When the spontaneous symmetry breaking occurs for systems without Lorentz covariance, there arises possible mismatch, $N_{\rm NG} < N_{\rm BG}$, between numbers of Nambu-Goldstone (NG) bosons ($N_{\rm NG}$) and the numbers of broken generators ($N_{\rm BG}$. In such a situation, so-called type-II NG bosons emerge. We study how the gauge bosons acquire masses through the Higgs mechanism under this mismatch by employing gauge theories with complex scalar field at finite chemical potential and by enforcing "charge" neutrality. To separate the physical spectra from unphysical ones, the $R_ξ$ gauge is adopted. Not only massless NG bosons but also massive scalar bosons generated by the chemical potential are absorbed into spatial components of the gauge bosons. Although the chemical potential induces a non-trivial mixings among the scalar bosons and temporal components of the gauge bosons, it does not affect the structure of the physical spectra, so that the total number of physical modes is not modified even for $N_{\rm NG} < N_{\rm BG}$.
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 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 …
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 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.
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 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 pin down the origin of a peculiar dispersion relation of domain wall fluctuation, the so-called ripplon, in a superfluid-superfluid interface. A ripplon has a dispersion relation $ω\propto k^{3/2}$ due to the nonlocality of the effective Lagrangian, which is mediated by gapless superfluid phonons in the bulk. We point out the analogy to the longitudinal phonon in the two-dimensional Wigner crystal.
The optimized perturbation theory (OPT) at finite temperature recently developed by the present authors is reviewed by using O(N) phi^4 theory with spontaneous symmetry breaking. The method resums automatically higher loops (including the hard thermal loops) at high $T$ and simultaneously cures the problem of tachyonic poles at relatively low $T$. We prove that (i) the renormalization of the ultra-violet divergences can be carried out systematically in any given order of OPT, and (ii) the Nambu-Goldstone theorem is satisfied for arbitrary $N$ and for any given order of OPT.
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
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.
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 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.
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.
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 show that quasi-Nambu-Goldstone (NG) modes, which play prominent roles in high energy physics but have been elusive experimentally, can be realized with atomic Bose-Einstein condensates. The quasi-NG modes emerge when the symmetry of a ground state is larger than that of the Hamiltonian. When they appear, the conventional vacuum manifold should be enlarged. Consequently topological defects that are stable within the conventional vacuum manifold become unstable and decay by emitting the quasi-NG modes. Contrary to conventional wisdom, however, we show that the topological defects are stabili…
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 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 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 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…
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.
We develop the effective field theory of diffusive Nambu-Goldstone (NG) modes associated with spontaneous internal symmetry breaking taking place in nonequilibrium open systems. The effective Lagrangian describing semi-classical dynamics of the NG modes is derived and matching conditions for low-energy coefficients are also investigated. Due to new terms peculiar to open systems, the associated NG modes show diffusive gapless behaviors in contrast to the propagating NG mode in closed systems. We demonstrate two typical situations relevant to the condensed matter physics and high-energy physics…
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.
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.
We discuss the dispersion relations of Nambu-Goldstone (NG) modes associated with spontaneous breaking of internal symmetries at finite temperature and/or density. We show that the dispersion relations of type-A (I) and type-B (II) NG modes are linear and quadratic in momentum, whose imaginary parts are quadratic and quartic, respectively. In both cases, the real parts of the dispersion relations are larger than the imaginary parts when the momentum is small, so that the NG modes can propagate far away. We derive the gap formula for NG modes in the presence of a small explicit breaking term. W…
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…
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.
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.
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 …
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 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 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…
Motivated by recent constructions of TeV-scale strongly-coupled dynamics, either associated with the Higgs sector itself as in pseudo-Nambu-Goldstone boson (pNGB) Higgs models or in theories of asymmetric dark matter, we show that stable solitonic Q- balls can be formed from light pion-like pNGB fields carrying a conserved global quantum number in the presence of the Higgs field. We focus on the case of thick-wall Q-balls, where solutions satisfying all constraints are shown to exist over a range of parameter values. In the limit that our approximations hold, the Q-balls are weakly bound and p…
We show that the Nambu-Goldstone(NG) boson restricted on the light-front(LF) can only exist if we regularize the theory by introducing the explicit breaking NG-boson mass $m_π$. The NG-boson zero mode, when integrated over the LF, must have a singular behavior $\sim 1/m^2_π$ in the symmetric limit of $m^2_π\rightarrow 0$. In the discretized LF quantization this peculiarity is clarified in terms of the zero-mode constraints in the linear $σ$ model. The LF charge annihilates the vacuum, while it is not conserved in the symmetric limit in the NG phase.
