Vacuum Expectation Value Research Articles

The effective potential for conformal factor and GL(4) symmetry

We revisit the issue of whether the effective potential for the conformal factor of the metric, which is generated by quantized matter fields, possesses a non-vanishing vacuum expectation value (VEV) or not. We prove that the effective potential has a vanishing vacuum expectation value on the basis of a global GL(4) symmetry. We also account for why there seems to be two different effective potentials for the conformal factor in a theory, one of which gives rise to a vanishing VEV for the conformal factor, whereas the other has a non-vanishing VEV.

Phase transition and gravitational waves in maximally symmetric composite Higgs model

In this paper we study phase transitions in a maximally symmetric composite Higgs model with next-to-minimal coset, where a pseudoscalar singlet emerges alongside the Higgs doublet. The maximal symmetry guarantees the finiteness of the radiatively generated scalar potential. We explore the scenario involving an explicit source of CP violation in the strong sector, which induces a ℤ2 asymmetric scalar potential, and consequently leads to nonzero vacuum expectation value for the singlet. Current experimental bounds from the LHC are imposed on the masses of the composite resonances, while the CP violating interactions of the pseudo Nambu-Goldstone bosons are tightly constrained from the measurements of the electric dipole moment of the electron. We compute the finite temperature corrections to the potential, incorporating the momentum-dependent form factors in the loop integrals to capture the effect of the strong dynamics. The impact of the resonances from the strong sector on the finite temperature potential are exponentially suppressed. The presence of explicit CP violation leads to strong first-order phase transition from a false vacuum to the electroweak vacuum where the pseudoscalar singlet has a non-zero vacuum expectation value. We illustrate that, as a result of such phase transitions, the production of potentially observable gravitational waves at future detectors will offer a complementary avenue to probe the composite Higgs models, distinct from collider experiments.

Revisiting the decoupling limit of the Georgi-Machacek model with a scalar singlet

We study the connection between collider and dark matter phenomenology in the singlet extension of the Georgi-Machacek model. In this framework, the singlet scalar serves as a suitable thermal dark matter (DM) candidate. Our focus lies on the region vχ< 1 GeV, where vχ is the common vacuum expectation value of the neutral components of the scalar triplets of the model. Setting bounds on the model parameters from theoretical, electroweak precision and LHC experimental constraints, we find that the BSM Higgs sector is highly constrained. Allowed values for the masses of the custodial fiveplets, triplets and singlet are restricted to the range 140 GeV <MH50\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {M}_{H_5^0} $$\\end{document}< 350 GeV, 150 GeV <MH30\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {M}_{H_3^0} $$\\end{document}< 270 GeV and 145 GeV < MH< 300 GeV. The extended scalar sector provides new channels for DM annihilation into BSM scalars that allow to satisfy the observed relic density constraint while being consistent with direct DM detection limits. The allowed region of the parameter space of the model can be explored in the upcoming DM detection experiments, both direct and indirect. In particular, the possible high values of BR(H50\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {H}_5^0 $$\\end{document} → γγ) can lead to an indirect DM signal within the reach of CTA. The same feature also provides the possibility of exploring the model at the High-Luminosity run of the LHC. In a simple cut-based analysis, we find that a signal of about 4σ significance can be achieved in final states with at least two photons for one of our benchmark points.

Complete electroweak ONc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( N_c^2\\right) $$\\end{document} two-loop contributions to the Higgs boson masses in the MSSM and aspects of two-loop renormalisation

