Search

A one-loop Dyson-Schwinger-like resummation scheme is applied to scalar High-Electric-Charge compact Objects (HECOs), extending previous work on spin-1/2 case. The electromagnetic interactions of HECOs are considered within the framework of strongly coupled scalar Quantun Electrodynamics. The resummation amounts to determining non-trivial ultraviolet (UV) fixed points, at which the effective Lagrangian, which will lead to the pertinent predictions on the cross sections, is computed. In contrast to the fermionic HECO case, in which the fixed point structure was determined solely by the interactions of the HECOs with the photon field, in the scalar case the existence of non-trivial UV fixed points requires the presence of additional strong self interactions among the HECOs. Our resummation scheme, which is notably different from a lattice strong-coupling approach, makes the computation of the pertinent scalar-HECO-production cross sections reliable, thus allowing revisiting the mass bounds obtained from searches for such objects in current or future colliders. Our MadGraph implementation of the results leads to enhanced (up to ~30%) lower bounds on the mass of scalar HECOs, as compared to those extracted from the tree-level processes typically used in LHC collider searches by ATLAS and MoEDAL experiments., Comment: 18 pages, RevTex, 7 figures, 6 tables. arXiv admin note: text overlap with arXiv:2310.17452

High-Electric-Charge compact Objects (HECOs) appear in several theoretical particle physics models beyond the Standard Model, and are actively searched for in current colliders, such as the Large Hadron Collider (LHC). In such searches, mass bounds of these objects have been placed, using Drell-Yan and Photon-Fusion processes at tree level so far. However, such estimates are not reliable, given that, as a result of the large values of the electric charge of the HECO, perturbative QED calculations break down. We present a Dyson-Schwinger-like resummation scheme, which allows for a large gauge coupling and thus makes the computation of the pertinent HECO-production cross sections reliable, thus allowing us to extract improved mass bounds for such objects from ATLAS and MoEDAL searches., Comment: 6 pages, 1 figure, Proceedings for the 42nd International Conference on High Energy Physics (ICHEP 2024), 18-24 July 2024; submitted to Proceedings of Science (PoS)

Two fundamental signatures of Quantum Mechanics are tunnelling and the Casimir effect. We examine the ground state energetic properties of a scalar field confined on a $D$-dimensional sphere, and subjected to these two effects. We focus on $D=2$ and $D=3$, with a non-minimal coupling of a massless scalar field to curvature, which provides a radius-dependent effective mass. This scenario allows tunnelling to be more important than the Casimir effect, in a certain regime of parameters, and potential implications in Early Cosmology are discussed for the case $D=3$, which could avoid a cosmological singularity., Comment: 5 pages, 2 figures

We study bounce solutions and associated negative modes in the class of piecewise linear triangular-shaped potentials that may be viewed as approximations of smooth potentials. In these simple potentials, the bounce solution and action can be obtained analytically for a general spacetime dimension $D$. The eigenequations for the fluctuations around the bounce are universal and have the form of a Schr\"odinger-like equation with delta-function potentials. This Schr\"odinger equation is solved exactly for the negative modes whose number is confirmed to be one. The latter result may justify the usefulness of such piecewise linear potentials in the study of false vacuum decay.

Both black hole thermodynamics and finite volume effects in quantum field theory violate the null energy condition. Motivated by this, we compare thermodynamic features between two 1+1-dimensional systems: (i) a scalar field confined to a periodic spatial interval of length $a$ and tunneling between two degenerate vacua; (ii) a dilatonic black hole at temperature $T$ in the presence of matter fields. If we identify $a\propto T^{-1}$, we find similar thermodynamic behaviours, which suggests some deeper connection arising from the presence of non-trivial boundary conditions in both systems., Comment: 28 pages, 4 figures

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., Comment: 28 pages, 6 figures

