Search

The mass–action equivalence emerges naturally as the consequence of Relativistic Heisenberg Uncertainty (RHU). It changes the structure of relativistic energy–momentum equation that has been underpinning the chosen Lagrangian of the Standard Model, i.e., the Lagrangian which the Higgs mechanism works. The transition from the mass–energy to the mass–action equivalence zone occurs at a certain value of the particle’s wave group velocity $$v_{{\text{g}}}$$ indicating the crossing curve between relativistic energy and action. Due to this transition, particles in the Standard Model are not going to gain inertial mass coming from the Higgs mechanism and related Higgs field, but from another mechanism which can break the Lagrangian symmetry of the Standard Model. This mechanism corresponds to Explicit Symmetry Breaking by generating the new type of field, i.e., the X-Higgs-like field and works based on the mass–action equivalence. This field provides the mass for the X Matter as well as Higgs field for Ordinary Matter. The gaining mass of particles due to this mechanism is not related to the form of ordinary relativistic energy, but to the form of relativistic action. It leads us to the new dynamical equation instead of the ordinary Klein–Gordon and Dirac equation. There are two phenomena due to the increasing and decreasing of particle’s velocity in this mechanism. From the lower to the higher velocity, particle gains additional inertial mass from the X Matter, while conversely particle loses its inertial mass. It is reasonable for us to view that the missing inertial mass of particles in the Standard Model is compensated as the Dark Matter. The X-Higgs-like field breaking to be the Dark-Higgs-like and recognized Higgs field can be considered to explain the origin of the Dark and Ordinary Matter from the X Matter.

In order to study electrically and magnetically charged vortices in fractional quantum Hall effect and anyonic superconductivity, the Maxwell–Chern–Simons (MCS) model was introduced by Lee et al. (Phys Lett B 252:79–83, 1990) as a unified system of the classical Abelian–Higgs model (AH) and the Chern–Simons (CS) model. In this article, the first goal is to obtain the uniform (CS) limit result of (MCS) model with respect to the Chern–Simons parameter, without any restriction on either a particular class of solutions or the number of vortex points, as the Chern–Simons mass scale tends to infinity. The most important step for this purpose is to derive the relation between the Higgs field and the neutral scalar field. Our (CS) limit result also provides the critical clue to answer the open problems raised by Ricciardi and Tarantello (Comm Pure Appl Math 53:811–851, 2000) and Tarantello (Milan J Math 72:29–80, 2004), and we succeed to establish the existence of periodic Maxwell–Chern–Simons vortices satisfying the concentrating property of the density of superconductive electron pairs. Furthermore, we expect that the (CS) limit analysis in this paper would help to study the stability, multiplicity, and bubbling phenomena for solutions of the (MCS) model.

By virtue of Hirota bilinear form of the coupled Higgs field equation, some higher-order rogue wave, the Ma breather, the Akhmediev breather and the general breather solutions are constructed through symbolic computation. With the help of the contour line method, we investigate the localization characters of the first-order rogue wave, which is different from the case of its in nonlinear Schrodinger equation. The Ma breather and the Akhmediev breather solutions of the coupled Higgs field equation possess time-periodic and space-periodic, respectively. The results of this paper show us the generation and evolutions of novel nontraveling wave with several interesting structures.

Renormalization group methods are applied to a scalar field within a finite, nonlocal quantum field theory formulated perturbatively in Euclidean momentum space. It is demonstrated that the triviality problem in scalar field theory, the Higgs boson mass hierarchy problem and the stability of the vacuum do not arise as issues in the theory. The scalar Higgs field has no Landau pole.

We study solutions to the Kapustin--Witten equations on ALE and ALF gravitational instantons. On any such space and for any compact structure group, we prove asymptotic estimates for the Higgs field. We then use it to prove a vanishing theorem in the case when the underlying manifold is $\mathrm{R}^4$ or $\mathrm{R}^3 \times \mathbb{S}^1$ and the structure group is $\mathrm{SU} (2)$., Comment: 12 pages, no figures. A mistake in the main theorem is fixed; supersedes published version

Two analytic examples of globally regular non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory in (3+1)-dimensions are presented. In both cases, the space-time geometries are of the Nariai type and the Yang-Mills field is completely regular and of meron type (namely, proportional to a pure gauge). However, while in the first family (type I) $X_{0} = 1/2$ (as in all the known examples of merons available so far) and the Higgs field is trivial, in the second family (type II) $X_{0}$ is not 1/2 and the Higgs field is non-trivial. We compare the entropies of type I and type II families determining when type II solitons are favored over type I solitons: the VEV of the Higgs field plays a crucial role in determining the phases of the system. The Klein-Gordon equation for test scalar fields coupled to the non-Abelian fields of the gravitating solitons can be written as the sum of a two-dimensional D'Alembert operator plus a Hamiltonian which has been proposed in the literature to describe the four-dimensional Quantum Hall Effect (QHE): the difference between type I and type II solutions manifest itself in a difference between the degeneracies of the corresponding energy levels., Comment: 18 pages, 9 figures