In massless QCD coupled to QED in an external magnetic field, a photon with the linear polarization in the direction of the external magnetic field mixes with the charge neutral pion through the triangle anomaly, leading to one gapless mode with the quadratic dispersion relation $ω\sim k^2$ and one gapped mode. We show that this gapless mode can be interpreted as the so-called type-B Nambu-Goldstone (NG) mode associated with the spontaneous breaking of generalized global symmetries and that its presence is solely dictated by the anomalous commutator in the symmetry algebra. We also argue a pos…
Spontaneous symmetry breaking is a general principle, that constitutes the underlying concept of a vast number of physical phenomena ranging from ferromagnetism and superconductivity in condensed matter physics to the Higgs mechanism in the standard model of elementary particles. I focus on manifestations of spontaneously broken symmetries in systems that are not Lorentz invariant, which include both, nonrelativistic systems as well as relativistic systems at nonzero density, providing a self-contained review of the properties of spontaneously broken symmetries specific to such theories. Topic…
We show that a momentum operator of a translational symmetry may not commute with an internal symmetry operator in the presence of a topological soliton in non-relativistic theories. As a striking consequence, there appears a coupled Nambu-Goldstone mode with a quadratic dispersion consisting of translational and internal zero modes in the vicinity of a domain wall in an O(3) sigma model, a magnetic domain wall in ferromagnets with an easy axis.
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…
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.
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…
Recent lattice QCD simulations of the scattering lengths of Nambu-Goldstone bosons off the $D$ mesons are studied using unitary chiral perturbation theory. We show that the Lattice QCD data are better described in the covariant formulation than in the heavy-meson formulation. The $D^*_{s0}(2317)$ can be dynamically generated from the coupled-channels $DK$ interaction without \textit{a priori} assumption of its existence. A new renormalization scheme is proposed which manifestly satisfies chiral power counting rules and has well-defined behavior in the infinite heavy-quark mass limit. Using thi…
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…
We theoretically study the properties of Nambu-Goldstone bosons in an interacting single-component Bose-Einstein condensate (BEC). We first point out that the proofs of Goldstone's theorem by Goldstone, et al. [Phys. Rev. {\bf 127} (1962) 965] may be relevant to distinct massless modes of the BEC: whereas the first proof deals with the poles of the single-particle Green's function $\hat{G}$, the second one concerns those of the two-particle Green's function. Thus, there may be multiple Nambu-Goldstone bosons even in the single-component BEC with broken U(1) symmetry. The second mode turns out …
These lectures provide an introduction to the low-energy dynamics of Nambu-Goldstone fields, associated with some spontaneous (or dynamical) symmetry breaking, using the powerful methods of effective field theory. The generic symmetry properties of these massless modes are described in detail and two very relevant phenomenological applications are worked out: chiral perturbation theory, the low-energy effective theory of QCD, and the (non-linear) electroweak effective theory. The similarities and differences between these two effective theories are emphasized, and their current status is revie…
If quarks and gluons are either gapped or confined in neutron stars (NSs), the most relevant light modes are Nambu-Goldstone (NG) modes. We study NG modes within a schematic quark model whose parameters at high density are constrained by the two-solar mass constraint. Our model has the color-flavor-locked phase at high density, with the effective couplings as strong as in hadron physics. We find that strong coupling effects make NG modes more massive than in weak coupling predictions, and would erase several phenomena caused by the stressed pairings in mismatched Fermi surfaces. For instance, …
After imposing current conservation together with the Gauss law as initial conditions on the Abelian Nambu model, we prove that the resulting theory is equivalent to standard QED in the non-linear gauge $\left(A_{μ}A^{μ}-n^{2}M^{2}\right)=0$, to all orders in perturbation theory. We show this by writing both models in terms of the same variables, which produce identical Feynman rules for the interactions and propagators. A crucial point is to verify that the Faddeev-Popov ghosts arising from the gauge fixing procedure in the QED sector decouple to all orders. We verify this decoupling by follo…
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）
We study the Nambu-Goldstone (NG) modes associated with spontaneous breaking of the continuous time-translation symmetry. To discuss a quantum time-crystal with the spontaneously-broken continuous time-translation symmetry, we introduce the van der Pol type nonlinear-friction to open quantum systems. By considering small fluctuations around a time-periodic mean-field solution, we show that a gapless collective mode necessarily appears; this is nothing but the NG mode associated with a time crystal. We show that its dispersion relation becomes $ω=-iC\bm p^2$. We also show that noncommutative br…
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.
When global continuous symmetries are spontaneously broken, there appear gapless collective excitations called Nambu-Goldstone modes (NGMs) that govern the low-energy property of the system. The application of this famous theorem ranges from high-energy, particle physics to condensed matter and atomic physics. When a symmetry breaking occurs in systems that lack the Lorentz invariance to start with, as is usually the case in condensed matter systems, the number of resulting NGMs can be fewer than that of broken symmetry generators, and the dispersion of NGMs is not necessarily linear. In this …
The idea to have Higgs doublets as pseudo Nambu-Goldstone (PsNG) multiplet is examined in the framework of supersymmetric E_6 unified theory. We show that extra PsNG multiplets other than the expected Higgs doublets necessarily appear in the E_6 case. If we demand that the extra PsNG multiplets neither disturb the gauge coupling unification nor make the color gauge coupling diverge before unification occurs, only possibility for the extra PsNG is 10+\bar{10} of SU(5). This is realized when the symmetry breaking E_6 \to SO(10) occurs in the ϕ(27)+ϕ(\bar{27}) sector while E_6 \to SU(4)_C\times S…
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 …
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.
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 …
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…
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…