We develop a method for accurately calculating vacuum decay rates beyond the thin-wall regime in a pure scalar field theory at the one-loop level of the effective action. It accounts for radiative effects resulting from quantum corrections to the classical bounce, including gradient effects stemming from the inhomogeneity of the bounce background. To achieve this, it is necessary to compute not only the functional determinant of the fluctuation operator in the background of the classical bounce but also its functional derivative evaluated at the classical bounce. The former is efficiently calculated using the Gel'fand-Yaglom method. We illustrate how the latter can also be calculated with the same method, combined with a computation of various Green's functions., Comment: 35 pages, 5 figures; v2: presentation improved, refs updated; v3: a typo in Eq. (27) corrected, matches the published version

High-Electric-Charge compact Objects (HECOs) appear in several theoretical particle physics models beyond the Standard Model, and are actively searched for in current colliders, such as the Large Hadron Collider at CERN. In such searches, mass bounds of these objects have been placed, using Drell-Yan and photon-fusion processes at tree level so far. However, such mass-bound estimates are not reliable, given that, as a result of the large values of the electric charge of the HECO, perturbative Quantum Electrodynamics calculations break down. In this work, we perform a Dyson-Schwinger resummation scheme (as opposed to lattice strong-coupling approach), which makes the computation of the pertinent HECO-production cross sections reliable, thus allowing us to extract improved mass bounds for such objects from ATLAS and MoEDAL searches., Comment: 24 pages, 6 figures, 10 tables; typo correction in photon propagator in (26) and in respective Feynman rules in Tables V, VI and Eq.(A.4), with no effect on numerical results and conclusions; clarification added on HECO-photon vertex Feynman rule below (26)

If we imagine rewinding the universe to early times, the scale factor shrinks and the existence of a finite spatial volume may play a role in quantum tunnelling effects in a closed universe. It has recently been shown that such finite volume effects dynamically generate an effective equation of state that could support a cosmological bounce. In this work we extend the analysis to the case in which a (homogeneous) anisotropy is present, and identify a criteria for a successful bounce in terms of the size of the closed universe and the properties of the quantum field., Comment: 9 pages, 5 figures, minor changes, version accepted for publication in Physical Review D

There is growing interest in viable quantum theories with PT-symmetric non-Hermitian Hamiltonians, but a formulation of transition matrix elements consistent with positivity and perturbative unitarity has so far proved elusive. This Letter provides such a formulation, which relies crucially on the ability to span the state space in such a way that the interaction and energy eigenstates are orthonormal with respect to the same positive-definite inner product. We mention possible applications to the oscillations of mesons and neutrinos., Comment: 5 pages, 3 figures, revtex format

We allow a scalar field on a flat FLRW background metric to tunnel between two degenerate vacua. The resulting true vacuum state then violates the Null Energy Condition, and the corresponding homogeneous fluid induces a bounce, after which it has a phantom-like equation of state and asymptotically leads to a de Sitter phase. The mechanism presented here requires no exotic matter or modified gravity, it is purely generated by quantum fluctuations and is valid for a generic double well potential., Comment: Comments added; 22 pages, 3 figures

We show that tunnelling between two degenerate minima, as allowed in a finite volume, leads to a non-extensive symmetric ground state. This results in Null Energy Condition violation for sufficiently low temperatures, when a continuous set of momenta in the box containing the field is assumed. Taking into account discrete momenta can modify this picture and is achieved via the addition of the Casimir energy to the tunnelling-induced ground state energy. Focusing on zero-temperature, these non-trivial effects are found to compete, depending on the typical length scales involved., Comment: 9 pages, 4 figures

We study the renormalisation of the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with the interaction $\phi^2(i\phi)^\varepsilon$ using the Wilsonian approach and without any expansion in $\varepsilon$. Specifically, we solve the Wetterich equation in the local potential approximation, both in the ultraviolet regime and with the loop expansion. We calculate the scale-dependent effective potential and its infrared limit. The theory is found to be renormalisable at the one-loop level only for integer values of $\varepsilon$, a result which is not yet established within the $\varepsilon$-expansion. Particular attention is therefore paid to the two interesting cases $\varepsilon=1,2$, and the one-loop beta functions for the coupling associated with the interaction $i\phi^3$ and $-\phi^4$ are computed. It is found that the $-\phi^4$ theory has asymptotic freedom in four-dimensional spacetime. Some general properties for the Euclidean partition function and $n$-point functions are also derived., Comment: 18 pages; v2: refs added, published version

