Pattern Of Chiral Symmetry Breaking Research Articles

Gravitational waves from SU(N)/SP(N) composite Higgs models

We study possible strong first-order electroweak phase transitions in Composite Higgs models and we quantify the part of parameter space that can be probed with future gravitational wave experiments. We focus on models where the Composite Higgs sector arises from underlying four-dimensional strongly interacting gauge theories with fermions, and where the Standard Model fermion masses are induced via linear mixing terms with composite fermions — the so-called fermion partial compositeness framework. We perform our analysis for the general class of Composite Higgs models arising from N Weyl fermions in a pseudo-real representation of the new strongly interacting gauge group that dynamically triggers the global chiral symmetry breaking pattern SU(N) → Sp(N). The minimal model has N = 4 and for N > 4 the models feature complex scalar dark matter candidates arising as pseudo-Nambu-Goldstone bosons. We find a large number of points in the models parameter space which yield strong first-order electroweak phase transitions and identify the most important operators characterizing the strength of the phase transition. Almost all of these points are testable with future GW detectors such as LISA, Taiji, Tianqin, BBO, DECIGO and Ultimate-DECIGO.

Consistency of chiral symmetry breaking in chiral Yang-Mills theory with adiabatic continuity

We study the pattern of chiral symmetry breaking in the $\ensuremath{\psi}\ensuremath{\chi}\ensuremath{\eta}$ model [with the chiral fermion sector containing ${\ensuremath{\psi}}^{{ij}}$, ${\ensuremath{\chi}}_{[ij]}$, and ${\ensuremath{\eta}}_{i}^{A}$; see Armoni and Shifman Phys. Rev. D 85, 105003 (2012)] on ${\mathbb{R}}^{3}\ifmmode\times\else\texttimes\fi{}{S}_{L}^{1}$ and derive implications forcing ${\mathbb{R}}^{4}$ physics. Center-symmetric vacua are stabilized by a double-trace deformation. With the center symmetry maintained at small $L({S}^{1})\ensuremath{\ll}{\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{-}1}$, i.e., at weak coupling, no phase transitions are expected in passing to large $L({S}^{1})\ensuremath{\gg}{\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{-}1}$ (here, $\mathrm{\ensuremath{\Lambda}}$ is the dynamical Yang-Mills scale). Starting with the small-$L$ limit, we find the leading-order nonperturbative corrections in the given theory. The instanton-monopole operators induce the adjoint chiral condensate $⟨{\ensuremath{\psi}}^{{ij}}{\ensuremath{\chi}}_{[jk]}⟩\ensuremath{\ne}0$ at weak coupling, i.e., at $L({S}^{1})\ensuremath{\ll}{\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{-}1}$. Then adiabatic continuity tells us that $⟨{\ensuremath{\psi}}^{{ij}}{\ensuremath{\chi}}_{[jk]}⟩\ensuremath{\ne}0$ exists on ${\mathbb{R}}^{4}$, in full accord with the prediction from Bolognesi et al. [Phys. Rev. D 97, 094007 (2018)]. Simultaneously with $⟨{\ensuremath{\psi}}^{{ij}}{\ensuremath{\chi}}_{[jk]}⟩\ensuremath{\sim}{\mathrm{\ensuremath{\Lambda}}}^{3}{\ensuremath{\delta}}_{k}^{i}$, the $\mathrm{SU}({N}_{c})$ gauge symmetry is spontaneously broken at strong coupling down to its maximal Abelian subgroup.

The θ-angle and axion physics of two-color QCD at fixed baryon charge

We analyze the impact of the θ-angle and axion dynamics for two-color (in fact any Sp(2N )) QCD at nonzero baryon charge and as a function of the number of matter fields on the vacuum properties, the pattern of chiral symmetry breaking as well as the spectrum of the theory. We show that the vacuum acquires a rich structure when the underlying CP violating topological operator is added to the theory. We discover novel phases and analyse the order of their transitions characterizing the dynamics of the odd and even number of flavours. We further determine the critical chemical potential as function of the θ angle separating the normal from the superfluid phase of the theory. Our results will guide numerical simulations and novel tests of the model’s dynamics. The results are also expected to better inform phenomenological applications of the model ranging from composite Higgs physics to strongly interacting massive dark matter models featuring number changing interactions. In the companion work [1] we repurpose and upgrade the approach to determine the impact of the θ-angle and axion physics on non-perturbative near conformal dynamics related to the fixed baryon charge sector.

