Numerical Study of Multiparticle Production in ϕ4 Theory: Comparison with Analytical Results

Demidov, S.V.; Farkhtdinov, B. R.; Levkov, D. G.

doi:10.1134/s0021364021230028

Cited by 4 publications

(4 citation statements)

References 23 publications

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“…In addition, scalar QFTs are afflicted by evidence of rapidly increasing rates of high-energy processes involving the production of a large number of particles. Perturbative as well as semiclassical 1 calculations of scattering amplitudes at the multiparticle threshold, in particular the n-particle decay of a highly virtual state 1 → n, suggest a rapid growth for large n [4][5][6][7][8][9][10][11][12][13][14], in line with recent numerical studies [15,16]. As this is, naively, in contradiction to the unitarity requirement of any consistent quantum theory, these results hint at the termination of the perturbative regime or perhaps the need for novel degrees of freedom at high energies.…”

Section: Introductionsupporting

confidence: 69%

Multiparticle amplitudes in a scalar EFT

Khoze

Schenk

2022

J. High Energ. Phys.

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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.

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Section: Introductionsupporting

confidence: 69%

Multiparticle amplitudes in a scalar EFT

Khoze

Schenk

2022

J. High Energ. Phys.

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“…We see that F monotonically decreases with λn. As expected, at λn 1 it coincides with the contribution of tree-level diagrams [62] (dashed line), see also [53]. In the opposite limit λn 1 our numerical data are well fitted by the linear function (solid line in the figure ):…”

Section: Jhep02(2023)205supporting

confidence: 82%

“…Up to our knowledge, no calculation of this kind was performed before, see ref. [53] for the accompanying work. We exploit the same semiclassical method [54] as in the studies on "Higgsplosion" [39,40], but do not make additional assumptions on the structure of saddle-point solutions.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Suppression exponent for multiparticle production in λϕ4 theory

Demidov

Farkhtdinov

Levkov

2023

J. High Energ. Phys.

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We compute the probability of producing n particles from few colliding particles in the unbroken (3 + 1)-dimensional λϕ4 theory. To this end we numerically implement semiclassical method of singular solutions which works at n ≫ 1 in the weakly coupled regime λ ≪ 1. For the first time, we obtain reliable results in the region of exceptionally large final-state multiplicities n ≫ λ−1 where the probability decreases exponentially with n, $$ \mathcal{P}\left(\textrm{few}\to n\right)\sim \exp \left\{{f}_{\infty}\left(\varepsilon \right)n\right\} $$ P few → n ~ exp f ∞ ε n , and its slope f∞ < 0 depends on the mean kinetic energy ε of produced particles. In the opposite case n ≪ λ−1 our data match well-known tree-level result, and they interpolate between the two limits at n ~ λ−1. Overall, this proves exponential suppression of the multiparticle production probability at n ≫ 1 and arbitrary ε in the unbroken theory. Using numerical solutions, we critically analyze the mechanism for multiple Higgs boson production suggested in the literature. Application of our technique to the scalar theory with spontaneously broken symmetry can eradicate (or confirm) it in the nearest future.

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