Restricting the $\mathbb{Z}_2$-graded tensor product of Clifford algebras $C\ell_4\hat{\otimes}C\ell_6 $ to the particle subspace allows a natural definition of the Higgs field $\Phi$, the scalar part of Quillen's superconnection, as an element of $C\ell_4^1$. We emphasize the role of the exactly conserved weak hypercharge Y, promoted here to a superselection rule for both observables and gauge transformations. This yields a change of the definition of the particle subspace adopted in recent work with Michel Dubois-Violette \cite{DT20}; here we exclude the zero eigensubspace of Y consisting of the sterile (anti)neutrinos which are allowed to mix. One thus modifies the Lie superalgebra generated by the Higgs field. Equating the normalizations of $\Phi$ in the lepton and the quark subalgebras we obtain a relation between the masses of the W boson and the Higgs that fits the experimental values within one percent accuracy., Comment: 23 pages; new section 5, minor corrections, reference added

The spectral properties of a set of local gauge (BRST) invariant composite operators are investigated in theSU(2) Yang–Mills–Higgs model with a single Higgs field in the fundamental representation, quantized in the ’t Hooft$$R_{\xi }$$Rξ-gauge. These operators can be thought of as a BRST invariant version of the elementary fields of the theory, the Higgs and gauge fields, with which they share a gauge independent pole mass. The two-point correlation functions of both BRST invariant composite operators and elementary fields, as well as their spectral functions, are investigated at one-loop order. It is shown that the spectral functions of the elementary fields suffer from a strong unphysical dependence from the gauge parameter$$\xi $$ξ, and can even exhibit positivity violating behaviour. In contrast, the BRST invariant local operators exhibit a well defined positive spectral density.

We construct a supersymmetric flipped SU(5) grand unified model that possesses an $R$ symmetry. This $R$ symmetry forbids dangerous non-renormalizable operators suppressed by a cut-off scale up to sufficiently large mass dimensions so that the SU(5)-breaking Higgs field develops a vacuum expectation value of the order of the unification scale along the $F$- and $D$-flat directions, with the help of the supersymmetry-breaking effect. The mass terms of the Higgs fields are also forbidden by the $R$ symmetry, with which the doublet-triplet splitting problem is solved with the missing partner mechanism. The masses of right-handed neutrinos are generated by non-renormalizable operators, which then yield a light neutrino mass spectrum and mixing through the seesaw mechanism that are consistent with neutrino oscillation data. This model predicts one of the color-triplet Higgs multiplets to lie at an intermediate scale, and its mass is found to be constrained by proton decay experiments to be $\gtrsim 5 \times 10^{11}$ GeV. If it is $\lesssim 10^{12}$ GeV, future proton decay experiments at Hyper-Kamiokande can test our model in the $p \to \pi^0 \mu^+$ and $p \to K^0 \mu^+$ decay modes, in contrast to ordinary grand unified models where $p \to \pi^0 e^+ $ or $p \to K^+ \bar{\nu}$ is the dominant decay mode. This characteristic prediction for the proton decay branches enables us to distinguish our model from other scenarios., Comment: 30 pages, 2 figures

The objective of the paper was to examine gravitational evolutions in the Higgs-dark matter sector toy model. The real part of the Higgs doublet was modelled by a neutral scalar. Two dark matter candidates introduced were the dark photon and a charged complex scalar. Non-minimal couplings of both scalars to gravity were included. The coupling channels between the ordinary and dark matter sectors were kinetic mixing between the electromagnetic and dark U(1) fields and the Higgs portal coupling among the scalars. The structures of emerging singular spacetimes were either of Schwarzschild or Reissner–Nordström types. The non-minimal scalar–gravity couplings led to an appearance of timelike portions of apparent horizons where they transform from spacelike to null. The features of dynamical black holes were described as functions of the model parameters. The black holes formed later and their radii and masses were smaller as the mass parameter of the complex scalar increased. The dependencies on the coupling of the Higgs field to gravity exhibited extrema, which were a maximum for the time of the black holes formation and minima in the cases of their radii and masses. A set of quantities associated with an observer moving with the evolving matter was proposed. The energy density, radial pressure and pressure anisotropy within dynamical spacetimes get bigger as the singularity is approached. The increase is more considerable in the Reissner–Nordström spacetimes. The apparent horizon local temperature changes monotonically in the minimally coupled case and non-monotonically when non-minimal scalar–gravity couplings are involved.

