arXiv subjects

Bjorn Garbrecht

Publications and source records attributed to Bjorn Garbrecht.

At least 19 recordsLinked to original sources

arXiv2026

CP conservation in the strong interactions

We discuss matters related to the point that topological quantization in the strong interaction is a consequence of an infinite spacetime volume. Because of the ensuing order of limits, i.e. infinite volume prior to summing over topological sectors, CP is conserved. Here, we show that this reasoning is consistent with the construction of the path integral from steepest-descent contours. We reply to some objections that aim to support the case for CP violation in the strong interactions that are based on the role of the CP-odd theta-parameter in three-form effective theories, the correct sampling of all configurations in the dilute instanton gas approximation and the volume dependence of the partition function. We also show that the chiral effective field theory derived from taking the volume to infinity first is in no contradiction with analyses based on partially conserved axial currents.

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arXiv2025

Bubble wall dynamics from nonequilibrium quantum field theory

We derive the coupled dynamics between the bubble wall and the plasma from first principles using nonequilibrium quantum field theory. The commonly used equation of motion of the bubble wall in the kinetic approach is shown to be incomplete. In the language of the two-particle-irreducible effective action, the conventional equation misses higher-loop terms generated by the condensate-particle type vertices (e.g.,~$φϕχ^2$, where $φ$ is the background field describing the bubble wall, $ϕ$ the corresponding particle excitation and $χ$ another particle species in the plasma). From the missing terms, we identify an additional dissipative friction which is contributed by particle production processes from the condensate-particle type vertices. We also show how other transmission processes beyond the 1-to-1 elementary transmission studied in the literature for ultrarelativistic bubble walls, e.g., 1-to-1 mixing and 1-to-2 transition radiation, can be understood from the kinetic approach.

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arXiv2024

Double-well instantons in finite volume

Assuming a toroidal space with finite volume, we derive analytically the full one-loop vacuum energy for a scalar field tunnelling between two degenerate vacua, taking into account discrete momentum. The Casimir energy is computed for an arbitrary number of dimensions using the Abel-Plana formula, while the one-loop instanton functional determinant is evaluated using the Green's functions for the fluctuation operators. The resulting energetic properties are non-trivial: both the Casimir effect and tunnelling contribute to the Null Energy Condition violation, arising from a non-extensive true vacuum energy. We discuss the relevance of this mechanism to induce a cosmic bounce, requiring no modified gravity or exotic matter.

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arXiv2024

The QCD theta-parameter in canonical quantization

The role of the QCD theta-parameter is investigated in pure Yang-Mills theory in the spacetime given by the four-dimensional Euclidean torus. While in this setting the introduction of possibly unphysical boundary conditions is avoided, it must be specified how the sum over the topological sectors is to be carried out. To connect with observables in real time, we perceive the partition function as the trace over the canonical density matrix. The system then corresponds to one of a finite temperature on a spatial three-torus. Carrying out the trace operation requires canonical quantization and gauge fixing. Fixing the gauge and demanding that the Hermiticity of the Hamiltonian is maintained leads to a restriction of the Hilbert space of physical wave functionals that generalizes the constraints derived from imposing Gauss' law. Consequently, we find that the states in the Hilbert space are properly normalizable under an inner product that integrates over each physical configuration represented by the gauge potential one time and one time only. The observables derived from the constrained Hilbert space do not violate charge-parity symmetry. We note that an exact hidden symmetry of the theory that is present for arbitrary values of theta in the Hamiltonian is effectively promoted to parity conservation in this constrained space. These results, derived on a torus in order to avoid the introduction of boundary conditions, also carry over to Minkowski spacetime when taking account of all possible gauge transformations.

