arXiv subjects

Björn Garbrecht

Publications and source records attributed to Björn Garbrecht.

At least 19 recordsLinked to original sources

arXiv2026

On the relaxation dynamics of non-equilibrium quantum systems

We investigate the relaxation of an approximately conserved charge in interacting quantum systems close to local equilibrium. To this end, we provide a pedagogical review of Zubarev's non-equilibrium statistical operator approach in the minimal setting of a single non-conserved charge and apply it to the problem at hand. We explicitly highlight the physical assumptions that lead to a local relaxation law: weak charge violation, a separation between the short timescale of microscopic correlations and the much longer timescale of charge relaxation, and the resulting loss of microscopic memory. Under these conditions, the leading relaxation rate is determined by an equilibrium correlation function of the charge-violating operator. We show that the same result follows from a simpler local-equilibrium construction based on the system's evolution over an intermediate timescale, providing a direct alternative for practical calculations and making the common physical ingredients of the two approaches explicit. Beyond the decay law itself, we relate the relaxation rate to the equilibrium diffusion of the same charge. We then allow the charge density to vary in space, which leads to a diffusion-relaxation equation. Finally, we illustrate the formalism through electroweak $\mathrm{B+L}$ washout and a perturbative scalar model, where agreement with the linearized Boltzmann equation establishes a direct connection between equilibrium-correlator and kinetic descriptions.

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arXiv2025

Baryogenesis and EDMs in the 2HDM+CS

We perform the first joint analysis of baryogenesis from initial Higgs charges (also called Higgsogenesis) and EDMs in a model with two Higgs doublets, a complex scalar and a Majorana fermion. In our proposed scenario, baryogenesis happens in three steps: (1) The decay of the scalar produces an asymmetry between the two Higgs doublets which is partly transferred to fermions via Standard Model processes. (2) This asymmetry is converted into a $B-L$ charge via interactions mediated by the Majorana fermion. (3) The weak sphaleron processes partially convert the resulting $B-L$ charge into a $B$ asymmetry. We perform a numerical analysis of baryogenesis and the EDM contributions and find that, due to resonant enhancement, baryogenesis is possible with singlet masses as low as $10^5$ GeV. We also find that for some parameters, the model can give large contributions to the electron and neutron EDM while also producing baryogenesis. The present scenario offers a new perspective on interpreting observational bounds in terms of cosmology: Because it relies on out-of-equilibrium decays, the questions of baryogenesis and $CP$ violation in the Higgs sector may be linked with EDM signals without the additional assumption of a first order electroweak phase transition.

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arXiv2025

Instantons meet resonances: Unifying two seemingly distinct approaches to quantum tunneling

In the study of quantum-mechanical tunneling processes, numerous approaches have been developed to determine the decay rate of states initially confined within a metastable potential region. Virtually all analytical treatments, however, fall into one of two superficially unrelated conceptual frameworks: the resonant-state approach and the instanton method. Whereas the concept of resonant states and their associated decay widths is grounded in physical reasoning by capturing the regime of uniform probability decay, the instanton method lacks a comparably clear physical interpretation. We demonstrate the equivalence of the two approaches, revealing that the contour-deformation prescription in the functional integral put forward by Callan and Coleman directly corresponds to the outgoing Gamow--Siegert boundary conditions defining resonant states.

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arXiv2025

Reply to "Clearing up the Strong $CP$ problem"

