Symmetry Breaking Scale Research Articles

Bottom quark and tau lepton masses in a toy textrm{SU}(6) model

We study a toy textrm{SU}(6) model with the symmetry breaking pattern of the extended 331 symmetry of textrm{SU}(3)_c otimes textrm{SU}(3)_W otimes textrm{U}(1)_X. A “fermion-Higgs mismatching” symmetry breaking pattern is proposed for more realistic model building. Within such symmetry breaking pattern, only one Higgs doublet develops vacuum expectation value for the spontaneous electroweak symmetry breaking, and gives tree-level top quark mass. A natural VEV splittings in the 331 breaking Higgs fields gives tree-level masses to both bottom quark and tau lepton. The 125,textrm{GeV} SM-like Higgs boson discovered at the LHC can have Yukawa couplings to bottom quark and tau lepton as in the SM prediction, and this suggests the 331 symmetry breaking scale to be sim {{{mathcal {O}}}}(10),textrm{TeV}.

Cosmological structure formation and soliton phase transition in fuzzy dark matter with axion self-interactions

ABSTRACT We investigate cosmological structure formation in fuzzy dark matter (FDM) with the attractive self-interaction (SI) with numerical simulations. Such a SI would arise if the FDM boson were an ultra-light axion, which has a strong CP symmetry-breaking scale (decay constant). Although weak, the attractive SI may be strong enough to counteract the quantum ‘pressure’ and alter structure formation. We find in our simulations that the SI can enhance small-scale structure formation, and soliton cores above a critical mass undergo a phase transition, transforming from dilute to dense solitons.

Probing intermediate scale Froggatt-Nielsen models at future gravitational wave observatories

The flavor symmetry-breaking scale in the Froggatt-Nielsen (FN) mechanism is very weakly constrained by present experiments, and can lie anywhere from a few TeV to the Planck scale. We construct two minimal, non-supersymmetric, ultraviolet (UV) complete models that generate the FN mechanism, with a global $U(1)_{\rm{FN}}$ flavor symmetry and a single flavon field. Using the one-loop finite temperature effective potential, we explore the possibility of a strong first order phase transition (SFOPT) induced by the flavon. We show that if the flavor symmetry-breaking occurs at intermediate scales $\sim 10^4-10^7$ GeV, then in certain regions of the parameter space, the associated stochastic gravitational wave (GW) background is strong enough to be detected by second generation GW observatories such as the Big Bang Observer (BBO), the Deci-hertz interferometer Gravitational Observatory (DECIGO), the Cosmic Explorer (CE) and the Einstein Telescope (ET). We identify viable regions of the parameter space for the best detection prospects. While both models of flavor can produce a detectable GW background, the GW signature cannot be used to discriminate between them.

E- and T-model hybrid inflation

We consider the impact of a kinetic pole of order one or two on the non-supersymmetric model of hybrid inflation. These poles arise due to logarithmic Kähler potentials which control the kinetic mixing of the inflaton field and parameterize hyperbolic manifolds with scalar curvature related to the coefficient (-N)<0 of the logarithm. Inflation is associated with the breaking of a local SU(2)times U(1) symmetry, which does not produce any cosmological defects after it, and remains largely immune from the minimal possible radiative corrections to the inflationary potential. For N=1 and equal values of the relevant coupling constants, lambda and kappa , the achievement of the observationally central value for the scalar spectral index, n_{textrm{s}}, requires the mass parameter, m, and the symmetry breaking scale, M, to be of the order of 10^{12}~{textrm{GeV}} and 10^{17}~{textrm{GeV}} respectively. Increasing N above unity the tensor-to-scalar ratio r increases above 0.002 and reaches its maximal allowed value for Nsimeq 10{-}20.

