We are launching FindBounce, a Mathematica package for the evaluation of the Euclidean bounce action that enters the decay rate of metastable states in quantum and thermal field theories. It is based ...on the idea of polygonal bounces, which is a semi-analytical approach to solving the bounce equation by discretizing the potential into piecewise linear segments. This allows for a fast and robust evaluation of arbitrary potentials with specified precision and any number of scalar fields. Time cost grows linearly with the number of fields and/or the number of segments. Computation with 20 fields takes ∼2 s with 0.5% accuracy of the action. The FindBounce function is simple to use with the native Mathematica look and feel, it is easy to install, and comes with detailed documentation and physical examples, such as the calculation of the nucleation temperature. We also provide timing benchmarks with comparisons to existing tools, where applicable.
Program title:FindBounce
CPC Library link to program files:http://dx.doi.org/10.17632/tysw84skx3.1
Developer’s repository link:https://github.com/vguada/FindBounce
Licensing provisions: GNU General Public License 3
Programming language:Mathematica
Nature of problem: Evaluation of the Euclidean bounce action that controls the decay rate of metastable local minima in thermal and quantum field theories.
Solution method: Semi-analytical solution of a system of coupled differential equations, based on the polygonal bounce idea (Guada et al., 2019).
Restrictions:Mathematica version 10 or above, works in D=3,4.
We consider the decay of a false vacuum in circumstances where the methods suggested by Coleman run into difficulties. We find that in these cases quantum fluctuations play a crucial role. Namely, ...they naturally induce both ultraviolet and infrared cutoff scales, determined by the parameters of the classical solution, beyond which this solution cannot be trusted anymore. This leads to the appearance of a broad class of new O(4) invariant instantons, which would have been singular in the absence of an ultraviolet cutoff. We apply our results to a case where the potential is unbounded from below in a linear way and in particular show how the problem of small instantons is resolved by taking into account the inevitable quantum fluctuations.
The decay of a false vacuum is considered in circumstances where the methods suggested by Coleman run into difficulties. It is found that in these cases quantum fluctuations play a crucial role. Namely, they naturally induce both ultraviolet and infrared cutoff scales, determined by the parameters of the classical solution, beyond which this solution cannot be trusted anymore. This leads to the appearance of a broad class of new O(4) invariant instantons, which would have been singular in the absence of an ultraviolet cutoff. The results will be applied to a case where the potential is unbounded from below in a linear way. In particular it will be shown how the problem of small instantons is resolved by taking into account the inevitable quantum fluctuations.
We consider radiative corrections to false vacuum decay in a four-dimensional scalar field theory with cubic and quartic potential. Using planar thin wall approximation we were able to get analytical ...expression for the decay rate up to two loop order. The results obtained employ dimensional regularization and MS‾ renormalization scheme.
We study the fate of a false vacuum in the case of a potential that contains a portion which is quartic and unbounded. We first prove that an O(4) invariant instanton with the Coleman boundary ...conditions does not exist in this case. This, however, does not imply that the false vacuum does not decay. We show how the quantum fluctuations may regularize the singular classical solutions. This gives rise to a new class of O(4) invariant regularized instantons which describe the vacuum instability in the absence of the Coleman instanton. We derive the corresponding solutions and calculate the decay rate they induce.
The authors study the fate of a false vacuum in the case of a potential that contains a portion which is quartic and unbounded. First they prove that an O(4) invariant instanton with the Coleman boundary conditions does not exist in this case. This, however, does not imply that the false vacuum does not decay. It will be shown how the quantum fluctuations may regularize the singular classical solutions. This gives rise to a new class of O(4) invariant regularized instantons which describe the vacuum instability in the absence of the Coleman instanton. What follows is both a derivation of the corresponding solutions and a calculation of the decay rate they induce.
We study tachyonic preheating associated with the spontaneous breaking of B−L, the difference of baryon and lepton number. Reheating occurs through the decays of heavy Majorana neutrinos which are ...produced during preheating and in decays of the Higgs particles of B−L breaking. Baryogenesis is an interplay of nonthermal and thermal leptogenesis, accompanied by thermally produced gravitino dark matter. The proposed mechanism simultaneously explains the generation of matter and dark matter, thereby relating the absolute neutrino mass scale to the gravitino mass.
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