Goldstone Bosons Research Articles

Celestial amplitudes from UV to IR

Celestial amplitudes represent 4D scattering of particles in boost, rather than the usual energy-momentum, eigenstates and hence are sensitive to both UV and IR physics. We show that known UV and IR properties of quantum gravity translate into powerful constraints on the analytic structure of celestial amplitudes. For example the soft UV behavior of quantum gravity is shown to imply that the exact four-particle scattering amplitude is meromorphic in the complex boost weight plane with poles confined to even integers on the negative real axis. Would-be poles on the positive real axis from UV asymptotics are shown to be erased by a flat space analog of the AdS resolution of the bulk point singularity. The residues of the poles on the negative axis are identified with operator coefficients in the IR effective action. Far along the real positive axis, the scattering is argued to grow exponentially according to the black hole area law. Exclusive amplitudes are shown to simply factorize into conformally hard and conformally soft factors. The soft factor contains all IR divergences and is given by a celestial current algebra correlator of Goldstone bosons from spontaneously broken asymptotic symmetries. The hard factor describes the scattering of hard particles together with the boost-eigenstate clouds of soft photons or gravitons required by asymptotic symmetries. These provide an IR safe mathcal{S} -matrix for the scattering of hard particles.

N = 2 PNGB quintessence dark energy

In this paper, we show that a pseudo-Nambu–Goldstone boson (PNGB) quintessence of spontaneous symmetry breaking (SSB) is responsible for an epoch of late-time cosmic acceleration. We suggest that an N = 2PNGB quintessence with SSB can give rise to the fast-roll cosmic acceleration in the evolution of the Universe. In the N = 2 PNGB quintessence model, the standard slow-roll condition in which the absolute value of the tachyonic mass squared \(|m_q^2|\) of this model is much less than the square of the Hubble constant \(H^2\), is broken down to the fast-roll condition, \(|m_q^2|=O(H^2)\). However, the fast-rolling associated with the N = 2 PNGB quintessence of SSB is shown to lead to the epoch of late-time cosmic acceleration. Indeed, in our PNGB model, this epoch can be quite long-lasting because the mass of the N = 2 PNGB quintessence field is extremely small at \(m_q \approx 10^{-33} \mathrm {eV}\).

Flavor-changing Majoron interactions with leptons

When the Standard Model Higgs sector is extended with a complex singlet that breaks global lepton number symmetry spontaneously, a massless Goldstone boson called the Majoron J arises. In addition to increasing Higgs invisible decay through mixing, the Majoron can generally have flavor-changing interactions with fermions. We find that type-III seesaw model poses such interesting properties with both charged leptons and neutrinos. This opens up new channels to search for the Majoron. We use the experimental data such as muonium-anti-muonium oscillation and flavor-changing neutrino and charged lepton decays to put constraints on the couplings. As a novel way to reveal the chiral properties of these interactions, we propose an experimentally measurable polarization asymmetry of flavor-changing l to l' J decays.

Dynamical inverse seesaw mechanism as a simple benchmark for electroweak breaking and Higgs boson studies

The Standard Model (SM) vacuum is unstable for the measured values of the top Yukawa coupling and Higgs mass. Here we study the issue of vacuum stability when neutrino masses are generated through spontaneous low-scale lepton number violation. In the simplest dynamical inverse seesaw, the SM Higgs has two siblings: a massive CP-even scalar plus a massless Nambu-Goldstone boson, called majoron. For TeV scale breaking of lepton number, Higgs bosons can have a sizeable decay into the invisible majorons. We examine the interplay and complementarity of vacuum stability and perturbativity restrictions, with collider constraints on visible and invisible Higgs boson decay channels. This simple framework may help guiding further studies, for example, at the proposed FCC facility.

Assessment of systematic theory uncertainties in IAM unitarization

Effective Field Theories (EFTs) for Goldstone Boson scattering at a low order allow the computation of near–threshold observables in terms of a few coefficients arranged by a counting. As a matter of principle they should make sense up to an energy scale E ∼ 4πF but the expansion in powers of momentum violates exact elastic unitarity and renders the derivative expansion unreliable at much lower energies. If new–physics deviations from the Standard Model are found and encoded in low-energy coefficients, perhaps at the LHC, it will be profitable to extend the reach of the EFT to regimes where partial waves are saturating unitarity. The methods known in hadron physics as “Unitarized Chiral Perturbation Theory” extend the EFT up to its nominal reach or up to the first new physics resonance or structure (if found below that energy reach) in the partial wave amplitude, but they usually have unknown uncertainties. We recapitulate our analysis of the systematic theory uncertainties of the well known Inverse Amplitude Method (IAM).