The coupled Higgs field equation is significant for describing a system of conserved scalar nucleons interacting with the neutral scalar meson. The improved Bernoulli sub-equation function method and the sine–Gordon expansion method have been put in used in the current article, to interpret the dynamism of the particles through analytical solutions modelled by the coupled Higgs field equation. The interaction among the electrons and mesons has been found out and it is observed that the particle moves along the smooth path from one state to another. It is also vital to mark that the wave profile of the waves are velocity dependent and the incident is shown in the figures. Different types of soliton shape like, bell shape soliton, kink soliton, consolidated bell shape; anti-bell shape soliton, compacton, singular soliton, flat kink soliton etc. are ascertained by assigning individual quantities of the unidentified parameters whose propagations are portrayed in 3D and 2D surfaces. The solutions established in this study are further comprehensive, broad–ranging and some are new which have not been found in earlier research. The executed schemes are effective, compatible to computer algebra and deliver ample wide–ranging wave solutions.

The work presents systematic investigations on invariant analysis and the analytic solution of the second order Higgs equation. On employing Lie classical approach, new symmetry and the corresponding reduction of the system are obtained. Explicit convergent infinite series solution of the reduced system is obtained. Local conservation laws of the system are derived by the multiplier approach.

The abundance of the QCD axion is known to be suppressed if the Hubble parameter during inflation, $H_{\rm inf}$, is lower than the QCD scale, and if the inflation lasts sufficiently long. We show that the tight upper bound on the inflation scale can be significantly relaxed if the eternal old inflation is driven by the standard-model Higgs field trapped in a false vacuum at large field values. Specifically, $H_{\rm inf}$ can be larger than $100\,$GeV if the false vacuum is located above the intermediate scale. We also discuss the slow-roll inflation after the tunneling from the false vacuum to the electroweak vacuum., 31 pages, 4 figures

In quantum many-body systems with spontaneous breaking of a continuous symmetry, Higgs modes emerge as collective amplitude oscillations of order parameters. Recently, Higgs modes have been observed in superconductors and in Bose gases in optical lattices. However, it has yet to be observed in Fermi gases. In the present paper, we use the time-dependent Bogoliubov–de Gennes equations to investigate Higgs amplitude oscillations of the superfluid order parameter in a trapped Fermi gas induced by a sudden changes of the $${ s}$$ -wave scattering length. In particular, we investigate the Higgs mode with different values of the initial scattering length and discuss how the frequency and damping of the Higgs mode changes around the unitarity regime.

We propose a simple non-supersymmetric grand unified theory (GUT) based on the gauge group $SO(10) \times U(1)_\psi$. The model includes 3 generations of fermions in ${\bf 16}$ ($+1$), ${\bf 10}$ ($-2$) and ${\bf 1}$ ($+4$) representations. The ${\bf 16}$-plets contain Standard Model (SM) fermions plus right-handed neutrinos, and the ${\bf 10}$-plet and the singlet fermions are introduced to make the model anomaly-free. Gauge coupling unification at $M_{GUT} \simeq 5 \times 10^{15}-10^{16}$ GeV is achieved by including an intermediate Pati-Salam breaking at $M_{I} \simeq 10^{12}-10^{11}$ GeV, which is a natural scale for the seesaw mechanism. For $M_{I} \simeq 10^{12}-10^{11}$, proton decay will be tested by the Hyper-Kamiokande experiment. The extra fermions acquire their masses from $U(1)_\psi$ symmetry breaking, and a $U(1)_\psi$ Higgs field drives a successful inflection-point inflation with a low Hubble parameter during inflation, $H_{inf} \ll M_{I}$. Hence, cosmologically dangerous monopoles produced from $SO(10)$ and PS breakings are diluted away. The reheating temperature after inflation can be high enough for successful leptogenesis. With the Higgs field contents of our model, a ${\bf Z}_2$ symmetry remains unbroken after GUT symmetry breaking, and the lightest mass eigenstate among linear combinations of the ${\bf 10}$-plet and the singlet fermions serves as a Higgs-portal dark matter (DM). We identify the parameter regions to reproduce the observed DM relic density while satisfying the current constraint from the direct DM detection experiments. The present allowed region will be fully covered by the future direct detection experiments such as LUX-ZEPLIN DM experiment. In the presence of the extra fermions, the SM Higgs potential is stabilized up to $M_{I}$., Comment: 25 pages, 5 figures, new references added

We discuss new mechanisms to stop the relaxion field during inflation. They can be realized in a generic model, including the original model but in a quite different parameter region. We consider a fast-rolling relaxion field, which can go over the bumps created by QCD-like dynamics. Then, in one of the mechanisms, we stop it with a parametric resonance of the Higgs field. The mechanisms are free from a super-Planckian field excursion or a gigantic number of e-folds of inflation. The relaxion has a mass around the weak scale and mixes with the Higgs boson, which enhances the testability of our mechanisms., 58 pages, 12 figures; added Appendix D; published version

