Goldstone Bosons Research Articles

Chiral excitations of open-beauty systems

We study the scattering of open-beauty mesons and Goldstone bosons as predicted by the chiral SU(3) Lagrangian. The impact of subleading order chiral interactions to systems with $J^P= 0^+$ and $J^P=1^+$ quantum numbers is worked out. We estimate the relevant low-energy coefficients from the open-charm sector, for which their values have been determined previously from sets of QCD lattice data. The leading order heavy-quark symmetry breaking effects are estimated by matching the $B$-meson ground-state chiral mass formula to the mass formula from the heavy-quark effective theory. We make refined predictions for the flavor anti-triplet and sextet resonances that are generated dynamically by coupled-channel interactions.

Restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry

In this paper, we elucidate the relation between the restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry. Using a scalar–tensor gravity, we show that the restricted Weyl symmetry leads to spontaneous symmetry breakdown of a global scale symmetry when the vacuum expectation value of a scalar field takes a nonzero value. It is then shown that this spontaneous symmetry breakdown induces spontaneous symmetry breakdown of special conformal symmetry in a flat Minkowski spacetime, but the resultant Nambu–Goldstone boson is not an independent physical mode but expressed in terms of the derivative of the dilaton which is the Nambu–Goldstone boson of the global scale symmetry. In other words, the theories which are invariant under the general coordinate transformation and the restricted Weyl transformation exhibit a Nambu–Goldstone phase where both special conformal transformation and dilatation are spontaneously broken while preserving the Poincaré symmetry.

Double nuclear spin relaxation in hybrid quantum Hall systems

Recent advances in quantum engineering have given us the ability to design hybrid systems with novel properties normally not present in the regime they operate in. The coupling of spin ensembles and magnons to microwave resonators has for instance lead to a much richer understanding of collective effects in these systems and their potential quantum applications. We can also hybridize electron and nuclear spin ensembles together in the solid-state regime to investigate collective effects normally only observed in the atomic, molecular, and optical world. Here we explore in the solid state regime the dynamics of a double domain nuclear spin ensemble coupled to the Nambu-Goldstone boson in GaAs semiconductors and show it exhibits both collective and individual relaxation (thermalization) on very different time scales. Further the collective relaxation of the nuclear spin ensemble is what one would expect from superradiant decay. This opens up the possibility for the exploration of novel collective behavior in solid state systems where the natural energies associated with those spins are much less than the thermal energy.

The SINDRUM-I Experiment

SINDRUM-I was the first nearly 4\pi4π spectrometer at SIN. It was initially designed to search for the forbidden decay \mu^+ \rightarrow e^+e^-e^+μ+→e+e−e+, but also successfully studied various other processes with high precision. The upper limit obtained for the branching ratio of B_{\mu \rightarrow 3e} = \Gamma (\mu^+ \rightarrow e^+e^-e^+)/\Gamma(\mu^+ \rightarrow e^+ \nu_e \bar{\nu}_{\mu}) < 1.0 \times 10^{-12}Bμ→3e=Γ(μ+→e+e−e+)/Γ(μ+→e+νeν‾μ)<1.0×10−12(90% CL) from 1988 is still the best. The first statistically significant observation of the rare decay \mu^+ \rightarrow e^+e^-e^+ \nu_e {\bar{\nu}_{\mu}}μ+→e+e−e+νeν‾μ, achieved in 1985, yielded a branching ratio of B_{\mu\to3e2\nu} = (3.4 \pm 0.2 \pm 0.2) \times 10^{-5}Bμ→3e2ν=(3.4±0.2±0.2)×10−5. Several other measurements of rare processes were undertaken. The first observation of the \piπ-decay \pi^+ \rightarrow e^+ \nu_e e^-e^+π+→e+νee−e+ resulted in the value \Gamma (\pi^+ \rightarrow e^+ \nu_e e^-e^+)/ \Gamma (\pi^+ \rightarrow \mu^+ \nu_{\mu})Γ(π+→e+νee−e+)/Γ(π+→μ+νμ) = (3.2 \pm 0.5 \pm 0.2) \times 10^{-9}(3.2±0.5±0.2)×10−9, also still the best measurement. The determination of the ratio of the weak axial- to vector-form factor F_A/F_V = (0.7 \pm 0.5)FA/FV=(0.7±0.5) resolved a long-standing ambiguity. In addition, upper limits for \mu^+ \rightarrow e^+ \phiμ+→e+ϕ and \pi^+ \rightarrow e^+ \nu_e \phiπ+→e+νeϕ with subsequent decay \phi \rightarrow e^+ e^-ϕ→e+e− (search for “massless” Goldstone bosons \phiϕ) and \pi^0 \rightarrow e^+e^- \gamma < 1.3 \times 10^{-7}π0→e+e−γ<1.3×10−7 were obtained.