Top–Bottom Condensation Model: Symmetries and Spectrum of the Induced 2HDM

Here, we use the Schwinger–DeWitt approach to address the four-fermion composite Higgs effective model proposed by Miransky, Tanabashi and Yamawaki (MTY). The surprising benefit of such an approach is that it is possible to ascribe to a SM-type Higgs a quark–antiquark structure of predominantly a b¯b nature with a small t¯t admixture, which in turn yields a Higgs mass compatible with the observed value of 125 GeV. We discuss this result in a detailed and pedagogical way, as it goes against the common belief that this model and akin composite descriptions should predict a Higgs mass-of-order of twice the top quark mass, contrary to empirical evidence. A further aspect of this approach is that it highlights the link of the SU(2)L×U(1)R symmetric four-fermion MTY model interactions of the heavy quark family to a specific two-Higgs-doublet model (2HDM), and the necessity to go beyond the one Higgs doublet to obtain the empirical Higgs mass within composite models. By appropriately fixing the symmetry-defining interaction parameters, we show that the resulting CP-preserving spectrum harbors the following collective states at the electroweak scale ΛEW=246 GeV: a light scalar to which the standard Higgs is associated; a heavier neutral state preconized as the Nambu partner of the standard Higgs within the Nambu sum rule; the expected triplet of Goldstone bosons associated with the longitudinal polarizations of the electroweak massive bosons; and a neutral pseudoscalar state that in the limit of a global U(1)A symmetry would be a Goldstone mode. The anomalous breaking of this axial symmetry is a subleading effect in a large Nc counting scheme, and we discuss how it modifies the leading-order Nambu sum rule result and its relevance for the qualitative description of the spectrum.

Softly shifting away from dark matter direct detection

We propose soft breaking mechanism for dark matter (DM) shift symmetry in a class of composite dark matter models, where both DM and the Higgs boson arise as pseudo Nambu-Goldstone bosons from novel strong dynamics. Our mechanism is utilized to suppress the non-derivative portal coupling between the Higgs boson and DM particle, which can evade the stringent bound of current DM direct detection experiments. Otherwise this non-derivative portal coupling would naturally be at the same order of the Higgs quartic, rendering this class of models under severe crisis. For realizing soft breaking mechanism, we introduce vector-like top partners, dubbed as "softons", to restore the shift symmetry of DM in top Yukawa sector, which however is only broken by the softon masses. The portal coupling would automatically vanish as the shift-symmetry-breaking softon masses approach zero. Specifically we present a proof-of-concept model of soft breaking, based on the coset $O(6)/O(5)$ and the simplest fermion embedding, and study its DM phenomenology, where we show a large amount of novel parameter space is opened up by using the soft breaking mechanism.

Model for the singlet-triplet leptoquarks

The deviations of $B$-meson decays measured in ${R}_{{D}^{(*)}}^{\ensuremath{\tau}\ensuremath{\ell}}$ and ${R}_{{K}^{(*)}}^{\ensuremath{\mu}e}$ can be explained by the presence of two scalar leptoquarks, a singlet ${S}_{1}$ and a triplet ${S}_{3}$, mostly coupled to the third generation. We consider a theory of resonances, as an effective description of a strongly interacting theory, that generates the leptoquarks and the Higgs as Nambu-Goldstone bosons, with the rest of the resonances at a scale of order 10--30 TeV. We assume anarchic partial compositeness for the flavor of the SM fermions. Under this hypothesis, we study whether it is possible to reproduce the deviations in the $B$ decays without being in conflict with flavor and electroweak bounds. We find a tension between ${R}_{{D}^{(*)}}^{\ensuremath{\tau}\ensuremath{\ell}}$ and some flavor observables, dominated by flavor violating $\ensuremath{\tau}$ decays and $\mathrm{\ensuremath{\Delta}}{m}_{{B}_{s}}$, that require a tuning of order 10%--25%. We also compute the potential of the scalars showing that leptoquarks with masses $O(2--3)\text{ }\text{ }\mathrm{TeV}$ can be naturally expected in the model. We discuss briefly the phenomenology of the other resonances.