A finite volume allows tunnelling between degenerate vacua in Quantum Field Theory, and leads to remarkable energetic features, arising from the competition of different saddle points in the partition function. We describe this competition for finite temperature at equilibrium, taking into account both static and (Euclidean) time-dependent saddle points. The effective theory for the homogeneous order parameter yields a non-extensive vacuum energy at low temperatures, implying a dynamical violation of the Null Energy Condition., Comment: 14 pages, two figures

Tunnelling between degenerate vacuua is allowed in finite-volume Quantum Field Theory, and features remarkable energetic properties, which result from the competition of different dominant configurations in the partition function. We derive the one-loop effective potential based on two homogeneous vacuua of the bare theory, and we discuss the resulting Null Energy Condition violation in O(4)-symmetric Euclidean spacetime, as a result of a non-extensive effective action., Comment: 8 pages, 5 figures

We extend to a non-Hermitian fermionic quantum field theory with PT symmetry our previous discussion of second quantization, discrete symmetry transformations, and inner products in a scalar field theory [arXiv:2006.06656]. For illustration, we consider a prototype model containing a single Dirac fermion with a parity-odd, anti-Hermitian mass term. In the phase of unbroken PT symmetry, this Dirac fermion model is equivalent to a Hermitian theory under a similarity transformation, with the non-Hermitian nature of the model residing only in the spinor structure, whereas the algebra of the creation and annihilation operators is just that of a Hermitian theory., Comment: 29 pages, revtex format; to match published version

The Null Energy Condition is considered the most fundamental of the energy conditions, on which several key results, such as the singularity theorems, are based. The Casimir effect is one of the rare equilibrium mechanisms by which it is breached without invoking modified gravity or non-minimal couplings to exotic matter. In this work we propose an independent dynamical mechanism by which it is violated, with the only ingredients being standard (but non-perturbative) QFT and a minimally coupled scalar field in a double-well potential. As for the Casimir effect, we explain why the Averaged Null Energy Condition should not be violated by this mechanism. Nevertheless, the transient behaviour could have profound impacts in Early Universe Cosmology., Comment: 7 pages, 1 figure

We discuss second quantization, discrete symmetry transformations and inner products in free non-Hermitian scalar quantum field theories with PT symmetry, focusing on a prototype model of two complex scalar fields with anti-Hermitian mass mixing. Whereas the definition of the inner product is unique for theories described by Hermitian Hamiltonians, its formulation is not unique for non-Hermitian Hamiltonians. Energy eigenstates are not orthogonal with respect to the conventional Dirac inner product, so we must consider additional discrete transformations to define a positive-definite norm. We clarify the relationship between canonical-conjugate operators and introduce the additional discrete symmetry C', previously introduced for quantum-mechanical systems, and show that the C'PT inner product does yield a positive-definite norm, and hence is appropriate for defining the Fock space in non-Hermitian models with PT symmetry in terms of energy eigenstates. We also discuss similarity transformations between PT-symmetric non-Hermitian scalar quantum field theories and Hermitian theories, showing that they would require modification in the presence of interactions. As an illustration of our discussion, we compare particle mixing in a Hermitian theory and in the corresponding non-Hermitian model with PT symmetry, showing how the latter maintains unitarity and exhibits mixing between scalar and pseudoscalar bosons., Comment: 44 pages, revtex format; to match published version, including a revised discussion of particle mixing and oscillations

We discuss dynamical mass generation for fermions and pseudoscalar fields (axion-like particles (ALP)), in the context of effective theories containing Yukawa type interactions between the fermions and ALPs. We discuss both Hermitian and non-Hermitian Yukawa interactions, which are motivated in the context of some scenarios for radiative (anomalous) Majorana sterile neutrino masses in some effective field theories. The latter contain shift-symmetry breaking Yukawa interactions between sterile neutrinos and ALPs. We show that, for a Hermitian Yukawa interaction, there is no (pseudo)scalar dynamical mass generation, but there is fermion dynamical mass generation, provided one adds a bare (pseudo)scalar mass. The situation is opposite for an anti-Hermitian Yukawa model: there is (pseudo)scalar dynamical mass generation, but no fermion dynamical mass generation.In the presence of additional attractive four-fermion interactions, dynamical fermion mass generation can occur in these models, under appropriate conditions and range of their couplings., Comment: 24 pages revtex, one eps figure incorporated; section IIIC contains material related to arXiv:2004.03699 [hep-ph]. Minor restructuring on sections, with section II added. Also discussion added, along with Figure 2 and ref. [25], on resummation of four-fermion loops, which justifies our approximations. Minor typos corrected. No effects on conclusions. Version to be published in Nuclear Physics B

