Abstract
At sufficiently high energies the production of a very large number of particles is kinematically allowed. However, it is well-known that already in the simplest case of a weakly-coupled massive λφ4 theory, n-particle amplitudes become non-perturbative in the limit where n scales with energy. In this case, the effective expansion parameter, λn, is no longer small and the perturbative approach breaks down. In general, the associated n-particle production rates were argued to be described by an exponential that, depending on the specifics of the underlying Quantum Field Theory model, could be either growing or decaying in the large-n regime. We investigate such processes in general settings of Effective Field Theory (EFT), involving arbitrary higher-dimensional operators of φ. We perform the resummation of all leading loop corrections arising from EFT vertices for amplitudes at the multiparticle threshold. We find that the net effect of higher-dimensional operators amounts to an exponentially growing factor. We show that if an exponential growth was already generated by the renormalizable interactions, it would then be further enhanced by the EFT contributions. On the other hand, if the multiparticle rates computed in the renormalizable part of the theory were suppressed, this suppression would not be lifted in the EFT.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G.F. Giudice, Naturally speaking: the naturalness criterion and physics at the LHC, arXiv:0801.2562 [INSPIRE].
D.J.E. Callaway, Triviality pursuit: can elementary scalar particles exist?, Phys. Rept. 167 (1988) 241 [INSPIRE].
V.V. Khoze and J. Reiness, Review of the semiclassical formalism for multiparticle production at high energies, Phys. Rept. 822 (2019) 1 [arXiv:1810.01722] [INSPIRE].
J.M. Cornwall, On the high-energy behavior of weakly coupled gauge theories, Phys. Lett. B 243 (1990) 271 [INSPIRE].
H. Goldberg, Breakdown of perturbation theory at tree level in theories with scalars, Phys. Lett. B 246 (1990) 445 [INSPIRE].
L.S. Brown, Summing tree graphs at threshold, Phys. Rev. D 46 (1992) R4125 [hep-ph/9209203] [INSPIRE].
M.B. Voloshin, Multiparticle amplitudes at zero energy and momentum in scalar theory, Nucl. Phys. B 383 (1992) 233 [INSPIRE].
E.N. Argyres, R.H.P. Kleiss and C.G. Papadopoulos, Amplitude estimates for multi-Higgs production at high-energies, Nucl. Phys. B 391 (1993) 42 [INSPIRE].
M.B. Voloshin, Summing one loop graphs at multiparticle threshold, Phys. Rev. D 47 (1993) R357 [hep-ph/9209240] [INSPIRE].
B.H. Smith, Summing one loop graphs in a theory with broken symmetry, Phys. Rev. D 47 (1993) 3518 [hep-ph/9209287] [INSPIRE].
M.V. Libanov, V.A. Rubakov, D.T. Son and S.V. Troitsky, Exponentiation of multiparticle amplitudes in scalar theories, Phys. Rev. D 50 (1994) 7553 [hep-ph/9407381] [INSPIRE].
V.V. Khoze, Multiparticle Higgs and vector boson amplitudes at threshold, JHEP 07 (2014) 008 [arXiv:1404.4876] [INSPIRE].
D.T. Son, Semiclassical approach for multiparticle production in scalar theories, Nucl. Phys. B 477 (1996) 378 [hep-ph/9505338] [INSPIRE].
V.V. Khoze, Multiparticle production in the large λn limit: realising Higgsplosion in a scalar QFT, JHEP 06 (2017) 148 [arXiv:1705.04365] [INSPIRE].
S.V. Demidov and B.R. Farkhtdinov, Numerical study of multiparticle scattering in λϕ4 theory, JHEP 11 (2018) 068 [arXiv:1806.10996] [INSPIRE].
S.V. Demidov, B.R. Farkhtdinov and D.G. Levkov, Numerical study of multiparticle production in ϕ4 theory: comparison with analytical results, JETP Lett. 114 (2021) 649 [Pisma Zh. Eksp. Teor. Fiz. 114 (2021) 723] [arXiv:2111.04760] [INSPIRE].
M.B. Voloshin, Estimate of the onset of nonperturbative particle production at high-energy in a scalar theory, Phys. Lett. B 293 (1992) 389 [INSPIRE].
J. Jaeckel and V.V. Khoze, Upper limit on the scale of new physics phenomena from rising cross sections in high multiplicity Higgs and vector boson events, Phys. Rev. D 91 (2015) 093007 [arXiv:1411.5633] [INSPIRE].
V.V. Khoze and M. Spannowsky, Higgsplosion: solving the hierarchy problem via rapid decays of heavy states into multiple Higgs bosons, Nucl. Phys. B 926 (2018) 95 [arXiv:1704.03447] [INSPIRE].
V.V. Khoze and M. Spannowsky, Higgsploding universe, Phys. Rev. D 96 (2017) 075042 [arXiv:1707.01531] [INSPIRE].
