Mass Renormalization in Lattice Simulations of False Vacuum Decay

TL;DR

This paper investigates how lattice simulations of false vacuum decay are affected by mass renormalization, providing theoretical predictions and numerical validation to improve the accuracy of decay rate calculations in quantum field theories.

Contribution

It computes the effective mass modifications in lattice simulations of false vacuum decay and compares theoretical predictions with numerical results, enhancing the understanding of parameter redefinition effects.

Findings

Excellent agreement between theory and simulations for effective mass modifications.

Decay rates depend qualitatively on the UV cutoff, indicating the need for further corrections.

Modeling uncertainties from non-linear effects are identified and explored.

Abstract

False vacuum decay, a quantum mechanical first-order phase transition in scalar field theories, is an important phenomenon in early universe cosmology. Recently, real-time semi-classical techniques based on ensembles of lattice simulations were applied to the problem of false vacuum decay. In this context, or any other lattice simulation, the effective potential experienced by long-wavelength modes is not the same as the bare potential. To make quantitative predictions using the real-time semi-classical techniques, it is therefore necessary to understand the redefinition of model parameters and the corresponding deformation of the vacuum state, as well as stochastic contributions that require modeling of unresolved subgrid modes. In this work, we focus on the former corrections and compute the expected modification of the true and false vacuum effective mass, which manifests as a modified dispersion relationship for linear fluctuations about the vacuum. We compare these theoretical predictions to numerical simulations and find excellent agreement. Motivated by this, we use the effective masses to fix the shape of a parameterized effective potential, and explore the modeling uncertainty associated with non-linear corrections. We compute the decay rates in both the Euclidean and real-time formalisms, finding qualitative agreement in the dependence on the UV cutoff. These calculations further demonstrate that a quantitative understanding of the rates requires additional corrections.