Abstract
We study numerically classical collisions of waves in λϕ4 theory. These processes correspond to multiparticle scattering in the semiclassical regime. Parameterizing initial and final wavepackets by energy E and particle numbers Ni, Nf we find classically allowed region in the parameter space. We describe properties of the scattering solutions at the boundary of the classically allowed region. We comment on the implications of our results for multiparticle production in the quantum regime.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.B. Voloshin, Nonperturbative methods, talk given at the 27th International Conference on High-energy Physics (ICHEP 94), July 20-27, Glasgow, U.K. (1994), hep-ph/9409344 [INSPIRE].
M.V. Libanov, V.A. Rubakov and S.V. Troitsky, Multiparticle processes and semiclassical analysis in bosonic field theories, Phys. Part. Nucl. 28 (1997) 217 [INSPIRE].
A. Ringwald, High-energy breakdown of perturbation theory in the electroweak instanton sector, Nucl. Phys. B 330 (1990) 1 [INSPIRE].
O. Espinosa, High-energy behavior of baryon and lepton number violating scattering amplitudes and breakdown of unitarity in the standard model, Nucl. Phys. B 343 (1990) 310 [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].
M.B. Voloshin, Multiparticle amplitudes at zero energy and momentum in scalar theory, Nucl. Phys. B 383 (1992) 233 [INSPIRE].
L.S. Brown, Summing tree graphs at threshold, Phys. Rev. D 46 (1992) R4125 [hep-ph/9209203] [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].
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].
S.Yu. Khlebnikov, V.A. Rubakov and P.G. Tinyakov, Instanton induced cross-sections below the sphaleron, Nucl. Phys. B 350 (1991) 441 [INSPIRE].
V.A. Rubakov and P.G. Tinyakov, Towards the semiclassical calculability of high-energy instanton cross-sections, Phys. Lett. B 279 (1992) 165 [INSPIRE].
D.T. Son, Semiclassical approach for multiparticle production in scalar theories, Nucl. Phys. B 477 (1996) 378 [hep-ph/9505338] [INSPIRE].
F.L. Bezrukov, M.V. Libanov and S.V. Troitsky, O(4) symmetric singular solutions and multiparticle cross-sections in \( \phi \) 4 theory at tree level, Mod. Phys. Lett. A 10 (1995) 2135 [hep-ph/9508220] [INSPIRE].
F.L. Bezrukov, Use of singular classical solutions for calculation of multiparticle cross-sections in field theory, Theor. Math. Phys. 115 (1998) 647 [hep-ph/9901270] [INSPIRE].
V.I. Zakharov, High-energy production of scalar bosons in weak coupling theories, Phys. Rev. Lett. 67 (1991) 3650 [INSPIRE].
V.A. Rubakov, Nonperturbative aspects of multiparticle production, talk given at the 2nd Rencontres du Vietnam: From the Sun and Beyond & Physics at the Frontiers of the Standard Model, October 21-28, Ho Chi Minh City, Vietnam (1995), hep-ph/9511236 [INSPIRE].
C. Bachas, A proof of exponential suppression of high-energy transitions in the anharmonic oscillator, Nucl. Phys. B 377 (1992) 622 [INSPIRE].
J.M. Cornwall and G. Tiktopoulos, Semiclassical matrix elements for the quartic oscillator, Ann. Phys. 228 (1993) 365.
J. Jaeckel and S. Schenk, Exploring high multiplicity amplitudes in quantum mechanics, arXiv:1806.01857 [INSPIRE].
V.V. Khoze, Multiparticle Higgs and vector boson amplitudes at threshold, JHEP 07 (2014) 008 [arXiv:1404.4876] [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].
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, Diagrammatic computation of multi-Higgs processes at very high energies: scaling log σ n with MadGraph, Phys. Rev. D 92 (2015) 014021 [arXiv:1504.05023] [INSPIRE].
C. Degrande, V.V. Khoze and O. Mattelaer, Multi-Higgs production in gluon fusion at 100 TeV, Phys. Rev. D 94 (2016) 085031 [arXiv:1605.06372] [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, Multiparticle production in the large λn limit: realising Higgsplosion in a scalar QFT, JHEP 06 (2017) 148 [arXiv:1705.04365] [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].
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, arXiv:1709.08655 [INSPIRE].
V.V. Khoze, Semiclassical computation of quantum effects in multiparticle production at large λn, arXiv:1806.05648 [INSPIRE].
A. Belyaev, F. Bezrukov, C. Shepherd and D. Ross, Problems with Higgsplosion, arXiv:1808.05641 [INSPIRE].
A. Monin, Inconsistencies of hIggsplosion, arXiv:1808.05810 [INSPIRE].
V.A. Rubakov and D.T. Son, Instanton like transitions at high-energies in (1 + 1)-dimensional scalar models. 2. Classically allowed induced vacuum decay, Nucl. Phys. B 424 (1994) 55 [hep-ph/9401257] [INSPIRE].