On the derivation of chiral symmetry breaking in QCD-like theories and S-confining theories

Recent works argue that the pattern of chiral symmetry breaking in QCD-like theories can be derived from supersymmetric (SUSY) QCD with perturbation of anomaly-mediated SUSY breaking (AMSB). Nevertheless, despite the fact that AMSB needs to be a small (but still exact) perturbation, two other major problems remain unsolved: first, in order to derive the chiral symmetry breaking pattern, one needs to minimize the potential along a certain specific direction, identifying this direction fully as an outcome is nontrivial given the moduli space of degenerate vacua in the SUSY limit; second, when SUSY is broken, non-holomorphic states might emerge and be relevant for determining the vacuum structure. In this work, we try to resolve these problems and discuss their physical implica- tions. For this purpose, we focus on SUSY QCD with Nf ≤ Nc + 1 and perturb the theories using AMSB. Without minimizing the potential along a certain specific direction in the moduli space, we successfully derive the expected chiral symmetry breaking pattern when Nf< Nc. However, when Nf = Nc and Nf = Nc + 1, we show that tree-level AMSB would induce runaway directions, along which baryon number is spontaneously broken, and the vacua with broken baryon number can be deeper while the field values are not far from the origin. This implies that phase transitions and/or non-holomorphic physics are necessary. In order to derive the expected chiral symmetry breaking pattern of non-SUSY QCD starting from the SUSY limit and AMSB, baryon number conservation is needed as an input rather than obtained as an output. Moreover, we perform explicit consistency checks on “ultraviolet insensitivity” for different Nf by adding the holomorphic mass term for the last flavor, we find that the “jump” of AMSB potential indeed matches the contribution from the holomorphic mass term. We also show in general that, when tree-level AMSB is not vanishing, the origin of the moduli space in s-confining theories does not persist as a minimum.

Singlet channel scattering in a composite Higgs model on the lattice

We present the first calculation of the scattering amplitude in the singlet channel beyond QCD. The calculation is performed in SU(2) gauge theory with N_f=2 fundamental Dirac fermions and based on a finite-volume scattering formalism. The theory exhibits a SU(4) rightarrow Sp(4) chiral symmetry breaking pattern that is used to design minimal composite Higgs models currently tested at the LHC. Our results show that, for the range of underlying fermion mass considered, the lowest flavour singlet state is stable.

Effect of the quark-gluon vertex on dynamical chiral symmetry breaking

In this work, we investigate how the details of the quark-gluon interaction vertex affect the quantitative description of chiral symmetry breaking through the gap equation for quarks. We start from two gluon propagator models widely used in literature and constructed in direct connection with our gradually improved understanding of infrared quantum chromodynamics coupled with its exact one-loop limit. The gap equation is then solved by employing a variety of vertex Ans\"atze, which have been constructed in order to implement some of the key aspects of quantum chromodynamics, namely, multiplicative renormalizability of the quark propagator, gauge invariance, matching with perturbation theory in the weak coupling regime, independence from unphysical kinematic singularities as well as manifestly correct transformation properties under charge conjugation and parity operations. On general grounds, all truncation schemes exhibit the same qualitative and quantitative pattern of chiral symmetry breaking, ensuring the overall robustness of this approach and its potentially reliable description of the hadron spectrum and properties.

Chiral symmetry breaking in a semilocalized magnetic field

In this work, I'm going to explore the pattern of chiral symmetry breaking and restoration in a solvable magnetic distribution within Nambu--Jona-Lasinio model. The special semi-localized static magnetic field can roughly simulate the realistic situation in peripheral heavy ion collisions, thus the study is important for the dynamical evolution of quark matter. I find that the magnetic field dependent contribution from discrete spectra usually dominates over that from continuum ones and chiral symmetry breaking is locally catalyzed by both the magnitude and scale of the magnetic field.

Nambu–Jona-Lasinio model in a parallel electromagnetic field

We explore the features of the UA(1) and chiral symmetry breaking of the Nambu–Jona-Lasinio model without the Kobayashi–Maskawa–'t Hooft determinant term in the presence of a parallel electromagnetic field. We show that the electromagnetic chiral anomaly can induce both finite neutral pion condensate and isospin-singlet pseudo-scalar η condensate and thus modifies the chiral symmetry breaking pattern. In order to characterize the strength of the UA(1) symmetry breaking, we evaluate the susceptibility associated with the UA(1) charge. The result shows that the susceptibility contributed from the chiral anomaly is consistent with the behavior of the corresponding η condensate. The spectra of the mesonic excitations are also studied.

