Abstract
Planar zeros are studied in the context of the five-point scattering amplitude for gauge bosons and gravitons. In the case of gauge theories, it is found that planar zeros are determined by an algebraic curve in the projective plane spanned by the three stereographic coordinates labelling the direction of the outgoing momenta. This curve depends on the values of six independent color structures. Considering the gauge group SU(N) with N = 2, 3, 5 and fixed color indices, the class of curves obtained gets broader by increasing the rank of the group. For the five-graviton scattering, on the other hand, we show that the amplitude vanishes whenever the process is planar, without imposing further kinematic conditions. A rationale for this result is provided using color-kinematics duality.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Elvang and Y.-t. Huang, Scattering Amplitudes, arXiv:1308.1697 [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
S. Stieberger and T.R. Taylor, Graviton as a Pair of Collinear Gauge Bosons, Phys. Lett. B 739 (2014) 457 [arXiv:1409.4771] [INSPIRE].
S. Stieberger and T.R. Taylor, Graviton Amplitudes from Collinear Limits of Gauge Amplitudes, Phys. Lett. B 744 (2015) 160 [arXiv:1502.00655] [INSPIRE].
A. Sabio Vera and M.A. Vazquez-Mozo, The Double Copy Structure of Soft Gravitons, JHEP 03 (2015) 070 [arXiv:1412.3699] [INSPIRE].
R.W. Brown, Understanding something about nothing: Radiation zeros, AIP Conf. Proc. 350 (1995) 261 [hep-th/9506018] [INSPIRE].
T. Han, Exact and approximate radiation amplitude zeros: Phenomenological aspects, AIP Conf. Proc. 350 (1995) 224 [hep-ph/9506286] [INSPIRE].
U. Baur and R.W. Brown, Zero zeros after all these (20) years, hep-ph/9909522 [INSPIRE].
R.W. Brown, D. Sahdev and K.O. Mikaelian, W ± Z 0 and W ± γ Pair Production in νe, pp and \( \overline{p}p \) Collisions, Phys. Rev. D 20 (1979) 1164 [INSPIRE].
K.O. Mikaelian, M.A. Samuel and D. Sahdev, The Magnetic Moment of Weak Bosons Produced in pp and \( \overline{p}p \) Collisions, Phys. Rev. Lett. 43 (1979) 746 [INSPIRE].
D0 collaboration, V.M. Abazov et al., First study of the radiation-amplitude zero in Wγ production and limits on anomalous WWγ couplings at \( \sqrt{s}=1.96 \) TeV, Phys. Rev. Lett. 100 (2008) 241805 [arXiv:0803.0030] [INSPIRE].
CMS collaboration, Measurement of the Wγ and Zγ inclusive cross sections in pp collisions at \( \sqrt{s}=7 \) TeV and limits on anomalous triple gauge boson couplings, Phys. Rev. D 89 (2014) 092005 [arXiv:1308.6832] [INSPIRE].
G. Passarino, Radiation zeros and gravity, Nucl. Phys. B 241 (1984) 48 [INSPIRE].
M. Heyssler and W.J. Stirling, Radiation zeros at HERA: More about nothing, Eur. Phys. J. C 4 (1998) 289 [hep-ph/9707373] [INSPIRE].
M. Heyssler and W.J. Stirling, Radiation zeros in high-energy e + e − annihilation into hadrons, Eur. Phys. J. C 5 (1998) 475 [hep-ph/9712314] [INSPIRE].
I. Rodriguez and O.A. Sampayo, Tau anomalous couplings and radiation zeros in the \( {e}^{+}{e}^{-}\to \tau \overline{\tau}\gamma \) process, hep-ph/0312316 [INSPIRE].
L.A. Harland-Lang, Planar radiation zeros in five-parton QCD amplitudes, JHEP 05 (2015) 146 [arXiv:1503.06798] [INSPIRE].
R. Kleiss and H. Kuijf, Multi-Gluon Cross-sections and Five Jet Production at Hadron Colliders, Nucl. Phys. B 312 (1989) 616 [INSPIRE].
B. Kol and R. Shir, Color structures and permutations, JHEP 11 (2014) 020 [arXiv:1403.6837] [INSPIRE].
S.J. Parke and T.R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].
D.H. Sattinger and O.L. Weaver, Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics, Springer Verlag (1986).
R.N. Mohapatra, Unification and Supersymmetry: The Frontiers of Quark-Lepton Physics, third edition, Springer Verlag (2003).
F.A. Berends, W.T. Giele and H. Kuijf, On relations between multi-gluon and multigraviton scattering, Phys. Lett. B 211 (1988) 91 [INSPIRE].
T. He, P. Mitra and A. Strominger, 2D Kac-Moody Symmetry of 4D Yang-Mills Theory, arXiv:1503.02663 [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1607.04605
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Jiménez, D.M., Vera, A.S. & Vázquez-Mozo, M.Á. Planar zeros in gauge theories and gravity. J. High Energ. Phys. 2016, 6 (2016). https://doi.org/10.1007/JHEP09(2016)006
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2016)006