Suppression exponent for multiparticle production in λϕ 4 theory

S. Demidov (Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary prospect 7a, Moscow, 117312, Russia; Moscow Institute of Physics and Technology, Institutsky per. 9, Dolgoprudny, 141700, Russia) ; B. Farkhtdinov (Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary prospect 7a, Moscow, 117312, Russia; Moscow Institute of Physics and Technology, Institutsky per. 9, Dolgoprudny, 141700, Russia; I.M. Sechenov First Moscow State Medical University, 8-2 Trubetskaya street, Moscow, 119991, Russia) ; D. Levkov (Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary prospect 7a, Moscow, 117312, Russia; Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University, Leninskie Gory, GSP-1, Moscow, 119991, Russia)

We compute the probability of producing n particles from few colliding particles in the unbroken (3 + 1)-dimensional λϕ 4 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, P few n ~ exp f ε n $$ \mathcal{P}\left(\textrm{few}\to n\right)\sim \exp \left\{{f}_{\infty}\left(\varepsilon \right)n\right\} $$ , 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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      "surname": "Farkhtdinov", 
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      "surname": "Levkov", 
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      "title": "Suppression exponent for multiparticle production in \u03bb\u03d5 4 theory"
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  "abstracts": [
    {
      "source": "Springer", 
      "value": "We compute the probability of producing n particles from few colliding particles in the unbroken (3 + 1)-dimensional \u03bb\u03d5 4 theory. To this end we numerically implement semiclassical method of singular solutions which works at n \u226b 1 in the weakly coupled regime \u03bb \u226a 1. For the first time, we obtain reliable results in the region of exceptionally large final-state multiplicities n \u226b \u03bb  \u22121 where the probability decreases exponentially with n,   <math> <mi>P</mi> <mfenced> <mrow> <mi>few</mi> <mo>\u2192</mo> <mi>n</mi> </mrow> </mfenced> <mo>~</mo> <mo>exp</mo> <mfenced> <mrow> <msub> <mi>f</mi> <mo>\u221e</mo> </msub> <mfenced> <mi>\u03b5</mi> </mfenced> <mi>n</mi> </mrow> </mfenced> </math>  $$ \\mathcal{P}\\left(\\textrm{few}\\to n\\right)\\sim \\exp \\left\\{{f}_{\\infty}\\left(\\varepsilon \\right)n\\right\\} $$ , and its slope f  \u221e  &lt; 0 depends on the mean kinetic energy \u03b5 of produced particles. In the opposite case n \u226a \u03bb  \u22121 our data match well-known tree-level result, and they interpolate between the two limits at n ~ \u03bb  \u22121. Overall, this proves exponential suppression of the multiparticle production probability at n \u226b 1 and arbitrary \u03b5 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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Published on:
21 February 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 2
Pages 1-36
DOI:
https://doi.org/10.1007/JHEP02(2023)205
arXiv:
2212.03268
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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