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arXiv2023

Instability of bubble expansion at zero temperature

In the context of false vacuum decay at zero temperature, it is well known that bubbles expand with uniform proper acceleration. We show that this uniformly accelerating expansion suffers from an instability related to the bubble size. This can be observed in Minkowski spacetime as a tachyonic mode in the spectrum of fluctuations for the energy functional in the reference frame in which the uniformly accelerating bubble wall appears static. In such a frame, arbitrary small perturbations cause an amplifying departure from the static wall solution. This implies that the nucleated bubble is not a critical point of the energy functional in the rest frame of nucleation but becomes one in the accelerating frame. The aforementioned instability for vacuum bubbles can be related to the well-known instability for the nucleated critical static bubbles during finite-temperature phase transitions in the rest frame of the plasma. It is therefore proposed that zero-temperature vacuum decays as seen from accelerating frames have a dual description in terms of finite-temperature phase transitions.

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arXiv2022

The limits of the strong $CP$ problem

While $CP$ violation has never been observed in the strong interactions, the QCD Lagrangian admits a $CP$-odd topological interaction proportional to the so called $θ$ angle, which weighs the contributions to the partition function from different topological sectors. The observational bounds are usually interpreted as demanding a severe tuning of $θ$ against the phases of the quark masses, which constitutes the strong $CP$ problem. Here we report on recent challenges to this view based on a careful treatment of boundary conditions in the path integral and of the limit of infinite spacetime volume, which leads to $θ$ dropping out of fermion correlation functions and becoming unobservable, implying that $CP$ is preserved in QCD.

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arXiv2022

Bubble wall velocities in local equilibrium

It is commonly expected that a friction force on the bubble wall in a first-order phase transition can only arise from a departure from thermal equilibrium in the plasma. Recently however, it was argued that an effective friction, scaling as $γ_w^2$ (with $γ_w$ being the Lorentz factor for the bubble wall velocity), persists in local equilibrium. This was derived assuming constant plasma temperature and velocity throughout the wall. On the other hand, it is known that, at the leading order in derivatives, the plasma in local equilibrium only contributes a correction to the zero-temperature potential in the equation of motion of the background scalar field. For a constant plasma temperature, the equation of motion is then completely analogous to the vacuum case, the only change being a modified potential, and thus no friction should appear. We resolve these apparent contradictions in the calculations and their interpretation and show that the recently proposed effective friction in local equilibrium originates from inhomogeneous temperature distributions, such that the $γ_w^2$-scaling of the effective force is violated. Further, we propose a new matching condition for the hydrodynamic quantities in the plasma valid in local equilibrium and tied to local entropy conservation. With this added constraint, bubble velocities in local equilibrium can be determined once the parameters in the equation of state are fixed, where we use the bag equation in order to illustrate this point. We find that there is a critical value of the transition strength $α_{\rm crit}$ such that bubble walls run away for $α>α_{\rm crit}$.

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arXiv2021

Absence of $CP$ violation in the strong interactions

We derive correlation functions for massive fermions with a complex mass in the presence of a general vacuum angle. For this purpose, we first build the Green's functions in the one-instanton background and then sum over the configurations of background instantons. The quantization of topological sectors follows for saddle points of finite Euclidean action in an infinite spacetime volume and the fluctuations about these. For the resulting correlation functions, we therefore take the infinite-volume limit before summing over topological sectors. In contrast to the opposite order of limits, the chiral phases from the mass terms and from the instanton effects then are aligned so that, in absence of additional phases, these do not give rise to observables violating charge-parity symmetry. This result is confirmed when constraining the correlations at coincident points by using the index theorem instead of instanton calculus.

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arXiv2020

Fat brane and seesaw mechanism in extra dimensions

In this paper we present a higher-dimensional seesaw mechanism. We consider a single, flat extra dimension, where a fat brane is localized and contains the standard model (SM) fields, similar to Universal Extra Dimension models. There is only one Dirac fermion in the bulk, and in four dimensions it results in two towers of Kaluza-Klein (KK) Majorana sterile neutrinos, whose mass mixing with the SM neutrinos is suppressed due to a brane-localized kinetic term. The interaction between the sterile neutrinos and the SM is through the usual coupling with the Higgs boson, where the coupling depends upon the compactification radius $R^{-1}=10^{-2}-1$ GeV and the width of the fat brane $L^{-1}=2$ TeV, where the latter value is chosen to avoid LHC constraints. Due to this suppression mechanism the mass of the lightest sterile neutrinos can be of order $\mathcal{O}(1-10)$~\text{TeV} while naturally explaining the small SM neutrino mass, which in turn is easily obtained for a large range of parameter choices. Furthermore, neutrino oscillations are not substantially influenced by the tower of sterile KK particles. Finally, leptogenesis is investigated in this setup, and it is viable for some values within the parameter space.