A scalar cosmological Higgs field is expected to exist in our universe in order to create inertial mass. Some results obtained at LHC suggest that this idea must be reconsidered. The cosmological effects of scalar fields have been proposed as a mechanism to drive the evolution of the universe in various scenarios. In this paper we investigate, from the dynamical systems perspective, the evolution of a Universe consisting of a matter component $$\rho $$ together with a scalar field $$\phi $$ exhibiting a quartic polynomial self-interacting potential. We consider an homogeneous and isotropic flat Friedmann–Robertson–Walker metric. Center Manifold Theory is employed to investigate the dynamics near a non-hyperbolic critical point. We prove that there are two possible late time attractors corresponding to stable de Sitter solutions.

We consider the impact on WW production of the unique dimension-six operator coupling gluons to the Higgs field. In order to study this process, we have to appropriately model the effect of a veto on additional jets. This requires the resummation of large logarithms of the ratio of the maximum jet transverse momentum and the invariant mass of the W boson pair. We have performed such resummation at the appropriate accuracy for the Standard Model (SM) background and for a signal beyond the SM (BSM), and devised a simple method to interface jet-veto resummations with fixed-order event generators. This resulted in the fast numerical code MCFM-RE, the Resummation Edition of the fixed-order code MCFM. We compared our resummed predictions with parton-shower event generators and assessed the size of effects, such as limited detector acceptances, hadronisation and the underlying event, that were not included in our resummation. We have then used the code to compare the sensitivity of WW and ZZ production at the HL-LHC to the considered higher-dimension operator. We have found that WW can provide complementary sensitivity with respect to ZZ, provided one is able to control theory uncertainties at the percent-level. Our method is general and can be applied to the production of any colour singlet, both within and beyond the SM., 48 pages, 14 figures, JHEP style files included; v2: added references, improved discussion in section 4; v3: added ratio plot to fig. 1, minor clarifications, published version

The study of generalized field associated with Abelian dyons has been undertaken and it has been demonstrated that topologically, a non-Abelian gauge theory is equivalent to a set of Abelian gauge theories supplemented by dyons which undergo condensation leading to confinement and consequently to superconducting model of QCD vacuum, where the Higgs field plays the role of a regulator only. Constructing the effective action for dyonic field in Abelian projection of QCD, it has been demonstrated that any charge (electrical or magnetic) of dyon screens its own direct potential to which it minimally couples and anti-screens the dual potential leading to dual superconductivity in accordance with generalized Meissner effect. In this Abelian projection of QCD an Abelian Higgs model (AHM) has been successfully constructed and it has been shown to incorporate dual superconductivity and confinement as the consequence of dyonic condensation. It has been demonstrated that in AHM t’ Hooft loop creates the string (AHM-string) around which the monopole current under London limit leads to vanishing coherence length in the chromo-magnetic superconductor. It has also been shown that in London limit the squared density of monopole current around AHM-string has a maximum at the distance of the order of penetration length.

Multi-condensate superconductors have multiple excitation modes. Among them, the Nambu-Goldstone mode, Leggett mode, and Higgs mode are important in superconductors. The dispersion relations and mass formulas of these modes in a multi-condensate superconductor are evaluated by using the functional integral method. At low temperatures, the Higgs mode is defined clearly with the action of a quadratic form. The Higgs mass in the BCS model has a non-relativistic correction compared to that of the relativistic Nambu-Jona-Lasinio model.

Supersymmetric see-saw slow roll inflection point inflation occurs along a MSSM D-flat direction associated with gauge invariant combination of Higgs, slepton and right-handed sneutrino at a scale set by the right-handed neutrino mass $M_{{\nu }^{c}} \sim 10^{6}\!\,-\,\!10^{13}$ GeV. The tensor to scalar perturbation ratio r∼10−3 can be achieved in this scenario. However, this scenario faced difficulty in being embedded in the realistic new minimal supersymmetric SO(10) grand unified theory (NMSO(10)GUT). The recent discovery of B-mode polarization by BICEP2, changes the prospects of NMSO(10)GUT inflation. Inflection point models become strongly disfavoured, as the trilinear coupling of SUSY see-saw inflation potential gets suppressed relative to the mass parameter favoured by BICEP2. Large values of r≈0.2 can be achieved with super-Planck scale inflaton values and mass scales of inflaton ≥10 13 GeV. In NMSO(10)GUT, this can be made possible with an admixture of heavy Higgs doublet fields, i.e., other than MSSM Higgs field, which are present and have masses of order GUT scale.