Radiative symmetry breaking, cosmic strings and observable gravity waves in \U0001d5b4(1)\U0001d5b1 symmetric \U0001d5b2\U0001d5b4(5) × \U0001d5b4(1)χ

We implement shifted hybrid inflation in the framework of supersymmetric SU(5) × U(1)χ GUT model which provides a natural solution to the monopole problem appearing in the spontaneous symmetry breaking of SU(5). The U(1)χ symmetry is radiatevely broken after the end of inflation at an intermediate scale, yielding topologically stable cosmic strings. The Planck's bound on the gravitational interaction strength of these strings, characterized by GNμs are easily satisfied with the U(1)χ symmetry breaking scale which depends on the initial boundary conditions at the GUT scale. The dimension-5 proton lifetime for the decay p → K + ν̅, mediated by color-triplet Higgsinos is found to satisfy current Super-Kamiokande bounds for SUSY breaking scale M SUSY ≳ 12.5 TeV. We show that with minimal Kähler potential, the soft supersymmetry breaking terms play a vital role in bringing the scalar spectral index n_s within the Planck's latest bounds, although with small tensor modes r ≲ 2.5 × 10-6 and SU(5) gauge symmetry breaking scale in the range (2 × 1015≲ Mα ≲ 2 × 1016) GeV. By employing non-minimal terms in the Kähler potential, the tensor-to-scalar ratio approaches observable values (r ≲ 10-3) with the SU(5) symmetry breaking scale Mα ≃ 2 × 1016 GeV.

Exploring Dynamics of A4 Flavour Symmetry Using Low Scale Seesaw Mechanisms

Low scale seesaw models, like low scale type II, inverse (ISS), and linear seesaw (LSS) models provide an interesting mechanism to obtain light neutrino masses and mixings, as they can be tested in future TeV scale experiments. Discrete flavour symmetry groups like $A_4$ can be incorporated to explain the flavour structure of particles. But, so far, nothing is known about dynamics of flavour symmetry - scale of its breaking, or VEV alignment of the flavon fields. In a recent study [1], we have investigated and shed light on how to pinpoint the favoured VEV alignment of the flavon field using light neutrino oscillation data. In this work, for the first time, we present an analysis on dependence of light neutrino masses on scale of flavon VEV in these three seesaw models, and comment on how this information can be used to discriminate among them. We also discuss about the estimated value of the constant $F$ which can constrain various coupling constants of the model, cut-off scale of the theory and scale of flavour symmetry breaking. This study can provide useful insight into the hitherto unknown dynamics of flavour symmetry and hence can contribute as an important ingredient in the model building for future studies.

W-Boson Mass Anomaly as a Manifestation of Spontaneously Broken Additional SU(2) Global Symmetry on a New Fundamental Scale

Recently, the CDF Collaboration has announced a new precise measurement of the W-boson mass MW that deviates from the Standard Model (SM) prediction by 7σ. The discrepancy in MW is about ΔW ≃ 70 MeV and is probably caused by a beyond the SM physics. Within a certain scenario of extension of the SM, we obtain the relation ΔW ≃ 3α8πMW ≃ 70 MeV, where α is the electromagnetic fine structure constant. The main conjecture is the appearance of longitudinal components of the W-bosons as the Goldstone bosons of a spontaneously broken additional SU(2) global symmetry at distances much smaller than the electroweak symmetry breaking scale rEWSB. We argue that within this scenario, the masses of charged Higgs scalars can obtain an electromagnetic radiative contribution which enhances the observed value of MW± with respect to the usual SM prediction. Our relation for ΔW follows from the known one-loop result for the corresponding effective Coleman–Weinberg potential in combination with the Weinberg sum rules.

Generalized symmetry breaking scales and weak gravity conjectures

We explore the notion of approximate global symmetries in quantum field theory and quantum gravity. We show that a variety of conjectures about quantum gravity, including the weak gravity conjecture, the distance conjecture, and the magnetic and axion versions of the weak gravity conjecture can be motivated by the assumption that generalized global symmetries should be strongly broken within the context of low-energy effective field theory, i.e. at a characteristic scale less than the Planck scale where quantum gravity effects become important. For example, the assumption that the electric one-form symmetry of Maxwell theory should be strongly broken below the Planck scale implies the weak gravity conjecture. Similarly, the violation of generalized non-invertible symmetries is closely tied to analogs of this conjecture for non-abelian gauge theory. This reasoning enables us to unify these conjectures with the absence of global symmetries in quantum gravity.