Results for the full electroweak two-loop contributions of ONc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( N_c^2\\right) $$\\end{document}, where Nc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c$$\\end{document} is the colour factor, to the Higgs-boson masses in the MSSM are obtained using a Feynman-diagrammatic approach including the full dependence on the external momentum. These corrections are expected to constitute the dominant part of the two-loop corrections that were still missing up to now. As a consequence of working at ONc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( N_c^2\\right) $$\\end{document}, the relevant two-loop self-energies decompose into products of one-loop integrals, giving rise to a transparent analytical structure of the self-energies. We compare different renormalisation schemes for tan(β)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ an (\\beta )$$\\end{document}, the ratio of the vacuum expectation values of the two Higgs doublets, and demonstrate under which conditions different renormalisation schemes can be related to each other via a simple reparametrisation. We explicitly show that this is in general not possible for mixed renormalisation schemes due to the presence of evanescent terms. In our numerical analysis, the new corrections are compared with already known two-loop contributions and the experimental uncertainty of the mass of the observed Higgs boson. While smaller than the already known two-loop corrections, the new terms are typically larger in size than the experimental uncertainty. This underlines the relevance of the so-far unknown electroweak two-loop contributions.

Finite temperature fermionic condensate and energy–momentum tensor in cosmic string spacetime

Here we analyze the expectation value of the fermionic condensate and the energy–momentum tensor associated with a massive charged fermionic quantum field with a nonzero chemical potential propagating in a magnetic-flux-carrying cosmic string in thermal equilibrium at finite temperature T. The expectation values of the fermionic condensate and the energy–momentum tensor are expressed as the sum of vacuum expectation values and the finite temperature contributions coming from the particles and antiparticles excitation. The thermal expectations values of the fermionic condensate and the energy–momentum tensor are even periodic functions of the magnetic flux with period being the quantum flux, and also even functions of the chemical potential. Because the analyses of vacuum expectation of the fermionic condensate and energy–momentum tensor have been developed in literature, here we are mainly interested in the investigation of the thermal corrections. In this way we explicitly study how these observable behaves in the limits of low and high temperatures, and also for points near the string. Besides the analytical discussions, we included some graphs that exhibit the behavior of these observable for different values of the physical parameters of the model.

Froggatt-Nielsen meets the SMEFT

We study the matching of Froggatt-Nielsen theories of flavour onto the Standard Model Effective Field Theory (SMEFT), upon integrating out a heavy Beyond-the-Standard-Model (BSM) scalar ‘flavon’ whose vacuum expectation value breaks an Abelian flavour symmetry at energies ΛFN well above the electroweak scale, ΛFN> ΛSM. We include matching contributions to the infrared dSM = 6 (Warsaw basis) SMEFT sourced from ultraviolet contact terms suppressed up to order 1/ΛUV2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Lambda}_{\ extrm{UV}}^2 $$\\end{document} in the Froggatt-Nielsen Lagrangian, where ΛUV> ΛFN is an arbitrary ultraviolet scale where further unspecified BSM particles are dynamical. This includes tree-level (one-loop) ultraviolet diagrams with dFN = 6 (5) effective vertices. We first do so with a toy model, but then generalize our findings to arbitrary Frogatt-Nielsen charges. Our results indicate a rich and non-trivial signature of Froggatt-Nielsen theories on the (otherwise) model-independent operators of the SMEFT, and we briefly speculate on extending our analysis to broader classes of BSM flavour models, e.g. non-Abelian and/or gauged theories. We thus take an important step towards determining how to use rapidly developing theoretical and experimental SMEFT technologies to gain unambiguous insight into the SM’s longstanding fermion flavour puzzle.

Unstable instantons in A-model localization

We apply localization techniques to A-twisted N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = (2) theories of vector multiplets on S2. We derive formulae for A-model partition functions and correlators as integrals along a real contour, as opposed to a complex one. Using the correlator formula, we successfully recover the unstable instanton partition function of pure two-dimensional Yang-Mills theory from the vacuum expectation value of an A-model operator.

Double-Higgs Production

A major focus in particle physics has been on understanding the interactions of the Higgs boson. Tremendous progress has been made in determining the strength of the couplings of the Higgs boson to fermions and vector bosons, but its self-interaction has yet to be established. Understanding the Higgs self-coupling and the form of the potential function of the Higgs field will illuminate the process by which the Higgs boson acquires a vacuum expectation value and could provide insight into the early Universe and, perhaps, its eventual fate. The most natural way to probe the Higgs self-interaction is via searches for Higgs boson pair (HH) production. Since the Standard Model makes a definite prediction for the Higgs self-coupling, enhanced rates and modified kinematic properties of HH production are a smoking-gun signature for new physics. This article reviews the current experimental status of HH searches, discusses the experimental challenges and limitations, and provides an outlook for the future of the field.

