Decay Rate Of False Vacuum Research Articles

Fate of false vacuum in non-perturbative regimes

We use some exact results in scalar field theory to revise the analysis by Coleman and Callan about false vacuum decay and propose a simple non-perturbative formalism. We introduce an exact Green’s function which incorporates non-perturbative corrections in the strong coupling regimes of the theory. The solution of the scalar field theory involves the Jacobi elliptical function and has been used to calculate the effective potential for any arbitrary coupling values. We demonstrate the use of this formalism in a simple λ ϕ 4 theory, and show that the effective potential exhibits a false minimum at the origin. We then calculate the false vacuum decay rate in the thin wall approximation, and suggest simple analytic formulae that may be useful for the analysis for the first-order phase transition beyond the perturbative regime. In our methodology, we show that the standard results obtained in perturbation theory are reproduced by making the coupling values very small.

Vacuum decay in the Lorentzian path integral

We apply the Lorentzian path integral to the decay of a false vacuum and estimate the false-vacuum decay rate. To make the Lorentzian path integral convergent, the deformation of an integration contour is performed by following the Picard-Lefschetz theory. We show that the nucleation rate of a critical bubble, for which the corresponding bounce action is extremized, has the same exponent as the Euclidean approach. We also extend our computation to the nucleation of a bubble larger or smaller than the critical one to which the Euclidean formalism is not applicable.

Analytic thin wall false vacuum decay rate

We derive a closed-form false vacuum decay rate at one loop in the thin wall limit, where the true and false vacua are nearly degenerate. We obtain the bounce configuration in D dimensions, together with the Euclidean action with a higher order correction, counter-terms and renormalization group running. We extract the functional determinant via the Gel’fand-Yaglom theorem for low and generic orbital multipoles. The negative and zero eigenvalues appear for low multipoles and the translational zeroes are removed. We compute the fluctuations for generic multipoles, multiply and regulate the orbital modes. We find an explicit finite renormalized decay rate in D = 3, 4 and give a closed-form expression for the finite functional determinant in any dimension.

Exact one-loop false vacuum decay rate

We discuss an exact false vacuum decay rate at one loop for a real and complex scalar field in a quartic-quartic potential with two tree-level minima. The bounce solution is used to compute the functional determinant from both fluctuations. We obtain the finite product of eigenvalues and remove translational zero modes. The orbital modes are regularized with the zeta function and we end up with a complete renormalized decay rate. We derive simple expansions in the thin and thick wall limits and determine their validity.

Precise calculation of the decay rate of false vacuum with multi-field bounce

We study the decay rate of a false vacuum in gauge theory at the one-loop level. We pay particular attention to the case where the bounce consists of an arbitrary number of scalar fields. With a multi-field bounce, which has a curved trajectory in the field space, the mixing among the gauge fields and the scalar fields evolves along the path of the bounce in the field space and the one-loop calculation of the vacuum decay rate becomes complicated. We consider the one-loop contribution to the decay rate with an arbitrary choice of the gauge parameter, and obtain a gauge invariant expression of the vacuum decay rate. We also give proper treatments of gauge zero modes and renormalization.

False vacuum decay in quantum mechanics and four dimensional scalar field theory

When the Higgs boson was discovered in 2012 it was realized that electroweak vacuum may suffer a possible metastability on the Planck scale and can eventually decay. To understand this problem it is important to have reliable predictions for the vacuum decay rate within the framework of quantum field theory. For now, it can only be done at one loop level, which is apparently is not enough. The aim of this work is to develop a technique for the calculation of two and higher order radiative corrections to the false vacuum decay rate in the framework of four dimensional scalar quantum field theory and then apply it to the case of the Standard Model. To achieve this goal, we first start from the case of d=1 dimensional QFT i.e. quantum mechanics. We show that for some potentials two and three loop corrections can be very important and must be taken into account. Next, we use quantum mechanical example as a template for the general d=4 dimensional theory. In it we are concentrating on the calculations of bounce solution and corresponding Green function in so called thin wall approximation. The obtained Green function is then used as a main ingredient for the calculation of two loop radiative corrections to the false vacuum decay rate.