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arXiv2020

Gradient effects on false vacuum decay in gauge theory

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 numerical calculation of Green's functions. In addition to the renormalization of couplings, we employ a covariant gradient expansion in order to systematically construct the counterterm for the wave-function renormalization. The result for the full decay rate however does not rely on such an expansion and accounts for all gradient corrections at the chosen truncation of the loop expansion. The ensuing gradient effects are shown to be of the same order of magnitude as non-derivative one-loop corrections.

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arXiv2020

Leptogenesis from Oscillations of Heavy Neutrinos with Large Mixing Angles

The extension of the Standard Model by heavy right-handed neutrinos can simultaneously explain the observed neutrino masses via the seesaw mechanism and the baryon asymmetry of the Universe via leptogenesis. If the mass of the heavy neutrinos is below the electroweak scale, they may be found at the LHC, BELLE II, NA62, the proposed SHiP experiment or a future high-energy collider. In this mass range, the baryon asymmetry is generated via CP-violating oscillations of the heavy neutrinos during their production. We study the generation of the baryon asymmetry of the Universe in this scenario from first principles of non-equilibrium quantum field theory,including spectator processes and feedback effects. We eliminate several uncertainties from previous calculations and find that the baryon asymmetry of the Universe can be explained with larger heavy neutrino mixing angles, increasing the chance for an experimental discovery. For the limiting cases of fast and strongly overdamped oscillations of right-handed neutrinos, the generation of the baryon asymmetry can be calculated analytically up to corrections of order one.

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arXiv2020

Why is there more matter than antimatter? Calculational methods for leptogenesis and electroweak baryogenesis

We review the production of the matter-antimatter asymmetry in the early Universe, that is baryogenesis, in out-of-equlibrium conditions induced by decays of heavy particles or by the presence of phase boundaries. The most prominent examples are given by leptogenesis and electroweak baryogenesis, respectively. For both cases, we derive the equations that govern the production of the asymmetries. We first use intuitive arguments based on classical fluid equations in combination with quantum-field-theoretical effects of CP-violation. As for a more thorough approach that is well-suited for systematic improvements, we obtain the real-time evolution of the system of interest using the closed time-path method. We thus provide a simple and practicable scheme to set up phenomenological fluid equations based on first principles of quantum field theory. Necessary for baryogenesis are both, CP even as well as odd phases in the amplitudes. A possibility of generating the even phases is the coherent superposition of quantum states, i.e. mixing. These coherence effects are essential in resonant leptogenesis as well as in some scenarios of electroweak baryogenesis. Recent theoretical progress on asymmetries from out-of-equlibrium decays may therefore also be applicable to baryogenesis at phase boundaries.

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arXiv2019

Functional methods for false vacuum decay in real time

We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum corrections. For this purpose, we use the well-known fact that Euclidean saddle points in terms of real fields can be analytically continued to complex saddles of the action in Minkowski space. We also use Picard-Lefschetz theory in order to determine the middle-dimensional steepest-descent surface in the complex field space, constructed from Lefschetz thimbles, on which the path integral is to be performed. As an alternative to extracting the decay rate from the imaginary part of the ground-state energy of the false vacuum, we use the optical theorem in order to derive it from the real-time amplitude for forward scattering. While this amplitude may in principle be obtained by analytic continuation of its Euclidean counterpart, we work out in detail how it can be computed to one-loop order at the level of the path integral, i.e. evaluating the Gaußian integrals of fluctuations about the relevant complex saddle points. To that effect, we show how the eigenvalues and eigenfunctions on a thimble can be obtained by analytic continuation of the Euclidean eigensystem, and we determine the path-integral measure on thimbles. This way, using real-time methods, we recover the one-loop result by Callan and Coleman for the decay rate. We finally demonstrate our real-time methods explicitly, including the construction of the eigensystem of the complex saddle, on the archetypical example of tunneling in a quasi-degenerate quartic potential.

