Abstract
We use generalized elastic positivity bounds to constrain the parameter space of multi-field spin-2 effective field theories. These generalized bounds involve inelastic scattering amplitudes between particles with different masses, which contain kinematic singularities even in the t = 0 limit. We apply these bounds to the pseudo-linear spin-2 theory, the cycle spin-2 theory and the line spin-2 theory respectively. For the pseudo-linear theory, we exclude the remaining operators that are unconstrained by the usual elastic positivity bounds, thus excluding all the leading (or highest cutoff) interacting operators in the theory. For the cycle and line theory, our approach also provides new bounds on the Wilson coefficients previously unconstrained, bounding the parameter space in both theories to be a finite region (i.e., every Wilson coefficient being constrained from both sides). To help visualize these finite regions, we sample various cross sections of them and estimate the total volumes.
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References
C. de Rham, J.T. Deskins, A.J. Tolley and S.-Y. Zhou, Graviton Mass Bounds, Rev. Mod. Phys. 89 (2017) 025004 [arXiv:1606.08462] [INSPIRE].
E. Babichev et al., Heavy spin-2 Dark Matter, JCAP 09 (2016) 016 [arXiv:1607.03497] [INSPIRE].
L. Marzola, M. Raidal and F.R. Urban, Oscillating Spin-2 Dark Matter, Phys. Rev. D 97 (2018) 024010 [arXiv:1708.04253] [INSPIRE].
N. Bernal, M. Dutra, Y. Mambrini, K. Olive, M. Peloso and M. Pierre, Spin-2 Portal Dark Matter, Phys. Rev. D 97 (2018) 115020 [arXiv:1803.01866] [INSPIRE].
A. Gromov and D.T. Son, Bimetric Theory of Fractional Quantum Hall States, Phys. Rev. X 7 (2017) 041032 [Addendum ibid. 8 (2018) 019901] [arXiv:1705.06739] [INSPIRE].
M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond. A 173 (1939) 211 [INSPIRE].
D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of Massive Gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
S.F. Hassan and R.A. Rosen, Bimetric Gravity from Ghost-free Massive Gravity, JHEP 02 (2012) 126 [arXiv:1109.3515] [INSPIRE].
K. Hinterbichler and R.A. Rosen, Interacting Spin-2 Fields, JHEP 07 (2012) 047 [arXiv:1203.5783] [INSPIRE].
C. de Rham, Massive Gravity, Living Rev. Rel. 17 (2014) 7 [arXiv:1401.4173] [INSPIRE].
K. Hinterbichler, Theoretical Aspects of Massive Gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE].
A. Schmidt-May and M. von Strauss, Recent developments in bimetric theory, J. Phys. A 49 (2016) 183001 [arXiv:1512.00021] [INSPIRE].
C. de Rham, A.J. Tolley and S.-Y. Zhou, The Λ2 limit of massive gravity, JHEP 04 (2016) 188 [arXiv:1602.03721] [INSPIRE].
G. Gabadadze, Scale-up of Λ3: Massive gravity with a higher strong interaction scale, Phys. Rev. D 96 (2017) 084018 [arXiv:1707.01739] [INSPIRE].
L. Alberte, C. de Rham, A. Momeni, J. Rumbutis and A.J. Tolley, EFT of Interacting Spin-2 Fields, JHEP 01 (2020) 131 [arXiv:1910.05285] [INSPIRE].
J.H.C. Scargill, J. Noller and P.G. Ferreira, Cycles of interactions in multi-gravity theories, JHEP 12 (2014) 160 [arXiv:1410.7774] [INSPIRE].
C. de Rham and A.J. Tolley, Vielbein to the rescue? Breaking the symmetric vielbein condition in massive gravity and multigravity, Phys. Rev. D 92 (2015) 024024 [arXiv:1505.01450] [INSPIRE].
C. Cheung and G.N. Remmen, Positive Signs in Massive Gravity, JHEP 04 (2016) 002 [arXiv:1601.04068] [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Positivity Bounds for Massive Spin-1 and Spin-2 Fields, JHEP 03 (2019) 182 [arXiv:1804.10624] [INSPIRE].
B. Bellazzini, F. Riva, J. Serra and F. Sgarlata, Beyond Positivity Bounds and the Fate of Massive Gravity, Phys. Rev. Lett. 120 (2018) 161101 [arXiv:1710.02539] [INSPIRE].
J. Bonifacio, K. Hinterbichler and R.A. Rosen, Positivity constraints for pseudolinear massive spin-2 and vector Galileons, Phys. Rev. D 94 (2016) 104001 [arXiv:1607.06084] [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].
L. Alberte, C. de Rham, A. Momeni, J. Rumbutis and A.J. Tolley, Positivity Constraints on Interacting Spin-2 Fields, JHEP 03 (2020) 097 [arXiv:1910.11799] [INSPIRE].
L. Alberte, C. de Rham, A. Momeni, J. Rumbutis and A.J. Tolley, Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields, JHEP 07 (2020) 121 [arXiv:1912.10018] [INSPIRE].
