We derive fermionic Green's functions in the background of the Euclidean solitons describing false vacuum decay in a prototypal Higgs-Yukawa theory. In combination with appropriate counterterms for the masses, couplings and wave-function normalization, these can be used to calculate radiative corrections to the soliton solutions and transition rates that fully account for the inhomogeneous background provided by the nucleated bubble. We apply this approach to the archetypal example of transitions between the quasi-degenerate vacua of a massive scalar field with a quartic self-interaction. The effect of fermion loops is compared with those from additional scalar fields, and the loop effects accounting for the spacetime inhomogeneity of the tunneling configuration are compared with those where gradients are neglected. We find that scalar loops lead to an enhancement of the decay rate, whereas fermion loops lead to a suppression. These effects get relatively amplified by a perturbatively small factor when gradients are accounted for. In addition, we observe that the radiative corrections to the solitonic field profiles are smoother when the gradients are included. The method presented here for computing fermionic radiative corrections should be applicable beyond the archetypal example of vacuum decay. In particular, we work out methods that are suitable for calculations in the thin-wall limit, as well as others that take account of the full spherical symmetry of the solution. For the latter case, we construct the Green's functions based on spin hyperspherical harmonics, which are eigenfunctions of the appropriate angular momentum operators that commute with the Dirac operator in the solitonic background.
Practical calculations in light-front dynamics are, as a general rule, complicated, since there is no consensus about how to treat the poles which come from the instantaneous parts of Feynman's propagators of the fields. An alternative to solve this difficulty is null-plane causal perturbation theory, a recent developed framework which prevents the appearance of the mentioned poles by avoiding the usage of Feynman's propagators in "loop distributions", requiring no regularization of the amplitudes. In this study, we treat the radiative corrections in the neutral Yukawa's model in that framewor…
We elaborate in this paper a translation-invariant model for fermions in 4-dimensional noncommutative Euclidean space. The construction is done on the basis of the renormalizable noncommutative translation-invariant Phi4 theory introduced by R. Gurau et al. We combine our model with the scalar model, in order to study the noncommutative pseudo-scalar Yukawa theory. After we derive the Feynman rules of the theory, we perform an explicit calculation of the quantum corrections at one loop level to the propagators and vertices.
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.
A new physical origin for electroweak symmetry breaking is proposed, involving compact spatial dimensions of scale 1/R \approx 1 TeV. The higher dimensional theory is supersymmetric, and hence requires the top-quark Yukawa coupling to be localized on some ``Yukawa brane'' in the bulk. The short distance divergence in the Higgs-boson mass is regulated because supersymmetry is unbroken in the vicinity of this Yukawa brane. A finite, negative Higgs mass-squared is generated radiatively by the top-quark supermultiplet propagating a distance of order R from the Yukawa brane to probe supersymmetry b…
With the Higgs mass now measured at the sub-percent level, the potential metastability of the electroweak vacuum of the Standard Model (SM) motivates renewed study of false vacuum decay in quantum field theory. In this note, we describe an approach to calculating quantum corrections to the decay rate of false vacua that is able to account fully and self-consistently for the underlying inhomogeneity of the solitonic tunneling configuration. We show that this method can be applied both to theories in which the instability arises already at the level of the classical potential and those in which …
We obtain the renormalization group(RG) functions for the $O(N)$ scalar field theory and the Higgs-Yukawa field theory with the Coleman-Weinberg mechanism in which the symmetry breaking occurs radiatively by using the method proposed previously in case of the neutral scalar field theory.
We study different properties of an anti-Hermitian Yukawa interaction, motivated by a scenario of radiative anomalous generation of masses for the right-handed sterile neutrinos. The model, involving either a pseudo-scalar or a scalar, is consistent both at the classical and quantum levels, and particular attention is given to its properties under improper Lorentz transformations. The path integral is consistently defined with a Euclidean signature, and we discuss the energetics of the model, which show that no dynamical mass generation can occur, unless extra interactions are considered.
We introduce a Green's function method for handling radiative effects on false vacuum decay. In addition to the usual thin-wall approximation, we achieve further simplification by treating the bubble wall in the planar limit. As an application, we take the $λϕ^4$ theory, extended with $N$ additional heavier scalars, wherein we calculate analytically both the functional determinant of the quadratic fluctuations about the classical soliton configuration and the first correction to the soliton configuration itself.
I consider a theory of a real scalar and a fermion field, with a Yukawa interaction and a potential term that admits two degenerate minima at the tree level. The quantum vacuum energy difference between these two vacua can be calculated using the renormalization group improved effective potential, and gives a finite, nonzero result, dependent on the relative strength of the scalar and the Yukawa interactions.
