Suppression exponent for multiparticle production in $\lambda {\varphi }^4$ theory

Abstract

We compute the probability of producing $n$ particles from few colliding particles in the unbroken $(3+1)$-dimensional $\lambda {\varphi }^4$ theory. To this end we numerically implement semiclassical method of singular solutions which works at $n\gg 1$ in the weakly coupled regime $\lambda \ll 1$. For the first time, we obtain reliable results in the region of exceptionally large final state multiplicities $n\gg {\lambda }^{-1}$ where the probability decreases exponentially with $n$, ${{\cal P}(\mbox{few} \to n) \sim \exp\{f_\infty(\varepsilon) \, n\}}$, and its slope $f_{\infty }<0$ depends on the mean kinetic energy $\epsilon$ of produced particles. In the opposite case $n\ll {\lambda }^{-1}$ our data match well-known tree-level result, and they interpolate between the two limits at $n\sim {\lambda }^{-1}$. Overall, this proves exponential suppression of the multiparticle production probability at $n\gg 1$ and arbitrary $\epsilon$ 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.

arXiv comment38 pages, 24 figures, 1 table, 3 ancillary data files, 3 videos

References in corpus (40)

• The Epsilon Expansion Meets Semiclassics
• Summing tree graphs at threshold
• Semiclassical approach for multiparticle production in scalar theories
• Semiclassical Study of Baryon and Lepton Number Violation in High-Energy Electroweak Collisions
• Exponentiation of Multiparticle Amplitudes in Scalar Theories
• Summing One-Loop Graphs at Multi-Particle Threshold
• Summing one-loop graphs in a theory with broken symmetry
• Suppression of baryon number violation in electroweak collisions: Numerical results
• Non-Perturbative Production of Multi-Boson States and Quantum Bubbles
• Higgsplosion: Solving the Hierarchy Problem via rapid decays of heavy states into multiple Higgs bosons
• Non-Perturbative Isotropic Multi-Particle Production in Yang--Mills Theory
• Exponentiation of multiparticle amplitudes in scalar theories. II. Universality of the exponent
• The Semiclassical Description of Tunneling in Scattering with Multiple Degrees of Freedom
• False Vacuum Decay Induced by Particle Collisions
• Computational Study of Baryon Number Violation in High Energy Electroweak Collisions
• Soliton-antisoliton pair production in particle collisions
• Review of the semiclassical formalism for multiparticle production at high energies
• Multiscalar production amplitudes beyond threshold
• Perturbative growth of high-multiplicity W, Z and Higgs production processes at high energies
• The fate of small classically stable Q-balls
• Induced tunneling in QFT: soliton creation in collisions of highly energetic particles
• The Higgsploding Universe
• Multiparticle Higgs and Vector Boson Amplitudes at Threshold
• O(4) symmetric singular solutions and multiparticle cross sections in ${\varphi }^4$ theory at tree level
• Real-Time Instantons and Suppression of Collision-Induced Tunneling
• Properties of perturbative multi-particle amplitudes in ${\varphi }^k$ and $O(N)$ theories
• Soliton pair creation in classical wave scattering
• Multiparticle production in the large lambda n limit: Realising Higgsplosion in a scalar QFT
• Signatures of unstable semiclassical trajectories in tunneling
• Tree amplitudes at multiparticle threshold in a model with softly broken $O(2)$ symmetry
• Semiclassical description of soliton-antisoliton pair production in particle collisions
• Problems with Higgsplosion
• Exploring High Multiplicity Amplitudes in Quantum Mechanics
• Use of singular classical solutions for calculation of multiparticle cross sections in field theory
• Loops with heavy particles in multi Higgs production amplitudes
• Exploring High Multiplicity Amplitudes: The QM Analogue of the Spontaneously Broken Case
• The Breakdown of Resummed Perturbation Theory at High Energies
• Numerical study of multiparticle scattering in $\lambda {\varphi }^4$ theory
• Numerical study of multiparticle production in ${\varphi }^4$ theory: comparison with analytic results
• Multiparticle Amplitudes in a Scalar EFT