Radiative corrections to false vacuum decay in quantum mechanics

We consider radiative corrections to false vacuum decay within the framework of quantum mechanics for the general potential of the form 1/2 M q^2 (q-A)(q-B), where M , A and B are arbitrary parameters. For this type of potential we provide analytical results for Green function in the background of corresponding bounce solution together with one loop expression for false vacuum decay rate. Next, we discuss the computation of higher order corrections for false vacuum decay rate and provide numerical expressions for two and three loop contributions.

On the gauge invariance of the decay rate of false vacuum

We study the gauge invariance of the decay rate of the false vacuum for the model in which the scalar field responsible for the false vacuum decay has gauge quantum number. In order to calculate the decay rate, one should integrate out the field fluctuations around the classical path connecting the false and true vacua (i.e., so-called bounce). Concentrating on the case where the gauge symmetry is broken in the false vacuum, we show a systematic way to perform such an integration and present a manifestly gauge-invariant formula of the decay rate of the false vacuum.

Renormalization-scale uncertainty in the decay rate of false vacuum

We study radiative corrections to the decay rate of false vacua, paying particular attention to the renormalization-scale dependence of the decay rate. The decay rate exponentially depends on the bounce action. The bounce action itself is renormalization scale dependent. To make the decay rate scale-independent, radiative corrections, which are due to the field fluctuations around the bounce, have to be included. We show quantitatively that the inclusion of the fluctuations suppresses the scale dependence, and hence is important for the precise calculation of the decay rate. We also apply our analysis to a supersymmetric model and show that the radiative corrections are important for the Higgs-stau system with charge breaking minima.

On the prefactor in false vacuum decay

This paper gives a survey of recent work in collaboration with G Dunne concerning a new method for computing determinants in quantum field-theoretic applications, using angular momentum cut-off regularization and renormalization. This method is generally applicable to the situation of computing the quantum fluctuations about a classical configuration that has a symmetry allowing the fluctuation operator to be radially separable. There are many such cases of interest in quantum field theory. Here I describe the case of the false vacuum decay rate in a self-interacting scalar field theory modelling the process of nucleation in a four-dimensional spacetime. The rate prefactor involves quantum fluctuations about the classical bounce solution, which is O(4) symmetric. The computational method is based on the Gelfand–Yaglom approach to determinants of ordinary differential operators, suitably extended to higher dimensions using angular momentum cut-off regularization. I also present a simple new formula for the zero-mode contribution to the fluctuation prefactor, expressed entirely in terms of the asymptotic behaviour of the classical bounce solution.

Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay

We present a general numerical method for computing precisely the false vacuum decay rate, including the prefactor due to quantum fluctuations about the classical bounce solution, in a self-interacting scalar field theory modeling the process of nucleation in four-dimensional space-time. This technique does not rely on the thin-wall approximation. The method is based on the Gelfand-Yaglom approach to determinants of differential operators, suitably extended to higher dimensions using angular momentum cutoff regularization. A related approach has been discussed recently by Baacke and Lavrelashvili, but we implement the regularization and renormalization in a different manner, and compare directly with analytic computations made in the thin-wall approximation. We also derive a simple new formula for the zero mode contribution to the fluctuation prefactor, expressed entirely in terms of the asymptotic behavior of the classical bounce solution.

One-loop corrections to the metastable vacuum decay

We evaluate the one-loop prefactor in the false vacuum decay rate in a theory of a self-interacting scalar field in $3+1$ dimensions. We use a numerical method, established some time ago, which is based on a well-known theorem on functional determinants. The proper handling of zero modes and of renormalization is discussed. The numerical results show in particular that the quantum corrections strongly increase when one approaches the thin-wall case. In the thin-wall limit the numerical results are found to join into those obtained by a gradient expansion.

