Symmetry Breaking Scale Research Articles

Berezinskii-Kosterlitz-Thouless transitions in classical and quantum long-range systems

In the past decades, considerable efforts have been made to understand the critical features of both classical and quantum long-range (LR) interacting models. The case of the Berezinskii-Kosterlitz-Thouless (BKT) universality class, as in the two-dimensional (2D) classical $XY$ model, is considerably complicated by the presence, for short-range interactions, of a line of renormalization group fixed points. In this paper, we discuss a field-theoretical treatment of the 2D $XY$ model with LR couplings, and we compare it with results from the self-consistent harmonic approximation. These methods lead to a rich phase diagram, where both power law BKT scaling and spontaneous symmetry breaking appear for the same (intermediate) decay rates of LR interactions. We also discuss the Villain approximation for the 2D $XY$ model with power law couplings, providing hints that, in the LR regime, it fails to reproduce the correct critical behavior. The obtained results are then applied to the LR quantum $XXZ$ spin chain at zero temperature. We discuss the relation between the phase diagrams of the two models, and we give predictions about the scaling of the order parameter of the quantum chain close to the transition.

Probing high scale Dirac leptogenesis via gravitational waves from domain walls

We propose a novel way of probing high-scale Dirac leptogenesis, a viable alternative to the canonical leptogenesis scenario where the total lepton number is conserved, keeping light standard model neutrinos purely Dirac. The simplest possible seesaw mechanism for generating light Dirac neutrinos involves heavy singlet Dirac fermions and a singlet scalar. In addition to unbroken global lepton number, a discrete ${Z}_{2}$ symmetry is imposed to forbid direct coupling between right and left chiral parts of light Dirac neutrinos. Generating light Dirac neutrino mass requires the singlet scalar to acquire a vacuum expectation value (VEV) that also breaks the ${Z}_{2}$ symmetry, leading to the formation of domain walls in the early Universe. These walls, if made unstable by introducing a soft ${Z}_{2}$-breaking term, generate gravitational waves (GWs) with a spectrum characterized by the wall tension or the singlet VEV, and the soft symmetry breaking scale. The scale of leptogenesis depends on the ${Z}_{2}$-breaking singlet VEV, which is also responsible for the tension of the domain wall, affecting the amplitude of GWs produced from the collapsing walls. We find that most of the near-future GW observatories will be able to probe Dirac leptogenesis scales all the way up to ${10}^{11}\text{ }\text{ }\mathrm{GeV}$.

Altered axion abundance from a dynamical Peccei-Quinn scale

We build a model in which the relic abundance of axions is altered from the standard misalignment mechanism, either increased or decreased, due to the presence of a new light scalar that couples to the radial part of the Peccei-Quinn (PQ) field. The light scalar makes the effective PQ symmetry-breaking scale dynamical, altering the early-time dynamics for the axion and affecting its late-time dark matter abundance. We analyze this new mechanism semianalytically and numerically, showing that we can accommodate both lighter or heavier axion dark matter, compared to the standard treatments. We discuss implications of the model for axion searches and fundamental physics.

Constraining the cosmic strings gravitational wave spectra in no-scale inflation with viable gravitino dark matter and nonthermal leptogenesis

We revisit the hybrid inflation model gauged by $U(1)_{B-L}$ extension of the Minimal Supersymmetric Standard Model (MSSM) in a no-scale background. Considering a single predictive framework, we study inflation, leptogenesis, gavitino cosmology, and the stochastic background of gravitational waves produced by metastable cosmic strings. The spontaneous breaking of $U(1)_{B-L}$ at the end of inflation produces a network of metastable cosmic strings while, the interaction between $U(1)_{B-L}$ Higgs field and the neutrinos generate heavy Majorana masses for the right-handed neutrinos. The heavy Majorana masses explain the tiny neutrino masses via the seesaw mechanism, a realistic scenario for reheating and non-thermal leptogenesis. We show that a successful non-thermal leptogenesis and a stable gravitino as a dark matter candidate can be achieved for a wide range of reheating temperatures and $U(1)_{B-L}$ symmetry breaking scales. The possibility of realizing metastable cosmic strings in a grand unified theory (GUT) setup is briefly discussed. We find that a successful reheating with non-thermal leptogenesis and gravitino dark matter restrict the allowed values of string tension to a narrow range $10^{-9} \lesssim G\mu_{CS} \lesssim 8 \times 10^{-6}$, predicting a stochastic gravitational-wave background that lies within the 1-$\sigma$ bounds of the recent NANOGrav 12.5-yr data, as well as within the sensitivity bounds of future GW experiments.

