arXiv subjects

Apostolos Pilaftsis

Publications and source records attributed to Apostolos Pilaftsis.

At least 37 records · Page 2Linked to original sources

arXiv2022

Charged and CP-violating Kink Solutions in the Two Higgs Doublet Model

Minimal extensions of the Standard Model (SM), such as the so-called Two Higgs Doublet Model (2HDM), can possess several accidental discrete symmetries whose spontaneous breakdown in the early universe usually lead to the formation of domain walls. We extend an earlier work [arXiv:2006.13273] on this topic by studying in more detail the analytic properties of electrically charged and CP-violating kink solutions in the $Z_{2}$-symmetric 2HDM. We derive the complete set of equations of motion that describe the 1D spatial profile of both the 2HDM vacuum parameters and the would-be Goldstone bosons $G^{1,2,3}$ of the SM. These equations are then solved numerically using the gradient flow technique, and the results of our analysis are presented in different parametrizations of the Higgs doublets. In particular, we show analytically how an electrically charged profile should arise in 1D kink solutions when asymmetric boundary conditions are imposed on the Goldstone mode $G^{2}$ at spatial infinities, i.e. as ${x\to \pm \infty}$. If asymmetric boundary conditions are selected at ${x\to \pm \infty}$ for the Goldstone mode $G^{3}$ or the longitudinal mode $θ$ corresponding to a would-be massive photon, the derived kink solutions are then shown to exhibit CP violation. Possible cosmological implications of the electrically charged and CP-violating domain walls in the 2HDM are discussed.

hep-ph↗

arXiv2022

Higgs-Sector Predictions from Maximally Symmetric multi-Higgs Doublet Models

Maximally Symmetric $n$-Higgs Doublet Models (MS-$n$HDMs)define very economic settings that enable sharp Higgs-sector predictions beyond the Standard Model (SM) potentially testable at high-energy colliders. The scalar potential of a MS-$n$HDM obeys an $\mathrm{Sp(2}n)$ symmetry, which is softly broken by bilinear scalar masses and explicitly by hypercharge and Yukawa couplings through renormalisation-group effects. The $\mathrm{Sp(2}n)$ also ensures natural SM alignment and allows for quartic coupling unification up to the Planck scale. As typical examples, we consider maximally symmetric realisations of the Type-II 2HDM and the Type-V 3HDM. We show how in terms of a few input parameters, definite predictions for the entire scalar mass spectrum of the MS-2HDM and MS-3HDM are obtained, including the SM-like Higgs-boson couplings to the gauge bosons and fermions.

hep-ph↗

arXiv2021

Frame Covariant Formalism for Fermionic Theories

We present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky-DeWitt (VDW) effective action. We explicitly construct a field-space supermanifold on which the quantum fields act as coordinates. We show how to define field-space tensors on this supermanifold from the classical action that are covariant under field reparametrisations. We then employ these tensors to equip the field-space supermanifold with a metric, thus solving a long-standing problem concerning the proper definition of a metric for fermionic theories. With the metric thus defined, we use well-established field-space techniques to extend the VDW effective action and express any fermionic theory in a frame- and field-reparametrisation-invariant manner.

hep-th↗

arXiv2021

Maximally Symmetric Three Higgs Doublet Model

We consider the general Three-Higgs Doublet Model (3HDM) and identify all limits that lead to exact SM alignment. After discussing the underlying symmetries that can naturally enforce such an alignment, we focus on the most economic setting, called here the Maximally Symmetric Three-Higgs Doublet Model (MS-3HDM). The potential of the MS-3HDM obeys an $\mathrm{Sp(6)}$ symmetry, softly broken by bilinear masses and explicitly by hypercharge and Yukawa couplings through renormalisation-group effects, whilst the theory allows for quartic coupling unification up to the Planck scale. Besides the two ratios of vacuum expectation values, $\tanβ_{1,2}$, the MS-3HDM is predominantly governed by only three input parameters: the masses of the two charged Higgs bosons, $M_{h_{1,2}^{\pm}}$, and their mixing angle $σ$. Most remarkably, with these input parameters, we obtain definite predictions for the entire scalar mass spectrum of the theory, as well as for the SM-like Higgs-boson couplings to the gauge bosons and fermions. The predicted deviations of these couplings from their SM values might be probed at future precision high-energy colliders. The new phenomenological aspects of the MS-3HDM with respect to the earlier studied MS-2HDM are discussed.