The conservation of $CP$ in QCD has been shown to follow from a careful treatment of the path integral and canonical quantization in arXiv:2001.07152 and arXiv:2403.00747. Here, we refute the critique of these results put forth in arXiv:2510.18951. First, using the quantum rotor as an analogue of QCD, it is argued in arXiv:2510.18951 that the topological susceptibility vanishes when using the limiting procedure of arXiv:2001.07152. When translated to QCD, this would contradict the observed $η^\prime$-mass. We show that this is not the case because the susceptibility is defined from the vacuum correlator of the topological charge density, which for the rotor is just fixed by the canonical commutation relation. The latter does not depend on the disputed order of limits. Second, it is suggested in arXiv:2510.18951 that $CP$ violation in QCD can be established by considering the low-energy effective theory alone. We show that here the argument relies on assuming from the start choices of couplings that lead to $CP$ violation but are not of the most general form allowed by spurion analysis. No valid reason is given for why allowed choices leading to $CP$ conservation, that match the computation of ultraviolet correlators as shown in arXiv:2001.07152 and arXiv:2403.00747, would be inconsistent.

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arXiv2025

False vacuum decay of excited states in finite-time instanton calculus

Extracting information about a system's metastable ground state energy employing functional methods usually hinges on utilizing the late-time behavior of the Euclidean propagator, practically impeding the possibility of determining decay widths of excited states. We demonstrate that such obstacles can be surmounted by working with bounded time intervals, adapting the standard instanton formalism to compute a finite-time amplitude corresponding to excited state decay. This is achieved by projecting out the desired resonant energies utilizing carefully chosen approximations to the excited state wave functions in the false vacuum region. To carry out the calculation, we employ unconventional path integral techniques by considering the emerging amplitude as a single composite functional integral that includes fluctuations at the endpoints of the trajectories. This way, we explicitly compute the sought-after decay widths, including their leading quantum corrections, for arbitrary potentials, demonstrating accordance with traditional WKB results. While the initial starting point of weighting Euclidean propagator contributions according to their endpoints using false vacuum states has been proposed earlier, we find several flaws in the published evaluation of the relevant amplitudes. Although we show that the previous proposition of employing a sequential calculation scheme -- where the functional integral is evaluated around extremal trajectories with fixed endpoints, weighted only at a subsequent stage -- can lead to the desired goal, the novel composite approach is found to be more concise and transparent.

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arXiv2025

Path integral analysis of Schrödinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states

Schrödinger-type eigenvalue problems are ubiquitous in theoretical physics, with quantum-mechanical applications typically confined to cases for which the eigenfunctions are required to be normalizable on the real axis. However, seeking the spectrum of resonant states for metastable potentials or comprehending $\mathcal{PT}$-symmetric scenarios requires the broader study of eigenvalue problems for which the boundary conditions are provided in specific angular sectors of the complex plane. We generalize the conventional path integral treatment to such nonstandard boundary value problems, allowing the extraction of spectral information using functional methods. We find that the arising functional integrals are naturally defined on a complexified integration contour, encapsulating the demanded sectorial boundary conditions of the associated eigenvalue problem. The attained results are applied to the analysis of resonant ground-state energies, through which we identify the previously elusive one-to-one correspondence between decay rates derived from real-time quantum tunneling dynamics and those obtained via the Euclidean instanton method.

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arXiv2025

Curvature perturbations from vacuum transition during inflation

We demonstrate that in the presence of a light scalar spectator field, vacuum transitions taking place during inflation can produce large, potentially detectable non-Gaussian signatures in the primordial curvature perturbation. Such transitions are common in theories with multiple scalar fields when the potential has several minima. Our computation proceeds by numerically finding the instanton solution that describes quantum tunnelling between vacuum states in a de Sitter background, calculating its dependence on the spectator field and, thereby, its effect on the expansion of space. For a scenario with Higgs inflation, we obtain the non-Gaussianity parameter $f_\mathrm{NL} \sim O(10)$ and study its parameter dependence.

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arXiv2025

False vacuum decay beyond the quadratic approximation: summation of non-local self-energies

Using the 2PI effective action formalism, we study false vacuum decay beyond the quadratic approximation of the path integral. We derive a coupled system of equations for the bounce and the propagator, and we compute a semi-analytic expression for the self-energy of a real scalar field with cubic and quartic interactions from the 2PI effective action truncated at two loops and without further approximations. Deriving numerical results, we can show that the Hartree approximation, where non-local contributions to the self-energy are neglected, is generally not justified. The procedure we develop is a key step towards the explicit computation of the quantum corrected bounce, the determinant of fluctuations about it and the decay rate in the presence of classical zero-modes that are lifted by quantum effects, e.g. classically scale-invariant models relevant for assessing the Higgs stability.

