Abstract
The purely on-shell approach to effective field theories requires the construction of independent contact terms. Employing the little-group-covariant massive-spinor formalism, we present the first systematic derivation of independent four-point contact terms involving massive scalars, spin-1/2 fermions, and vectors. Independent three-point amplitudes are also listed for massive particles up to spin-3. We make extensive use of the simple relations between massless and massive amplitudes in this formalism. Our general results are specialized to the (broken-phase) particle content of the electroweak sector of the standard model. The (anti)symmetrization among identical particles is then accounted for. This work opens the way for the on-shell computation of massive four-point amplitudes.
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References
C. Cheung and C.-H. Shen, Nonrenormalization theorems without supersymmetry, Phys. Rev. Lett. 115 (2015) 071601 [arXiv:1505.01844] [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].
Z. Bern, J. Parra-Martinez and E. Sawyer, Nonrenormalization and operator mixing via on-shell methods, Phys. Rev. Lett. 124 (2020) 051601 [arXiv:1910.05831] [INSPIRE].
Z. Bern, J. Parra-Martinez and E. Sawyer, Structure of two-loop SMEFT anomalous dimensions via on-shell methods, JHEP 10 (2020) 211 [arXiv:2005.12917] [INSPIRE].
M. Jiang, T. Ma and J. Shu, Renormalization group evolution from on-shell SMEFT, arXiv:2005.10261 [INSPIRE].
J. Elias Miró, J. Ingoldby and M. Riembau, EFT anomalous dimensions from the S-matrix, JHEP 09 (2020) 163 [arXiv:2005.06983] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, Scattering amplitudes for all masses and spins, arXiv:1709.04891 [INSPIRE].
E. Conde and A. Marzolla, Lorentz constraints on massive three-point amplitudes, JHEP 09 (2016) 041 [arXiv:1601.08113] [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, Operator bases, S-matrices, and their partition functions, JHEP 10 (2017) 199 [arXiv:1706.08520] [INSPIRE].
Y. Shadmi and Y. Weiss, Effective field theory amplitudes the on-shell way: scalar and vector couplings to gluons, JHEP 02 (2019) 165 [arXiv:1809.09644] [INSPIRE].
B. Henning and T. Melia, Constructing effective field theories via their harmonics, Phys. Rev. D 100 (2019) 016015 [arXiv:1902.06754] [INSPIRE].
B. Henning and T. Melia, Conformal-helicity duality & the Hilbert space of free CFTs, arXiv:1902.06747 [INSPIRE].
R. Aoude and C.S. Machado, The rise of SMEFT on-shell amplitudes, JHEP 12 (2019) 058 [arXiv:1905.11433] [INSPIRE].
G. Durieux, T. Kitahara, Y. Shadmi and Y. Weiss, The electroweak effective field theory from on-shell amplitudes, JHEP 01 (2020) 119 [arXiv:1909.10551] [INSPIRE].
G. Durieux and C.S. Machado, Enumerating higher-dimensional operators with on-shell amplitudes, Phys. Rev. D 101 (2020) 095021 [arXiv:1912.08827] [INSPIRE].
T. Ma, J. Shu and M.-L. Xiao, Standard Model effective field theory from on-shell amplitudes, arXiv:1902.06752 [INSPIRE].
A. Falkowski, Bases of massless EFTs via momentum twistors, arXiv:1912.07865 [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].
T. Cohen, H. Elvang and M. Kiermaier, On-shell constructibility of tree amplitudes in general field theories, JHEP 04 (2011) 053 [arXiv:1010.0257] [INSPIRE].
R. Franken and C. Schwinn, On-shell constructibility of Born amplitudes in spontaneously broken gauge theories, JHEP 02 (2020) 073 [arXiv:1910.13407] [INSPIRE].
A. Falkowski and C.S. Machado, Soft matters, or the recursions with massive spinors, arXiv:2005.08981 [INSPIRE].
B. Bachu and A. Yelleshpur, On-shell electroweak sector and the Higgs mechanism, JHEP 08 (2020) 039 [arXiv:1912.04334] [INSPIRE].
N. Christensen and B. Field, Constructive Standard Model, Phys. Rev. D 98 (2018) 016014 [arXiv:1802.00448] [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].
R. Alonso, E.E. Jenkins and A.V. Manohar, Geometry of the scalar sector, JHEP 08 (2016) 101 [arXiv:1605.03602] [INSPIRE].
A. Helset, A. Martin and M. Trott, The geometric Standard Model effective field theory, JHEP 03 (2020) 163 [arXiv:2001.01453] [INSPIRE].
T. Cohen, N. Craig, X. Lu and D. Sutherland, Is SMEFT enough?, arXiv:2008.08597 [INSPIRE].
M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning conformal correlators, JHEP 11 (2011) 071 [arXiv:1107.3554] [INSPIRE].
M.L. Mangano and S.J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [INSPIRE].
V. Schomerus, E. Sobko and M. Isachenkov, Harmony of spinning conformal blocks, JHEP 03 (2017) 085 [arXiv:1612.02479] [INSPIRE].
P. Kravchuk and D. Simmons-Duffin, Counting conformal correlators, JHEP 02 (2018) 096 [arXiv:1612.08987] [INSPIRE].
J. Bonifacio and K. Hinterbichler, Bounds on amplitudes in effective theories with massive spinning particles, Phys. Rev. D 98 (2018) 045003 [arXiv:1804.08686] [INSPIRE].
R.H. Boels and H. Lüo, A minimal approach to the scattering of physical massless bosons, JHEP 05 (2018) 063 [arXiv:1710.10208] [INSPIRE].
E.W. Glover and M.E. Tejeda-Yeomans, Two loop QCD helicity amplitudes for massless quark massless gauge boson scattering, JHEP 06 (2003) 033 [hep-ph/0304169] [INSPIRE].
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ArXiv ePrint: 2008.09652
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Durieux, G., Kitahara, T., Machado, C.S. et al. Constructing massive on-shell contact terms. J. High Energ. Phys. 2020, 175 (2020). https://doi.org/10.1007/JHEP12(2020)175
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DOI: https://doi.org/10.1007/JHEP12(2020)175