Abstract
We present a map between the tree-level Standard Model Effective Theory (SMEFT) in the Warsaw basis and massive on-shell amplitudes. As a first step, we focus on the electroweak sector without fermions. We describe the Feynman rules for a particular choice of input scheme and compare them with the 3-point massive amplitudes in the broken phase. Thereby we fix an on-shell basis which allows us to study scattering amplitudes with recursion relations. We hope to open up new avenues of exploration to a complete formulation of massive EFTs in the on-shell language.
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].
S. Dittmaier, Weyl-van der Waerden formalism for helicity amplitudes of massive particles, Phys. Rev.D 59 (1998) 016007 [hep-ph/9805445] [INSPIRE].
D. Forde and D.A. Kosower, All-multiplicity amplitudes with massive scalars, Phys. Rev.D 73 (2006) 065007 [hep-th/0507292] [INSPIRE].
G. Rodrigo, Multigluonic scattering amplitudes of heavy quarks, JHEP09 (2005) 079 [hep-ph/0508138] [INSPIRE].
C. Schwinn and S. Weinzierl, SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks, JHEP03 (2006) 030 [hep-th/0602012] [INSPIRE].
C. Schwinn and S. Weinzierl, On-shell recursion relations for all Born QCD amplitudes, JHEP04 (2007) 072 [hep-ph/0703021] [INSPIRE].
A. Hall, Massive quark-gluon scattering amplitudes at tree level, Phys. Rev.D 77 (2008) 025011 [arXiv:0710.1300] [INSPIRE].
R.H. Boels and C. Schwinn, On-shell supersymmetry for massive multiplets, Phys. Rev.D 84 (2011) 065006 [arXiv:1104.2280] [INSPIRE].
R. Britto and A. Ochirov, On-shell recursion for massive fermion currents, JHEP01 (2013) 002 [arXiv:1210.1755] [INSPIRE].
T. Cohen, H. Elvang and M. Kiermaier, On-shell constructibility of tree amplitudes in general field theories, JHEP04 (2011) 053 [arXiv:1010.0257] [INSPIRE].
M. Kiermaier, The Coulomb-branch S-matrix from massless amplitudes, arXiv: 1105.5385 [INSPIRE].
N. Craig, H. Elvang, M. Kiermaier and T. Slatyer, Massive amplitudes on the Coulomb branch of N = 4 SYM, JHEP12 (2011) 097 [arXiv:1104.2050] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, Scattering amplitudes for all masses and spins, arXiv:1709.04891 [INSPIRE].
A. Herderschee, S. Koren and T. Trott, Massive on-shell supersymmetric scattering amplitudes, JHEP10 (2019) 092 [arXiv:1902.07204] [INSPIRE].
A. Herderschee, S. Koren and T. Trott, Constructing N = 4 Coulomb branch superamplitudes, JHEP08 (2019) 107 [arXiv:1902.07205] [INSPIRE].
A. Ochirov, Helicity amplitudes for QCD with massive quarks, JHEP04 (2018) 089 [arXiv:1802.06730] [INSPIRE].
N. Christensen and B. Field, Constructive Standard Model, Phys. Rev.D 98 (2018) 016014 [arXiv:1802.00448] [INSPIRE].
M.-Z. Chung, Y.-T. Huang, J.-W. Kim and S. Lee, The simplest massive S-matrix: from minimal coupling to black holes, JHEP04 (2019) 156 [arXiv:1812.08752] [INSPIRE].
A. Guevara, A. Ochirov and J. Vines, Scattering of spinning black holes from exponentiated soft factors, JHEP09 (2019) 056 [arXiv:1812.06895] [INSPIRE].
N. Moy nihan and J. Murugan, Comments on scattering in massive gravity, vDVZ and BCFW, Class. Quant. Grav.35 (2018) 155005 [arXiv:1711.03956] [INSPIRE].
I. Brivio and M. Trott, The Standard Model as an effective field theory, Phys. Rept.793 (2019) 1 [arXiv:1706.08945] [INSPIRE].
R. Aoude and C.S. Machado, in preparation.
B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the Standard Model Lagrangian, JHEP10 (2010) 085 [arXiv:1008.4884] [INSPIRE].
B. Henning, X. Lu, T. Melia and H. Murayama, Hilbert series and operator bases with derivatives in effective field theories, Commun. Math. Phys.347 (2016) 363 [arXiv:1507.07240] [INSPIRE].
B. Henning, X. Lu, T. Melia and H. Murayama, 2, 84, 30, 993, 560, 15456, 11962, 261485, .. .: higher dimension operators in the SM EFT, JHEP08 (2017) 016 [Erratum ibid.09 (2019) 019] [arXiv:1512.03433] [INSPIRE].
B. Henning and T. Melia, Constructing effective field theories via their harmonics, Phys. Rev.D 100 (2019) 016015 [arXiv:1902.06754] [INSPIRE].