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arXiv2025

The Neutrino Mass Bound from Leptogenesis Revisited

Recent years have seen a great improvement in the computation of $CP$-conserving and $CP$-violating equilibration rates for leptogenesis. These are relevant for the relativistic regime of the sterile Majorana fermions and the dynamics of the Standard Model particles acting as spectator processes. In order to probe the regime of large $({\cal O}(10^2))$ washout parameters, we add $ΔL = 2$ washout processes, which we derive in the CTP-formalism. To demonstrate their significance, we apply state-of-the-art computational techniques to a simple yet well-motivated phenomenological scenario: unflavored leptogenesis in a hierarchical type-I seesaw model. We then perform a parameter scan of the final baryon asymmetry and find a constraint $m_\text{lightest} \lesssim 0.15 \, \text{eV}$ on the absolute neutrino mass scale, which is slightly less stringent than previously reported bounds obtained without the aforementioned improvements. The relaxation of the bounds is mainly due to partially equilibrated spectator fields, which protect part of the asymmetry from washout and lead to larger final asymmetries. While this might seem like a minor correction, the actual dynamics of the fields is substantially altered by these effects. Even though we focused on a particularly simple scenario for leptogenesis, the methods employed here can and should be extended to other models, thus giving us a more accurate picture of the different leptogenesis scenarios.

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arXiv2025

A Scotogenic Model as a Prototype for Leptogenesis with One Single Gauge Singlet

We investigate the potential of a minimal Scotogenic model with two additional scalar doublets and a single heavy Majorana fermion to explain neutrino masses, dark matter, and the baryon asymmetry of the Universe. In this minimal setup, Leptogenesis is purely flavored, and a second Majorana neutrino is not necessary because the Yukawa couplings of the extra doublets yield the necessary $CP$-odd phases. The mechanism we employ can also be applied to a wide range of scenarios with at least one singlet and two gauge multiplets. Despite stringent limits from the dark matter abundance, direct detection experiments, and the baryon asymmetry of the Universe, we find a parametric region consistent with all bounds which could resolve the above shortcomings of the Standard Model of particle physics. Methodically, we improve on the calculation of correlations between the mixing scalar fields given their finite width. We also present an argument to justify the kinetic equilibrium approximation for out-of-equilibrium distribution functions often used in calculations of Baryogenesis and Leptogenesis.

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arXiv2022

Superradiance in Stars: Non-equilibrium approach to damping of fields in stellar media

Superradiance in black holes is well-understood but a general treatment for superradiance in stars has until now been lacking. This is surprising given the ease with which we can observe isolated neutron stars and the array of signatures which would result from stellar superradiance. In this work, we present the first systematic pipeline for computing superradiance rates in rotating stars. Our method can be used with any Lagrangian describing the interaction between the superradiant field and the constituents of the star. Our scheme falls into two parts: firstly we show how field theory at finite density can be used to express the absorption of long wavelength modes into the star in terms of microphsyical scattering processes. This allows us to derive a damped equation of motion for the bosonic field. We then feed this into an effective theory for long wavelengths (the so-called worldline formalism) to describe the amplification of superradiant modes of arbitrary multipole moment for a rapidly rotating star. Our method places stellar superradiance on a firm theoretical footing and allows the calculation of the superradiance rate arising from any interaction between a bosonic field and stellar matter.