Localised Dirac eigenmodes, chiral symmetry breaking, and Goldstone’s theorem at finite temperature

I show that a finite density of near-zero localised Dirac modes in the chirally broken phase of a gauge theory can lead to the disappearance of the massless excitations predicted by the Goldstone theorem at finite temperature.

Extranatural flux inflation

We propose a new inflation scenario in flux compactification, where a zero mode scalar field of extra components of the higher dimensional gauge field is identified with an inflaton. The scalar field is a pseudo Nambu-Goldstone boson of spontaneously broken translational symmetry in compactified spaces. The inflaton potential is non-local and finite, which is protected against the higher dimensional non-derivative local operators by quantum gravity corrections thanks to the gauge symmetry in higher dimensions and the shift symmetry originated from the translation in extra spaces. We give an explicit inflation model in a six dimensional scalar QED, which is shown to be consistent with Planck 2018 data.

Searching for pseudo Nambu-Goldstone boson dark matter production in association with top quarks

Pseudo Nambu-Goldstone bosons (pNGBs) are attractive dark matter (DM) candidates, since they couple to the Standard Model (SM) predominantly through derivative interactions. Thereby they naturally evade the strong existing limits inferred from DM direct detection experiments. Working in an effective field theory that includes both derivative and non-derivative DM-SM operators, we perform a detailed phenomenological study of the Large Hadron Collider reach for pNGB DM production in association with top quarks. Drawing on motivated benchmark scenarios as examples, we compare our results to other collider limits as well as the constraints imposed by DM (in) direct detection experiments and the relic abundance. We furthermore explore implications on the viable parameter space of pNGB DM. In particular, we demonstrate that DM direct detection experiments become sensitive to many pNGB DM realisations once loop-induced interactions are taken into account. The search strategies and pNGB DM benchmark models that we discuss can serve as a starting point for dedicated experimental analyses by the ATLAS and the CMS collaborations.

Two-loop mathcal{O} ((\u03b1t + \u03b1\u03bb + \u03b1\u03ba)2) corrections to the Higgs boson masses in the CP-violating NMSSM

We present our computation of the mathcal{O} ((αt + αλ + ακ)2) two-loop corrections to the Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric Standard Model (NMSSM) using the Feynman-diagrammatic approach in the gaugeless limit at vanishing external momentum. We choose a mixed overline{mathrm{DR}} -on-shell (OS) renormalisation scheme for the Higgs sector and apply both overline{mathrm{DR}} and OS renormalisation in the top/stop sector. For the treatment of the infrared divergences we apply and compare three different regularisation methods: the introduction of a regulator mass, the application of a small momentum expansion, and the inclusion of the full momentum dependence. Our new corrections have been implemented in the Fortran code NMSSMCALC that computes the Higgs mass spectrum of the CP-conserving and CP-violating NMSSM as well as the Higgs boson decays including the state-of-the-art higher-order corrections. Our numerical analysis shows that the newly computed corrections increase with rising λ and κ, remaining overall below about 3% compared to our previously computed mathcal{O} (αt(αt + αs)) corrections, in the region compatible with perturbativity below the GUT scale. The renormalisation scheme and scale dependence is of typical two-loop order. The impact of the CP-violating phases in the new corrections is small. We furthermore show that the Goldstone Boson Catastrophe due to the infrared divergences can be treated in a numerically efficient way by introducing a regulator mass that approximates the momentum-dependent results best for squared mass values in the permille range of the squared renormalisation scale. Our results mark another step forward in the program of increasing the precision in the NMSSM Higgs boson observables.

UV completed composite Higgs model with heavy composite partners

We study electroweak symmetry breaking in minimal composite Higgs models $SU(4)/Sp(4)$ with purely fermionic UV completions based on a confining Hypercolor gauge group and find that the extra Higgs potential from the underlying preon mass can destruct the correlation between the mass of Higgs and composite partners. Thus the composite partners can be very heavy for successful electroweak symmetry breaking without enhancing the separation between the new physical scale and Higgs VEV. So this kind of model can be easily realized by ordinary strong dynamics theories without artificial assumptions and more likely consistent with lattice simulations. The UV completion of partial compositeness predicts a light singlet Goldstone boson which interacts with QCD and electroweak gauge bosons through Wess-Zumino-Witten terms. It can be produced through gluon fusion at LHC and decay into gauge boson pairs. We briefly discuss its phenomenology and derive its bounds from LHC searches.

