Gauge Symmetry Breaking Research Articles

Supersymmetric Hybrid Inflation in Light of CMB Experiments and Swampland Conjectures

Abstract In this study, we revisited supersymmetric (SUSY) hybrid inflation considering the latest observations from CMB experiments and the swampland conjectures. We demonstrated that when incorporating radiative, soft mass, and SUGRA corrections to the scalar potential, SUSY hybrid inflation remains consistent with Planck 2018 data. It is commonly perceived that SUSY hybrid inflation with a minimal K"ahler potential results in a gauge symmetry breaking scale $M$ of ${\cal O}(10^{15})$ GeV, leading to issues with the proton decay rate. Our analysis introduces a new parameter space where the proton decay problem is mitigated by achieving $M \sim 10^{16}$ GeV with $M_{S}^{2}<0$ and $am_{3/2}>0$. This scenario necessitates a soft SUSY breaking scale $|M_{S}| \gtrsim 10^{6}$ GeV. Furthermore, we found that the tensor-to-scalar ratio $r$ spans from $10^{-16}$ to $10^{-6}$, indicating a very small value. This small ratio allows the modified swampland criteria to hold, although satisfying the trans-Planckian censorship conjecture remains challenging. To address this, we also explored non-minimal K"ahler potentials. By fixing the spectral index at $n_{S}=0.9665$, consistent with the central value of Planck 2018 data, and setting $M=2\times 10^{16}$ GeV, we presented our calculations. We showed that the canonical measure of primordial gravitational waves, $r$, for $M_{S}=$ 1 TeV, $m_{3/2}=$ 1 TeV, $\kappa_{S}<0$ for $\cal{N}=$1 and $\cal{N}=$2, ranges from $10^{-5}$ to $0.01$, making it detectable by Planck and upcoming experiments such as LiteBIRD, Simons Observatory, PRISM, PIXIE, CORE, CMB-S4, and CMB-HD. Additionally, we outlined the parametric space and provided benchmark points for the non-minimal case, ensuring compatibility with both the modified swampland and trans-Planckian censorship conjectures. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd

An effective gauge field theory of the nucleon interactions

We discuss the possibility of constructing an effective gauge field theory of the nucleon interactions based on the ideas of isotopic invariance as well as hypercharge invariance as a local gauge symmetry and spontaneous breaking of this symmetry. The constructed effective field theory predicts the structure of interactions of protons and neutrons with ρ- and σ-mesons, and with pi-mesons and photons, as well as interactions of these particles with each other. The Lagrangian of the theory consists of several parts involving dimension 4 and 5 gauge invariant operators. Feynman rules for physical degrees of freedom that follow on from the Lagrangian define the structure of diagrams for one-boson exchanges between nucleons, predicting the internucleon one-boson-exchange potential as well as nucleon scattering amplitudes. The range of applicability of the effective theory is discussed and estimates are made of the resulting coupling constants. The theory predicts the mass of the neutral ρ 0-meson to be about 1 MeV larger than the mass of the charged mesons ρ ±. The vector ω-meson, which is a sterile particle with respect to the considered gauge group SU I (2) × U Y (1), can be added to the scheme via a gauge-invariant operator of dimension 5, as shown in the appendix.

Deconstructing flavor anomalously

Flavor deconstruction refers to ultraviolet completions of the Standard Model where the gauge group is split into multiple factors under which fermions transform non-universally. We propose a mechanism for charging same-family fermions into different factors of a deconstructed gauge theory in a way that gauge anomalies are avoided. The mechanism relies in the inclusion of a strongly-coupled sector, responsible of both anomaly cancellation and the breaking of the non-universal gauge symmetry. As an application, we propose different flavor deconstructions of the Standard Model that, instead of complete families, uniquely identify specific third-family fermions. All these deconstructions allow for a new physics scale that can be as low as few TeV and provide an excellent starting point for the explanation of the Standard Model flavor hierarchies.