Conjecture about the 2-Flavour QCD Phase Diagram

The QCD phase diagram, in particular its sector of high baryon density, is one of the most prominent outstanding mysteries within the Standard Model of particle physics. We sketch a project how to arrive at a conjecture for the case of two massless quark flavours. The pattern of spontaneous chiral symmetry breaking is isomorphic to the spontaneous magnetisation in an O(4) non-linear σ-model, which can be employed as a low-energy effective theory to study the critical behaviour. We focus on the 3d O(4) model, where the configurations are divided into topological sectors, as in QCD. A topological winding with minimal Euclidean action is denoted as a skyrmion, and the topological charge corresponds to the QCD baryon number. This effective model can be simulated on a lattice with a powerful cluster algorithm, which should allow us to identify the features of the critical temperature, as we proceed from low to high baryon density. In this sense, this projected numerical study has the potential to provide us with a conjecture about the phase diagram of QCD with two massless quark flavours.

Extending chiral perturbation theory with an isosinglet scalar

We augment the chiral Lagrangian by an isosinglet scalar and compute the one-loop radiative corrections to the pion mass and decay constant, as well as the scalar mass. The calculations are carried out for different patterns of chiral symmetry breaking of immediate relevance for phenomenology and lattice investigations. By construction our results encompass several interesting limits, ranging from the dilaton to the linear sigma model.

Instanton-dyon ensemble with two dynamical quarks: The chiral symmetry breaking

This is the second paper of the series aimed at understanding the ensemble of instanton-dyons, now with two flavors of light dynamical quarks. The partition function is appended by the fermionic factor, $(det T)^{N_f}$ and Dirac eigenvalue spectra at small values are derived from the numerical simulation of 64 and 128 dyons. Those spectra show clear chiral symmetry breaking pattern at high dyon density.

Finite volume and partially quenched QCD-like effective field theories

We present a calculation of the meson masses, decay constants and quark-antiquark vacuum expectation value for the three generic QCD-like chiral symmetry breaking patterns SU(N-F) x SU(N-F) -> SU(N-F)(V), SU(N-F) -> SO(N-F) and SU(2N(F)) -> Sp(2N(F)) in the effective field theory for these cases. We extend the previous two-loop work to include effects of partial quenching and finite volume. The calculation has been performed using the quark flow technique. We reproduce the known in finite volume results in the unquenched case. The analytical results can be found in the supplementary material. Some examples of numerical results are given. The numerical programs for all cases are included in version 0.54 of the CHIRON package. The purpose of this work is the use in lattice extrapolations to zero mass for QCD-like and strongly interacting Higgs sector lattice calculations. (Less)

Stability of the pion and the pattern of chiral symmetry breaking

We investigate the pressure of the pion, which should be equal to zero to ensure the stability of the pion, within the framework of the chiral quark model beyond the chiral limit. The pressure of the pion vanishes nontrivially by the Gell-Mann-Oakes-Renner relation within the present framework. This implies that the stability of the pion might be deeply rooted in spontaneous chiral symmetry breaking. We also discuss physical quantities relevant to the energy-momentum tensor operator.

Implications of the Oklo Phenomenon in a Chiral Approach to Nuclear Matter

It has been customary to use data from the Oklo natural nuclear reactor to place bounds on the change that has occurred in the electromagnetic fine structure constant $\alpha$ over the last 2 billion years. Alternatively, an analysis could be based on a recently proposed expression for shifts in resonance energies which relates them to changes in both $\alpha$ and the average $m_q$ of the $u$ and $d$ current quark masses, and which makes explicit the dependence on mass number $A$ and atomic number $Z$. (Recent model independent results on hadronic $\sigma$-terms suggest sensitivity to the strange quark mass is negligible.) The most sophisticated analysis, to date, of the quark mass term invokes a calculation of the nuclear mean-field within the Walecka model of quantum hadrodynamics. We comment on this study and consider an alternative in which the link to low-energy quantum chromodynamics (QCD) and its pattern of chiral symmetry-breaking is more readily discernible. Specifically, we investigate the sensitivity to changes in the pion mass $M_\pi$ of a single nucleon potential determined by an in-medium chiral perturbation theory ($\chi$PT) calculation which includes virtual $\mathrm{\Delta}$-excitations. Subject to some reasonable assumptions about low-energy constants (LECs), we confirm that the $m_q$-contribution to resonance shifts is enhanced by a factor of 10 or so relative to the $\alpha$-term and deduce that the Oklo data for Sm imply that $|m_q(\mathrm{Oklo})- m_q(\mathrm{now})| \lesssim 10^{-9}m_q(\mathrm{now})$.