C. Rebbi and R.L. Singleton, Jr, Computational study of baryon number violation in high-energy electroweak collisions, Phys. Rev. D 54 (1996) 1020 [hep-ph/9601260] [INSPIRE].
C. Rebbi and R.L. Singleton, Jr, Numerical approaches to high-energy electroweak baryon number violation above and below the sphaleron barrier, in the proceedings of the High energy physics and cosmology, June 10-July 26, Trieste, Italy (1996), hep-ph/9706424 [INSPIRE].
S.V. Demidov and D.G. Levkov, Soliton pair creation in classical wave scattering, JHEP 06 (2011) 016 [arXiv:1103.2133] [INSPIRE].
H. Goldberg, D. Nash and M.T. Vaughn, Classical λ \( \phi \) 4 theory in (3 + 1)-dimensions, Phys. Rev. D 46 (1992) 2585 [INSPIRE].
K. Rajagopal and N. Turok, Classical high-energy scattering in the abelian Higgs model, Nucl. Phys. B 375 (1992) 299 [INSPIRE].
C. Gong, S.G. Matinyan, B. Müller and A. Trayanov, Manifestation of infrared instabilities in high-energy processes in nonAbelian gauge theories, Phys. Rev. D 49 (1994) 607 [Erratum ibid. D 49 (1994) 5629] [nucl-th/9310001] [INSPIRE].
C.R. Hu et al., Wave packet dynamics in Yang-Mills theory, Phys. Rev. D 52 (1995) 2402 [hep-ph/9502276] [INSPIRE].
C.R. Hu, S.G. Matinyan, B. Müller and D. Sweet, Wave packet collisions in Yang-Mills Higgs theory, Phys. Rev. D 53 (1996) 3823 [hep-ph/9509305] [INSPIRE].
S.A. Teukolsky et al., Numerical recipes: the art of scientific computing, third edition, Cambridge University Press, Cambridge U.K. (2007).
M. Frigo and S. G. Johnson, The design and implementation of FFTW3, IEEE Proc. 93 (2005) 216.
N. Metropolis et al., Equation of state calculations by fast computing machines, J. Chem. Phys. 21 (1953) 1087.
S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the bayesian restoration of images, IEEE Trans. Pattern Anal. 6 (1984) 721.
F.L. Bezrukov et al., Semiclassical study of baryon and lepton number violation in high-energy electroweak collisions, Phys. Rev. D 68 (2003) 036005 [hep-ph/0304180] [INSPIRE].
F.L. Bezrukov et al., Suppression of baryon number violation in electroweak collisions: numerical results, Phys. Lett. B 574 (2003) 75 [hep-ph/0305300] [INSPIRE].
D.G. Levkov and S.M. Sibiryakov, Induced tunneling in QFT: soliton creation in collisions of highly energetic particles, Phys. Rev. D 71 (2005) 025001 [hep-th/0410198] [INSPIRE].
S.V. Demidov and D.G. Levkov, Soliton-antisoliton pair production in particle collisions, Phys. Rev. Lett. 107 (2011) 071601 [arXiv:1103.0013] [INSPIRE].
V.A. Rubakov, D.T. Son and P.G. Tinyakov, Classical boundary value problem for instanton transitions at high-energies, Phys. Lett. B 287 (1992) 342 [INSPIRE].
P.G. Tinyakov, Multiparticle instanton induced processes and B violation in high-energy collisions, Phys. Lett. B 284 (1992) 410 [INSPIRE].
A.H. Mueller, Comparing two particle and multiparticle initiated processes in the one instanton sector, Nucl. Phys. B 401 (1993) 93 [INSPIRE].
G.F. Bonini, A.G. Cohen, C. Rebbi and V.A. Rubakov, The semiclassical description of tunneling in scattering with multiple degrees of freedom, Phys. Rev. D 60 (1999) 076004 [hep-ph/9901226] [INSPIRE].
D.G. Levkov, A.G. Panin and S.M. Sibiryakov, Signatures of unstable semiclassical trajectories in tunneling, J. Phys. A 42 (2009) 205102 [arXiv:0811.3391] [INSPIRE].
S. Demidov and D. Levkov, High-energy limit of collision-induced false vacuum decay, JHEP 06 (2015) 123 [arXiv:1503.06339] [INSPIRE].
S.V. Demidov and D.G. Levkov, Semiclassical description of soliton-antisoliton pair production in particle collisions, JHEP 11 (2015) 066 [arXiv:1509.07125] [INSPIRE].
S.V. Demidov, B.R. Farkhtdinov and D.G. Levkov, in progress.
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: 1806.10996
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
Demidov, S.V., Farkhtdinov, B.R. Numerical study of multiparticle scattering in λϕ4 theory. J. High Energ. Phys. 2018, 68 (2018). https://doi.org/10.1007/JHEP11(2018)068
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2018)068