We extend the study of a previous publication \cite{amsot} on Schwinger-Dyson dynamical mass generation for fermions and pseudoscalar fields (axion-like particles (ALP)), in field theories containing Yukawa type interactions between the fermions and ALPs, by incorporating anomaly terms and/or (constant) axial background fields. The latter are linked to some Lorentz (and CPT) violating scenarios for leptogenesis in the early Universe. We discuss both Hermitian and non-Hermitian Yukawa interactions, anomaly terms and axial backgrounds, which are all motivated in the context of some scenarios for…
We consider the effect of radiative corrections on the maximum velocity of propagation of neutral scalar fields in a uniform electromagnetic field. The propagator of neutral scalar fields interacting with charged fields depends on the electromagnetic field through charged particle loops. The kinetic terms of the scalar fields are corrected and the maximum velocity of the scalar particle becomes greater or less than unity. We show that the maximum velocity becomes greater than unity in a simple example, a neutral scalar field coupled with two charged Dirac fields by Yukawa interaction. The maxi…
We calculate the triangular anomaly in the next order in the Abelian-Higgs theory with an appropriate number of families of chiral fermions and with Yukawa couplings. The calculation is performed with the method of subtraction aided by the Ward- Takahashi identities. This anomaly amplitude is performed without any regularization and is found to vanish.
In this paper, we establish the analysis of noncommutative Yukawa theory, encompassing neutral and charged scalar fields. We approach the analysis by considering carefully the derivation of the respective effective actions. Hence, based on the obtained results, we compute the one-loop contributions to the neutral and charged scalar field self-energy, as well as to the Chern-Simons polarization tensor. In order to properly define the behaviour of the quantum fields, the known UV/IR mixing due to radiative corrections is analysed in the one-loop physical dispersion relation of the scalar and gau…
We study false vacuum decay for a gauged complex scalar field in a polynomial potential with nearly degenerate minima. Radiative corrections to the profile of the nucleated bubble as well as the full decay rate are computed in the planar thin-wall approximation using the effective action. This allows to account for the inhomogeneity of the bounce background and the radiative corrections in a self-consistent manner. In contrast to scalar or fermion loops, for gauge fields one must deal with a coupled system that mixes the Goldstone boson and the gauge fields, which considerably complicates the …
The most direct experimental signature of a compactified extra dimension is the appearance of towers of Kaluza-Klein particles obeying specific mass and coupling relations. However, such masses and couplings are subject to radiative corrections. In this paper, using techniques developed in previous work, we investigate the extent to which such radiative corrections deform the expected tree-level relations between Kaluza-Klein masses and couplings. As toy models for our analysis, we investigate a flat five-dimensional scalar λϕ^4 model and a flat five-dimensional Yukawa model involving both sca…
In this mini review, we discuss some recent developments regarding properties of (quantum) field-theory models containing anti-Hermitian Yukawa interactions between pseudoscalar fields (axions) and Dirac (or Majorana) fermions. Specifically, after motivating physically such interactions, in the context of string-inspired low-energy effective field theories, involving right-handed neutrinos and axion fields, we proceed to discuss their formal consistency within the so-called Parity-Time-reversal(PT)-symmetry framework, as well as dynamical mass generation, induced by the Yukawa interactions, fo…
This paper studies false vacuum lumps surrounded by the true vacuum in a real scalar field potential in flat spacetime. Fermions reside in the core of the lump, which are coupled with the scalar field via Yukawa interaction. Such lumps are stable against spherical collapse and deformation from spherical shape based on energetics considerations. The fermions inside the lump are treated as a uniform Fermi gas. We consider the Fermi gas in both ultrarelativistic and nonrelativistic limits. The mass and size of these lumps depend on the scale characterizing the scalar field potential as well as th…
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 $\overline{MS}$ renormalization scheme.
It is shown that tunneling rates can be defined in terms of a false-vacuum effective action whose reality and convexity properties differ from those of the corresponding groundstate functional. The tunneling rate is directly related to the false-vacuum effective action evaluated at an extremal "quantum bounce". The Nielsen identities of the false-vacuum functional ensure that the rate remains independent of the choice of gauge-fixing. Our results are nonperturbative and clarify issues related with convexity and radiative corrections.
Recently it was discovered that the Standard Model vacuum may suffer an essential metastability near the Planck scale. In this regard it makes sense to study in more detail the decay processes of the metastable vacuum and to develop methods for their more accurate analysis. In this article we develop a technique to calculate two loop radiative corrections to false vacuum decay rate in thin-wall approximation and apply it to false vacuum decay in scalar quantum field theory with cubic and quartic interactions. The results obtained use dimensional regularization and given in two different renorm…