Selection rules for the S-Matrix bootstrap

We examine the space of allowed S-matrices on the Adler zeros' plane using the recently resurrected (numerical) S-matrix bootstrap program for pion scattering. Two physical quantities, an averaged total scattering cross-section, and an averaged entanglement power for the boundary S-matrices, are studied. Emerging linearity in the leading Regge trajectory is correlated with a reduction in both these quantities. We identify two potentially viable regions where the S-matrices give decent agreement with low energy S- and P-wave scattering lengths and have leading Regge trajectory compatible with experiments. We also study the line of minimum averaged total cross section in the Adler zeros' plane. The Lovelace-Shapiro model, which was a precursor to modern string theory, is given by a straight line in the Adler zeros' plane and, quite remarkably, we find that this line intersects the space of allowed S-matrices near both these regions.

Revealing the structure of light pseudoscalar mesons at the electron–ion collider

The questions of how the bulk of the Universe’s visible mass emerges and how it is manifest in the existence and properties of hadrons are profound, and probe the heart of strongly interacting matter. Paradoxically, the lightest pseudoscalar mesons appear to be key to a further understanding of the emergent mass and structure mechanisms. These mesons, namely, the pion and kaon, are the Nambu–Goldstone boson modes of quantum chromodynamics (QCD). Unravelling their partonic structure and the interplay between emergent and Higgs-boson mass mechanisms is a common goal of three interdependent approaches—continuum QCD phenomenology, lattice-regularised QCD, and the global analysis of parton distributions—linked to experimental measurements of hadron structure. Experimentally, the anticipated electron–ion collider will enable a revolution in our ability to study pion and kaon structures, accessed by scattering from the ‘meson cloud’ of the proton through the Sullivan process. With the goal of enabling a suite of measurements that can address these questions, we examine key reactions that identify the critical detector-system requirements needed to map tagged pion and kaon cross-sections over a wide range of kinematics. The excellent prospects for extracting pion structural, functional, and form-factor data are outlined, and similar prospects for kaon structures are discussed in the context of a worldwide programme. The successful completion of the programme outlined herein will deliver deep, far-reaching insights into the emergence of pions and kaons, their properties, and their role as QCD’s Goldstone boson modes.

Downfolding approaches to electron-ion coupling: Constrained density-functional perturbation theory for molecules

Constrained electronic-structure theories enable the construction of effective low-energy models consisting of partially dressed particles. However, the interpretation and physical content of these theories is not straightforward. Here, we carefully explore the properties of downfolding theories for electron-ion problems, in particular constrained density-functional perturbation theory (cDFPT). We show that the dipole selection rules determine whether the partially dressed phonons satisfy Goldstone's theorem, and we prove that electronic screening always lowers the phonon frequencies. We illustrate the theory with cDFPT calculations for minimal example systems: the nitrogen and benzene molecule as well as graphene.

Comments on gauge anomalies at dimension-six in the Standard Model Effective Field Theory

We study whether higher-dimensional operators in effective field theories, in particular in the Standard Model Effective Field Theory (SMEFT), can source gauge anomalies via the modification of the interactions involved in triangle diagrams. We find no evidence of such gauge anomalies at the level of dimension-6 operators that can therefore be chosen independently to each others without spoiling the consistency of SMEFT, at variance with recent claims. The underlying reason is that gauge-invariant combinations of Goldstone bosons and massive gauge fields are allowed to couple to matter currents which are not conserved. We show this in a toy model by computing the relevant triangle diagrams, as well as by working out Wess-Zumino terms in the bosonic EFT below all fermion masses. The same approach applies directly to the Standard Model both at the renormalisable level, providing a convenient and unusual way to check that the SM is anomaly free, as well as at the non-renormalisable level in SMEFT.

