Goldstone Bosons Research Articles

Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit

It has been observed that when the gauge fields are present on the link, fermion propagation is possible in the weak coupling limit due to the dominance of the hopping term, which corresponds to the colour gauge interaction in the lattice QCD formulation. The production of low energy skyrmionic excitation at the fermionic site destroys the underlying antiferromagnetic order. In the continuum limit, the kinetic term in the lattice QCD corresponds to the rearrangement of the fermionic constituents through their propagation within the confined domain of the bound stateconfigurations of the interacting system which gives rise to a running coupling constant leading to asymptotic freedom. When one can assign a colour to a particular quantum number of a fermionic component in a limited state, it shows that QCD may be thought of as a generalised non-Abelian gauge field theory since these degrees of freedom play a part in the restricted area of the system and examines the continuous limit of the Hubbard-like model and the weak coupling limit that results from the abolition of the antiferromagnetic order and fermion propagation. This is equivalent to the non-Abelian color gauge field interaction. It is noted that the generalised spin fluctuation may be linked to the colour gauge field. This formalism's discovery of pseudoscalar Goldstone bosons associated with chiral symmetry breaking is in line with (3+1)D continuum QCD.

Inflationary Adler conditions

We derive a new soft theorem that corresponds to the spontaneous breaking of Lorentz boosts. This is motivated by the dynamics of inflation in the sub-horizon (flat-space) limit, where spacetime becomes flat but Lorentz boosts are still broken. In this limit, the scattering amplitudes become sensible observables. We relate the soft emission of a Goldstone boson to the (non-relativistic) Lorentz boost of the hard scattering amplitudes. This is the on-shell avatar of the spontaneous breaking of Lorentz boosts, analogous to the Adler zero of pions in the chiral symmetry breaking. We comment on several applications to inflation, including the demonstration that Dirac-Born-Infeld Inflation is the unique theory that has an emergent Lorentz invariance when the boosts are spontaneously broken.

Discrete Goldstone bosons

Exact discrete symmetries, if non-linearly realized, can reduce the ultraviolet sensitivity of a given theory. The scalars stemming from spontaneous symmetry breaking are massive without breaking the discrete symmetry, and those masses are protected from divergent quadratic corrections. This is in contrast to non-linearly realized continuous symmetries, for which the masses of pseudo-Goldstone bosons require an explicit breaking mechanism. The symmetry-protected masses and potentials of those discrete Goldstone bosons offer promising physics avenues, both theoretically and in view of the blooming experimental search for ALPs. We develop this theoretical setup using invariant theory and focusing on the maximally natural minima of the potential. For these, we show that typically a subgroup of the ultraviolet discrete symmetry remains explicit in the spectrum, i.e. realized "\`a la Wigner"; this subgroup can be either abelian or non-abelian. This suggests tell-tale experimental signals for those minima: at least two (three) degenerate scalars produced simultaneously if abelian (non-abelian), while the specific ratios of multi-scalar amplitudes provide a hint of the full ultraviolet discrete symmetry. Examples of exact ultraviolet $A_4$ and $A_5$ symmetries are explored in substantial detail.

A model of pseudo-Nambu–Goldstone dark matter from a softly brokenSU(2) global symmetry with aU(1) gauge symmetry

AbstractA 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 results of the direct detection experiments. The small momentum transfer suppresses the scattering amplitudes thanks to the low-energy behavior of the Nambu–Goldstone boson. In our model, the soft symmetry-breaking term is uniquely determined. This is the advantage of our model compared to some earlier works in which some soft symmetry-breaking terms cannot be forbidden but are simply assumed to be absent to avoid the constraints from the direct detection experiments. We calculate the thermal relic abundance of the pNG DM and find that the model can explain the measured value of the DM energy density under some constraints from perturbative unitarity.

Unifying baryogenesis with dark matter production

We here propose a mechanism that predicts, at early times, both baryon asymmetry and dark matter origin and that recovers the spontaneous baryogenesis during the reheating. Working with U(1)-invariant quark Q and lepton L effective fields, with an interacting term that couples the evolution of Universe’s environment field $$\psi $$ , we require a spontaneous symmetry breaking and get a pseudo Nambu–Goldstone boson $$\theta $$ . The pseudo Nambu–Goldstone boson speeds the Universe up during inflation, playing the role of inflaton, enabling baryogenesis to occur. Thus, in a quasi-static approximation over $$\psi $$ , we impressively find both baryon and dark matter quasi-particle production rates, unifying de facto the two scenarios. Moreover, we outline particle mixing and demonstrate dark matter takes over baryons. Presupposing that $$\theta $$ field energy density dominates as baryogenesis stops and employing recent limits on reheating temperature, we get numerical bounds over dark matter constituent, showing that the most likely dark matter would be consistent with MeV-scale mass candidates. Finally, we briefly underline our predictions are suitable to explain the the low-energy electron recoil event excess between 1 and 7 keV found by the XENON1T collaboration.