Asymptotic Weak Gravity Conjecture in M-theory on K3× K3

Abstract The Asymptotic Weak Gravity Conjecture (WGC) has been proposed as a special case of the Tower WGC that probes infinite distances in the moduli space corresponding to weakly coupled gauge regimes. The conjecture has been studied in M-theory on a Calabi–Yau threefold (CY3) with finite volume inducing a 5D effective quantum field theory. In this paper, we extend the scope of the previous study to encompass lower dimensions, particularly we generalize the obtained 5D Asymptotic WGC to the effective field theory (EFT$_{3D}$) coupled to 3D gravity that descends from M-theory compactified on a Calabi–Yau fourfold with an emphasis on $K3\times K3$. We find that the CY4 has three fibration structures labeled as line Type-$\mathbb {T}^{2}$, surface Type-$\mathbb {S}$, and bulk Type-$\mathbb {V}$. The emergent EFT$_{3D}$ is shown to have 2+2 towers of particle states termed as the BPS $\mathcal {T}_{M_{\mathrm{k}}\rightarrow 0}^{\rm{{\small BPS}}}$ and $\mathcal {T}_{M_{\mathrm{k}}\rightarrow \infty }^{\rm{{\small BPS}}}$ as well as the non-BPS $\mathcal {T}_{M_{\mathrm{k}}\rightarrow 0}^{\rm{{\small N-BPS}}}$ and $\mathcal {T}_{M_{\mathrm{k}}\rightarrow \infty }^{\rm{{\small N-BPS}}}$. To ensure the viability of the 3D Asymptotic WGC, we give explicit calculations to thoroughly test the Swampland constraint for both the weakly and strongly gauge coupled regimes. Additional aspects, including the gauge symmetry breaking and duality symmetry, are also investigated.

Scotogenic gauge mechanism for neutrino mass and dark matter

Scotogenic is a scheme for neutrino mass generation through the one-loop contribution of an inert scalar doublet and three sterile neutrinos. This work argues that such inert scalar doublet is a Goldstone boson mode associated with a gauge symmetry breaking. Hence, the resultant scotogenic gauge mechanism is very predictive, generating neutrino mass as contributed by a new gauge boson doublet that eats such Goldstone bosons. The dark matter stability is manifestly ensured by a matter parity as residual gauge symmetry for which a vector dark matter candidate is hinted.

Quantisation across bubble walls and friction

We quantise from first principles field theories living on the background of a bubble wall in the planar limit with particular focus on the case of spontaneous breaking of gauge symmetry. Using these tools, we compute the average momentum transfer from transition radiation: the soft emission of radiation by an energetic particle passing across the wall, with a particular focus on the longitudinal polarisation of vectors. We find these to be comparable to transverse polarisations in symmetry-breaking transitions with mild super-cooling, and dominant in broken to broken transitions with thin wall. Our results have phenomenological applications for the expansion of bubbles during first order phase transitions. Our general framework allows for the robust calculation of any particle processes of interest in such translation breaking backgrounds.

Measurement of the superfluid fraction of a supersolid by Josephson effect.

A new class of superfluids and superconductors with spatially periodic modulation of the superfluid density is arising1-12. It might be related to the supersolid phase of matter, in which the spontaneous breaking of gauge and translational symmetries leads to a spatially modulated macroscopic wavefunction13-16. This relation was recognized only in some cases1,2,5-9 and there is the need for a universal property quantifying the differences between supersolids and ordinary matter, such as the superfluid fraction, which measures the reduction in superfluid stiffness resulting from the spatial modulation16-18. The superfluid fraction was introduced long ago16, but it has not yet been assessed experimentally. Here we demonstrate an innovative method to measure the superfluid fraction based on the Josephson effect, a ubiquitous phenomenon associated with the presence of a physical barrier between two superfluids or superconductors19, which might also be expected for supersolids20, owing to the spatial modulation. We demonstrate that individual cells of a supersolid can sustain Josephson oscillations and we show that, from the current-phase dynamics, we can derive directly the superfluid fraction. Our study of a cold-atom dipolar supersolid7 reveals a relatively large sub-unity superfluid fraction that makes realistic the study of previously unknown phenomena such as partially quantized vortices and supercurrents16-18. Our results open a new direction of research that may unify the description of all supersolid-like systems.

