Exploring High Multiplicity Amplitudes: The QM Analogue of the Spontaneously Broken Case

Abstract

Calculations of high multiplicity Higgs amplitudes exhibit a rapid growth that may signal an end of perturbative behavior or even the need for new physics phenomena. As a step towards this problem we consider the quantum mechanical equivalent of $1\to n$ scattering amplitudes in a spontaneously broken ${\varphi }^4$-theory by extending our previous results on the quartic oscillator with a single minimum to transitions $⟨n|\hat{x}|0⟩$ in the symmetric double-well potential with quartic coupling $\lambda$. Using recursive techniques to high order in perturbation theory, we argue that these transitions are of exponential form $⟨n|\hat{x}|0⟩\sim \exp \left(F(\lambda n)/\lambda \right)$ in the limit of large $n$ and $\lambda n$ fixed. We apply the methods of "exact perturbation theory" put forward by Serone et al. to obtain the exponent $F$ and investigate its structure in the regime where tree-level perturbation theory violates unitarity constraints. We find that the resummed exponent is in agreement with unitarity and rigorous bounds derived by Bachas.

arXiv comment21 pages, 7 figures. v2: minor updates and corrections

References in corpus (35)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations
• Summing tree graphs at threshold
• Theta dependence, sign problems and topological interference
• Semiclassical approach for multiparticle production in scalar theories
• Exponentiation of Multiparticle Amplitudes in Scalar Theories
• Summing One-Loop Graphs at Multi-Particle Threshold
• Instantons in Quantum Mechanics and Resurgent Expansions
• The Power of Perturbation Theory
• Fast Summation of Divergent Series and Resurgent Transseries in Quantum Field Theories from Meijer-G Approximants
• Valley Views: Instantons, Large Order Behaviors, and Supersymmetry
• Summing one-loop graphs in a theory with broken symmetry
• 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
• Instantons from 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
• The Higgsploding Universe
• Valleys in Quantum Mechanics
• Multiparticle production in the large lambda n limit: Realising Higgsplosion in a scalar QFT
• Inconsistencies of higgsplosion
• Properties of perturbative multi-particle amplitudes in ${\varphi }^k$ and $O(N)$ theories
• Problems with Higgsplosion
• Exploring High Multiplicity Amplitudes in Quantum Mechanics
• Precision measurements for the Higgsploding Standard Model
• Singular Classical Solutions and Tree Multiparticle Cross Sections in Scalar Theories
• Multiparticle Threshold Amplitudes Exponentiate in Arbitrary Scalar Theories
• Numerical study of multiparticle scattering in $\lambda {\varphi }^4$ theory
• Semiclassical computation of quantum effects in multiparticle production at large lambda n
• A Higgsploding Theory of Dark Matter

Cited by in corpus (5)

• Weak-Coupling, Strong-Coupling and Large-Order Parametrization of the Hypergeometric-Meijer Approximants
• The Breakdown of Resummed Perturbation Theory at High Energies
• Numerical study of multiparticle production in ${\varphi }^4$ theory: comparison with analytic results
• Suppression exponent for multiparticle production in $\lambda {\varphi }^4$ theory
• Multiparticle Amplitudes in a Scalar EFT