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., Comment: 7 pages, comments added

We formulate supersymmetric non-Hermitian quantum field theories with PT symmetry, starting with free chiral boson/fermion models and then including trilinear superpotential interactions. We consider models with both Dirac and Majorana fermions, analyzing them in terms of superfields and at the component level. We also discuss the relation between the equations of motion, the (non-)invariance of the Lagrangian and the (non-)conservation of the supercurrents in the two models. We exhibit a similarity transformation that maps the free-field supersymmetric PT-symmetric Dirac model to a supersymmetric Hermitian theory, but there is, in general, no corresponding similarity transformation for the Majorana model. In this model, we find generically a mass splitting between bosons and fermions, even though its construction is explicitly supersymmetric, offering a novel non-Hermitian mechanism for soft supersymmetry breaking., Comment: 23 pages, revtex format; to match published version

We generalise our previous formulation of gauge-invariant PT-symmetric field theories to include models with non-Abelian symmetries and discuss the extension to such models of the Englert-Brout-Higgs-Kibble mechanism for generating masses for vector bosons. As in the Abelian case, the non-Abelian gauge fields are coupled to non-conserved currents. We present a consistent scheme for gauge fixing, demonstrating Becchi-Rouet-Stora-Tyutin invariance, and show that the particle spectrum and interactions are gauge invariant. We exhibit the masses that gauge bosons in the simplest two-doublet SU(2)xU(1) model acquire when certain scalar fields develop vacuum expectation values: they and scalar masses depend quartically on the non-Hermitian mass parameter mu. The bosonic mass spectrum differs substantially from that in a Hermitian two-doublet model. This non-Hermitian extension of the Standard Model opens a new direction for particle model building, with distinctive predictions to be explored further., Comment: 30 pages, 4 figures, revtex format; to match published version

Setting aside anthropic arguments, there is no reason why the universe should initially favour a net expanding phase rather than one experiencing a net contraction. However, a collapsing universe containing "normal" matter will end at a singularity in a finite time. We point out that there is a mechanism, derived from non-perturbative effects in Quantum Field Theory in a finite volume, which may provide a bias towards expansion when the spacetime volume shrinks, by dynamically violating the null energy condition, without the need for modified gravity or exotic matter. We describe a scalar field component subjected to this non-perturbative effect in a cosmological background and consider its impact on a contracting phase. We discuss how this could dynamically generate the necessary initial conditions for inflation to get started, or form part of the mechanism for a non-singular cosmological bounce., Comment: 8 pages, 2 figures, comments and references added

We present a gauge and Lorentz invariant model for the scattering of matter off magnetic poles, which justifies the presence of velocity-dependent magnetic charges as an effective description of either the behaviour of monopoles in scattering with matter or their production from matter particles at colliders. Hence, in such an approach, perturbativity of the magnetic charge is ensured for relative low velocities of monopoles with respect to matter particles. The model employs a ${\rm U(1)}_{\rm weak} \times {\rm U(1)}_{\rm strong}$ effective gauge field theory under which electrons and monopoles (assumed to be fermions) are appropriately charged. The non-perturbative quantum effects of the strongly coupled sector of the theory lead to dressed effective couplings of the monopole/dyon with the electromagnetic photon, due to non-trivial wave-function renormalization effects. For slowly-moving monopole/dyons, such effects lead to weak coupling, thus turning the bare non-perturbative magnetic charge, which is large due to the Dirac/Schwinger quantization rule, into a perturbative effective, velocity-("$\beta$")-dependent magnetic coupling. Our work thus offers formal support to previous conjectural studies, employing effective U(1)-electromagnetic gauge field theories for the description of monopole production from Standard Model matter, which are used in contemporary collider searches of such objects. This work necessarily pertains to composite monopoles, as seems to be the case of all known monopoles so far, that are solutions of specific particle physics models. This is a consequence of the fact that the wave-function renormalization of the (slowly-moving) monopole fermion turns out to violate unitarity bounds that would characterise asymptotic elementary particle states., Comment: 23 pages, 2 figures