Catastrogenesis: DM, GWs, and PBHs from ALP string-wall networks

Axion-like particles (ALPs), a compelling candidate for dark matter (DM), are the pseudo Nambu-Goldstone bosons of a spontaneously and explicitly broken global U(1) symmetry. When the symmetry breaking happens after inflation, the ALP cosmology predicts the formation of a string-wall network which must annihilate early enough, producing gravitational waves (GWs) and primordial black holes (PBHs), as well as non-relativistic ALPs. We call this process catastrogenesis. We show that, under the generic assumption that the potential has several degenerate minima, GWs from string-wall annihilation at temperatures below 100 eV could be detected by future CMB and astrometry probes, for ALPs with mass from 10-16 to 106 eV. In this case, structure formation could limit ALPs to constitute a fraction of the DM and the annihilation would produce mostly “stupendously large” PBHs. For larger annihilation temperatures, ALPs can constitute 100% of DM, and the annihilation could produce supermassive black holes with a mass of up to 109 M ⊙ as found at the center of large galaxies. Therefore our model can solve two mysteries, the nature of the DM and the origin of these black holes.

Leptonic CP asymmetry and Light flavored scalar

We consider a situation where right-handed neutrinos couple to a light scalar which is possibly a Nambu-Goldstone boson resulting from high-energy symmetry breaking. Its coupling is typically complex-valued and flavor-dependent. In this work, we investigate the possibility of the leptonic asymmetry generation in the Universe from the right-handed neutrino decay to flavorful light scalar. Furthermore a new source of asymmetry generation from a single decay process is pointed out, which is characteristic of the present setting.

Wigner crystallization versus Goldstone theorem in a 2D surface one component plasma

Wigner crystallization versus Goldstone theorem in a 2D surface one component plasma

Chiral symmetry restoration and properties of Goldstone bosons at finite temperature* *Supported in part by the National Natural Science Foundation of China (12075117, 11775112, 11535005, 11690030, 11905104, 11805024, 11947406) and Jiangsu Provincial Natural Science Foundation of China (BK20180323)

We study chiral symmetry restoration by analyzing thermal properties of QCD's(pseudo-) Goldstone bosons, especially the pion. The meson properties are obtained from the spectral densities of mesonic imaginary-time correlation functions. To obtain the correlation functions, we solve the Dyson-Schwinger equations and the inhomogeneous Bethe-Salpeter equations in the leading symmetry-preserving rainbow-ladder approximation. In chiral limit, the pion and its partner sigma degenerate at the critical temperature . At , it was found that the pion rapidly dissociates, which signals deconfinement phase transition. Beyond the chiral limit, the pion dissociation temperature can be used to define the pseudo-critical temperature of the chiral phase crossover, which is consistent with that obtained by the maximum point of chiral susceptibility. A parallel analysis for kaon and pseudoscalar suggests that heavy mesons may survive above .

Dilaton Effective Field Theory

We review and extend recent studies of dilaton effective field theory (dEFT) that provide a framework for the description of the Higgs boson as a composite structure. We first describe the dEFT as applied to lattice data for a class of gauge theories with near-conformal infrared behavior. This includes the dilaton associated with the spontaneous breaking of (approximate) scale invariance and a set of pseudo-Nambu–Goldstone bosons (pNGBs) associated with the spontaneous breaking of an (approximate) internal global symmetry. The theory contains two small symmetry-breaking parameters. We display the leading-order (LO) Lagrangian and review its fit to lattice data for the SU(3) gauge theory with Nf=8 Dirac fermions in the fundamental representation. We then develop power-counting rules to identify the corrections emerging at next-to-leading order (NLO) in the dEFT action. We list the NLO operators that appear and provide estimates for the coefficients. We comment on implications for composite Higgs model building.