Glauber gluons in annihilation amplitudes for heavy meson decays

We investigate the Glauber divergences in nonfactorizable annihilation amplitudes for two-body hadronic heavy meson decays in the kT factorization theorem at one-loop level. These divergences can be absorbed into the Glauber factors in the dominant kinematic regions of small parton momenta, which modify the interference between a nonfactorizable annihilation amplitude and other amplitudes by rotating it with a phase. We postulate that only the Glauber effect associated with a pion is significant, due to its special role as a qq̄ bound state and as a pseudo Nambu–Goldstone boson simultaneously. It is elaborated that the data of the D→ππ and πK branching ratios have revealed prominent Glauber effects. This work provides a solid theoretical ground for the factorization-assisted topological-amplitude parametrization of two-body hadronic D meson decays.

Confinement in 4D: An Attempt at Classical Understanding

In this review, we revisit our approach to constructing an effective theory for Abelian and Non-Abelian gauge theories in 4D. Our goal is to have an effective theory that provides a simple classical picture of the main qualitatively important features of these theories. We set out to ensure the presence of the massless photons—Goldstone bosons in Abelian theory and their disappearance in the Non-Abelian case—accompanied by the formation of confining strings between charged states. Our formulation avoids using vector fields and instead operates with the basic degrees of freedom that are the scalar fields of a nonlinear σ-model. The Mark 1 model we study turns out to have a large global symmetry group-the 2D diffeomorphism invariance in the Abelian limit, which is isomorphic to the group of all canonical transformations in the classical two dimensional phase space. This symmetry is not present in QED, and we eliminate it by “gauging” this infinite dimensional global group. Introducing additional modifications to the model (Mark 2), we are able to prove that the “Abelian” version is equivalent to the theory of a free photon. Achieving the desired property in the “Non-Abelian” regime turns out to be tricky. We are able to introduce a perturbation that leads to the formation of confining strings in our Mark 1 model. These strings have somewhat unusual properties, in that their profile does not decay exponentially away from the center of the string. In addition, the perturbation explicitly breaks the diffeomorphism invariance. Preserving this invariance in the gauged model as well as achieving confining strings in Mark 2 model remains an open question.

Regarding the Distribution of Glue in the Pion

Understanding why the scale of emergent hadron mass is obvious in the proton but hidden in the pion may rest on mapping the distribution functions (DFs) of all partons within the pion and comparing them with those in the proton; and since glue provides binding in quantum chromodynamics, the glue DF could play a special role. Producing reliable predictions for the proton’s DFs is difficult because the proton is a three-valence-body bound-state problem. As sketched herein, the situation for the pion, a two-valence-body problem, is much better, with continuum and lattice predictions for the valence-quark and glue DFs in agreement. This beginning of theory alignment is timely because experimental facilities now either in operation or planning promise to realize the longstanding goal of providing pion targets, thereby enabling precision experimental tests of rigorous theory predictions concerning Nature’s most fundamental Nambu–Goldstone bosons.

Exploring the landscape for soft theorems of nonlinear sigma models

We generalize soft theorems of the nonlinear sigma model beyond the mathcal{O} (p2) amplitudes and the coset of SU(N) × SU(N)/SU(N). We first discuss the universal flavor ordering of the amplitudes for the Nambu-Goldstone bosons, so that we can reinterpret the known mathcal{O} (p2) single soft theorem for SU(N) × SU(N)/SU(N) in the context of a general symmetry group representation. We then investigate the special case of the fundamental representation of SO(N), where a special flavor ordering of the “pair basis” is available. We provide novel amplitude relations and a Cachazo-He-Yuan formula for such a basis, and derive the corresponding single soft theorem. Next, we extend the single soft theorem for a general group representation to mathcal{O} (p4), where for at least two specific choices of the mathcal{O} (p4) operators, the leading non-vanishing pieces can be interpreted as new extended theory amplitudes involving bi-adjoint scalars, and the corresponding soft factors are the same as at mathcal{O} (p2). Finally, we compute the general formula for the double soft theorem, valid to all derivative orders, where the leading part in the soft momenta is fixed by the mathcal{O} (p2) Lagrangian, while any possible corrections to the subleading part are determined by the mathcal{O} (p4) Lagrangian alone. Higher order terms in the derivative expansion do not contribute any new corrections to the double soft theorem.

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.