Anomaly inflow and holography

We systematically study the perturbative anomaly inflow by the bulk Chern-Simons (CS) theory in a slice of five-dimensional anti-de Sitter spacetime (AdS5). The introduction of UV and IR 3-branes makes the anomaly story remarkably rich and many interesting aspects can be obtained, including weakly gauging and spontaneous symmetry breaking of the global symmetries of the dual 4D CFT. Our main contribution is to provide a unified and comprehensive discussion of the subject, together with a detailed description of the dual CFT picture for each case. To this end, we employ a gauge-fixed effective action suitable for a holographic study, which allows us to incorporate general UV and IR boundary conditions (BCs). As part of the process, we reproduce many known results in the literature, such as ’t Hooft anomaly matching for unbroken symmetry (Neumann IR-BC) and (gauged) Wess-Zumino-Witten (WZW) action for broken symmetry (IR-BC breaks the bulk group G → H). In addition, we show that anomaly matching occurs for ABJ anomalies as well as ’t Hooft anomalies, which suggests anomalies inflowed from the bulk CS theory are necessarily free of mixed anomalies with the confining gauge force of the 4D dual CFT. In the case of broken symmetry, we prove that the “would-be” Goldstone bosons associated with the weakly gauged symmetry are completely removed by a proper field redefinition, provided the anomaly from the bulk is exactly cancelled by the boundary contribution, hence confirming the standard expectation. Moreover, we present a holographic formulation of Witten’s argument for the quantization condition for the WZW action, and argue in favor of an alternative way to obtain the same condition using a “deformed” theory (different BCs). We work out several examples, including a product group with mixed anomaly, and identify the corresponding dual CFT picture. We consider a fully general case typically arising in the context of dynamical electroweak symmetry breaking.

Quark distribution inside a pion in many-flavor ( 2+1 )-dimensional QCD using lattice computations: UV listens to IR

We study the changes in the short-distance quark structure of the Nambu-Goldstone boson when the long-distance symmetry-breaking scales are depleted controllably. We achieve this by studying the valence Parton Distribution Function (PDF) of pion in 2+1 dimensional two-color QCD, with the number $N$ of massless quarks as the tunable parameter that slides the theory from being strongly broken for $N=0$ to the conformal window for $N>4$, where the theory is gapped by the fixed finite volume. We perform our study non-perturbatively using lattice simulations with $N=0,2,4,8$ flavors of nearly massless two-component Wilson-Dirac sea quarks and employ the leading-twist formalism (LaMET/SDF) to compute the PDF of pion at a fixed valence mass. We find that the relative variations in the first few PDF moments are only mild compared to the changes in decay constant, but the shape of the reconstructed $x$-dependent PDF itself dramatically changes from being broad in the scale-broken sector to being sharply peaked in the near-conformal region, best reflected in PDF shape observables such as the cumulants.

Hydrodynamic attractor and novel fixed points in superfluid Bjorken flow

Extending the quantum effective approach of Son and Nicolis and incorporating dissipation, we develop a MIS formalism for describing a superfluid out of equilibrium by including the Goldstone boson and the condensate together with the hydrodynamic modes as the effective degrees of freedom. We find that the evolution of the superfluid undergoing Bjorken flow is governed by the conventional hydrodynamic attractor with unbroken symmetry and an even number of novel non-dissipative fixed points with broken symmetry. If the initial temperature is super-critical, then the condensate becomes exponentially small very rapidly and the system is trapped by the hydrodynamic attractor for a long intermediate time before it reheats rapidly and switches to one of the symmetry-breaking fixed points eventually. Finally, we show that the fixed points are unstable against inhomogeneous perturbations that should lead to spinodal decomposition. We conclude that these features should be generic beyond the MIS formalism.

Mass structure of hadrons and light-front sum rules in the t′ Hooft model

We study the mass/energy structure of the bound state of hadrons in two-dimensional quantum chromodynamics in the large number of color limit (t' Hooft model). We analyze separately the contributions from the traceless and trace part of the energy-momentum tensor, and show that the masses are related to the matrix elements of the scalar charge and Coulomb energy. We derive the light-front sum rules for the scalar charge and Coulomb energy, expressed in terms of the light-front wave functions, and find that they are regular at $x=0$ without the delta function contribution. We also consider the result for the massless Goldstone boson, as well as the structure of the gravitational form factors of the bound meson states.