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Positivity bounds for scalar field theories, Phys. Rev. D 96 (2017) 081702 [arXiv:1702.06134] [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, UV complete me: Positivity Bounds for Particles with Spin, JHEP 03 (2018) 011 [arXiv:1706.02712] [INSPIRE].
N. Arkani-Hamed, Y.-t. Huang and T.-C. Huang, Build the Wall and Drain the Swampland: the EFThedron, unpublished.
A.V. Manohar and V. Mateu, Dispersion Relation Bounds for ππ Scattering, Phys. Rev. D 77 (2008) 094019 [arXiv:0801.3222] [INSPIRE].
B. Bellazzini, Softness and amplitudes’ positivity for spinning particles, JHEP 02 (2017) 034 [arXiv:1605.06111] [INSPIRE].
A.J. Tolley, Z.-Y. Wang and S.-Y. Zhou, New positivity bounds from full crossing symmetry, arXiv:2011.02400 [INSPIRE].
B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau and F. Riva, Positive Moments for Scattering Amplitudes, arXiv:2011.00037 [INSPIRE].
S. Caron-Huot and V. Van Duong, Extremal Effective Field Theories, arXiv:2011.02957 [INSPIRE].
A. Guerrieri, J. Penedones and P. Vieira, S-matrix Bootstrap for Effective Field Theories: Massless Pions, arXiv:2011.02802 [INSPIRE].
C. Zhang and S.-Y. Zhou, Positivity bounds on vector boson scattering at the LHC, Phys. Rev. D 100 (2019) 095003 [arXiv:1808.00010] [INSPIRE].
Q. Bi, C. Zhang and S.-Y. Zhou, Positivity constraints on aQGC: carving out the physical parameter space, JHEP 06 (2019) 137 [arXiv:1902.08977] [INSPIRE].
K. Yamashita, C. Zhang and S.-Y. Zhou, Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings, JHEP 01 (2021) 095 [arXiv:2009.04490] [INSPIRE].
G.N. Remmen and N.L. Rodd, Flavor Constraints from Unitarity and Analyticity, Phys. Rev. Lett. 125 (2020) 081601 [arXiv:2004.02885] [INSPIRE].
G.N. Remmen and N.L. Rodd, Consistency of the Standard Model Effective Field Theory, JHEP 12 (2019) 032 [arXiv:1908.09845] [INSPIRE].
B. Bellazzini, F. Riva, J. Serra and F. Sgarlata, The other effective fermion compositeness, JHEP 11 (2017) 020 [arXiv:1706.03070] [INSPIRE].
B. Bellazzini and F. Riva, New phenomenological and theoretical perspective on anomalous ZZ and Zγ processes, Phys. Rev. D 98 (2018) 095021 [arXiv:1806.09640] [INSPIRE].
G.N. Remmen and N.L. Rodd, Signs, Spin, SMEFT: Positivity at Dimension Six, arXiv:2010.04723 [INSPIRE].
C. Zhang and S.-Y. Zhou, Convex Geometry Perspective on the (Standard Model) Effective Field Theory Space, Phys. Rev. Lett. 125 (2020) 201601 [arXiv:2005.03047] [INSPIRE].
B. Fuks, Y. Liu, C. Zhang and S.-Y. Zhou, Positivity in electron-positron scattering: testing the axiomatic quantum field theory principles and probing the existence of UV states, Chin. Phys. C 45 (2021) 023108 [arXiv:2009.02212] [INSPIRE].
J. Gu, L.-T. Wang and C. Zhang, An unambiguous test of positivity at lepton colliders, arXiv:2011.03055 [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Massive Galileon Positivity Bounds, JHEP 09 (2017) 072 [arXiv:1702.08577] [INSPIRE].
K. Hinterbichler, Ghost-Free Derivative Interactions for a Massive Graviton, JHEP 10 (2013) 102 [arXiv:1305.7227] [INSPIRE].
G. Cohen-Tannoudji, A. Morel and H. Navelet, Kinematical singularities, crossing matrix and kinematical constraints for two-body helicity amplitudes, Annals Phys. 46 (1968) 239 [INSPIRE].
J. Bonifacio, K. Hinterbichler and L.A. Johnson, Pseudolinear spin-2 interactions, Phys. Rev. D 99 (2019) 024037 [arXiv:1806.00483] [INSPIRE].
C. de Rham, S. Melville and A.J. Tolley, Improved Positivity Bounds and Massive Gravity, JHEP 04 (2018) 083 [arXiv:1710.09611] [INSPIRE].
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ArXiv ePrint: 2011.05190
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Wang, ZY., Zhang, C. & Zhou, SY. Generalized elastic positivity bounds on interacting massive spin-2 theories. J. High Energ. Phys. 2021, 217 (2021). https://doi.org/10.1007/JHEP04(2021)217
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DOI: https://doi.org/10.1007/JHEP04(2021)217