We investigate the potential stochastic gravitational waves from first-order electroweak phase transitions in a model with pseudo-Nambu-Goldstone dark matter and two Higgs doublets. The dark matter candidate can naturally evade direct detection bounds, and can achieve the observed relic abundance via the thermal mechanism. Three scalar fields in the model obtain vacuum expectation values, related to phase transitions at the early Universe. We search for the parameter points that can cause first-order phase transitions, taking into account the existed experimental constraints. The resulting gravitational wave spectra are further evaluated. Some parameter points are found to induce strong gravitational wave signals, which have the opportunity to be detected in future space-based interferometer experiments LISA, Taiji, and TianQin.
We show that perforation of the three-brane by mass impinging upon it from the five-dimensional bulk excites Nambu-Goldstone spherical wave propagating outwards with the velocity of light. It is speculated that such an effect can give rise to "`unmotivated" energy release events in the brane-world cosmological models.
A pseudo-Nambu Goldstone Boson (pNGB) arising from the breaking of a global symmetry ($G\rightarrow H$) can be one of the most promising candidates for the quintessence model, to explain the late-time acceleration of our universe. Motivated from the Composite Higgs scenario, we have investigated the case where the pNGB associated with $SO(N)/ SO(N-1)$ develops a potential through its couplings with the particles that do not form the complete representations of $G$. The Coleman Weinberg (CW) potential is generated via the external particles in the loop which are linked with the strongly interac…
Gravitational Waves and Nambu-Goldstone Bosons from Infrared-Finite Cosmic Strings
The University of Tokyo（东京大学）；The University of Chicago（芝加哥大学）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；The University of Tokyo Institutes for Advanced Study, The University of Tokyo（东京大学国际高等研究所）
Nambu-Goldstone emissions from the cosmological evolution of global monopoles
Institute for Cosmic Ray Research, The University of Tokyo（宇宙线研究所，东京大学）；Frontier Research Institute for Interdisciplinary Sciences, Tohoku University（跨学科前沿科学研究所，东北大学）；Department of Physics, Tohoku University（物理学系，东北大学）
The Affleck-Dine mechanism creates the baryon asymmetry of the universe from an angular motion of a complex scalar field. The mechanism is efficient and allows for a low reheating temperature of the universe if the scalar field has a flat potential along its radial direction. We consider a possibility where the scalar field is a pseudo-Nambu-Goldstone boson arising from spontaneous breaking of an approximate global symmetry, so that the flatness of the potential is naturally understood. We construct a concrete realization of the idea based on chiral symmetry breaking in an SU(N) gauge theory. …
We discuss the cosmic ray spectra in annihilating/decaying Nambu-Goldstone dark matter models. The recent observed positron/electron excesses at PAMELA and Fermi experiments are well fitted by the dark matter with a mass of 3TeV for the annihilating model, while with a mass of 6 TeV for the decaying model. We also show that the Nambu-Goldstone dark matter models predict a distinctive gamma-ray spectrum in a certain parameter space.
We review the cosmological implications of a relic population of pseudo Nambu-Goldstone bosons (pNGB) with an anomalous coupling to two photons, often called axion-like particles (ALPs). We establish constraints on the pNGB mass and two-photon coupling by considering big bang nucleosynthesis, the physics of the cosmic microwave background, and the diffuse photon background. The bounds from WMAP7 and other large-scale-structure data on the effective number of neutrino species can be stronger than the traditional bounds from the primordial helium abundance. These bounds, together with those from…
We reconsider the two different facets of $π$ and $K$ mesons as $q \bar q$ bound states and approximate Nambu-Goldstone bosons. We address several topics, including masses, mass splittings between $π$ and $ρ$ and between $K$ and $K^*$, meson wavefunctions, charge radii, and the $K-π$ wavefunction overlap.
The counting rule for Nambu-Goldstone modes is discussed using Mori's projection operator method in nonrelativistic systems at zero and finite temperatures. We show that the number of Nambu-Goldstone modes is equal to the number of broken charges, Q_a, minus half the rank of the expectation value of [Q_a,Q_b].
The composite Higgs scenario, in which the Higgs emerges as a composite pseudo-Nambu-Goldstone boson, is extensively reviewed in these Notes. The material is presented in a pedagogical fashion, with great emphasis on the conceptual and technical foundations of the construction. A comprehensive summary of the flavor, collider and electroweak precision phenomenology is also presented.