Strong-coupling-expansion analysis of the false-vacuum decay rate of the lattice ϕ4model in 1 + 1 dimensions

Strong-coupling expansion is performed for the lattice phi^4 model in 1+1 dimensions. Because the strong-coupling limit itself is not solvable, we employed numerical calculations so as to set up unperturbed eigensystems. Restricting the number of Hilbert-space bases, we performed linked-cluster expansion up to eleventh order. We carried out alternative simulation by means of the density-matrix renormalization group. Thereby, we confirmed that our series-expansion data with a convergence-acceleration trick are in good agreement with the simulation result. Through the analytic continuation to the domain of negative biquadratic interaction, we obtain the false-vacuum decay rate. Contrary to common belief that tunnelling phenomenon lies out of perturbative treatments, our series expansion reproduces the instanton-theory behaviour for high potential barrier. For shallow barrier, on the contrary, our result tells that the relaxation is no more described by instanton, but the decay rate acquires notable enhancement.

Derivative expansion and gauge independence of the false vacuum decay rate in various gauges

In theories with radiative symmetry breaking, the calculation of the false vacuum decay rate requires the inclusion of higher-order terms in the derivative expansion of the effective action. I show here that, in the case of covariant gauges, the presence of infrared singularities forbids the consistent calculation by keeping the lowest-order terms. The situation is remedied, however, in the case of $R_{\xi}$ gauges. Using the Nielsen identities I show that the final result is gauge independent for generic values of the gauge parameter $v$ that are not anomalously small.

Can cosmic-ray catalysed vacuum decay dominate over tunnelling?

We consider the question of whether cosmic-ray catalysed false-vacuum decay can be phenomenologically more important than spontaneous decay via quantum tunnelling. We extend the zero bubble wall width Landau-WKB analysis of catalysed false-vacuum decay to include the leading order effects of finite wall width and derive an expression for the thin-wall bubble action. Using this we calculate the exponential suppression factor for the catalysed decay rate at the critical bubble energy, corresponding to the largest probability of catalysed decay. We show that, in general, cosmic-ray catalysed decay is more important than spontaneous decay for sufficiently thin-walled bubbles (wall thickness less than about 30% of the initial bubble radius), but that spontaneous decay will dominate for the case of thick-walled bubbles. Since any perturbative model with a cosmologically significant false-vacuum decay rate will produce thick-walled bubbles, we can conclude that cosmic-ray catalysed false-vacuum decay will never dominate over tunnelling in imposing phenomenological constraints on perturbative particle physics models.

Phase transitions and vacuum tunneling into charge- and color-breaking minima in the MSSM.

The scalar potential of the MSSM may have local and global minima characterized by non-zero expectation values of charged and colored bosons. Even if the true vacuum is not color and charge conserving, the early Universe is likely to occupy the minimum of the potential in which only the neutral Higgs fields have non-zero vev's. The stability of this false vacuum with respect to quantum tunneling imposes important constraints on the values of the MSSM parameters. We analyze these constraints using some novel methods for calculating the false vacuum decay rate. Some regions of the MSSM parameter space are ruled out because the lifetime of the corresponding physically acceptable false vacuum is small in comparison to the present age of the Universe. However, there is a significant fraction of the parameter space that is consistent with the hypothesis that the Universe rests in the false vacuum that is stable on a cosmological time scale.

Improved action method for analyzing tunneling in quantum field theory

We describe a new method which allows one to evaluate the false vacuum decay rate for a general potential which may depend on an arbitrary number of scalar fields.

Tunneling in quantum field theory with spontaneous symmetry breaking

Tunneling in quantum field theory is well understood in the case of a single scalar field. However, in theories with spontaneous symmetry breaking, one has to take into account the additional zero modes which appear due to the Goldstone phenomenon. We calculate the false vacuum decay rate in this case. The result may differ significantly from the tunneling rates in the absence of symmetry breaking.