V.V. Khoze, J. Reiness, M. Spannowsky and P. Waite, Precision measurements for the higgsploding standard model, J. Phys. G 46 (2019) 065004 [arXiv:1709.08655] [INSPIRE].
V.V. Khoze, J. Reiness, J. Scholtz and M. Spannowsky, A higgsploding theory of dark matter, arXiv:1803.05441 [INSPIRE].
A. Belyaev, F. Bezrukov, C. Shepherd and D. Ross, Problems with higgsplosion, Phys. Rev. D 98 (2018) 113001 [arXiv:1808.05641] [INSPIRE].
A. Monin, Inconsistencies of higgsplosion, arXiv:1808.05810 [INSPIRE].
V.V. Khoze and M. Spannowsky, Consistency of higgsplosion in localizable QFT, Phys. Lett. B 790 (2019) 466 [arXiv:1809.11141] [INSPIRE].
M.V. Libanov, D.T. Son and S.V. Troitsky, Exponentiation of multiparticle amplitudes in scalar theories. 2. Universality of the exponent, Phys. Rev. D 52 (1995) 3679 [hep-ph/9503412] [INSPIRE].
S. Schenk, The breakdown of resummed perturbation theory at high energies, JHEP 03 (2022) 100 [arXiv:2109.00549] [INSPIRE].
J. Jaeckel and S. Schenk, Exploring high multiplicity amplitudes in quantum mechanics, Phys. Rev. D 98 (2018) 096007 [arXiv:1806.01857] [INSPIRE].
J. Jaeckel and S. Schenk, Exploring high multiplicity amplitudes: the quantum mechanics analogue of the spontaneously broken case, Phys. Rev. D 99 (2019) 056010 [arXiv:1811.12116] [INSPIRE].
S. Schenk, How many Higgs bosons does it take: consistency of scalar field theories at high energies, Ph.D. thesis, University of Heidelberg, Heidelberg, Germany (2019).
A.S. Gorsky and M.B. Voloshin, Nonperturbative production of multiboson states and quantum bubbles, Phys. Rev. D 48 (1993) 3843 [hep-ph/9305219] [INSPIRE].
V.V. Khoze, Semiclassical computation of quantum effects in multiparticle production at large λn, arXiv:1806.05648 [INSPIRE].
M. Dine, H.H. Patel and J.F. Ulbricht, Behavior of cross sections for large numbers of particles, arXiv:2002.12449 [INSPIRE].
M.B. Voloshin, Loops with heavy particles in production amplitudes for multiple Higgs bosons, Phys. Rev. D 95 (2017) 113003 [arXiv:1704.07320] [INSPIRE].
M.V. Libanov, Multiparticle threshold amplitudes exponentiate in arbitrary scalar theories, Mod. Phys. Lett. A 11 (1996) 2539 [hep-th/9610036] [INSPIRE].
H. Goldberg and M.T. Vaughn, Tree and nontree multiparticle amplitudes, Phys. Rev. Lett. 66 (1991) 1267 [INSPIRE].
V.V. Khoze, Perturbative growth of high-multiplicity W, Z and Higgs production processes at high energies, JHEP 03 (2015) 038 [arXiv:1411.2925] [INSPIRE].
M.B. Voloshin, Zeros of tree level amplitudes at multiboson thresholds, Phys. Rev. D 47 (1993) 2573 [hep-ph/9210244] [INSPIRE].
M.B. Voloshin, Some properties of amplitudes at multiboson thresholds in spontaneously broken scalar theory, Phys. Rev. D 47 (1993) 3525 [hep-ph/9211242] [INSPIRE].
E.N. Argyres, C.G. Papadopoulos and R.H.P. Kleiss, On amplitude zeros at threshold, Phys. Lett. B 302 (1993) 70 [Addendum ibid. 319 (1993) 544] [hep-ph/9212280] [INSPIRE].
E.N. Argyres, R.H.P. Kleiss and C.G. Papadopoulos, Nullification of multi-Higgs threshold amplitudes in the standard model, Phys. Lett. B 308 (1993) 315 [Addendum ibid. 319 (1993) 544] [hep-ph/9303322] [INSPIRE].
B.H. Smith, Effects of amplitude nullification in the standard model, Phys. Rev. D 49 (1994) 1081 [hep-ph/9309231] [INSPIRE].
E.N. Argyres, R.H.P. Kleiss and C.G. Papadopoulos, Multiscalar amplitudes to all orders in perturbation theory, Phys. Lett. B 308 (1993) 292 [Addendum ibid. 319 (1993) 544] [hep-ph/9303321] [INSPIRE].
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: 2203.03654
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
Khoze, V.V., Schenk, S. Multiparticle amplitudes in a scalar EFT. J. High Energ. Phys. 2022, 134 (2022). https://doi.org/10.1007/JHEP05(2022)134
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2022)134