We pursue a possibility that a pseudo-Nambu-Goldstone boson is lurking around or below the intermediate scale. To this end we consider an anomaly-free global flavor symmetry, and construct models where the pseudo-Nambu-Goldstone boson is coupled preferentially to leptons. The experimental and astrophysical bounds derived from couplings to photons and nucleons are significantly relaxed. If sufficiently light, the pseudo-Nambu-Goldstone boson contributes to dark matter, and interestingly, it generally decays into photons through couplings arising from threshold corrections. We show that the rece…
In the standard model extended by a single complex scalar boson with a softly broken global U(1) symmetry, a pseudo Nambu-Goldstone boson becomes a candidate for dark matter. In this paper, we discuss the direct detection of the pseudo Nambu-Goldstone boson dark matter. Since the tree-level amplitude for dark matter-nucleon scattering vanishes, higher order quantum corrections for the amplitude should be taken into account. We perform the calculation at the next-to-leading order in QCD in a systematic manner.
We derive some properties of the Nambu-Goldstone boson coupling in theories that have CP violation and Majorana masses. We show explicitly that its diagonal coupling to a Majorana fermion is pseudoscalar not scalar. This clarifies some confusion in the literature. Some potentially useful off-diagonal properties are also derived. We also show, in the process, that the Goldstone theorem often produces interesting and nontrivial identities in matrix theory which may be hard to prove otherwise.
We study gravitational quantum mechanics violating (QMV) effects to masses of Nambu-Goldstone bosons, taking majoron as an example. We show a supersymmetric majoron has either mass of O(keV) for the dimension five potential or smaller mass for effective potentials with higher dimensions. We extend the Dashen's formula for pseudo Nambu-Goldstone bosons to include possible effects of QMV.
Pseudo-Nambu-Goldstone dark matter connected to Standard Model fermion through the Higgs portal has the property that its direct detection vanishes in the zero momentum transfer limit due to a cancellation mechanism. This feature helps the Pseudo-Nambu-Goldstone dark matter to escape the stringent constraints from direct detection experiments. In this paper we explore new constraints on parameter space of non-zero momentum transfer from the direct detection experiments, and also from the neutron star temperature via the dark matter reheating mechanism.
The fate of the Nambu-Goldstone modes arising from spontaneous Lorentz violation is investigated. Using the vierbein formalism, it is shown that up to 10 Lorentz and diffeomorphism Nambu-Goldstone modes can appear and that they are contained within the 10 modes of the vierbein associated with gauge degrees of freedom in a Lorentz-invariant theory. A general treatment of spontaneous local Lorentz and diffeomorphism violation is given for various spacetimes, and the fate of the Nambu-Goldstone modes is shown to depend on both the spacetime geometry and the dynamics of the tensor field triggering…
We calculate the scattering lengths of Nambu-Goldstone bosons interacting with $D$ mesons in a covariant formulation of chiral perturbation theory, which satisfies heavy-quark spin symmetry and analytical properties of loop amplitudes. We compare our results with previous studies performed using heavy meson chiral perturbation theory and show that recoil corrections are sizable in most cases.
We discuss spontaneous symmetry breaking of open classical and quantum systems. When a continuous symmetry is spontaneously broken in an open system, a gapless excitation mode appears corresponding to the Nambu-Goldstone mode. Unlike isolated systems, the gapless mode is not always a propagation mode, but it is a diffusion one. Using the Ward-Takahashi identity and the effective action formalism, we establish the Nambu-Goldstone theorem in open systems, and derive the low-energy coefficients that determine the dispersion relation of Nambu-Goldstone modes. Using these coefficients, we classify …
We discuss the Top Mode pseudo Nambu-Goldstone boson Higgs (TMpNGBH) model which has recently been proposed as a variant of the top quark condensate model in light of the 125 GeV Higgs boson discovered at the LHC. In this talk, we focus on the vacuum alignment and the phenomenologies of characteristic particles of the TMpNGBH model.