Topological defects in nonlocal field theories

In this paper we study for the first time topological defects in the context of nonlocal field theories in which Lagrangians contain infinite-order differential operators. In particular, we analyze domain walls. Despite the complexity of non-linear infinite-order differential equations, we are able to find an approximate analytic solution. We first determine the asymptotic behavior of the nonlocal domain wall close to the vacua. Then, we find a linearized nonlocal solution by perturbing around the well-known local ‘kink’, and show that it is consistent with the asymptotic behavior. We develop a formalism to study the solution around the origin, and use it to verify the validity of the linearized solution. We find that nonlocality makes the width of the domain wall thinner, and the energy per unit area smaller as compared to the local case. For the specific domain wall solution under investigation we derive a theoretical constraint on the energy scale of nonlocality which must be larger than the corresponding symmetry-breaking scale. We also briefly comment on other topological defects like string and monopole.

Searching for cosmic string induced stochastic gravitational wave background with the Parkes Pulsar Timing Array

We search for stochastic gravitational wave background emitted from cosmic strings using the Parkes Pulsar Timing Array data over 15 years. While we find that the common power-law excess revealed by several pulsar timing array experiments might be accounted for by the gravitational wave background from cosmic strings, the lack of the characteristic Hellings-Downs correlation cannot establish its physical origin yet. The constraints on the cosmic string model parameters are thus derived with conservative assumption that the common power-law excess is due to unknown background. Two representative cosmic string models with different loop distribution functions are considered. We obtain constraints on the dimensionless string tension parameter $G\mu<10^{-11}\sim10^{-10}$, which is more stringent by two orders of magnitude than that obtained by the high-frequency LIGO-Virgo experiment for one model, and less stringent for the other. The results provide the chance to test the Grand unified theories, with the spontaneous symmetry breaking scale of $U(1)$ being two-to-three orders of magnitude below $10^{16}$ GeV. The pulsar timing array experiments are thus quite complementary to the LIGO-Virgo experiment in probing the cosmic strings and the underlying beyond standard model physics in the early Universe.

Phenomenological implications of the new Littlest Higgs model with T-parity

We investigate the parameter space of the new Littlest Higgs model with T-parity (NLHT) recently introduced to cure some pathologies of the original LHT. The model requires extra fermion content and additional pseudo-Goldstone bosons. While the heavy top quark sector is similar, there are both T-odd and T-even heavy quarks and leptons with masses proportional to just two sets of Yukawa matrices in flavor space, one more than in the LHT. The new scalars are a singlet and real triplet, T-odd, with masses controlled by gauge and Yukawa couplings, independent of the spontaneous symmetry breaking scale f, and hence potentially light. Imposing that no mass exceeds the cutoff scale, applying current lower bounds on vector-like quarks and assuming a simplified model with mass degenerate heavy fermions compatible with the heavy photon as dark matter constituent, we find that f gets constrained within the interval between 2 and 3 TeV, the common Yukawa coupling of heavy leptons gets fixed and the Yukawa coupling of heavy quarks becomes greatly correlated to the top quark Yukawa couplings. The particle spectrum is then bounded from below and above, with the (lightest) heavy photon at about 0.5 TeV, not far from the heavy leptons, the new scalars below 1 TeV, the usual complex scalar triplet close to the heavy weak bosons at about 1.5 to 2.5 TeV, and the heavy quarks and top quark partners between 2 and 5 TeV. The new scalars decay predominantly to a standard and a T-odd lepton and have a width comparable to that of the Higgs.