Two types of Witten zeta functions

We define two types of Witten’s zeta functions according to Cartan’s classification of compact symmetric spaces. The type II is the original Witten zeta function constructed by means of irreducible representations of the simple compact Lie group U. The type I Witten zeta functions, we introduce here, are related to the irreducible spherical representations of U. They arise in the harmonic analysis on compact symmetric spaces of the form U/K, where K is the maximal subgroup of U. To construct the type I zeta function we calculate the partition functions of 2d YM theory with broken gauge symmetry using the Migdal–Witten approach. We prove that for the rank one symmetric spaces the generating series for the values of the type I functions with integer arguments can be defined in terms of the generating series of the Riemann zeta-function.

Hunting for hypercharge anapole dark matter in all spin scenarios

We conduct a combined analysis to investigate dark matter (DM) with hypercharge anapole moments, focusing on scenarios where Majorana DM particles with spin 1/2, 1, 3/2, and 2 interact exclusively with Standard Model particles through U(1)Y hypercharge anapole terms for the first time. For completeness, we construct general effective U(1) gauge-invariant three-point vertices. These enable the generation of hypercharge gauge-invariant interaction vertices for both a virtual photon γ and a virtual Z boson with two identical massive Majorana particles of any nonzero spin s, after the spontaneous breaking of electroweak gauge symmetry. For complementarity, we adopt effective operators tailored to each dark matter spin allowing crossing symmetry. We calculate the relic abundance, analyze current constraints and future sensitivities from dark matter direct detection and collider experiments, and apply the conceptual naive perturbativity bound. Our estimations based on a generalized vertex calculation demonstrate that the scenario with a higher-spin DM is more stringently constrained than a lower-spin DM, primarily due to the reduced annihilation cross section and/or the enhanced rate of LHC monojet events. As a remarkable outcome, the spin-2 anapole DM scenario is almost entirely excluded, while the high-luminosity LHC exhibits high sensitivities in probing spin-1 and -3/2 scenarios, except for a tiny parameter range of DM mass around 1 TeV. A significant portion of the remaining parameter space in the spin-1/2 DM scenario can be explored through upcoming Xenon experiments, with more than 20 ton-yr exposure equivalent to approximately 5 years of running the XENONnT experiment. Published by the American Physical Society 2024

Electrodynamics with violations of Lorentz and U(1) gauge symmetries and their Hamiltonian structures* *Supported by the National Key Research and Development Program of China (2020YFC2201503, the Zhejiang Provincial Natural Science Foundation of China (LR21A050001, LY20A050002) and the National Natural Science Foundation of China (12275238, 11675143). B.-F. Li is supported by the National Natural Science Foundation of China (NNSFC) (12005186)

This study aims to investigate Lorentz/U(1) gauge symmetry-breaking electrodynamics in the framework of the standard-model extension and analyze the Hamiltonian structure for the theory with a specific dimension of Lorentz breaking operators. For this purpose, we consider a general quadratic action of the modified electrodynamics with Lorentz/gauge-breaking operators and calculate the number of independent components of the operators at different dimensions in gauge invariance and breaking. With this general action, we then analyze how Lorentz/gauge symmetry-breaking can change the Hamiltonian structure of the theories by considering Lorentz/gauge-breaking operators with dimension as examples. We show that the Lorentz-breaking operators with gauge invariance do not change the classes of the theory constrains and the number of physical degrees of freedom of the standard Maxwell electrodynamics. When U(1) gauge symmetry-breaking operators are present, the theories generally lack a first-class constraint and have one additional physical degree of freedom compared to the standard Maxwell electrodynamics.