A possibility of existence of a pseudovector-type quark-antiquark condensate in the quark matter and Nambu-Goldstone modes on that condensate in the Nambu-Jona-Lasinio model
In a two-flavor color superconductor, the SU(3)_c gauge symmetry is spontaneously broken by diquark condensation. The Nambu-Goldstone excitations of the diquark condensate mix with the gluons associated with the broken generators of the original gauge group. It is shown how one can decouple these modes with a particular choice of 't Hooft gauge. We then explicitly compute the spectral density for transverse and longitudinal gluons of adjoint color 8. The Nambu-Goldstone excitations give rise to a singularity in the real part of the longitudinal gluon self-energy. This leads to a vanishing gluo…
We study a dark matter model with one singlet complex scalar and two Higgs doublets. The scalar potential respects a softly broken global symmetry, which makes the imaginary part of the singlet become a pseudo-Nambu-Goldstone boson acting as a dark matter candidate. The pseudo-Nambu-Goldstone nature of the boson leads to the vanishing of its tree-level scattering amplitude off nucleons at zero momentum transfer. Therefore, although the interaction strength could be sufficiently large to yield a viable relic abundance via thermal mechanism, direct detection is incapable of probing this candidat…
Axion cosmology is reexamined taking into account effect of kinetic pseudo Nambu-Goldstone modes, with its importance recently pointed out. When Peccei-Quinn (PQ) symmetry is broken by a chiral U(1) singlet, it is found that the effect of kinetic Nambu-Goldstone mode makes the axion dark matter untenable. When PQ symmetry is extended and is broken by two singlets, we find axion cosmology to work, but there are several differences from the axion cosmology studied in the literature. The differences are (1) ordinary type of dark matter scaling as $1/{\rm cosmic \; scale\; factor}^3$ arising from …
This is an introduction to theories where the Higgs is a composite Nambu-Goldstone boson of a new strongly-interacting dynamics not much above the weak scale. A general discussion is presented based on the pattern of global symmetries at low energy, and the analogy with the QCD pion is analyzed. The last part of the lectures shows how a composite Higgs can emerge as the hologram of a 5-dimensional gauge field.
We investigate a possibility that our four-dimensional world is a brane-like object embedded in a higher dimensional spacetime. In such a situation, the transverse coordinates of the brane become the Nambu-Goldstone bosons which appear as a result of spontaneous breaking of the translation symmetry. We determine the form of the effective action of the system, finding the explicit form of the vierbein induced on the brane in terms of the Nambu-Goldstone boson variables and the bulk vielbein. As was pointed out in the previous paper, the Kaluza-Klein mode couplings are suppressed by the effect o…
A canonical pseudo-Nambu Goldstone Boson (pNGB) can play the role of a dark energy field responsible for present cosmic acceleration. Confronting with the recent cosmological data, we find that the pNGB field requires spontaneous symmetry breaking scale $f$ close to $M_P$ and the initial field value fine-tuned. It is difficult to achieve a large $f$ in a theoretically consistent set-up. A possible resolution can be achieved by increasing the Hubble friction in well motivated particle physics models in the general set-up of modified gravity theories. We show two phenomenological examples of thi…
We study a scalar zero mode originated from extradimensional components of a gauge field in a six-dimensional theory compactified on a magnetized torus. We confirm it is a Nambu-Goldstone boson of the translational symmetry on the torus which is breaking spontaneously due to magnetic flux. We also show explicitly it is massless up to the two-loop level. Moreover, we discuss full order contributions by considering the effective potential.
We investigate spontaneous global symmetry breaking in the absence of Lorentz invariance, and study technical Naturalness of Nambu-Goldstone (NG) modes whose dispersion relation exhibits a hierarchy of multicritical phenomena with Lifshitz scaling and dynamical exponents $z>1$. For example, we find NG modes with a technically natural quadratic dispersion relation which do not break time reversal symmetry and are associated with a single broken symmetry generator, not a pair. The mechanism is protected by an enhanced `polynomial shift' symmetry in the free-field limit.
We discuss the counting of Nambu-Goldstone (NG) modes associated with the spontaneous breaking of higher-form global symmetries. Effective field theories of NG modes are developed based on symmetry breaking patterns, using a generalized coset construction for higher-form symmetries. We derive a formula of the number of gapless NG modes, which involves expectation values of the commutators of conserved charges, possibly of different degrees.