Structure of flavor changing Goldstone boson interactions

General flavor changing Goldstone boson (GB) interactions with fermions from a spontaneous global U(1)G symmetry breaking are discussed. This GB may be the Axion, solving the strong QCD CP problem, if there is a QCD anomaly for the assignments of quarks U(1)G charge. Or it may be the Majoron, producing seesaw Majorana neutrino masses by lepton number violation, if the symmetry breaking scale is much higher than the electroweak scale. It may also, in principle, play the roles of Axion and Majoron simultaneously as far as providing solution for the strong CP problem and generating a small Majorana neutrino masses are concerned. Great attentions have been focused on flavor conserving GB interactions. Recently flavor changing Axion and Majoron models have been studied in the hope to find new physics from rare decays in the intensity frontier. In this work, we will provide a systematic model building aspect study for flavor changing neutral current (FCNC) GB interactions in the fermion sectors, or separately in the quark, charged lepton and neutrino sectors and will identify in detail the sources of FCNC interactions in a class of beyond standard model with a spontaneous global U(1)G symmetry breaking. We also provide a general proof of the equivalence of using physical GB components and GB broken generators for calculating GB couplings to two gluons and two photons, and discuss some issues related to spontaneous CP violation models. Besides, we will also provide some details for obtaining FCNC GB interactions in several popular models, such as the Type-I, -II, -III seesaw and Left-Right symmetric models, and point out some special features in these models.

Scattering of Goldstone bosons and resonance production in a composite Higgs model on the lattice

We calculate the coupling between a vector resonance and two Goldstone bosons in SU(2) gauge theory with Nf = 2 Dirac fermions in the fundamental representation. The considered theory can be used to construct a minimal Composite Higgs models. The coupling is related to the width of the vector resonance and we determine it by simulating the scattering of two Goldstone bosons where the resonance is produced. The resulting coupling is gVPP = 7.8 ± 0.6, not far from gρππ ≃ 6 in QCD. This is the first lattice calculation of the resonance properties for a minimal UV completion. This coupling controls the production cross section of the lightest expected resonance at the LHC and enters into other tests of the Standard Model, from Vector Boson Fusion to electroweak precision tests. Our prediction is crucial to constrain the model using lattice input and for understanding the behavior of the vector meson production cross section as a function of the underlying gauge theory. We also extract the coupling {g}_{mathrm{VPP}}^{mathrm{KSRF}} = 9.4 ± 0.6 assuming the vector-dominance and find that this phenomenological estimate slightly overestimates the value of the coupling.

Renormalization group improvement of the effective potential: an EFT approach

We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the O(N) model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop β-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem.

Chiral waves on the Fermi-Dirac sea: Quantum superfluidity and the axial anomaly

We show that as a result of the axial anomaly, massless fermions at zero temperature define a relativistic quantum superfluid. The anomaly pole implies the existence of a gapless Chiral Density Wave (CDW), i.e. an axion-like acoustic mode of an irrotational and dissipationless Hamiltonian perfect fluid, that is a correlated fermion/anti-fermion pair excitation of the Fermi-Dirac sea. In D=2 dimensions the chiral superfluid effective action coincides with that of the Schwinger model as e→0, and the CDW acoustic mode is precisely the Schwinger boson. Since this identity holds also at zero chiral chemical potential, the Dirac vacuum itself may be viewed as a quantum superfluid state. The CDW collective boson is a U(1) chiral phase field, which is gapless as a result of a novel, non-linear realization of Goldstone's theorem, extended to this case of symmetry breaking by an anomaly. A new local form of the axial anomaly bosonic effective action in any D even spacetime is given, consistent with superfluidity, and its quantization is shown to be required by the anomalous Schwinger terms in fermion current commutators. In QED4 this collective Goldstone mode appears as a massless pole in the axial anomaly triangle diagram, and is responsible for the macroscopic non-dissipative currents of the Chiral Magnetic and Chiral Separation Effects, as well as the Anomalous Hall Effect. In a constant uniform magnetic field an exact dimensional reduction from D=4 to D=2 occurs and the collective e+e− CDW chiral pair excitation propagating along the magnetic field direction is a Chiral Magnetic Wave, which acquires a mass gap M2=e3B/2π2. Possible realizations and tests of the theory of collective bosonic excitations due to the anomaly in Dirac/Weyl materials are briefly discussed.