hep-ph↗

arXiv2021

Quantizing the Eisenhart Lift

The classical Eisenhart lift is a method by which the dynamics of a classical system subject to a potential can be recreated by means of a free system evolving in a higher-dimensional curved manifold, known as the lifted manifold. We extend the formulation of the Eisenhart lift to quantum systems, and show that the lifted manifold recreates not only the classical effects of the potential, but also its quantum mechanical effects. In particular, we find that the solutions of the Schrodinger equations of the lifted system reduce to those of the original system after projecting out the new degrees of freedom. In this context, we identify a conserved quantum number, which corresponds to the lifted momentum of the classical system. We further apply the Eisenhart lift to Quantum Field Theory (QFT). We show that a lifted field space manifold is able to recreate both the classical and quantum effects of a scalar field potential. We find that, in the case of QFT, the analogue of the lifted momentum is a quantum charge that is conserved not only in time, but also in space. The different possible values for this charge label an ensemble of Fock spaces that are all disjoint from one another. The relevance of these extended Fock spaces to the cosmological constant and gauge hierarchy problems is considered.

hep-th↗

arXiv2020

Domain Wall Constraints on Two Higgs Doublet Models with $Z_2$ Symmetry

The Two Higgs Doublet Model (2HDM) with spontaneously broken $Z_2$ symmetry predicts a production of domain walls at the electroweak scale. We derive cosmological constraints on model parameters for both Type-I and Type-II 2HDMs from the requirement that domain walls do not dominate the Universe by the present day. For Type-I 2HDMs, we deduce the lower bound on the key parameter $\tanβ> 10^5$ for a wide range of Higgs-boson masses $\sim$ 100 GeV or greater close to the Standard Model alignment limit. In addition, we perform numerical simulations of the 2HDM with an approximate as well as an exact $Z_2$ symmetry but biased initial conditions. In both cases, we find that domain wall networks are unstable and, hence, do not survive at late times. The domain walls experience an exponential suppression of scaling in these models which can help ameliorate the stringent constraints found in the case of an exact discrete symmetry. For a 2HDM with softly-broken $Z_2$ symmetry, we relate the size of this exponential suppression to the soft-breaking bilinear parameter $m_{12}$ allowing limits to be placed on this parameter of order $μ$eV, such that domain wall domination can be avoided. In particular, for Type-II 2HDMs, we obtain a corresponding lower limit on the CP-odd phase $θ$ generated by QCD instantons, $θ\ \stackrel{>}{{}_\sim}\ 10^{-11}/(\sinβ\cosβ)$, which is in some tension with the upper limit of $θ\ \stackrel{<}{{}_\sim}\ 10^{-11}$--$10^{-10}$, as derived from the non-observation of a non-zero neutron electric dipole moment. For a $Z_2$-symmetric 2HDM with biased initial conditions, we are able to relate the size of the exponential suppression to a biasing parameter $\varepsilon$ so as to avoid domain wall domination.

hep-ph↗

arXiv2020

Radiative Neutrino Masses in the $ν_R$MSSM

We present a complete analysis of scenarios with radiatively generated neutrino masses that may occur in the Minimal Supersymmetric Standard Model with low-scale right-handed neutrinos. For brevity, we call such a model the $ν_R$MSSM. We pay particular attention to the impact of the non-renormalization theorem of supersymmetry (SUSY) on the loop-induced neutrino masses, by performing our computations in the weak and flavour bases. In particular, we find that the smallness of the observed light neutrino masses may naturally arise due to a soft SUSY-screening effect from a nearly supersymmetric singlet neutrino sector. The profound phenomenological and cosmological implications that may originate from this screening phenomenon in the $ν_R$MSSM and its minimal extensions are discussed.