Chiral symmetry breaking patterns in theUL(n)×UR(n)meson model

Chiral symmetry breaking patterns are investigated in the U_L(n)xU_R(n) meson model. It is shown that new classes of minima of the effective potential belonging to the center of the Lie algebra exist for arbitrary flavor number n. The true ground state of the system is searched nonperturbatively and although multiple local minima of the effective potential may exist, it is argued that in regions of the parameter space applicable for the strong interaction, strictly a U_L(n)xU_R(n)->U_V(n) spontaneous symmetry breaking is possible. The reason behind this is the existence of a discrete subset of axial symmetries, which connects various U_V(n) symmetric vacua of the theory. The results are in agreement with the Vafa-Witten theorem of QCD, illustrating that it remains valid, even without gauge fields, for an effective model of the strong interaction.

Bethe-Salpeter equation at leading order in Coulomb gauge

The Bethe-Salpeter equation and leptonic decay constants for pseudoscalar and vector quark-antiquark mesons with arbitrary quark masses are studied in Coulomb gauge, under a leading order truncation. As input, we use a pure linear rising potential, supplemented by a contact term arising from the conservation of total color charge. It is shown how the equations can be written in terms of manifestly finite functions, despite the infrared singular interaction. The resulting equations are solved numerically. Both the pattern of dynamical chiral symmetry breaking and the leading order heavy quark limit are visible.

Determining the chiral condensate from the distribution of the winding number beyond topological susceptibility

Abstract The first two non-trivial moments of the distribution of the topological charge (or gluonic winding number), i.e., the topological susceptibility and the fourth cumulant, can be computed in lattice QCD simulations and exploited to constrain the pattern of chiral symmetry breaking. We compute these two topological observables at next-to-leading order in three-flavour Chiral Perturbation Theory, and we discuss the role played by the η propagation in these expressions. For hierarchies of light-quark masses close to the physical situation, we show that the fourth cumulant has a much better sensitivity than the topological susceptibility to the three-flavour quark condensate, and thus constitutes a relevant tool to determine the pattern of chiral symmetry breaking in the limit of three massless flavours. We provide the complete formulae for the two topological observables in the isospin limit, and predict their values in the particular setting of the recent analysis of the RBC/UKQCD collaboration. We show that a combination of the topological susceptibility and the fourth cumulant is able to pin down the three flavour condensate in a particularly clean way in the case of three degenerate quarks.

Mesons and nucleons in the soft-wall AdS/QCD model with constrained infrared background

The purpose of this paper is to further study the soft-wall AdS/QCD model with constrained IR background. By including a quartic bulk scalar potential we study various meson and nucleon spectra. This model naturally realizes the asymptotical linearity of these mass spectra simultaneously, together with correctly pattern of explicit and dynamical chiral symmetry breaking. The agreement between the theoretical calculations and the experimental data is good.

Nonlinear boundary dynamics and chiral symmetry in holographic QCD

In a hard-wall model of holographic QCD, we find that nonlinear boundary dynamics are required in order to maintain the correct pattern of explicit and spontaneous chiral symmetry breaking beyond leading order in the pion fields. With the help of a field redefinition, we relate the requisite nonlinear boundary conditions to a standard Sturm-Liouville system. Observables insensitive to the chiral limit receive only small corrections in the improved description, and classical calculations in the hard-wall model remain surprisingly accurate.

Vector-axial vector correlators in weak electric field and the holographic dynamics of the chiral condensate

Abstract The transverse part of the vector-axial vector flavor current correlator in the presence of weak external electric field is studied using holography. The correlator is calculated using a bottom-up model proposed recently, that includes both contributions of higher string states and the non-linear dynamics of the chiral condensate. It is shown that for low momenta the result agrees with the relation proposed by Son and Yamamoto motivated by a simpler holographic model. This suggests that the Son-Yamamoto relation is generically valid in the IR of models with the proper chiral symmetry breaking pattern.