Electron scattering at a potential temporal step discontinuity

We solve the problem of electron scattering at a potential temporal step discontinuity. For this purpose, instead of the Schrödinger equation, we use the Dirac equation, for access to back-scattering and relativistic solutions. We show that back-scattering, which is associated with gauge symmetry breaking, requires a vector potential, whereas a scalar potential induces only Aharonov–Bohm type energy transitions. We derive the scattering probabilities, which are found to be of later-forward and later-backward nature, with the later-backward wave being a relativistic effect, and compare the results with those for the spatial step and classical electromagnetic counterparts of the problem. Given the unrealizability of an infinitely sharp temporal discontinuity—which is of the same nature as its spatial counterpart!—we also provide solutions for a smooth potential step and demonstrate that the same physics as for the infinitely sharp case is obtained when the duration of the potential transition is sufficiently smaller than the de Broglie period of the electron (or deeply sub-period).

Pseudo-Goldstone dark matter in a radiative inverse seesaw scenario

We consider a scale-invariant inverse seesaw model with dynamical breaking of gauge symmetry and lepton number. In some regions of the parameter space, the Majoron — the pseudo-Goldstone of lepton number breaking — is a viable dark matter candidate. The bound on the Majoron decay rate implies a very large dilaton vacuum expectation value, which also results in a suppression of other dark matter couplings. Because of that, the observed dark matter relic abundance can only be matched via the freeze-in mechanism. The scalar field which gives mass to heavy neutrinos can play the role of the inflaton, resulting in a tensor-to-scalar ratio r ≲ 0.01 for metric inflation and r ≲ 0.21 for Palatini gravity.

Identifying the group-theoretic structure of machine-learned symmetries

Deep learning was recently successfully used in deriving symmetry transformations that preserve important physics quantities. Being completely agnostic, these techniques postpone the identification of the discovered symmetries to a later stage. In this letter we propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. We design loss functions which probe the subalgebra structure either during the deep learning stage of symmetry discovery or in a subsequent post-processing stage. We illustrate the new methods with examples from the U(n) Lie group family, obtaining the respective subalgebra decompositions. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries like SU(3) and SU(5) which are commonly used in model building.

Dark photon dark matter from cosmic strings and gravitational wave background

Dark photon dark matter may be produced by the cosmic strings in association with the dark U(1) gauge symmetry breaking. We perform three-dimensional lattice simulations of the Abelian-Higgs model and follow the evolution of cosmic strings. In particular, we simulate the case of (very) light vector boson and find that such vector bosons are efficiently produced by the collapse of small loops while the production is inefficient in the case of heavy vector boson. We calculate the spectrum of the gravitational wave background produced by the cosmic string loops for the light vector boson case and find characteristic features in the spectrum, which can serve as a probe of the dark photon dark matter scenario. In particular, we find that the current ground-based detectors may be sensitive to such gravitational wave signals and also on-going/future pulsar timing observations give stringent constraint on the dark photon dark matter scenario.

Gradient-flowed order parameter for spontaneous gauge symmetry breaking

The gauge-invariant two-point function of the Higgs field at the same spacetime point can make a natural gauge-invariant order parameter for spontaneous gauge symmetry breaking. However, this composite operator is ultraviolet divergent and is not well defined. We propose using a gradient flow to cure the divergence from putting the fields at the same spacetime point. As a first step, we compute it for the Abelian Higgs model with a positive mass squared at the one-loop order in the continuum theory using the saddle-point method to estimate the finite part. The order parameter consistently goes to zero in the infrared limit of the infinite flow time.