In this article normalization of a Hamiltonian system with reflection symmetry is performed by means of Lie transforms. The periodic solutions are computed by means of inverse transformation and they are compared with numerical results for the efficiency of the applied method. On the other hand approximate integrals are constructed with the same procedure, and the level curves obtained from those integrals are compared with Poincare surface of section (P.S.S.). The Hamiltonian under consideration is a gauge theoretical model resulting from classical SU(2) Yang–Mills–Higgs system which possesses quartic nonlinear term. The stabilizing effect of Higgs field, suppress the chaotic nature of pure Yang–Mills fields so that regular behaviour becomes dominant. Especially for lower energies the regularity of the system is manifested as invariant curves in P.S.S. Not only periodic orbits but also approximate integrals shows good agreement with numerical results, which improve the reliability of the procedure done.

Extra dimensions can be very useful tools when constructing new physics models. Previously, we began investigating toy models for the 5-D analog of the kinetic mixing/vector portal scenario where the interactions of bulk dark matter with the brane-localized fields of the Standard Model are mediated by a massive $U(1)_D$ dark photon also living in the bulk. In that setup, where the dark matter was taken to be a complex scalar, a number of nice features were obtained such as $U(1)_D$ breaking by boundary conditions without the introduction of a dark Higgs field, the absence of potentially troublesome SM Higgs-dark singlet mixing, also by boundary conditions, the natural similarity of the dark matter and dark photon masses and the decoupling of the heavy gauge Kaluza-Klein states from the Standard Model. In the present paper we extend this approach by examining the more complex cases of Dirac and Majorana fermionic dark matter. In particular, we discuss a new mechanism that can occur in 5-D (but not in 4-D) that allows for light Dirac dark matter in the $\sim 100$ MeV mass range, even though it has an $s$-wave annihilation into Standard Model fields, by avoiding the strong constraints that arise from both the CMB and 21 cm data. This mechanism makes use of the presence of the Kaluza-Klein excitations of the dark photon to extremize the increase in the annihilation cross section usually obtained via resonant enhancement. In the Majorana dark matter case, we explore the possibility of a direct $s$-channel dark matter pair-annihilation process producing the observed relic density, due to the general presence of parity-violating dark matter interactions, without employing the usual co-annihilation mechanism which is naturally suppressed in this 5-D setup., Comment: 22 pages, 7 Figs; discussions and refs. added, typos fixed; title changed to match earlier work

Particle physics suggests that the Universe may have undergone several phase transitions, including the well-known inflationary event associated with the separation of the strong and electroweak forces in grand unified theories. The accelerated cosmic expansion during this transition, at cosmic time $$t\sim 10^{-36}-10^{-33}$$ s, is often viewed as an explanation for the uniformity of the CMB temperature, T, which would otherwise have required inexplicable initial conditions. With the discovery of the Higgs particle, it is now quite likely that the Universe underwent another (electroweak) phase transition, at $$T=159.5\pm 1.5$$ GeV – roughly $$\sim 10^{-11}$$ s after the big bang. During this event, the fermions gained mass and the electric force separated from the weak force. There is currently no established explanation, however, for the apparent uniformity of the vacuum expectation value of the Higgs field which, like the uniformity in T, gives rise to its own horizon problem in standard $$\varLambda $$ CDM cosmology. We show in this paper that a solution to the electroweak horizon problem may be found in the choice of cosmological model, and demonstrate that this issue does not exist in the alternative Friedmann–Robertson–Walker cosmology known as the $$R_\mathrm{h}=ct$$ universe.

In new Higgs inflation the Higgs kinetic terms are non-minimally coupled to the Einstein tensor, allowing the Higgs field to play the role of the inflaton. The new interaction is non-renormalizable, and the model only describes physics below some cutoff scale. Even if the unknown UV physics does not affect the tree level inflaton potential significantly, it may still enter at loop level and modify the running of the Standard Model (SM) parameters. This is analogous to what happens in the original model for Higgs inflation. A key difference, though, is that in new Higgs inflation the inflationary predictions are sensitive to this running. Thus the boundary conditions at the EW scale as well as the unknown UV completion may leave a signature on the inflationary parameters. However, this dependence can be evaded if the kinetic terms of the SM fermions and gauge fields are non-minimally coupled to gravity as well. Our approach to determine the model's UV dependence and the connection between low and high scale physics can be used in any particle physics model of inflation., Comment: 21+6 pages, 1 figure; final version accepted by the journal, improvements of section 4