Correlations of mixed systems in confining backgrounds

We show that the entanglement of purification and the critical distance between the two mixed systems is a powerful measure in probing the phase structures of QCD and confining backgrounds, as it can distinguish the scale of chiral symmetry breaking versus the scale of confinement/deconfinement phase transitions. For two symmetric strips with equal and finite width and infinite length, and in the background of several confining geometries, we numerically calculate the critical distance between them where the mutual information vanishes and show that this quantity can probe the very rich phase structures of these backgrounds. The geometries that we study here are AdS-soliton, Witten–Sakai–Sugimoto and deformed Sakai–Sugimoto, Witten-QCD, Klebanov–Strassler, Klebanov–Tseytlin, Klebanov–Witten, Maldacena–Nunez, Nunez–Legramandi metric, and Domain-Wall QCD model. For each background we also present the relation for the entanglement of purification. Finally, we show that the Crofton forms of these geometries also behave in a universal form where a “well” is being observed around the IR wall, and therefore for all confining backgrounds, the Crofton form would also be capable of distinguishing the confining versus conformal backgrounds as it is also a tool in the reconstruction of various bulk geometries.

Testing super heavy dark matter from primordial black holes with gravitational waves

Ultra-light primordial black holes with masses M BH < 109 g evaporate before big-bang nucleosynthesis producing all matter fields, including dark matter, in particular super-heavy dark matter: M DM ≳ 1010 GeV. If the dark matter gets its mass via U(1) symmetry-breaking, the phase transition that gives a mass to the dark matter also produces cosmic strings which radiate gravitational waves. Because the symmetry-breaking scale ΛCS is of the same order as M DM, the gravitational waves radiated by the cosmic strings have a large enough amplitude to be detectable across all frequencies accessible with current and planned experimental facilities. Moreover, an epoch of early primordial black hole domination introduces a unique spectral break in the gravitational wave spectrum whose frequency is related to the super-heavy dark matter mass. Hence, the features of a stochastic background of primordial gravitational waves could indicate that super-heavy dark matter originated from primordial black holes. In this perspective, the recent finding of a stochastic common-spectrum process across many pulsars by two nano-frequency pulsar timing arrays would fix the dark matter mass to be 3 × 1013 GeV ≲ M DM ≲ 1014 GeV. The (non-)detection of a spectral break at 0.2 Hz ≲ f * ≲ 0.4 Hz would (exclude) substantiate this interpretation of the signal.

Multiphase critical Higgs boson at colliders

The recently proposed multi-phase criticality principle in Coleman-Weinberg models can provide a new explanation for the hierarchy between the electroweak and new physics scales. When applied to the Standard Model, a Higgs boson as light as the pseudo-Goldstone boson of broken scale invariance occurs. The suppressed mixing between the two light fields still carries information about the large scale of symmetry breaking, albeit up to logarithmic corrections. In this work we probe this scenario with the present LHC data and assess the impact of future lepton and hadron colliders. Our results show that the multi-phase criticality can easily explain the apparent absence of new physics at the energy scales tested in current experiments.

Dilaton in scalar QFT: a no-go theorem in 4-epsilon and 3-epsilon dimensions

Spontaneous scale invariance breaking and the associated Goldstone boson, the dilaton, is investigated in renormalizable, unitary, interacting non-supersymmetric scalar field theories in 4-\varepsilon4−ε dimensions. At leading order it is possible to construct models which give rise to spontaneous scale invariance breaking classically and indeed a massless dilaton can be identified. Beyond leading order, in order to have no anomalous scale symmetry breaking in QFT, the models need to be defined at a Wilson-Fisher fixed point with exact conformal symmetry. It is shown that this requirement on the couplings is incompatible with having the type of flat direction which would be necessary for an exactly massless dilaton. As a result spontaneous scale symmetry breaking and an exactly massless dilaton can not occur in renormalizable, unitary 4-\varepsilon4−ε dimensional scalar QFT. The arguments apply to \phi^6ϕ6 theory in 3-\varepsilon3−ε dimensions as well.

A Natural Inflation inspired model

We propose a modification of the Natural Inflation (NI) potential in such a way that the spontaneous symmetry breaking scale $f$ can take values less than one (in Planck units). The proposed potential seems simple enough, however, its consequences are difficult to calculate analytically. Therefore, we illustrate the feasibility of the model by considering some numerical examples that easily satisfy the conditions imposed on the observables $n_s$ and $r$ by the most recent observations, while at the same time maintaining the number of e-folds during the inflationary epoch within the expected range.