We present a new mechanism of fluctuation-induced Nambu-Goldstone bosons in a scalar field theory of Higgs-Josephson systems. We consider a simple scalar field model with $U(1)^n$ rotational symmetry. When there is an interaction which violates the rotational symmetry, the Nambu-Goldstone bosons become massive and massless bosons are concealed. We present a model where the massive boson becomes a massless boson as a result of the perturbative fluctuation. In our model the ${\bf Z}_2$-symmetry associated with the chirality is also broken. The transition occurs as a (weak) first-order transition…
The masses of the pseudo-Nambu-Goldstone bosons in the color superconducting phase of dense QCD with two light flavors are estimated by making use of the Cornwall-Jackiw-Tomboulis effective action. Parametrically, the masses of the doublet and antidoublet bosons are suppressed by a power of the coupling constant as compared to the value of the superconducting gap. This is qualitatively different from the mass expression for the singlet pseudo-Nambu-Goldstone boson, resulting from non-perturbative effects. It is argued that the (anti-) doublet pseudo-Nambu-Goldstone bosons form colorless [with …
We investigate the existence of double copy structure, or the lack thereof, in higher derivative operators for Nambu-Goldstone bosons. At the leading ${\cal O}(p^2)$, tree amplitudes of Nambu-Goldstone bosons in the adjoint representation can be (trivially) expressed as the double copy of itself and the cubic bi-adjoint scalar theory, through the Kawai-Lewellen-Tye bilinear kernel. At the next-to-leading ${\cal O}(p^4)$ there exist four operators in general, among which we identify one operator whose amplitudes exhibit the flavor-kinematics duality and can be written as the double copy of ${\c…
We derive the general structure of dimension-six derivative interactions in the N Higgs doublet models, where Higgs fields arise as pseudo Nambu-Goldstone modes of a strongly interacting sector. We show that there are several relations among the dimension-six operators, and therefore the number of independent operators decreases compared with models on which only SU(2)_L x U(1)_Y invariance is imposed. As an explicit example, we derive scattering amplitudes of longitudinal gauge bosons and Higgs bosons at high energy on models involving two Higgs doublets, and compare them with the amplitudes …
Using the effective Lagrangian approach, we clarify general issues about Nambu-Goldstone bosons without Lorentz invariance. We show how to count their number and study their dispersion relations. Their number is less than the number of broken generators when some of them form canonically conjugate pairs. The pairing occurs when the generators have a nonzero expectation value of their commutator. For non-semi-simple algebras, central extensions are possible. The underlying geometry of the coset space in general is partially symplectic.
We review the spectrum of lightest scalar resonances recently determined using dispersion techniques. The conceptual difference between the pole mass and the bare mass (or the line--shape mass) is stressed. The nature of the lightest scalars are discussed and we argue, without relying on any model details, that the $σ(500)$, $κ(700)$, $a_0(980)$ and $f_0(980)$ may be understood as chiral partners of the Nambu--Goldstone bosons in the linear realization of chiral symmetry. But there remains some difficulties in understanding the role of $f_0(980)$ in this picture.
Nicolis and Piazza have recently pointed out the existence of Nambu-Goldstone-like excitations in relativistic systems at finite density, whose gap is exactly determined by the chemical potential and the symmetry algebra. We show that the phenomenon is much more general than anticipated and demonstrate the presence of such modes in a number of systems from (anti)ferromagnets in magnetic field to superfluid phases of quantum chromodynamics. Furthermore, we prove a counting rule for these massive Nambu-Goldstone bosons and construct a low-energy effective Lagrangian that captures their dynamics.
We consider a model of dynamical neutrino masses via the see-saw mechanism. Nambu-Goldstone bosons (majorons) arise associated with the formation of the heavy right-handed majorana masses. These bosons then acquire naturally soft masses (become pNGB's) at loop level via the Higgs-Yukawa mass terms. These models, like the original neutrino pNGB quintessence schemes of the 1980's that proceed through the Dirac masses, are natural, have cosmological implications through mass varying neutrinos, long range forces, and provide a soft potential for dark energy. We further argue that these models can …
We propose a model of dark matter identified with a pseudo-Nambu-Goldstone boson in the dynamical supersymmetry breaking sector in a gauge mediation scenario. The dark matter particles annihilate via a below-threshold narrow resonance into a pair of R-axions each of which subsequently decays into a pair of light leptons. The Breit-Wigner enhancement explains the excess electron and positron fluxes reported in the recent cosmic ray experiments PAMELA, ATIC and PPB-BETS without postulating an overdensity in halo, and the limit on anti-proton flux from PAMELA is naturally evaded.