It is shown that in the Einstein-conformally coupled Higgs--Maxwell system with Friedman-Robertson-Walker symmetries the energy density of the Higgs field has stable local minimum only if the mean curvature of the $t={\rm const}$ hypersurfaces is less than a finite critical value $\chi_c$, while for greater mean curvature the energy density is not bounded from below. Therefore, there are extreme gravitational situations in which even quasi-locally defined instantaneous vacuum states of the Higgs sector cannot exist, and hence one cannot at all define the rest mass of all the classical fields. On hypersurfaces with mean curvature less than $\chi_c$ the energy density has the `wine bottle' (rather than the familiar `Mexican hat') shape, and the gauge field can get rest mass via the Brout--Englert--Higgs mechanism. The spacelike hypersurface with the critical mean curvature represents the moment of `genesis' of rest masses., Comment: 21 pages, 3 figures; short, journal version of arXiv:1603.06997

The issue of vacuum stability of standard model (SM) is discussed by embedding it within the TeV scale left–right quark see-saw model. The Higgs potential in this case has only two coupling parameters (λ 1, λ 2) and two mass parameters. There are only two physical neutral Higgs bosons (h,H), the lighter one being identified with the 126 GeV Higgs boson. We explore the range of values for (λ 1, λ 2) for which the vacuum is stable for all values of the Higgs fields till 1016 GeV. Combining with the further requirement that the scalar self-couplings remain perturbative till 1016 GeV, we find (i) an upper and lower limit on the second Higgs (H) mass to be within the range: 0.4 ≤ (M H /v R ) ≤ 0.7, where v R is the parity breaking scale and (ii) the masses of heavy vector-like top, bottom and τ partner fermions (P 3, N 3,E 3) have an upper bound ≤ v R . These predictions can be tested at LHC and future higher energy colliders.

We consider integral geometry inverse problems for unitary connections and skew-Hermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without boundary, and also in the presence of trapped geodesics. In the boundary case, we show injectivity of the attenuated ray transform on tensor fields with values in a Hermitian bundle (i.e. vector valued case). We also show that a connection and Higgs field on a Hermitian bundle are determined up to gauge by the knowledge of the parallel transport between boundary points along all possible geodesics. The main tools are an energy identity, the Pestov identity with a unitary connection, which is presented in a general form, and a precise analysis of the singularities of solutions of transport equations when there are trapped geodesics. In the case of closed manifolds, we obtain similar results modulo the obstruction given by twisted conformal Killing tensors, and we also study this obstruction., 48 pages, 1 figure, final version to appear in CMP

We consider the general case of the temperature evolution of the two-doublet Higgs potential of the minimal supersymmetric standard model when vacuum condensates of the Higgs doublets arbitrarily propagate along the equilibrium surface (or along the extremum surface) passing through bifurcation domains. In the framework of catastrophe theory, the two-doublet Higgs potential of the minimal supersymmetric standard model is a special case of a gradient system potential. We obtain nonlinear transformations of the vacuum condensates of this model, which reduce the two-doublet potential to a canonical form, and catastrophe functions of types A3 and A5 corresponding to an electroweak first-order phase transition in the considered model.

We describe a geometric theory of Virasoro constraints in generalized Drinfeld-Sokolov hierarchies. Solutions of Drinfeld-Sokolov hierarchies are succinctly described by giving a principal bundle on a complex curve together with the data of a Higgs field near infinity. String solutions for these hierarchies are defined as points having a big stabilizer under a certain Lie algebra action. We characterize principal bundles coming from string solutions as those possessing connections compatible with the Higgs field near infinity. We show that tau-functions of string solutions satisfy second-order differential equations generalizing the Virasoro constraints of 2d quantum gravity., 28 pages

Within the framework of the confinement mechanism proposed earlier by the author in QCD the problem of masses for fundamental fermions in particle physics is discussed by the example of τ-lepton τ −. It is shown that the observed parameters of τ-lepton such as its mass and magnetic moment can be obtained in a preon model dynamically due to a preon gauge interaction. The radius of τ-lepton is also estimated. Under the circumstances preons might be massless in virtue of existence of the nonzero chiral limit for the preon interaction energy.

We give, for the first time, self-consistent large-N analytical solutions of inhomogeneous condensates in the quantum ℂP N − 1 model in the large-N limit. We find a map from a set of gap equations of the ℂP N − 1 model to those of the Gross-Neveu (GN) model (or the gap equation and the Bogoliubov-de Gennes equation), which enables us to find the self-consistent solutions. We find that the Higgs field of the ℂP N − 1 model is given as a zero mode of solutions of the GN model, and consequently only topologically non-trivial solutions of the GN model yield nontrivial solutions of the ℂP N − 1 model. A stable single soliton is constructed from an anti-kink of the GN model and has a broken (Higgs) phase inside its core, in which ℂP N − 1 modes are localized, with a symmetric (confining) phase outside. We further find a stable periodic soliton lattice constructed from a real kink crystal in the GN model, while the Ablowitz-Kaup-Newell-Segur hierarchy yields multiple solitons at arbitrary separations.