Casimir energy with perfect electromagnetic boundary conditions and duality: A field-theoretic approach

Using functional integral methods, we study the Casimir effect for the case of two infinite parallel plates in the QED vacuum, with (different) perfect electromagnetic boundary conditions applied to both plates. To enforce these boundary conditions, we add two Lagrange multiplier fields to the action. We subsequently recover the known Casimir energy in two ways: once directly from the path integral and once as the vacuum expectation value of the 00 component of the energy-momentum tensor. Comparing both methods, we show that the energy-momentum tensor must be modified and that it picks up boundary contributions as a consequence. We also discuss electromagnetic duality invariance of the theory and its interplay with the boundaries by generalizing the Deser-Teitelboim implementation of the duality transformation. Published by the American Physical Society 2024

Fermion mass generation without symmetry breaking

We study the generation of fermion mass in a context where interactions break a discrete chiral symmetry. Then, fermion mass is not protected by a symmetry, no symmetry is broken by the generation of mass, and a vanishing mass no longer enhances a symmetry. We elaborate these scenarios for template fermionic and Yukawa theories in three dimensions where mass can be generated either by fluctuations, strong dynamics, or the vacuum expectation value of a scalar field. We find that fluctuation-induced contributions to fermion mass are parametrically suppressed in the number of fermion flavors N. The generation of fermion mass then takes the form of a rapid crossover which turns into a second order quantum phase transition for large N, much like in settings with fundamental chiral symmetry. We further discuss theories where fermion mass can be generated spontaneously without breaking any symmetry other than scale symmetry. Implications of our findings are discussed. Published by the American Physical Society 2024

Spontaneous CP violation in supersymmetric QCD

We investigate a composite model of spontaneous CP violation based on a new supersymmetric QCD as a solution to the strong CP problem. The scalar components of the meson chiral superfields obtain complex vacuum expectation values to break CP symmetry spontaneously. Then, wavefunction renormalization for the quark kinetic terms provides the Cabibbo-Kobayashi-Maskawa (CKM) phase, while the strong CP phase θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ heta} $$\\end{document} is protected by nonrenormalization of the superpotential and hermiticity of the wavefunction renormalization factor. In our model, the right-handed down-type quark multiplets are given by composite states, enhancing their couplings to CP breaking fields, which is essential to realize the observed CKM phase. The non-perturbative dynamics generates the scale of spontaneous CP violation hierarchically lower than the Planck scale. We discuss potential corrections to θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ heta} $$\\end{document} and find a viable parameter space of the model to solve the strong CP problem without fine-tuning.

A Goldstone boson equivalence for inflation

The effective field theory of single-field inflation characterizes the inflationary epoch in terms of a pattern of symmetry breaking. An operator acquires a time-dependent vacuum expectation value, defining a preferred spatial slicing. In the absence of dynamical gravity, the fluctuations around the time-dependent background are described by the Goldstone boson associated with this symmetry breaking process. With gravity, the Goldstone is eaten by the metric, becoming the scalar metric fluctuation. In this paper, we will show that in general single-field inflation, the statistics of scalar metric fluctuations are given by the statistics of this Goldstone boson decoupled from gravity up to corrections that are controlled as an expansion in slow-roll parameters. This even holds in the presence of additional parameters, like the speed of sound, that naively enhance the impact of the gravitational terms. In the process, we derive expressions for leading and sub-leading gravitational corrections to all-orders in the Goldstone boson.