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arXiv2020

Relativistic and spectator effects in leptogenesis with heavy sterile neutrinos

For leptogenesis with heavy sterile neutrinos above the electroweak scale, asymmetries produced at early times (in the relativistic regime) are relevant, if they are protected from washout. This can occur for weak washout or when the asymmetry is partly protected by being transferred to spectator fields. We thus study the relevance of relativistic effects for leptogenesis in a minimal seesaw model with two sterile neutrinos in the strongly hierarchical limit. Starting from first principles, we derive a set of momentum-averaged fluid equations to calculate the final $B-L$ asymmetry as a function of the washout strength and for different initial conditions at order one accuracy. For this, we take the leading fluid approximation for the relativistic $CP$-even and odd rates. Assuming that spectator fields remain in chemical equilibrium, we find that for weak washout, relativistic corrections lead to a sign flip and an enhancement of the asymmetry for a vanishing initial abundance of sterile neutrinos. As an example for the effect of partially equilibrated spectators, we consider bottom-Yukawa and weak-sphaleron interactions in leptogenesis driven by sterile neutrinos with masses $\gtrsim 5\times10^{12}$ GeV. For a vanishing initial abundance of sterile neutrinos, this can give rise to another flip and an absolute enhancement of the final asymmetry in the strong washout regime by up to two orders of magnitude relative to the cases either without spectators or with fully equilibrated ones. These effects are less pronounced for thermal initial conditions for the sterile neutrinos. The $CP$-violating source in the relativistic regime at early times is important as it is proportional to the product of lepton-number violating and lepton-number conserving rates, and therefore less suppressed than an extrapolation of the nonrelativistic approximations may suggest.

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arXiv2017

Combining Experimental and Cosmological Constraints on Heavy Neutrinos

We study experimental and cosmological constraints on the extension of the Standard Model by three right handed neutrinos with masses between those of the pion and W boson. We combine for the first time direct, indirect and cosmological constraints in this mass range. This includes experimental constraints from neutrino oscillation data, neutrinoless double $β$ decay, electroweak precision data, lepton universality, searches for rare lepton decays, tests of CKM unitarity and past direct searches at colliders or fixed target experiments. On the cosmological side, big bang nucleosynthesis has the most pronounced impact. Our results can be used to evaluate the discovery potential of searches for heavy neutrinos at LHCb, BELLE II, SHiP, ATLAS, CMS or a future lepton collider.

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arXiv2015

Probing leptogenesis with GeV-scale sterile neutrinos at LHCb and BELLE II

We show that existing laboratory experiments have the potential to unveil the origin of matter by probing leptogenesis in the type-I seesaw model with three right-handed neutrinos and Majorana masses in the GeV range. The baryon asymmetry is generated by CP-violating flavour oscillations during the production of the right-handed neutrinos. In contrast to the case with only two right-handed neutrinos, no degeneracy in the Majorana masses is required. The right-handed neutrinos can be found in meson decays at BELLE II and LHCb.

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arXiv2015

A facility to Search for Hidden Particles at the CERN SPS: the SHiP physics case

This paper describes the physics case for a new fixed target facility at CERN SPS. The SHiP (Search for Hidden Particles) experiment is intended to hunt for new physics in the largely unexplored domain of very weakly interacting particles with masses below the Fermi scale, inaccessible to the LHC experiments, and to study tau neutrino physics. The same proton beam setup can be used later to look for decays of tau-leptons with lepton flavour number non-conservation, $τ\to 3μ$ and to search for weakly-interacting sub-GeV dark matter candidates. We discuss the evidence for physics beyond the Standard Model and describe interactions between new particles and four different portals - scalars, vectors, fermions or axion-like particles. We discuss motivations for different models, manifesting themselves via these interactions, and how they can be probed with the SHiP experiment and present several case studies. The prospects to search for relatively light SUSY and composite particles at SHiP are also discussed. We demonstrate that the SHiP experiment has a unique potential to discover new physics and can directly probe a number of solutions of beyond the Standard Model puzzles, such as neutrino masses, baryon asymmetry of the Universe, dark matter, and inflation

