A pseudo-Nambu-Goldstone boson (pNGB) is an attractive candidate for dark matter since the current severe limits of dark matter direct detection experiments are naturally evaded by its nature. We construct a model with pNGB dark matter based on a {\it gauged} $U(1)_{B-L}$ symmetry, where no ad-hoc global symmetry is assumed. The model keeps natural suppression mechanism for the dark matter direct detection cross section. On the other hand, the pNGB can decay through the new high scale suppressed operators. We show that the pNGB has long enough lifetime to be a dark matter in the wide range of the parameter space of the model. The thermal relic abundance of pNGB dark matter can be fit with the observed value against the constraints on the dark matter decays from the cosmic-ray observations.
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.
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.
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 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.
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…
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 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 …
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…
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.
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.
We propose an ultraviolet completion model for pseudo-Nambu-Goldstone dark matter with a hidden $\mathrm{U}(1)$ gauge symmetry. Compared to previous studies, this setup is simpler, introducing less interactions. Dark matter scattering off nucleons is highly suppressed by the ultraviolet scale and direct detection constraints can be easily evaded. The kinetic mixing between the hidden $\mathrm{U}(1)$ and the $\mathrm{U}(1)_\mathrm{Y}$ gauge fields would lead to dark matter decays. We find that the current bound on the dark matter lifetime implies that the ultraviolet scale should be higher than…
We consider an extension of the Standard Model with the global symmetry breaking pattern SO(5)/SO(4), where the Higgs boson arises as a pseudo-Nambu-Goldstone boson. The scalar content of the theory consists of a Standard-Model-like Higgs field and an extra real scalar field. The flavour sector of the model is extended by two right-handed neutrinos compatible with the observed light-neutrino phenomenology, and we find that the correct vacuum alignment determines the mass of the heavier neutrino eigenstate to be around 80 TeV. The new singlet-scalar state generates dynamically a Majorana mass t…
We consider a scale invariant extension of the standard model (SM) with a combined breaking of conformal and electroweak symmetry in a strongly interacting hidden $SU(n_c)$ gauge sector with $n_f$ vector-like hidden fermions. The (pseudo) Nambu-Goldstone bosons that arise due to dynamical chiral symmetry breaking are dark matter (DM) candidates. We focus on $n_f=n_c=3$, where $SU(3)$ is the largest symmetry group of hidden flavor which can be explicitly broken into either $U(1) \times U(1)$ or $SU(2)\times U(1)$. We study DM properties and discuss consistent parameter space for each case. Beca…
We propose an axionic QCD string scenario based on the original flux-tube model by Kogut and Susskind, and then incorporate it into a gauged Nambu-Jona-Lasinio (NJL) model. Axial anomaly is studied by a new topological coupling from the string side, and by the 't Hooft vortex from the NJL side, respectively. The nontrivial phase distribution of the quark condensate plays an important role in this scenario.
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].
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 study the early kinetic decoupling effect in a pseudo-Nambu-Goldstone (pNG) dark matter (DM) model. The pNG DM scattering processes with particles in the thermal bath in the early Universe are suppressed by the small momentum transfer. As a result, kinetic equilibrium is not maintained, and the temperature of DM is different from the temperature of the thermal bath at the freeze-out era. This temperature difference affects the thermal relic abundance of DM. We investigate the early kinetic decoupling in the Higgs resonance region, 50 GeV $\lesssim m_χ\lesssim m_h/2$, where $m_χ$ is the mass…
The hierarchy of the Yukawa couplings is an outstanding problem of the standard model. We present a class of models in which the first and second generation fermions are SUSY partners of pseudo-Nambu-Goldstone bosons that parameterize a non-compact Kahler manifold, explaining the small values of these fermion masses relative to those of the third generation. We also provide an example of such a model. We find that various regions of the parameter space in this scenario can give the correct dark matter abundance, and that nearly all of these regions evade other phenomenological constraints. We …
A model of the pseudo-Nambu-Goldstone (pNG) dark matter (DM) is proposed. We assume that there is an $SU(2)_g$ global symmetry and a $U(1)_X$ gauge symmetry in the dark sector, and they are spontaneously broken into a $U(1)_D$ global symmetry after a scalar field develops a vacuum expectation value. We add a soft symmetry breaking term that breaks the $SU(2)_g$ global symmetry into the $U(1)_g$ global symmetry explicitly. Our model predicts a stable complex pNG particle under the $U(1)_D$ global symmetry. One of the virtues of the pNG DM models is that the models can explain the current null r…
We propose a pseudo-Nambu-Goldstone boson (pNGB) dark matter (DM) model based on an additional non-Abelian gauge symmetry $SU(2)_D$. The gauge symmetry $SU(2)_D$ is spontaneously broken to a global custodial symmetry $U(1)_V$ via the nonvanishing vacuum expectation values of $SU(2)_D$ doublet and triplet scalar fields. Due to the exact global symmetry $U(1)_V$, the lightest $U(1)_V$ charged particle becomes stable. We assume that the lightest charged particle in the model is the charged complex pNGB, which we regard as DM. It avoids the strong constraints from current DM direct detection exper…
We calculate the leading radiative corrections to the dark-matter-nucleon scattering in the pseudo-Nambu-Goldstone dark matter model augmented with a second Higgs doublet (S2HDM). In this model, the cross sections for the scattering of the dark-matter on nuclei vanishes at tree-level in the limit of zero momentum-transfer due to a U(1) symmetry. However, this symmetry is softly broken in order to give a mass to the dark-matter particle. As a consequence, non-vanishing scattering cross sections arise at the loop level. We find that the current cross-section limits from dark-matter direct-detect…
We outline a scenario where both the Higgs and a complex scalar dark matter candidate arise as the pseudo-Nambu-Goldstone bosons of breaking a global $SO(7)$ symmetry to $SO(6)$. The novelty of our construction is that the symmetry partners of the Standard Model top-quark are charged under a hidden color group and not the usual $SU(3)_c$. Consequently, the scale of spontaneous symmetry breaking and the masses of the top partners can be significantly lower than those with colored top partners. Taking these scales to be lower at once makes the model more natural and also reduces the induced non-…
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 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 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 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…
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.
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 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.