Dark matter phenomenology in 2HDMS in light of the 95 GeV excess

The Two Higgs Doublet model extended with a complex scalar singlet (2HDMS) is a well-motivated Beyond Standard Model candidate addressing several open problems of nature. In this work, we focus on the dark matter (DM) phenomenology of the complex scalar singlet where the real part of the complex scalar obtains a vacuum expectation value. The model is characterized by an enlarged Higgs spectrum comprising six physical Higgs bosons and a pseudoscalar DM candidate. We address the impact of accommodating the 95 GeV excess on the 2HDMS parameter space and DM observables after including all theoretical and experimental constraints. Finally, we look into the prospects of this scenario at HL-LHC and future lepton colliders for a representative benchmark.

Split Majoron model confronts the NANOGrav signal and cosmological tensions

In the light of the evidence of a gravitational wave background from the NANOGrav 15 yr dataset, we reconsider the split Majoron model as a new physics extension of the standard model able to generate a needed contribution to solve the current tension between the data and the standard interpretation in terms of inspiraling supermassive black hole massive binaries. In the split Majoron model the seesaw right-handed neutrinos acquire Majorana masses from spontaneous symmetry breaking of global U(1)B−L in a strong first order phase transition of a complex scalar field occurring above the electroweak scale. The final vacuum expectation value couples to a second complex scalar field undergoing a low scale phase transition occurring after neutrino decoupling. Such a coupling enhances the strength of this second low scale first order phase transition and can generate a sizeable primordial gravitational wave background contributing to the NANOGrav 15 yr signal. Some amount of extraradiation is generated after neutron-to-proton ration freeze-out but prior to nucleosynthesis. This can be either made compatible with the current upper bound from primordial deuterium measurements or even be used to solve a potential deuterium problem. Moreover, the free streaming length of light neutrinos can be suppressed by their interactions with the resulting Majoron background, and this mildly ameliorates existing cosmological tensions. Thus cosmological observations nicely provide independent motivations for the model. Published by the American Physical Society 2024

A4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_4$$\\end{document} modular invariance and the strong CP problem

We present simple effective theory of quark masses, mixing and CP violation with level N=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=3$$\\end{document} (A4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_4$$\\end{document}) modular symmetry, which provides solution to the strong CP problem without the need for an axion. The vanishing of the strong CP-violating phase θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{\ heta }}$$\\end{document} is ensured by assuming CP to be a fundamental symmetry of the Lagrangian of the theory. The CP symmetry is broken spontaneously by the vacuum expectation value (VEV) of the modulus τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}. This provides the requisite large value of the CKM CP-violating phase while the strong CP phase θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{\ heta }}$$\\end{document} remains zero or is tiny. Within the considered framework we discuss phenomenologically viable quark mass matrices with three types of texture zeros, which are realized by assigning both the left-handed and right-handed quark fields to A4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_4$$\\end{document} singlets 1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{1}$$\\end{document}, 1′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbf{1'}}$$\\end{document} and 1′′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbf{1''}$$\\end{document} with appropriate weights. The VEV of τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document} is restricted to reproduce the observed CKM parameters. We discuss cases in which the modulus VEV is close to the fixed points i, ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} and i∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$i\\infty $$\\end{document}. In particular, we focus on the VEV of τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}, which gives the absolute minima of the supergravity-motivated modular- and CP-invariant potentials for the modulus τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}, so called, modulus stabilisation. We present a successful model, which is consistent with the modulus stabilisation close to τ=ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au =\\omega $$\\end{document}.

Flavino dark matter in a non-Abelian discrete flavor model

We study a relic density of the “flavino” dark matter in modified Altarelli and Feruglio A4 model which is respecting the SU(2)L × A4 × Z3 × U(1)R symmetry. We calculate the Lagrangian from the superpotential in the model. In estimating the relic density, we consider the relevant interactions from the Lagrangian that realize the vacuum expectation value alignments and charged lepton masses where we assume that the supersymmetry breaking effects are small for “flavon” sector. As a result, we find the degenerate masses between the lightest “flavon” and “flavino”, and only two parameters in the potential determines the relic density. Then the allowed parameter space of these parameters are estimated from the relic density calculation taking a constraint from lepton flavor violation into account. We also briefly discuss other dark matter physics such as the direct detection, indirect detection, and collider search.