A new model of dressed photons (DPs) as photons in virtual modes is presented by extending conventional electromagnetic field into the one with full energy–momentum support. At first glance, such an extension of electromagnetic field seems to be quite unfamiliar, but, according to one of the fundamental results in mathematical theory on quantum fields, the energy–momentum support covering the whole p-space including timelike, lightlike, and spacelike domains is indispensable for describing their interactions. Virtual photons as mediators of electromagnetic field interactions would be a familiar example: in perturbative calculations of quantum electrodynamics, the concept of virtual photons emerges as photon modes with four polarization vectors, since the theory of virtual photons necessarily involves longitudinal and scalar modes. We show that a new model presented here can be formulated on the basis of vortex (or spin) dynamics and we call Clebsch-dual electromagnetic field which is similar to twistor theory from the group theoretical viewpoint. Since Clebsch-dual vortex dynamics is closely related to scalar photon dynamics, we show here how scalar photons can be interpreted from the viewpoint of micro–macro duality proposed by Ojima in combination with a new interpretation of gauge condition which becomes important in formulating Clebsch-dual vortex dynamics as an extended electromagnetic field in a spacelike domain.

D-Wave system shows quantum computers can learn to detect particle signatures in mountains of data, but doesn’t outpace conventional methods — yet.

The ‘hierarchy problem’ plagues the Standard Model of particle physics. The source of this problem is our inability to answer the following question: Why is the Higgs mass so much below the GUT or Planck scale? A brief description about how ‘supersymmetry’ and ‘composite Higgs’ address this problem is given here.

Local or gauge symmetries are fundamental in elementary-particle physics to describes electroweak and strong interactions in the standard model. The gauge symmetry underlies the dynamics and is employed to describe the interaction between fields. For obtaining a gauge-invariant Lagrangian, the gauge-covariant derivative is defined such that any gauge fields are associated with the generators of the local symmetry group. In this paper, we obtain the gauge-covariant derivative and the gauge-invariant Lagrangian density in de Sitter ambient space formalism.

The effect of spontaneous breaking of gauge symmetry in cosmological models with expansion and rotation in Bianchi metrics of types VII and IX is considered.

This article has two aims. First, I undertake an extensive review of the Higgs mechanism and its connections with spontaneous symmetry breaking and the Goldstone theorem. I take the opportunity to expound and discuss a certain number of philosophical issues, amongst them surplus structure and redundancies. Second, I offer a defence of the metaphor according to which 'gauge fields eat Goldstone bosons to gain a mass’ as sensible rather than merely misleading. It is sensible because there is a direct physical correspondence between the longitudinal polarization of massive gauge fields and Goldstone bosons, which is not merely set by a gauge-fixing procedure. In these terms, I wish to argue that the mechanism which allows for the discovery of the Higgs boson has more than merely heuristic and methodological virtue.

On the occasion of the recent experimental detection of a Higgs-type particle at the Large Hadron Collider at CERN, the paper reviews philosophical aspects of the Higgs mechanism as the presently preferred account of the generation of particle masses in the Standard Model of elementary particle physics and its most discussed extensions. The paper serves a twofold purpose: on the one hand, it offers an introduction to the Higgs mechanism and its most interesting philosophical aspects to readers not familiar with it; on the other hand, it clarifies widespread misunderstandings related to the role of gauge symmetries and their breaking in it.

The properties of 125 GeV new particle, which was discovered in 2012 at the Large Hadron Collider (LHC), are found to be consistent with those of the Higgs boson in the standard model (SM). Hereafter the new particle is dubbed as SM-like Higgs boson. However there is still spacious room for physics beyond the SM (BSM) due to the limited energy and luminosity of the LHC. With more data, experiments will scrutinize whether the new particle is indeed the SM one or not. At the same time, one believes that discovery of the SM-like Higgs boson is just the start of the new era of particle physics. The predominant topic is whether there are others new Higgs bosons as speculated in various BSM models. In this short review we willdescribe the current status of Higgs physics at the LHC and several BSM models which contain more Higgs sectors. In literature there are numerous studies on extended Higgs sector and a comprehensive review is beyond the scopeof this review. Instead, we will present two latest studies on Higgs physics: (1) how to detect the charged Higgs boson and measure $\tan\beta$ after including the top polarization information, and (2) how todiscover the extra neutral Higgs boson via the pair production of SM-like Higgs boson., Comment: 20 pages, 3 figures, 3 tables

We briefly review how successfully the Scalar-Tensor-Theory applies to the Accerelating Universe, particularly through the unique way in resolving the Fine-Tuning Problem. An emphasis is placed also on the role of the scalar field as a (pseudo) Nambu-Goldstone boson (dilaton) for the mass generation of the Higgs field.