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arXiv2018

Radiative effects on false vacuum decay in Higgs-Yukawa theory

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.

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arXiv2018

Probing Leptogenesis at Future Colliders

We investigate the question whether leptogenesis, as a mechanism for explaining the baryon asymmetry of the universe, can be tested at future colliders. Focusing on the minimal scenario of two right-handed neutrinos, we identify the allowed parameter space for successful leptogenesis in the heavy neutrino mass range between $5$ and $50$ GeV. Our calculation includes the lepton flavour violating contribution from heavy neutrino oscillations as well as the lepton number violating contribution from Higgs decays to the baryon asymmetry of the universe. We confront this parameter space region with the discovery potential for heavy neutrinos at future lepton colliders, which can be very sensitive in this mass range via displaced vertex searches. Beyond the discovery of heavy neutrinos, we study the precision at which the flavour-dependent active-sterile mixing angles can be measured. The measurement of these mixing angles at future colliders can test whether a minimal type I seesaw mechanism is the origin of the light neutrino masses, and it can be a first step towards probing leptogenesis as the mechanism of baryogenesis. We discuss how a stronger test could be achieved with an additional measurement of the heavy neutrino mass difference.

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arXiv2018

Fluctuations about the Fubini-Lipatov instanton for false vacuum decay in classically scale invariant models

For a scalar theory whose classical scale invariance is broken by quantum effects, we compute self-consistent bounce solutions and Green's functions. Deriving analytic expressions, we find that the latter are similar to the Green's functions in the archetypal thin-wall model for tunneling between quasi-degenerate vacua. The eigenmodes and eigenspectra are, however, very different. Large infrared effects from the modes of low angular momentum $j=0$ and $j=1$, which include the approximate dilatational modes for $j=0$, are dealt with by a resummation of one-loop effects. For a parametric example, this resummation is carried out numerically.

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arXiv2018

Flavor effects in leptogenesis

Flavor effects can have a significant impact on the final estimate of the lepton (and therefore baryon) asymmetry in scenarios of leptogenesis. It is therefore necessary to account fully for this flavor dynamics in the relevant transport equations that describe the production (and washout) of the asymmetry. Doing so can both open up and restrict viable regions of parameter space relative to the predictions of more approximate calculations. In this review, we identify the regimes in which flavor effects can be relevant and illustrate their impact in a number of phenomenological models. These include type I and type II seesaw embeddings, and low-scale resonant scenarios. In addition, we provide an overview of the semi-classical and field-theoretic methods that have been developed to capture flavor effects in a consistent way.

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arXiv2018

Probing the Seesaw Mechanism and Leptogenesis with the International Linear Collider

We investigate the potential of the International Linear Collider (ILC) to probe the mechanisms of neutrino mass generation and leptogenesis within the minimal seesaw model. Our results can also be used as an estimate for the potential of a Compact Linear Collider (CLIC). We find that heavy sterile neutrinos that simultaneously explain both, the observed light neutrino oscillations and the baryon asymmetry of the universe, can be found in displaced vertex searches at ILC. We further study the precision at which the flavour-dependent active-sterile mixing angles can be measured. The measurement of the ratios of these mixing angles, and potentially also of the heavy neutrino mass splitting, can test whether minimal type I seesaw models are the origin of the light neutrino masses, and it can be a first step towards probing leptogenesis as the mechanism of baryogenesis. Our results show that the ILC can be used as a discovery machine for New Physics in feebly coupled sectors that can address fundamental questions in particle physics and cosmology.

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