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arXiv2014

Testing Inflation and Curvaton Scenarios with CMB Distortions

Prior to recombination, Silk damping causes the dissipation of energy from acoustic waves into the monopole of the Cosmic Microwave Background (CMB), resulting in spectral distortions. These can be used to probe the primordial scalar power spectrum on smaller scales than it is possible with CMB anisotropies. An enhancement of power on these scales is nevertheless required for the resulting distortions to be detectable by future experiments like PIXIE. In this paper, we examine all 49 single-field inflation models listed by Martin et al. in the Encyclopaedia Inflationaris [1] and find that only one of these may lead to a detectable level of distortions in a tuned region of its parameter space, namely the original hybrid model. Three effective multi-field scenarios are also studied: with softly and suddenly turning trajectories, and with a mild waterfall trajectory. Softly turning trajectories do not induce distortions at any detectable level, whereas a sudden turn in the field space or a mild waterfall trajectory predicts a peak (plus damped oscillations in the sudden turn case) in the scalar power spectrum, which can lead to an observable amount of CMB distortions. Finally, another scenario leading to potentially detectable distortions involves a curvaton whose blue spectrum is subdominant on CMB angular scales and overtakes the inflaton spectrum on smaller scales. In this case however, we show that the bounds from ultra compact minihaloes are not satisfied. Expectations for an ultimate PRISM-class experiment characterized by an improvement in sensitivity by a factor of ten are discussed for some models.

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arXiv2013

Non-Gaussianities and Curvature Perturbations from Hybrid Inflation

For the original hybrid inflation as well as the supersymmetric F-term and D-term hybrid models, we calculate the level of non-gaussianities and the power spectrum of curvature perturbations generated during the waterfall, taking into account the contribution of entropic modes. We focus on the regime of mild waterfall, in which inflation continues for more than about 60 e-folds N during the waterfall. We find that the associated f_nl parameter goes typically from f_nl \simeq -1 / N_exit in the regime with N >> 60, where N_exit is the number of e-folds between the time of Hubble exit of a pivot scale and the end of inflation, down to f_nl ~-0.3 when N \gtrsim 60, i.e. much smaller in magnitude than the current bound from Planck. Considering only the adiabatic perturbations, the power spectrum is red, with a spectral index n_s = 1 - 4 / N_exit, in the case N >> 60, whereas in the case N \gtrsim 60, it increases up to unity. Including the contribution of entropic modes does not change the observable predictions in the first case. However, in the second case, they are a relevant source for the power spectrum of curvature perturbations, of which the amplitude increases by several orders of magnitudes and can lead to black hole formation. We conclude that due to the important contribution of entropic modes, the parameter space leading to a mild waterfall phase is excluded by CMB observations for all the considered models.

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arXiv2012

Slow Roll during the Waterfall Regime: The Small Coupling Window for SUSY Hybrid Inflation

It has recently been pointed out that a substantial amount of e-folds can occur during the waterfall regime of hybrid inflation. Moreover, Kodama et.al. have derived analytic approximations for the trajectories of the inflaton and of the waterfall fields. Based on these, we derive here the consequences for F- and D-term SUSY hybrid inflation: A substantial amount of e-folds may occur in the waterfall regime, provided kappa << M^2/M_P^2, where kappa is the superpotential coupling, M the scale of symmetry breaking and M_P the reduced Planck mass. When this condition is amply fulfilled, a number of e-folds much larger than N_e\approx60 can occur in the waterfall regime and the scalar spectral index is then given by the expression found by Kodama et.al. n_s=1-4/N_e. This value may be increased up to unity, if only about N_e e-folds occur during the waterfall regime, such that the largest observable scale leaves the horizon close to the critical point of hybrid inflation, what can be achieved for kappa\approx10^(-13) and M\approx5x10^(12) GeV in F-term inflation. Imposing the normalization of the power spectrum leads to a lower bound on the scale of symmetry breaking.

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