Chiral sum rule on the light front and the 3D image of the pion

The lightest meson, the pion, features two faces – one is the elementary Goldstone boson of QCD and the other is the structured bound state of quarks and gluons. To accommodate both in a single light-front wave function in the valence space, we obtain a sum rule by analyzing the conserved axial-vector current and the general structures of the wave functions. Using an analytic model motivated by holography, we show this sum rule is consistent with requirements of chiral symmetry breaking in AdS/QCD. Within this model, we find a remarkable feature of the pion, namely that the density is mostly uniform inside its radius; furthermore, we obtain good agreement with the experimental pion form factor at spacelike momenta.

W-Boson Mass Anomaly as a Manifestation of Spontaneously Broken Additional SU(2) Global Symmetry on a New Fundamental Scale

Recently, the CDF Collaboration has announced a new precise measurement of the W-boson mass MW that deviates from the Standard Model (SM) prediction by 7σ. The discrepancy in MW is about ΔW ≃ 70 MeV and is probably caused by a beyond the SM physics. Within a certain scenario of extension of the SM, we obtain the relation ΔW ≃ 3α8πMW ≃ 70 MeV, where α is the electromagnetic fine structure constant. The main conjecture is the appearance of longitudinal components of the W-bosons as the Goldstone bosons of a spontaneously broken additional SU(2) global symmetry at distances much smaller than the electroweak symmetry breaking scale rEWSB. We argue that within this scenario, the masses of charged Higgs scalars can obtain an electromagnetic radiative contribution which enhances the observed value of MW± with respect to the usual SM prediction. Our relation for ΔW follows from the known one-loop result for the corresponding effective Coleman–Weinberg potential in combination with the Weinberg sum rules.

Testing the charge-radius coupling of composite Goldstone (Higgs) bosons at hadron colliders

We explore the collider relevance of a charge-radius coupling among light mesons in composite Higgs models. In particular, we focus of a coupling of the photon to the composite Higgs and a composite singlet, arising from isospin violation in the underlying theory. This coupling offers a deep probe of the composite nature of the Higgs mechanism, being sensitive to the electromagnetic and weak isospin structure of its constituents. The main collider effect consists in the production of the Higgs boson in association with a light composite pseudo-scalar. We present an exploratory cut-and-count analysis at hadron colliders, like the LHC, showing that an efficient background suppression can be achieved. More sophisticated techniques, however, are necessary to select a sufficient number of signal events, due to the small production rates. This justifies further investigation of this channel, which is highly complementary to other searches for compositeness in the Higgs sector.

Higgs-boson visible and invisible constraints on hidden sectors

We investigate the impact of interactions between hidden sectors and the discovered Higgs boson h_{125}, allowing for additional invisible decay channels of h_{125}. We perform chi ^2-fits to the measurements of the Higgs-boson cross sections as a function of the invisible branching ratio and different combinations of coupling modifiers, where the latter quantify modifications of the couplings of h_{125} compared to the predictions of the Standard Model. We present generic results in terms of exclusion limits on the coupling modifiers and the invisible branching ratio of h_{125}. Additionally, we apply our results to a variety of concrete model realizations containing a hidden sector: dark matter within Higgs- and singlet-portal scenarios, models featuring (pseudo) Nambu–Goldstone bosons and two Higgs doublet extensions. One of the main conclusions of our work is that in a wide class of models the indirect constraints resulting from the measurements of the cross sections of h_{125} provide substantially stronger constraints on the invisible Higgs-boson branching ratio compared to the direct limits obtained from searches for the invisible decay of h_{125}. However, we demonstrate that the presence of an invisible decay mode of h_{125} can also open up parameter space regions which otherwise would be excluded as a result of the indirect constraints. As a byproduct of our analysis, we show that in light of the new results from the LZ collaboration a fermionic DM candidate within the simplest Higgs-portal scenario is ruled out under standard assumptions.

Pion superfluid phase transition under an external magnetic field including the inverse magnetic catalysis effect

Pion superfluid phase transition under external magnetic field including the inverse magnetic catalysis (IMC) effect is investigated by the Pauli-Villars regularized NJL model. Based on the Goldstone's theorem, we apply the massless Goldstone boson ($\pi^+$ meson) to determine the onset of pion superfluid phase. The inverse magnetic catalysis effect is introduced by the magnetic field dependent coupling $G(eB)$, which is a decreasing function of magnetic field. At fixed temperature and baryon chemical potential, the critical isospin chemical potential for pion superfluid phase transition including IMC effect increases as the magnetic field grows, which is similar as the case without IMC effect. This demonstrates that magnetic field disfavors the pion superfluid phase when considering or ignoring IMC effect. The critical isospin chemical potential at fixed magnetic field, temperature and baryon chemical potential is shifted to higher value by the IMC effect. Since it is more difficult to form pion superfluid with weaker coupling.

