Multiparticle Amplitudes in a Scalar EFT

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 $\lambda {\phi }^4$ theory, $n$-particle amplitudes become non-perturbative in the limit where $n$ scales with energy. In this case, the effective expansion parameter, $\lambda n$, 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 $\phi$. 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.

arXiv comment25 pages, 3 figures. v2: minor corrections

References in corpus (29)

• Summing tree graphs at threshold
• Semiclassical approach for multiparticle production in scalar theories
• 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
• 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
• Exponentiation of multiparticle amplitudes in scalar theories. II. Universality of the exponent
• Zeros of Tree-Level Amplitudes at Multi-Boson Thresholds
• Multiscalar amplitudes to all orders in perturbation theory
• An upper limit on the scale of new physics phenomena from rising cross sections in high multiplicity Higgs and vector boson events
• Review of the semiclassical formalism for multiparticle production at high energies
• Perturbative growth of high-multiplicity W, Z and Higgs production processes at high energies
• The Higgsploding Universe
• On amplitude zeros at threshold
• Multiparticle Higgs and Vector Boson Amplitudes at Threshold
• Nullification of multi-Higgs threshold amplitudes in the Standard Model
• Multiparticle production in the large lambda n limit: Realising Higgsplosion in a scalar QFT
• Problems with Higgsplosion
• Exploring High Multiplicity Amplitudes in Quantum Mechanics
• Precision measurements for the Higgsploding Standard Model
• Effects of Amplitude Nullification in the Standard Model
• Some Properties of Amplitudes at Multi Boson Thresholds in Spontaneously Broken Scalar Theory
• Loops with heavy particles in multi Higgs production amplitudes
• Exploring High Multiplicity Amplitudes: The QM Analogue of the Spontaneously Broken Case
• Multiparticle Threshold Amplitudes Exponentiate in Arbitrary Scalar Theories
• 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

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