Spontaneous CP violation and partially broken modular flavor symmetries

We study the realization of spontaneous CP violation through moduli stabilization. In modular flavor models, the source of CP violation is the vacuum expectation values of the complex structure moduli of toroidal compact space. We demonstrate that the combined effects of Type IIB flux compactifications with modular invariant couplings between the moduli and matter fields can induce spontaneous CP violation without or with supersymmetry breaking. Furthermore, some general properties of CP and modular invariant scalar potentials are presented. It is found that certain modifications or partial breakings of modular symmetry are useful in generating spontaneous CP violation.

Discrete Z4 Symmetry in Quantum Gravity

We consider the discrete Z4 symmetry i^, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter—the vacuum expectation value of the bilinear combination of fermionic operators. Under this symmetry operation, i^, the emerging tetrads are multiplied by the imaginary unit, i^eμa=−ieμa. The existence of such symmetry and the spontaneous breaking of this symmetry are also supported by the consideration of the symmetry breaking scheme in the topological superfluid 3He-B. The order parameter in 3He-B is also the bilinear combination of the fermionic operators. This order parameter is the analog of the tetrad field, but it has complex values. The i^-symmetry operation changes the phase of the complex order parameter by π/2, which corresponds to the Z4 discrete symmetry in quantum gravity. We also considered the alternative scenario of the breaking of this Z4 symmetry, in which the i^-operation changes sign of the scalar curvature, i^R=−R, and thus the Einstein–Hilbert action violates the i^-symmetry. In the alternative scenario of symmetry breaking, the gravitational coupling K=1/16πG plays the role of the order parameter, which changes sign under i^-transformation.

Geodesics structure and deflection angle of electrically charged black holes in gravity with a background Kalb–Ramond field

This article investigates the geodesic structure and deflection angle of charged black holes in the presence of a nonzero vacuum expectation value background of the Kalb–Ramond field. Topics explored include null and timelike geodesics, energy extraction by collisions, and the motion of charged particles. The photon sphere radius is calculated and plotted to examine the effects of both the black hole charge (Q) and the Lorentz-violating parameter (b) on null geodesics. The effective potential for timelike geodesics is analyzed, and second-order analytical orbits are derived. We further show that the combined effects of Lorentz-violating parameter and electric charge can mimic a Kerr black hole spin parameter up to its maximum values, i.e., a/M∼1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a/M \\sim 1$$\\end{document} thus suggesting that the current precision of measurements of highly spinning black hole candidates may not rule out the effect of Lorentz-violating parameter. The center of mass energy of colliding particles is also considered, demonstrating a decrease with increasing Lorentz-violating parameter. Circular orbiting particles of charged particles are discovered, with the minimum radius for a stable circular orbit decreasing as both b and Q increase. Results show that this circular orbit is particularly sensitive to changes in the Lorentz-violating parameter. Additionally, a timelike particle trajectory is demonstrated as a consequence of the combined effects of parameters b and Q. Finally, the light deflection angle is analyzed using the weak field limit approach to determine the Lorentz-breaking effect, employing the Gauss–Bonnet theorem for computation. Findings are visualized with appropriate plots and thoroughly discussed.

Stable Lorentz-breaking model for an antisymmetric two-tensor

In this work we investigate possible actions for antisymmetric two-tensor field models subject to constraints that force the field to acquire a nonzero vacuum expectation value, thereby spontaneously breaking Lorentz invariance. In order to assure stability, we require that the associate Hamiltonian be bounded from below. It is shown that this requirement rules out any quadratic action constructed only from the antisymmetric tensor field. We then explicitly construct a hybrid model consisting of the antisymmetric two-tensor field together with a vector field, subject to constraints forcing nonzero expectation values, that is stable in Minkowski space. Published by the American Physical Society 2024