Gravitational shine of dark domain walls

Cosmic domain walls are harmless, provided that their tension decreases with expansion of the Universe. This setup can be realized, if the scale of spontaneous symmetry breaking is induced dynamically through the interaction with hot primordial plasma. In that case, the domain wall tension can attain large values in the early Universe without any conflict with observations. Owing to the large initial tension, these topological defects may serve as a powerful source of gravitational waves. We make a preliminary estimate of the gravitational wave spectrum and argue that it is distinct from the spectrum produced by other sources, in particular by domain walls of a constant tension. The resulting gravitational wave signal is in the range accessible by Einstein Telescope, DECIGO, TianQin, LISA, IPTA, or SKA, if the field constituting the domain walls is very feebly coupled with hot primordial plasma and has tiny self-interactions. In particular, one can consider this field for the role of Dark Matter. We discuss various Dark Matter production mechanisms and properties of the emitted gravitational waves associated with them. We find that the conventional freeze-out and freeze-in mechanisms lead to large and perhaps unobservable frequency of gravitational waves. However, the Dark Matter production is also possible at the second order phase transition leading to the domain wall formation or at the inverse phase transition, when the domain walls get dissolved eventually. In both cases, there is essentially no lower bound on the frequency of emitted gravitational waves.

The minimal UV-induced effective QCD axion theory

The characteristic axion couplings could be generated via effective couplings between the Standard Model (SM) fermions to a pseudo-Goldstone from a high-scale U(1) Peccei–Quinn (PQ) symmetry breaking. Assuming that the UV-induced effective operators generate necessary couplings before the PQ symmetry breaking, and any low-scale couplings to the SM are restricted to the Yukawa sector, three minimal natural scenarios can be formulated, which provide a connection between the QCD axions and mediators at the GUT/string scales. We find that the PQ symmetry breaking scale could be about [Formula: see text] GeV, higher than the classical QCD dark matter axion window but possible if the anthropic window is considered. We also propose an experiment to probe such scenarios. If the dark matter axion is discovered, they might suggest that we live in an atypical Hubble volume.

On-shell Higgsing for EFTs

We study the on-shell version of the Higgs mechanism in effective theories (EFTs) containing particles of different spins, focusing on contact terms as a simple starting point. We derive the massive contact terms and their coefficients from the massless amplitudes of the EFT above the symmetry breaking scale, by covariantizing the massless contact terms under the massive little group. In the little-group-covariant massive-spinor formalism, this notationally amounts to bolding spinor labels. Mass-suppressed contributions to the contact-term coefficients arise from higher-point contact terms with additional soft Higgs legs. We apply this procedure to obtain massive four-point amplitudes featuring scalars, spin 1/2 fermions and vectors, in the standard-model EFT. The subleading helicity-flipped components of each massive contact term, which are dictated by little-group covariance, are associated with the residues of factorizable massless amplitudes. Extra “frozen” Higgses emitted from each leg of a massless contact term supply the additional light-like momentum component, needed to form a massive leg of the same polarization. As another application, we derive various components of massive three-point amplitudes from massless amplitudes with up to three additional Higgses, in a standard-model-like toy model.

Massive Gravitons as Feebly Interacting Dark Matter Candidates.

We detail our discovery of a chiral enhancement in the production cross sections of massive spin-2 gravitons, below the electroweak symmetry breaking scale, that makes them ideal dark matter candidates for the freeze-in mechanism. The result is independent of the physics at high scales and points toward masses in the keV-MeV range. The graviton is, therefore, a sub-MeV dark matter particle, as favored by the small scale galaxy structures. We apply the novel calculation to a Randall-Sundrum model with multiple branes, showing a significant parameter space where the first two massive gravitons saturate the dark matter relic density.

Fifth forces and broken scale symmetries in the Jordan frame

We study the origin of fifth forces in scalar-tensor theories of gravity in the so-called Jordan frame, where the modifications to the gravitational sector are manifest. We focus on theories of Brans-Dicke type in which an additional scalar field is coupled directly to the Ricci scalar of General Relativity. We describe how the necessary diffeomorphism invariance of the modified gravitational sector leads to a modification of the usual gauge fixing term (for the harmonic gauge), as compared to Einstein gravity. This allows us to perform a consistent linearization of the gravitational sector in the weak-field limit, which gives rise to a kinetic mixing between the non-minimally coupled scalar field and the graviton. It is through this mixing that a fifth force can arise between matter fields. We are then able to compute the matrix elements for fifth-force exchanges directly in the Jordan frame, without the need to perform a conformal transformation to the so-called Einstein frame, wherein the gravitational sector is of Einstein-Hilbert form. We obtain results that are in agreement with the equivalent Einstein-frame calculations and illustrate, still in the Jordan frame, the pivotal role that sources of explicit scale symmetry breaking in the matter sector play in admitting fifth-force couplings.