In this paper, using Donaldson’s heat flow, we show that the semi-stability of a Higgs bundle over a compact Kahler manifold implies the existence of approximate Hermitian–Einstein structure.

Solutions to the SU(2) monopole equations in the Bogolmony limit are constructed that look very much like Bolognesis conjectured magnetic bag solutions. Three theorems are also stated and proved that give bounds in terms of the topological charge for the radii of balls where the solutions Higgs field has very small norm.

In this note we will introduce our recent work on the existence of approximate Hermitian-Einstein structures on semi-stable Higgs bundles, and the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity.

Higgs type excitations are the excitations which give mass to particles. The Higgs type excitations has a critical role both in particle physics and condensed matter physics. In particle physics, the suspected Higgs boson has been found by the Large Hadron Collider (LHC) in 2012. In condensed matter physics, the Higgs type excitations relate to order phase of the system. In this review, we present an overview of recent studies on the Higgs type excitations both in non-interacting and interacting cold atom systems. First, in non-interacting cold atom system, by synthesizing artificial non-Abelian gauge potential, we demonstrate that when a non-Abelian gauge potential is reduced to Abelian potential, the Abelian part constructs spin-orbit coupling, and the non-Abelian part emerges Higgs excitations. Secondly, the Higgs excitations which are the reputed Higgs amplitude mode in interacting cold atom system are discussed. We review the theoretical model and the experimental detection of Higgs amplitude mode in two dimensional superfluid. The observation of both Higgs type excitations in real experiments are also discussed.

Within the framework of the law of conservation of energy, ranges of values of the temperature and effective size of an early Higgs Universe have been found, for which the superstring-generated quarks, and also other massive particles of the Standard Model with nonzero spin and, consequently, the Universe itself with the set of particles of the Standard Model, arising after the decay of the Higgs bosons, fall into our space with dimensionality n = 3.

UDC 530.12 Based on the concept of an initial Higgs Universe as one of the variants of a Multi-Universe with temperature distribution of massive nonrelativistic degenerate Higgs bosons over spaces with different dimensionalities and in line with their role as the mechanism of mass assignment within the framework of the law of conservation of energy, the ranges of values of the temperature and effective size of the Universe have been found, at which the superstring-generated quarks and also other massive particles of the Standard Model with nonzero spin and, consequently, the Universe itself, together with the set of particles of the Standard Model arising after the decay of the Higgs bosons, fall into the space with dimensionality t. Incidentally, the total thermodynamic functions of the Higgs universe have been found in all spaces.

The existence of dark matter is explained by a new neutral vector boson, C-boson, of mass (900 GeV), predicted by the Wu mechanisms for mass generation of gauge field. According to the Standard Model (SM) W, Z-bosons normally get their masses through coupling with the SM Higgs particle of mass 125 GeV. We compute the self-annihilation cross section of the vector gauge boson C-dark matter and calculate its relic abundance. We also study the constraints suggested by dark-matter direct-search experiments. The problem on the stability of C-particle is left as an open question for future research.

In this article, a variety of solitary wave solutions are found for some nonlinear equations. In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into the corresponding partial differential equation and the rational exp (−φ(η))-expansion method is implemented to find exact solutions of nonlinear equation. We find hyperbolic, trigonometric, rational and exponential function solutions using the above equation. The results of various studies show that the suggested method is very effective and can be used as an alternative for finding exact solutions of nonlinear equations in mathematical physics. A comparative study with the other methods gives validity to the technique and shows that the method provides additional solutions. Graphical representations along with the numerical data reinforce the efficacy of the procedure used. The specified idea is very effective, pragmatic for partial differential equations of fractional order and could be protracted to other physical phenomena.

We discuss the present status of the Higgs sector of the CP-violating minimal supersymmetric Standard Model (CPVMSSM). In the Standard Model (SM) of particle physics, the only source of CP violation is the complex phase in the Cabibbo–Kobayashi–Maskawa (CKM) matrix. By now we all know that this single phase is not large enough to explain the observed baryon asymmetry of our Universe. Hence, one require additional sources of CP violation. The MSSM with several complex phases is one such scenario. The tree-level CP invariance of the MSSM Higgs potential is broken at one-loop level in the presence of complex phases in the MSSM Lagrangian. The presence of these additional phases modifies Higgs masses, mixings and couplings significantly. These additional phases have non-trivial impact on several low-energy observables; like the electric dipole moments (EDMs) of atoms and molecules, the CP asymmetry in rare b-decays etc. We first present a brief outline of the CPVMSSM Higgs sector, and then discuss the current limits /bounds obtained from the measurements of several low-energy observables. We also comment on the current bounds coming from the high-energy collider experiments, specially the Large Electron Positron (LEP) Collider and the ongoing Large Hadron Collider (LHC) at the CERN.