hep-ph↗

arXiv2020

Accidental Symmetries in the 2HDMEFT

We construct accidentally symmetric potentials in the framework of Two Higgs Model Effective Field Theory (2HDMEFT) including higher-order operators of dimension 6 and dimension 8. Our construction is facilitated by an earlier developed technique based on prime invariants. In addition, we employ an alternative method that utilises the generators of each symmetry in the bi-adjoint representation and show how this method can be used to identify operators of any higher dimension. The accidentally symmetric 2HDMEFT potentials exhibit two classes of symmetries: (i) continuous symmetries and (ii) discrete symmetries. The number of continuous symmetries in the 2HDMEFT remains the same as in the 2HDM. However, the introduction of higher-order operators allows additional higher-order discrete symmetries, such as $Z_n$ and CP$n$. We classify the full list of the 17 accidental symmetries in the 2HDMEFT including dimension-6 and dimension-8 operators, and derive the relations that govern the theoretical parameters of the corresponding effective potentials.

hep-ph↗

arXiv2020

Frame Covariance in Quantum Gravity

We develop a quantum effective action for scalar-tensor theories of gravity which is both spacetime diffeomorphism invariant and field reparameterisation (frame) invariant beyond the classical approximation. We achieve this by extending the Vilkovisky-DeWitt formalism, treating both the scalar fields and the components of the gravitational tensor field as coordinates describing a manifold. By using tensors covariant under diffeomorphisms of this manifold, we show that scalar-tensor theories can be written in a form that is manifestly frame invariant at both classical and quantum levels. In~the same context, we show that in order to maintain manifest frame invariance, we must modify the Feynman rules of theories with a non-trivial field space. We show that one such theory is General Relativity by demonstrating explicitly that it has a non-zero field-space Riemann tensor. Thus, when constructing theories of quantum gravity, we must deal not only with curved spacetime, but also with a curved field space. Finally, we address the cosmological frame problem by tracing its origin to the existence of a new model function that appears in the path integral measure. Once this function is fixed, we find that frame transformations have no effect on the quantisation of the theory. The uniqueness of our improved quantum effective action is discussed.

hep-th↗

arXiv2020

Simulations of Domain Walls in Two Higgs Doublet Models

The Two Higgs Doublet Model predicts the emergence of 3 distinct domain wall solutions arising from the breaking of 3 accidental global symmetries, $Z_2$, CP1 and CP2, at the electroweak scale for specific choices of the model parameters. We present numerical kink solutions to the field equations in all three cases along with dynamical simulations of the models in (2+1) and (3+1) dimensions. For each kink solution we define an associated topological current. In all three cases simulations produce a network of domain walls which deviates from power law scaling in Minkowski and FRW simulations. This deviation is attributed to a winding of the electroweak group parameters around the domain walls in our simulations. We observe a local violation of the neutral vacuum condition on the domain walls in our simulations. This violation is attributed to relative electroweak transformations across the domain walls which is a general feature emerging from random initial conditions.

hep-ph↗

arXiv2020

Goldstone Boson Effects on Vacuum Decay

We study the effects of Goldstone modes on the stability of the vacuum in a $U(1)$ theory for a complex scalar field. The dynamics of the field resemble those of Keplerian motion in the presence of time-dependent friction, whose equations of motion imply a conserved quantity, $L$, reminiscent of conserved angular momentum. They also imply a persistent infinite barrier at $ρ=0$ and a divergent field value at the origin of coordinates in flat spacetime, rendering any solution physically unattainable. However, in a spacetime punctured at the origin of coordinates, we find finite-action solutions to the equations of motion, which correspond to the size of the hole $a_0$, which in turn determines the tunneling point $ρ_0$ and $L$. We find that the rates of vacuum decay get drastically enhanced by many orders of magnitude for all possible orderings in which the false and true vacua are placed in the potential. Finally, we show how Goldstone modes provide the necessary energy to overcome drag forces yielding finite-action solutions for any potential, including those that no such solutions exist for real scalar fields.