It has been found that a pseudo-Nambu-Goldstone boson dark matter suppresses the amplitude for elastic scattering with nuclei in non-relativistic limit, and thus can naturally evade the strong constraint of dark matter direct detection experiments. In this paper, we show that non-zero elastic scattering cross section can be induced if the mediator mass is as small as momentum transfer. The predicted recoil energy spectrum can differ from that for usual thermal dark matter. Together with the relevant constraints such as thermal relic abundance, indirect detection and Higgs decays, we investigat…
Quark matter at high density may exhibit color superconductivity. As magnetic flux tubes in metallic superconductors, color magnetic flux tubes as non-Abelian vortices appear in the color-flavor locked phase of high density QCD. ${\mathbb C}P^2$ Nambu-Goldstone bosons and Majorana fermions belonging to the triplet representation are known to be localized around a non-Abelian vortex. In this paper, we determine the coupling of these bosonic and fermionic modes by using the nonlinear realization method.
It is shown that a true Nambu-Goldstone (NG) boson develops a coherent long-range field whenever the charge associated with it that is carried by the other particles is not conserved in a macroscopic scale. The source of a NG field is the time rate of quantum number violation. If the lepton numbers are spontaneously broken at a scale below 1 TeV, the neutrino oscillation processes generate long-range majoron fields that are strong enough in Supernovae to modify the neutrino flavor dynamics. Two examples are given: NG fields may improve the adiabaticity of $ν_{e}\leftrightarrow ν_{X}$ transitio…
Nambu-Goldstone (NG) modes for 0-form and higher-form symmetries can become unstable in the presence of background fields. Examples include the instability of a photon with a time-dependent axion background or with a chirality imbalance, known as the chiral plasma instability, and the instability of a dynamical axion with a background electric field. We show that all these phenomena can be universally described by a symmetry algebra for 0-form and higher-form symmetries. We prove a counting rule for the number of unstable NG modes in terms of correlation functions of broken symmetry generators…
We study the q \bar q structure embedded in chiral mesons in response to external magnetic fields, using the chiral Lagrangian with q \bar q degrees of freedom derived earlier. We show that GMOR relations hold true for neutral chiral mesons, while they are violated for the charged ones for eB>sigma=0.2 GeV^2. The standard chiral perturbation theory also fails in this region. Masses of pi^+ and pi^0 mesons are calculated and compared to lattice data.
If the Higgs boson is a pseudo Nambu-Goldstone boson (PNGB), the $hZγ$ contact interaction induced by the $\mathcal{O}(p^4)$ invariants of the non-linear sigma model is free from its nonlinearity effects. The process $h\rightarrow Zγ$ can be used to eliminate the universal effects of heavy particles, which can fake the nonlinearity effects of the PNGB Higgs boson in the process $h\rightarrow V^*V$ ($V=W^\pm$,\ $Z$). We demonstrate that the ratio of the signal strength of $h\rightarrow Zγ$ and $h\rightarrow V^*V$ is good to distinguish the signature of the PNGB Higgs boson from Higgs coupling d…
We study the soft behavior of two seemingly different particles that are both referred to as dilatons in the literature, namely the one that appears in theories of gravity and in string theory and the Nambu-Goldstone boson of spontaneously broken conformal invariance. Our primary result is the discovery of a soft theorem at subsubleading order for each dilaton, which in both cases contains the operator of special conformal transformations. Interesting similarities as well as differences between the dilaton soft theorems are discussed.
Pions and kaons have double nature: the chiral dynamics of Nambu-Goldstone bosons together with the usual string dynamics common to all mesons. To uncover the interplay of both dynamics the effective chiral Lagrangian is derived from the QCD Lagrangian using the Field Correlator Method and the pion self-energy (mass) operator is written explicitly. The latter contains an infinite number of poles, but normalized to zero at zero momentum because of spontaneous chiral symmetry breaking. As a result one obtains the Gell-Mann-Oakes-Renner relation for the ground state pion and (slightly shifted by …
Searching for pseudo-Nambu--Goldstone bosons (pNGBs) in weak-coupling domains is crucial for understanding the dark components in the universe. We propose searching for pNGBs coupled to two photons in the mass range from 0.1~eV to 10~keV. This could provide opportunities to test string-theory-based pNGBs beyond the GUT scale $M \sim 10^{16}$~GeV included in the weak coupling proportional to $M^{-1}$. We provide formulae that are applicable to photon--photon scattering via a pNGB resonance exchange with a stimulation process in an asymmetric head-on photon--photon collider by mixing three laser…
We describe a class of relativistic models incorporating finite density of matter in which spontaneous breakdown of continuous symmetries leads to a lesser number of Nambu-Goldstone bosons than that required by the Goldstone theorem. This class, in particular, describes the dynamics of the kaon condensate in the color-flavor locked phase of high density QCD. We describe the spectrum of low energy excitations in this dynamics and show that, despite the presence of a condensate and gapless excitations, this system is not a superfluid.
