glue by glue on the light-cone worldsheet. II. Helicity conserving amplitudes, Phys. Rev. D 74 (2006) 045018 [Erratum ibid. 76 (2007) 089901] [hep-th/0602026] [INSPIRE].
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
K. Bardakci and C.B. Thorn, A World sheet description of large Nc quantum field theory, Nucl. Phys. B 626 (2002) 287 [hep-th/0110301] [INSPIRE].
C.B. Thorn, Notes on one-loop calculations in light-cone gauge, hep-th/0507213 [INSPIRE].
M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory, Addison-Wesley, Reading, U.S.A. (1995).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2208.11000
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Kakkad, H., Kotko, P. & Stasto, A. One-Loop effective action approach to quantum MHV theory. J. High Energ. Phys. 2022, 132 (2022). https://doi.org/10.1007/JHEP11(2022)132
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2022)132