BRST formalism of Weyl conformal gravity

We present the BRST formalism of a Weyl conformal gravity in Weyl geometry. Choosing the extended de Donder gauge-fixing condition (or harmonic gauge condition) for the general coordinate invariance and the new scalar gauge-fixing for the Weyl invariance we find that there is a Poincar${\rm{\acute{e}}}$-like $\IOSp(10|10)$ supersymmetry as in a Weyl invariant scalar-tensor gravity in Riemann geometry. We also point out that there is a gravitational conformal symmetry in quantum gravity although there is a massive Weyl gauge field as a result of spontaneous symmetry breakdown of Weyl gauge symmetry and account for how the gravitational conformal symmetry is spontaneously broken to the Poincar\'e symmetry. The corresponding massless Nambu-Goldstone bosons are the graviton and the dilaton. We also prove the unitarity of the physical S-matrix on the basis of the BRST quartet mechanism.

Formation of a supergiant quantum vortex in a relativistic Bose-Einstein condensate driven by rotation and a parallel magnetic field

Analysis based on the energy spectrum of noninteracting bosons shows that, under the circumstance of parallel rotation and magnetic field, charged bosons form a Bose-Einstein condensate because of the lift of the Landau level degeneracy by rotation [\textcolor{blue}{Y. Liu and I. Zahed, Phys. Rev. Lett. {\bf120}, 032001 (2018)}]. In this work, we study the interaction effect on the ground state of this Bose-Einstein condensate of charged bosons from the viewpoint of spontaneous symmetry breaking. We employ a minimal model for charged bosons with repulsive self-interaction. We find that the ground state of such a Bose-Einstein condensate is a supergiant quantum vortex, i.e., a quantized vortex with a large circulation. The size of the vortex is as large as the system size. The low-energy dispersion of the excitation spectra exhibits quadratic behavior, which is an anisotropic realization of the type-II Goldstone boson. Our study may give some implications to off-central relativistic heavy ion collisions, where large vorticity and magnetic fields can be generated.

Following the muon track of hierarchical sectors at LHCb

This paper reports a study of the experimental signatures of hierarchical sectors beyond the Standard Model characterized by a flavour-violating heavy vector and a set of light pseudo-Goldstone bosons a1,2, spanning a large range of lifetimes. The non-minimal scalar spectrum triggers novel B decays into multiple leptons that would have escaped the reach of current searches. Novel displaced vertex analyses at LHCb are therefore discussed to probe the hierarchical new physics, extending the scope of the tracking system of the detector. Additionally, the reach of the proposed CODEX-b experiment is studied. By exploiting the use of tracks only reconstructed in subsystems of the detector at the high-level LHCb trigger, mathcal{B}left({B}_{s}^{0}to {a}_{1}{a}_{2}right)<{10}^{-8} and ℬ(B+ → K+a1a2) < 10−9 could be reached in the muon channel across seven orders of magnitude in the lifetime of the Goldstone bosons. Correspondingly, heavy-light particle couplings of order ≲ 1 could be tested, potentially ruling out composite Higgs scenarios where the heavy and light sectors couple strongly.

Techni-composite Higgs models with symmetric and asymmetric dark matter candidates

We propose a novel class of composite models that feature both a technicolor and a composite Higgs vacuum limit, resulting in an asymmetric dark matter candidate. These techni-composite Higgs models are based on an extended left-right electroweak symmetry with a pseudo-Nambu Goldstone boson Higgs and stable dark matter candidates charged under a global $\mathrm{U}(1{)}_{X}$ symmetry, connected to the baryon asymmetry at high temperatures via the $\mathrm{SU}(2{)}_{\mathrm{R}}$ sphaleron. We consider, as explicit examples, four-dimensional gauge theories with fermions charged under a new confining gauge group ${G}_{\mathrm{HC}}$.

Recursion relations for one-loop Goldstone boson amplitudes

In this paper, we construct the recursion relations for one-loop planar integrands in the $SU(N)$ nonlinear sigma model. This generalizes the soft recursions for tree-level amplitudes in a variety of quantum field theories with special soft limits. The main ingredient is the definition of the one-loop planar integrand, which is fixed by cuts in the sense of generalized unitarity and by requiring the Adler zero on all external legs. We show that this does not uniquely fix the integrand, so additional constraints on the soft behavior of the loop momentum have to be imposed. Our work is the first step in extending modern amplitudes methods for loop amplitudes to effective field theories with special soft limits.