Natural inflation after Planck 2018

We calculate high-precision constraints on Natural Inflation relative to current observational constraints from Planck 2018 + BICEP/Keck(BK15) Polarization + BAO on r and n S, including post-inflationary history of the universe. We find that, for conventional post-inflationary dynamics, Natural Inflation with a cosine potential is disfavored at greater than 95% confidence out by current data. If we assume protracted reheating characterized by w̅>1/3, Natural Inflation can be brought into agreement with current observational constraints. However, bringing unmodified Natural Inflation into the 68% confidence region requires values of T re below the scale of electroweak symmetry breaking. The addition of a SHOES prior on the Hubble Constant H 0 only worsens the fit.

Axion model with the SU(6) unification

We propose an SU(6) unified theory that solves the strong $CP$ problem with a high-quality axion. This is achieved by an automatic global Peccei-Quinn $\mathrm{U}(1{)}_{\mathrm{PQ}}$ symmetry and the gauged discrete ${\mathbb{Z}}_{4\mathcal{R}}$ symmetry. With the axion mass predictions of ${m}_{a}\ensuremath{\sim}\mathcal{O}({10}^{\ensuremath{-}3})\ensuremath{-}\mathcal{O}(0.1)\text{ }\text{ }\mathrm{eV}$, as well as a universal axion-photon coupling in the unification models, the QCD axion can be probed in the upcoming experiments of IAXO. An intermediate gauge symmetry breaking scale characterized by the axion decay constant is obtained by the Peccei-Quinn quality argument, which is likely to achieve a successful leptogenesis through the type-I seesaw mechanism. The Higgs sector at the electroweak scale is a type-II two-Higgs-doublet model. The gauge coupling unification is possible with the supersymmetric extension.

Dark matter from a complex scalar singlet and the role of dark CP

A complex scalar singlet could provide a pseudo-scalar dark matter candidate, whose stability is guaranteed by a discrete symmetry: dark CP. The scalar singlet is also charged under a global U(1) symmetry, which is broken both explicitly and spontaneously. We analyze the phenomenology of different models with just one explicit symmetry breaking term and we also consider the case with more than one symmetry breaking term. Finally, we discuss the possibility that the explicit symmetry breaking term is much smaller than the symmetry breaking scale, leading to a pseudo-Nambu-Goldstone boson as a DM candidate.2

Yukawa coupling unification in non-supersymmetric SO(10) models with an intermediate scale

We discuss the possibility of unifying in a simple and economical manner the Yukawa couplings of third generation fermions in a non-supersymmetric SO(10) model with an intermediate symmetry breaking, focusing on two possible patterns with intermediate Pati-Salam and minimal left-right groups. For this purpose, we assume a minimal Yukawa sector at high energy, starting with two Higgs bi-doublets at the intermediate scale which then simply reduce to a two Higgs doublet model at the electroweak scale. We first enforce gauge coupling unification at the two-loop level by including the threshold corrections in the renormalization group running which are generated by the heavy fields that appear at the intermediate symmetry breaking scale. We then study the running of the Yukawa couplings of the top quark, bottom quark and tau lepton at two-loops in these two breaking schemes, when the appropriate matching conditions are imposed. We find that the unification of the third family Yukawa couplings can be achieved while retaining a viable spectrum, provided that the ratio of the vacuum expectation values of the two Higgs doublet fields is large, tan⁡β≈60.

Photon interactions with superconducting topological defects

Using a toy model for the interactions between a defect-forming field and the photon field where the photon becomes massive in the defect core (motivated by recent work on defects in the 2HDM), we study the impact on photon propagation in the background of the defect. We find that, when the photon frequency (in natural units) is much lower than the symmetry breaking scale, domain walls reflect most of an incoming photon signal leading to potential interesting astrophysical signals. We also adapt the calculations for vortices and monopoles. We find that the case of strings is very similar to the standard case for massive scalar particles, but in the case of monopoles the cross-section is proportional to the geometrical area of the monopole.

Filtered asymmetric dark matter during the Peccei-Quinn phase transition

In this paper, we propose a bubble filtering-out mechanism for an asymmetric dark matter scenario during the Peccei-Quinn (PQ) phase transition. Based on a QCD axion model, extended by extra chiral neutrinos, we show that the PQ phase transition can be first order in the parameter space of the model and regarding the PQ symmetry breaking scale, the mechanism can generate PeV-scale heavy neutrinos as a dark matter candidate. Considering a CP-violating source, during the phase transition, discriminating between the neutrino and antineutrino number density, we find the observed dark matter relic abundance, such that the setup can be applied to the first order phase transition with different strengths. We then calculate effective couplings of the QCD axion addressing the strong CP problem within the model. We also study the energy density spectrum of gravitational waves generated from the first order phase transition and show that the signals can be detected by future ground-based detectors such as Einstein Telescope. In particular, for a visible heavy axion case of the model, it is shown that gravitational waves can be probed by DECIGO and BBO interferometers. Furthermore, we discuss the dark matter-standard model neutrino annihilation process as a source for the creation of PeV-scale neutrinos.