hep-th↗

arXiv2020

Classifying Accidental Symmetries in Multi-Higgs Doublet Models

The potential of $n$-Higgs Doublet Models ($n$HDMs) contains a large number of SU(2)$_L$-preserving accidental symmetries as subgroups of the symplectic group Sp(2$n)$. To classify these, we introduce prime invariants and irreducible representations in bilinear field space that enable us to explicitly construct accidentally symmetric $n$HDM potentials. We showcase the classifications of symmetries and present the relationship among the theoretical parameters of the scalar potential for; (i) the Two Higgs Doublet Model (2HDM) and (ii) the Three Higgs Doublet Model (3HDM). We recover the maximum number of $13$ accidental symmetries for the 2HDM potential and for the first time, we present the complete list of $40$ accidental symmetries for the 3HDM potential.

hep-ph↗

arXiv2020

Natural Alignment in Multi-Higgs Doublet Models

We present the complete set of continuous maximal symmetries that the potential of an $n$-Higgs Doublet Model ($n$HDM) should satisfy for natural Standard Model (SM) alignment. As a result, no large mass scales or fine-tuning is required for such alignment, which still persists even if these symmetries were broken softly by bilinear mass terms. In particular, the Maximal Symmetric $n$HDM (MS-$n$HDM) can provide both natural SM alignment and quartic coupling unification up to the Planck scale. Most remarkably, we show that the MS-2HDM is a very predictive extension of the SM governed by two only additional parameters: (i) the charged Higgs mass $M_{h^{\pm}}$ (or $m^2_{12}$) and (ii) $\tanβ$, whilst the quartic coupling unification scale $μ_X$ is predicted to assume two discrete values. With these two input parameters, the entire Higgs-mass spectrum of the model can be determined. Moreover, we obtain definite predictions of misalignment for the SM-like Higgs-boson couplings to the gauge bosons and to the quarks, which might be testable at future precision high-energy colliders.

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arXiv2019

Quartic Coupling Unification in the Maximally Symmetric 2HDM

We consider the Maximally Symmetric Two-Higgs Doublet Model (MS-2HDM) in which the so-called Standard Model (SM) alignment can be naturally realised as a consequence of an accidental SO(5) symmetry in the Higgs sector. This symmetry is broken (i) explicitly by renormalization-group (RG) effects and (ii) softly by the bilinear scalar mass term $m^2_{12}$. We find that in the MS-2HDM all quartic couplings can unify at large RG scales $μ_X \sim 10^{11}\,$-$\,10^{20}$ GeV. In particular, we show that quartic coupling unification can take place in two different conformally invariant points, where all quartic couplings vanish. We perform a vacuum stability analysis of the model in order to ensure that the electro-weak vacuum is sufficiently long-lived. The MS-2HDM is a minimal and very predictive extension of the SM governed by only three additional parameters: the unification scale $μ_X$, the charged Higgs mass $M_{h^{\pm}}$ (or $m^2_{12}$) and $\tanβ$, which allow one to determine the entire Higgs sector of the model. In terms of these input parameters, we present illustrative predictions of misalignment for the SM-like Higgs-boson couplings to the $W^\pm$ and $Z$ bosons and, for the first time, to the top and bottom quarks.