We discuss $\mathcal{PT}$-symmetric Abelian gauge field theories, as well as their extension to the Englert-Brout-Higgs mechanism for generating a mass for a vector boson. Gauge invariance is not straightforward, and we discuss the different related problems, as well as a solution which consists in coupling the gauge field to a current that is not conserved. Non-Hermiticity then necessarily precludes the Lorenz gauge condition but nevertheless allows for a consistent formulation of the theory. We therefore generalise the Englert-Brout-Higgs mechanism to $\mathcal{PT}$-symmetric field theories, opening the way to constructing non-Hermitian extensions of the Standard Model and new scenarios for particle model-building., Comment: 19 pages

We demonstrate the extension to PT-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimisation of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a basis for our analysis, we first show how the conventional quantisation of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering PT conjugation instead of Hermitian conjugation. The extension of the Goldstone theorem to a PT-symmetric field theory is made possible by the existence of a conserved current that does not, however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition to extending the proof of the Goldstone theorem to a PT-symmetric theory, we exhibit a specific example in which we verify the existence of a massless boson at the tree and one-loop levels., Comment: 20 pages, revtex format; to match published version

Motivated by neutrino astronomy, we consider a plane wave of coupled and massive flavours, scattered by a static black hole, and describe analytically and numerically the corresponding oscillation probability in the surrounding space. Both the interpretation as particles travelling along geodesics and as scattered waves are studied, and consistently show a non-trivial and potentially long range interference pattern, in contrast to the spatially uniform transition probability in a flat spacetime. We introduce a numerical method for studying the oscillations around black holes, which accounts for the full curved geometry and flavour wave mixing. Whilst limited to the region immediately around the black hole, this numerical approach has the potential to be used in more general contexts, revealing the complex interference patterns which defy analytic methods., Comment: 17 pages, 4 figures, updated for journal version

We review how to describe a field theory that includes a non-Hermitian mass term in the region of parameter space where the Lagrangian is $PT$-symmetric. The discrete symmetries of the system are essential for understanding the consistency of the model, and the link between conserved current and variation of the Lagrangian has to be revisited in the case of continuous symmetries.

Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for PT-symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the PT-conjugate variables, allowing for an unambiguous definition of the equations of motion. After discussing the resulting constraints on the consistency of the variational procedure, we show that the invariance of a non-Hermitian Lagrangian under a continuous symmetry transformation does not imply the existence of a corresponding conserved current. Conserved currents exist, but these are associated with transformations under which the Lagrangian is not invariant and which reflect the well-known interpretation of PT-symmetric theories in terms of systems with gain and loss. A formal understanding of this unusual feature of non-Hermitian theories requires a careful treatment of Noether's theorem, and we give specific examples for illustration., Comment: Discussions extended

Working within the context of PT-symmetric quantum mechanics, we begin by describing a non-Hermitian extension of QED that is both Lorentz invariant and consistent with unitarity. We show that the non-Hermitian Dirac mass matrix of this theory exhibits an exceptional point, corresponding to an effectively massless theory whose conserved current is either right- or left-chiral dominated. With this inspiration, we are able to construct a non-Hermitian model of light Dirac neutrino masses from Hermitian and anti-Hermitian Yukawa couplings that are both of order unity. We finish by highlighting potential phenomenological implications of this model., Comment: 10 pages, 1 figure. Prepared for the proceedings of DISCRETE2016: the Fifth Symposium on Prospects in the Physics of Discrete Symmetries, 28 November-3 December 2016, University of Warsaw, Poland, to appear in the Journal of Physics: Conference Series (JPCS). Presented by P. Millington