GUTs, hybrid topological defects, and gravitational waves

The symmetry breaking of grand unified gauge groups in the early Universe often leaves behind relic topological defects such as cosmic strings, domain walls, or monopoles. For some symmetry breaking chains, hybrid defects can form where cosmic strings attach to domain walls or monopoles attach to strings. In general, such hybrid defects are unstable, with one defect ``eating'' the other via the conversion of its rest mass into the other's kinetic energy and, subsequently, decaying via gravitational waves. In this work, we determine the gravitational wave spectrum from 1) the destruction of a cosmic string network by the nucleation of monopoles which cut up and ``eat'' the strings, 2) the collapse and decay of a monopole-string network by strings that eat the monopoles, 3) the destruction of a domain wall network by the nucleation of string-bounded holes on the wall that expand and eat the wall, and 4) the collapse and decay of a string-bounded wall network by walls that eat the strings. We call the gravitational wave signals produced from the eating of one topological defect by another ``gravitational wave gastronomy.'' We find that the four gravitational wave gastronomy signals considered yield unique spectra that can be used to narrow down the $SO(10)$ symmetry breaking chain to the Standard Model and the scales of symmetry breaking associated with the consumed topological defects. Moreover, the systems we consider are unlikely to have a residual monopole or domain wall problem.

Gravitational wave pathway to testable leptogenesis

We analyze the classically scale-invariant $B-L$ model in the context of resonant leptogenesis with the recently proposed mass-gain mechanism. The $B-L$ symmetry breaking in this scenario is associated with a strong first order phase transition that gives rise to detectable gravitational waves (GWs) via bubble collisions. The same $B-L$ symmetry breaking also gives Majorana mass to right-handed neutrinos inside the bubbles, and their out of equilibrium decays can produce the observed baryon asymmetry of the Universe via leptogenesis. We show that the current LIGO-VIRGO limit on stochastic GW background already excludes part of the $B-L$ parameter space, complementary to the collider searches for heavy $Z^{\prime}$ resonances. Moreover, future GW experiments like Einstein Telescope and Cosmic Explorer can effectively probe the parameter space of leptogenesis over a wide range of the $B-L$ symmetry-breaking scales and gauge coupling values.

Thermal transitions in domain wall AdS/QCD

We study thermal transitions in a Domain Wall AdS/QCD model. The model is based on the D5/probe D7 system with a discontinuous mass profile which restricts chiral fermions to 3+1 dimensional domain walls. Fluctuations on the domain wall are dual to the quark mass and condensate and reveal the relation between domain wall separation and the quark mass. The massive quarks exhibit a second order thermal, meson melting transition. Witten's multi-trace prescription can be used to interpret these configurations as having a dynamical mass from a Nambu-Jona-Lasinio interaction - here the transition is first order. Confinement can be introduced into the gauge sector by compactifying one direction of the D5. Compactification induces chiral symmetry breaking and there is a first order thermal restoration transition. If an NJL interaction is also introduced then the confinement and chiral symmetry breaking scales can be separated.

Monopoles, exotic states and muon g-2 in TeV scale trinification

We study the low energy implications of a trinification model based on the gauge symmetry G= SU(3)_c times SU(3)_L times SU(3)_R, without imposing gauge coupling unification. A minimal model requires two Higgs multiplets that reside in the bi-fundamental representation of G, and this is shown to be adequate for accommodating the Standard Model (SM) fermion masses and generate, via loop corrections and seesaw mechanism, suitable masses for the heavy neutral leptons as well as the observed SM neutrinos. We estimate a lower bound of around 15 TeV for the masses of the new down- type quarks that are required by the SU(3)_L times SU(3)_R symmetry. We examine the resonant production at the LHC of the new gauge bosons, which leads to a lower bound of 16 TeV for the symmetry breaking scale of G. We also show how the muon g-2 anomaly can be resolved in the presence of these new gauge bosons and the heavy charged leptons present in the model. Finally, the model predicts the presence of a topologically stable monopole carrying three quanta (6 pi /e) of Dirac magnetic charge and mass gtrsim 160 TeV. If new matter fields lying in the fundamental representations of G are included, the model predicts the presence of exotic leptons, mesons and baryons carrying fractional electric charges such as pm e/3 and pm 2e/3, fully compatible with the Dirac quantization condition.

Instability of the model with spontaneously broken scale symmetry

The viability of the phase with spontaneous breaking of scale symmetry observed in the infinite N limit of the O(N) symmetric phi-six theory in three dimensions is scrutinized against quantum corrections at the next-to-leading order in 1/N expansion. It is shown that inclusion of such corrections disrupt the flatness and the global real-valuedness of the effective potential which develops an imaginary part for some values of the fields in a strong coupling regime that covers the BMB and the nontrivial ultraviolet fixed points. This signals instability of the phase with spontaneously broken approximate scale invariance which is doomed to decay by higher 1/N radiative corrections.

