Mass renormalization in lattice simulations of false vacuum decay

Apr 25, 2022
15 pages
Published in:
  • Phys.Rev.D 107 (2023) 8, 083509
  • Published: Apr 12, 2023
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Abstract: (APS)
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 semiclassical 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 semiclassical 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 parametrized effective potential, and explore the modeling uncertainty associated with nonlinear 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.
Note:
  • 15 pages, 5 figures, accepted. Additional clarifications added. Main results unchanged
  • false vacuum: decay
  • field theory: scalar
  • fluctuation: linear
  • mass: renormalization
  • correction: nonlinear
  • lattice
  • effective potential
  • critical phenomena
  • decay rate
  • quantum mechanics
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