hep-ph↗

arXiv2019

Charged Higgs Bosons in Naturally Aligned Two Higgs Doublet Models at the LHC

Measurements of a Higgs boson at the Large Hadron Collider (LHC) have become increasingly consistent with the predictions of the Standard Model (SM). This fact puts severe constraints on many potential low-energy extensions of the Higgs sector of the SM. In the well-known Two Higgs Doublet Model (2HDM), an `alignment limit' of parameters readily furnishes one SM-like scalar, and can be achieved naturally through an underlying symmetry. Among the other physical states of the 2HDM, a charged scalar $H^\pm$ would provide striking evidence of new physics if observed. We propose a novel technique for the observation of the process $pp\to t b H^\pm \to t\bar{t}b\bar{b}$ in the dileptonic decay channel at the LHC. The reconstruction of events in this channel is complicated by multiple $b$-jets and unobserved neutrinos in the final state. To determine the neutrino momenta, we implement a neutrino weighting procedure to study, for the first time, the $t\bar{t}b\bar{b}$ signature. We further train a pair of boosted decision trees to reconstruct and classify signal events. We determine the resulting reach within the context of naturally aligned 2HDMs, such as the Maximally Symmetric Two Higgs Doublet Model (MS-2HDM). By testing at the integrated luminosity of 150 fb$^{-1}$ achieved in Run 2 of the LHC, we find that this channel may restrict the parameter space of a Type-II MS-2HDM with charged Higgs masses as high as 680 GeV.

hep-ph↗

arXiv2019

Gauge-Independent Approach to Resonant Dark Matter Annihilation

In spontaneously broken gauge theories, transition amplitudes describing dark-matter (DM) annihilation processes through a resonance may become highly inaccurate close to a production threshold, if a Breit-Wigner (BW) ansatz with a constant width is used. To partially overcome this problem, the BW propagator needs to be modified by including a momentum dependent decay width. However, such an approach to resonant transition amplitudes generically suffers from gauge artefacts that may also give rise to a bad or ambiguous high-energy behaviour for such amplitudes. We address the two problems of gauge dependence and high-energy unitarity within a gauge-independent framework of resummation implemented by the so-called Pinch Technique. We study DM annihilation via scalar resonances in a gauged U(1)$_X$ complex-scalar extension of the Standard Model that features a massive stable gauge field which can play the role of the DM. We find that the predictions for the DM abundance may vary significantly from previous studies based on the naive BW ansatz and propose an alternative simple approximation which leads to the correct DM phenomenology. In particular, our results do not depend on the gauge-fixing parameter and are consistent with considerations from high-energy unitarity.

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arXiv2018

Protecting the Stability of the EW Vacuum from Planck-Scale Gravitational Effects

We investigate the stability of the Standard-Model Electroweak (EW) vacuum in the presence of Planck-scale suppressed operators of the type $ϕ^{2n}/M^{2n-4}_{\rm P}$ that involve the Higgs field $ϕ$ and could in principle be induced by quantum gravity effects. We show how minimal embeddings of the Standard Model (SM) in supergravity (SUGRA) can stabilize the EW vacuum against such operators up to very high values of the induced supersymmetry breaking scale $M_{\cal S}$, which may well be above the onset of the so-called SM metastability scale of $10^{11}$ GeV. In particular, we explicitly demonstrate how discrete $R$ symmetries could be invoked to suppress the occurrence of harmful Planck-scale operators of the form $ϕ^{2n}/M^{2n-4}_{\rm P}$ to arbitrary higher powers of $n$. We analyze different scenarios of Planck-scale gravitational physics and derive lower limits on the power $n$ that is required in order to protect our EW vacuum from dangerous rapid decay. The significance of our results for theories of low-scale quantum gravity is illustrated.

hep-ph↗

arXiv2018

The Eisenhart Lift for Field Theories

We present the Eisenhart-lift formalism in which the dynamics of a system that evolves under the influence of a conservative force is equivalent to that of a free system embedded in a curved manifold with one additional generalised coordinate. As an illustrative example in Classical Mechanics, we apply this formalism to simple harmonic motion. We extend the Eisenhart lift to homogeneous field theories by adding one new field. Unlike an auxiliary field, this field is fully dynamical and is therefore termed fictitious. We show that the Noether symmetries of a theory with a potential are solutions of the Killing equations in the lifted field space. We generalise this approach to field theories in four and higher spacetime dimensions by virtue of a mixed vielbein that links the field space and spacetime. Possible applications of the extended Eisenhart-lift formalism including the gauge hierarchy problem and the initial conditions problem in inflation are briefly discussed.

physics.class-ph↗