It is shown that a Nambu-Goldstone (NG) field may be coherently produced by a large number of particles in spite of the fact that the NG bosons do not couple to flavor conserving scalar densities like $\barψψ$. If a flavor oscillation process takes place the phases of the pseudo-scalar or flavor violating densities of different particles do not necessarily cancel each other. The NG boson gets a macroscopic source whenever the total (spontaneously broken) quantum number carried by the source particles suffers a net increase or decrease in time. If the lepton numbers are spontaneously broken suc…
We consider cases where the dark matter-nucleon interaction is naturally suppressed. We explicitly show that by extending the standard model scalar sector by a number of singlets, can lead to a vanishing direct detection cross section, if some softly broken symmetries are imposed in the dark sector. In particular, it is shown that if said symmetries are $SU(2)$ ($SU(N)$) and $U(1) \times S_N$, then the resulting pseudo-Nambu-Goldstone bosons can constitute the dark matter of the Universe, while naturally explaining the missing signal in nuclear recoil experiments.
A semiclassical calculation of particle production by a scalar field in a potential is performed. We focus on the particular case of production of fermions by a Nambu-Goldstone boson $θ$. We have derived a (non)local equation of motion for the $θ$-field with the backreaction of the produced particles taken into account. The equation is solved in some special cases, namely for purely Nambu-Goldstone bosons and for the tilted potential $ U(θ) \propto m^2 θ^2 $. Enhanced production of bosons due to parametric resonance is investigated; we argue that the resonance probably disappears when the expa…
We propose a pseudo-Nambu-Goldstone inflation where twin waterfall fields coupled to the inflaton are responsible for the graceful exit from inflation by a waterfall transition. In this scenario, the $Z_2$ symmetry for the waterfall fields and the inflaton protects the inflaton potential against dangerous quantum corrections coming from the waterfall couplings. We show that there is a wide range of natural model parameters and initial conditions for a successful inflation and discuss the reheating process by the perturbative decay of the waterfall field with a $Z_2$ invariant Higgs portal. We …
Production of single neutrinos as well as neutrino-antineutrino pairs by photons interacting with pseudo Nambu-Goldstone bosons is studied within the Standard Model. The corresponding cross sections are found analytically. The energy loss due to neutrino emission in a thermal plasma of photons and pions is calculated. It is shown that the obtained neutrino emissivity may be significantly enhanced in hot and dense matter due to in-medium modification of the pion decay constant. Phenomenological consequences for ultrarelativistic heavy-ion collisions and astrophysics are discussed.
We study Kelvin modes and translational zero modes excited along a quantized vortex and relativistic global string in superfluids and a relativistic field theory, respectively, by constructing the low-energy effective theory of these modes. We find that they become exact gapless Nambu-Goldstone modes only in a system with infinite volume limit. On the other hand, in a system with the finite volume, we find an imaginary massive gap causing the tachyonic instability above some critical wavelength in the relativistic theory. We also find in the non-relativistic theory that Kelvin modes with wavel…
We review recent progress of understanding and resolving instabilities driven by mismatch between the Fermi surfaces of the pairing quarks in 2-flavor color superconductor. With the increase of mismatch, the 2SC phase exhibits chromomagnetic instability as well as color neutral baryon current instability. We describe the 2SC phase in the nonlinear realization framework, and show that each instability indicates the spontaneous generation of the corresponding pseudo Nambu-Golstone current. The Nambu-Goldstone currents generation state covers the gluon phase as well as the one-plane wave LOFF sta…
We propose a Clifford algebra based model, which treats both gravity and Yang-Mills interactions as gauge fields. There are two sectors of boson fields as electroweak and Majorana bosons. The electroweak boson sector induces fermion masses via spontaneous symmetry breaking. It is composed of scalar Higgs, pseudoscalar Higgs, and antisymmetric tensor components. The Majorana boson sector contributes to flavor mixing and Majorana masses of right-handed neutrinos. It is comprised of neutrino Higgs and pseudo-Nambu-Goldstone bosons. The LHC 750 GeV diphoton resonance might possibly be identified a…