Naturally light Dirac and pseudo-Dirac neutrinos from left-right symmetry

We develop a class of left-right symmetric theories based on the gauge group SU(3)c × SU(2)L × SU(2)R × U(1) with a generalized seesaw mechanism for generating the charged fermion masses. Neutrinos are naturally Dirac particles in this setup with their small masses arising from two-loop quantum corrections. We evaluate these two-loop diagrams exactly and analyze the flavor structure of the lepton sector. We find excellent fits to neutrino oscillation data, independent of the right-handed gauge symmetry breaking scale. We also explore the possibility that neutrinos are pseudo-Dirac particles in this framework, with the tiny mass splittings between active and sterile neutrinos arising from Planck-induced corrections and find possible realizations. These models can be tested in the near future with precision cosmological measurements of ∆Neff in CMB which is predicted to be ≃ 0.14. This class of models allows for a solution to the strong CP problem via parity symmetry without the need for an axion.

Probing left-right symmetry via gravitational waves from domain walls

We study the possibility of probing the scale of left-right symmetry breaking in the context of left-right symmetric models (LRSM). In LRSM, the right handed fermions transform as doublets under a newly introduced $SU(2{)}_{R}$ gauge symmetry. This, along with a discrete parity symmetry $\mathcal{P}$ ensuring identical gauge couplings of left and right sectors make the model left-right symmetric, providing a dynamical origin of parity violation in electroweak interactions via spontaneous symmetry breaking. The spontaneous breaking of $\mathcal{P}$ leads to the formation of domain walls in the early universe. These walls, if made unstable by introducing an explicit parity breaking term, generate gravitational waves (GW) with a spectrum characterized by the wall tension or the spontaneous $\mathcal{P}$ breaking scale, and the explicit $\mathcal{P}$ breaking term. Considering explicit $\mathcal{P}$ breaking terms to originate from Planck suppressed operators provides one-to-one correspondence between the scale of left-right symmetry and sensitivities of near future GW experiments. This is not only complementary to collider and low energy probes of TeV scale LRSM but also to GW generated from first order phase transition in LRSM with different spectral shape, peak frequencies as well as symmetry breaking scales.

Tracking down the route to the SM with inflation and gravitational waves

We explore supersymmetric SO(10) models predicting observable proton decay and various topological defects which produce different shapes and strengths of gravitational wave backgrounds depending on the scales of intermediate symmetry breaking and inflation as well. We compare these to their non-supersymmetric counterparts. By identifying the scales at which gravitational wave signals appear, we would be able to track down a particular breaking chain and discern if it has a supersymmetric origin or not. It would also be useful to observe gravitational waves from more than one source among all possible topological defects and first order phase transitions for a realistic breaking chain. For these purposes, we work out specific examples in which the grand unification and relevant intermediate scales are calculable explicitly. It turns out that examples with gravitational waves from different sources are quite difficult to obtain, and the predicted gravitational wave profiles from domain walls and first order phase transitions obtained in some examples will require detectors in the kHz to MHz region.

Scale symmetry and composition of compact star matter

The dense compact star matter is studied by using the skyrmion crystal approach. The chiral effective theory used includes the lightest scalar meson, the lowest-lying vector mesons as well as pions. Consistency with the vector manifestation and the dilaton limit fixed point at high density constrains the anomalous dimension of the gluon field $1.0 \lesssim |\gamma_{G^2}| \lesssim 2.0$ and leads to the significance of the scale symmetry breaking in the intrinsic parity-odd part of the effective theory. The speed of sound $v_s^2 \simeq 1/3$ and the polytropic index $\gamma \simeq 1$ -- both satisfy the conformal limits -- after the dilaton limit fixed point at high density but the matter is still in the hadronic phase. This means that neither the conformal speed of sound nor the smallness of the polytropic index can be used as a criterion of the onset of quark matter. These conclusions are significant for constructing the equation of state of nuclear matter.