A two-generational SU(7) model with extended weak sector: mass hierarchies, mixings, and the flavor non-universality

We study a possible gauge symmetry breaking pattern in an SU(7) grand unified theory, which describes the mass origins of all electrically charged SM fermions of the second and the third generations. Two intermediate gauge symmetries of {mathcal{G}}_{341}equiv textrm{SU}{(3)}_cotimes textrm{SU}{(4)}_Wotimes textrm{U}{(1)}_{X_0} and {mathcal{G}}_{331}equiv textrm{SU}{(3)}_cotimes textrm{SU}{(4)}_Wotimes textrm{U}{(1)}_{X_1} arise above the electroweak scale. SM fermion mass hierarchies between two generations can be obtained through a generalized seesaw mechanism. The mechanism can be achieved with suppressed symmetry breaking VEVs from multiple Higgs fields that are necessary to avoid tadpole terms in the Higgs potential. Some general features of the SU(7) fermion spectrum will be described, which include the existence of vectorlike fermions, the tree-level flavor changing weak currents between the SM fermions and heavy partner fermions, and the flavor non-universality between different SM generations from the extended weak sector.

A Chern-Simons model for baryon asymmetry

In search of a phenomenological model that would describe physics from Big Bang to the Standard Model (SM), we propose a model with the following properties (i) above an energy about Λcr>1016 GeV there are Wess-Zumino supersymmetric preons and Chern-Simons (CS) fields, (ii) at Λcr∼1016 GeV spontaneous gauge symmetry breaking takes place in the CS sector and the generated topological mass provides an attractive interaction to equal charge preons, (iii) well below 1016 GeV the model reduces to the standard model with essentially pointlike quarks and leptons, having a radius ∼1/Λcr≈10−31 m. The baryon asymmetry turns out to have a fortuitous ratio nB/nγ≪1.

Higgs boson origin from a gauge symmetric theory of massive composite particles and massless W± and Z0 bosons at the TeV scale

The ultraviolet completion is the Standard Model (SM) gauge-symmetric four-fermion couplings at the high-energy cutoff. Composite particles appear in the gauge symmetric phase in contrast with SM particles in the spontaneous symmetry-breaking phase. The critical point between the two phases is a weak first-order transition. It relates to an ultraviolet fixed point for an SM gauge symmetric theory of composite particles in the strong coupling regime. The low-energy SM realizes at an infrared fixed point in the weak coupling regime. Composite bosons dissolve into SM particles at the phase transition, and in the top-quark channel, they become a composite SM Higgs boson and three Goldstone bosons. Extrapolation of SM renormalization-group solutions to high energies implies that the gauge-symmetric theory of composite particles has a characteristic scale of about 5.1 TeV. We discuss the phenomenological implications of composite SM Higgs boson in the gauge symmetry-breaking phase, and massive composite bosons coupling to massless W± and Z0 gauge bosons in the gauge symmetric phase.

PBH-infused seesaw origin of matter and unique gravitational waves

The Standard Model, extended with three right-handed (RH) neutrinos, is the simplest model that can explain light neutrino masses, the baryon asymmetry of the Universe, and dark matter (DM). Models in which RH neutrinos are light are generally easier to test in experiments. In this work, we show that, even if the RH neutrinos are super-heavy (Mi=1,2,3> 109 GeV)—close to the Grand Unification scale—the model can be tested thanks to its distinct features on the stochastic Gravitational Wave (GW) background. We consider an early Universe filled with ultralight primordial black holes (PBH) that produce a super-heavy RH neutrino DM via Hawking radiation. The other pair of RH neutrinos generates the baryon asymmetry via thermal leptogenesis, much before the PBHs evaporate. GW interferometers can test this novel spectrum of masses thanks to the GWs induced by the PBH density fluctuations. In a more refined version, wherein a U(1) gauge symmetry breaking dynamically generates the seesaw scale, the PBHs also cause observable spectral distortions on the GWs from the U(1)-breaking cosmic strings. Thence, a low-frequency GW feature related to DM genesis and detectable with a pulsar-timing array must correspond to a mid- or high-frequency GW signature related to baryogenesis at interferometer scales.

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.