L.J. Dixon, E.W.N. Glover and V.V. Khoze, MHV rules for Higgs plus multi-gluon amplitudes, JHEP12 (2004) 015 [hep-th/0411092] [INSPIRE].
L.J. Dixon and Y. Shadmi, Testing gluon selfinteractions in three jet events at hadron colliders, Nucl. Phys.B 423 (1994) 3 [Erratum ibid.B 452 (1995) 724] [hep-ph/9312363] [INSPIRE].
A. Azatov, R. Contino, C.S. Machado and F. Riva, Helicity selection rules and noninterference for BSM amplitudes, Phys. Rev.D 95 (2017) 065014 [arXiv:1607.05236] [INSPIRE].
C. Cheung and C.-H. Shen, Nonrenormalization theorems without supersymmetry, Phys. Rev. Lett.115 (2015) 071601 [arXiv:1505.01844] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, On-shell recursion relations for effective field theories, Phys. Rev. Lett.116 (2016) 041601 [arXiv:1509.03309] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, A periodic table of effective field theories, JHEP02 (2017) 020 [arXiv:1611.03137] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen, J. Trnka and C. Wen, Vector effective field theories from soft limits, Phys. Rev. Lett.120 (2018) 261602 [arXiv: 1801.01496] [INSPIRE].
H. Elvang, M. Hadjiantonis, C.R.T. Jones and S. Paranjape, Soft bootstrap and supersymmetry, JHEP01 (2019) 195 [arXiv:1806.06079] [INSPIRE].
C. Cheung, C.-H. Shen and J. Trnka, Simple recursion relations for general field theories, JHEP06 (2015) 118 [arXiv:1502.05057] [INSPIRE].
Y. Shadmi and Y. Weiss, Effective field theory amplitudes the on-shell way: scalar and vector couplings to gluons, JHEP02 (2019) 165 [arXiv:1809.09644] [INSPIRE].
T. Ma, J. Shu and M.-1. Xiao, Standard Model effective field theory from on-shell amplitudes, arXiv:1902.06752 [INSPIRE].
G. Durieux, T. Kitahara, Y. Shadmi and Y. Weiss, The electroweak effective field theory from on-shell amplitudes, arXiv:1909.10551 [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].
F. Cachazo, P. Svrcek and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP09 (2004) 006 [hep-th/0403047] [INSPIRE].
D.A. McGady and L. Rodina, Higher-spin massless S-matrices in four-dimensions, Phys. Rev.D 90 (2014) 084048 [arXiv:1311.2938] [INSPIRE].
R. Alonso, E.E. Jenkins and A.V. Manohar, Holomorphy without supersymmetry in the Standard Model effective field theory, Phys. Lett.B 739 (2014) 95 [arXiv:1409.0868] [INSPIRE].
H.K. Dreiner, H.E. Haber and S.P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys. Rept.494 (2010) 1 [arXiv:0812.1594] [INSPIRE].
E. Conde and A. Marzolla, Lorentz constraints on massive three-point amplitudes, JHEP09 (2016) 041 [arXiv:1601.08113] [INSPIRE].
A. Dedes, W. Materkowska, M. Paraskevas, J. Rosiek and K. Suxho, Feynman rules for the Standard Model effective field theory in Re-gauges, JHEP06 (2017) 143 [arXiv:1704.03888] [INSPIRE].
B. Feng and M. Luo, An introduction to on-shell recursion relations, Front. Phys. (Beijing)7 (2012) 533 [arXiv:1111.5759] [INSPIRE].
S.D. Badger, E.W.N. Glover, V.V. Khoze and P. Svrcek, Recursion relations for gauge theory amplitudes with massive particles, JHEP07 (2005) 025 [hep-th/0504159] [INSPIRE].
S.D. Badger, E.W.N. Glover and V.V. Khoze, Recursion relations for gauge theory amplitudes with massive vector bosons and fermions, JHEP01 (2006) 066 [hep-th/0507161] [INSPIRE].
C. Cheung, On-shell recursion relations for generic theories, JHEP03 (2010) 098 [arXiv:0808.0504] [INSPIRE].
K. Zhou and C. Qiao, General tree-level amplitudes by factorization limits, Eur. Phys. J.C 75 (2015) 163 [arXiv:1410.5042] [INSPIRE].
A. Falkowski and R. Rattazzi, Which EFT, JHEP10 (2019) 255 [arXiv:1902.05936] [INSPIRE].
S. Chang and M.A. Luty, The Higgs trilinear coupling and the scale of new physics, arXiv:1902.05556 [INSPIRE].
R. Alonso, E.E. Jenkins and A.V. Manohar, A geometric formulation of Higgs effective field theory: measuring the curvature of scalar field space, Phys. Lett.B 754 (2016) 335 [arXiv:1511.00724] [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: 1905.11433
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Aoude, R., Machado, C.S. The rise of SMEFT on-shell amplitudes. J. High Energ. Phys. 2019, 58 (2019). https://doi.org/10.1007/JHEP12(2019)058
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2019)058