Goldstone Bosons Research Articles

Cosmic birefringence and electroweak axion dark energy

Taking the recently reported non-zero rotation angle of the cosmic microwave background (CMB) linear polarization $\beta=0.35\pm0.14{\rm\, deg}$ as the hint for a pseudo Nambu-Goldstone boson quintessence dark energy (DE), we study the electroweak (EW) axion quintessence DE model where the axion mass is generated by the EW instantons. We find that the observed value of $\beta$ implies a non-trivial $U(1)$ electromagnetic anomaly coefficient ($c_{\gamma}$), once the current constraint on the DE equation of state is also taken into account. With the aid of the hypothetical high energy structure of the model inspired by the experimentally inferred $c_{\gamma}$, the model is shown to be able to make prediction for the current equation of state ($w_{\rm DE,0}$) of the quintessence DE. This is expected to make our scenario distinguishable in comparison with the cosmological constant ($w=-1$) and testable in future when the error in the future measurement of $w_{\rm DE,0}$ is reduced to $\mathcal{O}(1)\%$ level ($\delta w=\mathcal{O}(10^{-2})$).

Cosmic axion force

Nambu-Goldstone bosons, or axions, may be ubiquitous. Some of the axions may have small masses and thus serve as mediators of long-range forces. In this paper, we study the force mediated by an extremely light axion, $\ensuremath{\phi}$, between the visible sector and the dark sector, where dark matter lives. Since nature does not preserve the $CP$ symmetry, the coupling between dark matter and $\ensuremath{\phi}$ is generically $CP$ violating. In this case, the induced force is extremely long range and behaves as an effective magnetic field. If the force acts on electrons or nucleons, the spins of them on Earth precess around a fixed direction toward the Galactic Center. This provides an experimental opportunity for $\ensuremath{\phi}$ with mass, ${m}_{\ensuremath{\phi}}$, and decay constant, ${f}_{\ensuremath{\phi}}$, satisfying ${m}_{\ensuremath{\phi}}\ensuremath{\lesssim}{10}^{\ensuremath{-}25}\text{ }\text{ }\mathrm{eV}$, ${f}_{\ensuremath{\phi}}\ensuremath{\lesssim}{10}^{14}\text{ }\text{ }\mathrm{GeV}$ if the daily modulation of the effective magnetic field signals in magnetometers is measured by using the coherent averaging method. The effective magnetic field induced by an axionic compact object, such as an axion domain wall, is also discussed.

Comagnetometer probes of dark matter and new physics

Modern comagnetometry is—in absolute energy units—the most sensitive experimental technique for measuring the energy splitting between quantum states, with certain implementations measuring the nuclear spin-up/spin-down splitting at the 10−26 eV level. By measuring and subtracting the leading magnetic effects on the spins, comagnetometry can be used to study non-standard-model spin interactions. New physics scenarios that comagnetometers can probe include EDMs, violations of Lorentz invariance, Goldstone bosons from new high-energy symmetries, spin-dependent and CP-violating long-range forces, and axionic dark matter. We describe the many implementations that have been developed and optimized for these applications, and consider the prospects for improvements in the technique. Based purely on existing technology, there is room for several orders of magnitude in further improvement in statistical sensitivity. We also evaluate sources of systematic error and instability that may limit attainable improvements.

Ωcc resonances with negative parity in the chiral constituent quark model

Spectrum of the low-lying $\Omega_{cc}$ resonances with negative parity, which are assumed to be dominated by $sccq\bar{q}$ pentaquark components, is investigated using the chiral constituent quark model. Energies of the $\Omega_{cc}$ resonances are obtained by considering the hyperfine interaction between quarks by exchanging Goldstone boson. Possible $sccq\bar{q}$ configurations with spin-parity $1/2^{-}$, $3/2^{-}$ and $5/2^{-}$ are taken into account. Numerical results show that the lowest $\Omega_{cc}$ resonances with negative parity may lie at $4050 \pm 100$ MeV. In addition, the transitions of the $\Omega_{cc}$ resonance to a pseudoscalar meson and a ground baryon state are also investigated within the chiral Lagrangian approach. We expect that these $\Omega_{cc}$ resonances could be observed in the $\bar{D}\Xi_{c}$ channel by future experiments.

An ultraviolet completion for the Scotogenic model

The Scotogenic model is an economical scenario that generates neutrino masses at the 1-loop level and includes a dark matter candidate. This is achieved by means of an ad-hocZ2 symmetry, which forbids the tree-level generation of neutrino masses and stabilizes the lightest Z2-odd state. Neutrino masses are also suppressed by a quartic coupling, usually denoted by λ5. While the smallness of this parameter is natural, it is not explained in the context of the Scotogenic model. We construct an ultraviolet completion of the Scotogenic model that provides a natural explanation for the smallness of the λ5 parameter and induces the Z2 parity as the low-energy remnant of a global U(1) symmetry at high energies. The low-energy spectrum contains, besides the usual Scotogenic states, a massive scalar and a massless Goldstone boson, hence leading to novel phenomenological predictions in flavor observables, dark matter physics and colliders.

Hidden photon and axion dark matter from symmetry breaking

A light hidden photon or axion-like particle is a good dark matter candidate and they are often associated with the spontaneous breaking of dark global or gauged U(1) symmetry. We consider the dark Higgs dynamics around the phase transition in detail taking account of the portal coupling between the dark Higgs and the Standard Model Higgs as well as various thermal effects. We show that the (would-be) Nambu-Goldstone bosons are efficiently produced via a parametric resonance with the resonance parameter q ∼ 1 at the hidden symmetry breaking. In the simplest setup, which predicts a second order phase transition, this can explain the dark matter abundance for the axion or hidden photon as light as sub eV. Even lighter mass, as predicted by the QCD axion model, can be consistent with dark matter abundance in the case of first order phase transition, in which case the gravitational wave signals may be detectable by future experiments such as LISA and DECIGO.

Natural-scalaron inflation

A pseudo Nambu-Goldstone boson (such as an axion-like particle) is a theoretically well-motivated inflaton as it features a naturally flat potential (natural inflation). This is because Goldstone's theorem protects its potential from sizable quantum corrections. Such corrections, however, generically generates an R 2 term in the action, which leads to another inflaton candidate because of the equivalence between the R 2 term and a scalar field, the scalaron, with a quasi flat potential (Starobinsky inflation). Here it is investigated a new multifield scenario in which both the scalaron and a pseudo Nambu-Goldstone boson are active (natural-scalaron inflation). For generality, also a non-minimal coupling is included, which is shown to emerge from microscopic theories. It is demonstrated that a robust inflationary attractor is present even when the masses of the two inflatons are comparable. Moreover, the presence of the scalaron allows to satisfy all observational bounds in a large region of the parameter space, unlike what happens in pure-natural inflation.

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.