Effects Of Chiral Symmetry Breaking Research Articles

Probing the hadron mass spectrum in dense two-color QCD with the linear sigma model

We investigate modifications of hadron masses at finite quark chemical potential in two-flavor and two-color QCD, data of which are available from lattice simulations, within a linear sigma model based on approximate Pauli-Gursey $SU(4)$ symmetry. The model describes not only ground-state scalar diquarks and pseudoscalar mesons but also the excited pseudoscalar diquarks and scalar mesons; each ground-state diquark (meson) has the corresponding excited diquark (hadron) with opposite parity as a chiral partner. Effects of chiral symmetry breaking and diquark condensates are incorporated by a mean-field treatment. We show that various mixings among the hadrons, which are triggered by the breakdown of baryon number conservation in the superfluid phase, lead to a rich hadron mass spectrum. We discuss the influence of $U(1{)}_{A}$ anomaly on the density dependence of the mass spectrum and also manifestations of the chiral partner structures as the density increases in the superfluid phase. The predicted hadron masses are expected to provide future lattice simulations with useful information on such symmetry properties in dense two-color QCD.

Gluon string breaking and meson spectrum in the holographic Soft Wall model

We propose a general method for finding a string-like meson spectrum which is based on a certain condition for the breaking of closed gluon string. A model is constructed that successfully realizes the proposed method. The model is based on the holographic Soft Wall model for QCD and the use of the Wilson confinement criterion. We applied our approach to the vector and scalar cases and obtained numerical predictions for the intercepts of corresponding Regge like radial meson spectra. A good agreement is obtained both with the existing experimental data and with some other known phenomenological approaches. Remarkably, our closed string breaking condition has two branches. We argue that they should correspond to states of opposite parity. The Wilson confinement criterion leads then to a natural mass splitting between parity partners. The constructed model represents thus the first example of bottom-up holographic model in which the effects of chiral symmetry breaking can emerge automatically, i.e., without additional assumptions taken outside of the holographic approach.

Light scalars: Four-quark versus two-quark states in the complex energy plane from Bethe-Salpeter equations

We study the dynamical generation of scalar mesons in the light quark sector ($q\in\{u,d,s\}$) and calculate the masses and widths for the $f_0(500),a_0(980)$ and $f_0(980)$. To this end we study the mixing of conventional $q\bar{q}$ and `exotic' $q\bar{q}q\bar{q}$ states via a coupled set of two-body Bethe-Salpeter equations based on a symmetry-preserving truncation of the underlying Dyson-Schwinger equations. This allows us to determine the dominant components of each state. Furthermore, we extend our previous framework into the complex energy plane such that we can study the analytic structure of the states in question and extract their width. At the physical point of small quark masses, the $\sigma$ meson is predominantly a $\pi\pi$ resonance. Consequently, its mass and width is driven by the effects of chiral symmetry breaking. At larger quark masses, however, the conventional $q\bar{q}$ components take over. Furthermore, we find a strong molecular $K\bar{K}$ component for both, the strange-light $f_0(980)$ and the $a_0(980)$.

Asymptotically Safe Gravity-Fermion Systems on Curved Backgrounds

We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to Nf Dirac fermions on maximally symmetric backgrounds. Based on Wetterich’s equation, we perform a detailed study of the resulting fixed point structure in a projection including the Einstein–Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermion bilinears to the spacetime curvature. The latter constitutes a mass-type term that breaks chiral symmetry explicitly. Our analysis identified two infinite families of interacting RG fixed points, which are viable candidates to provide a high-energy completion through the asymptotic safety mechanism. The fixed points exist for all values of Nf outside of a small window situated at low values Nf and become weakly coupled in the large Nf-limit. Symmetry-wise, they correspond to “quasi-chiral” and “non-chiral” fixed points. The former come with enhanced predictive power, fixing one of the couplings via the asymptotic safety condition. Moreover, the interplay of the fixed points allows for cross-overs from the non-chiral to the chiral fixed point, giving a dynamical mechanism for restoring the symmetry approximately at intermediate scales. Our discussion of chiral symmetry breaking effects provides strong indications that the topology of spacetime plays a crucial role when analyzing whether quantum gravity admits light chiral fermions.

Chiral transition and the chiral charge density of the hot and dense QCD matter.

We study the chirally imbalanced hot and dense strongly interacting matter by means of the Dyson-Schwinger equations (DSEs). The chiral phase diagram is studied in the presence of chiral chemical potential μ5. The chiral quark condensate leftlangle overline{psi}psi rightrangle is obtained with the Cornwall-Jackiw-Tomboulis (CJT) effective action in concert with the Rainbow truncation. Catalysis effect of dynamical chiral symmetry breaking (DCSB) by μ5 is observed. We examine with two popular gluon models and consistency is found within the DSE approach, as well as in comparison with lattice QCD. The critical end point (CEP) location (μE, TE ) shifts toward larger TE but constant μE as μ5 increases. A technique is then introduced to compute the chiral charge density n5 from the fully dressed quark propagator. We find the n5 generally increases with temperature T , quark number chemical potential μ and μ5. Since the chiral magnetic effect (CME) is typically investigated with peripheral collisions, we also investigate the finite size effect on n5 and find an increase in n5 with smaller system size.

K1 and K* in nuclear matter

In this talk, I will discuss why previous experiments and theoretical considerations inevitably lead us to consider K* and K1 in nuclear matter [T. Song, T. Hatsuda and S.H. Lee, Phys. Lett. B 792, 160 (2019)]. I will also discuss the Weinberg type sum rule in the strangeness sector and derive a relation between chiral symmetry restoration and their mass difference. Using the kaon beam at JPARC, one could observe the mass shift of both of these particles in a nuclear target experiment, which will be the first step towards understanding the effects of chiral symmetry breaking in hadron masses.

Strange Stars in the Vector Interaction Enhanced Bag Model

The vector interaction enhanced Bag model (vBag) for dense quark matter extends the commonly used thermodynamic Bag model (tdBag) by incorporating effects of dynamical chiral symmetry breaking (D χ SB) and vector repulsion. Motivated by the suggestion that the stability of strange matter is in tension with chiral symmetry breaking (D χ SB) we examine the parameter space for its stability in the vBag model in this work. Assuming the chiral transition occurs at sufficiently low density, we determine the stability region of strange matter as a function of the effective Bag constant and the vector coupling. As an astrophysical application, we construct contours of maximum mass M max and radius at maximum mass R max in this region of parameter space. We also study the stability of strange stars in the vBag model with maximum mass in the 2 M ⊙ range by computing the spectrum of radial oscillations, and comparing to results from the tdBag model, find some notable differences.

Interplay of dynamical and explicit chiral symmetry breaking effects on a quark

The relative contributions of explicit and dynamical chiral symmetry breaking in QCD models of the quark-gap equation are studied in dependence of frequently employed ans\"atze for the dressed interaction and quark-gluon vertex. The explicit symmetry breaking contributions are defined by a constituent-quark sigma term whereas the combined effects of explicit and dynamical symmetry breaking are described by a Euclidean constituent-mass solution. We extend this study of the gap equation to a quark-gluon vertex beyond the Abelian approximation complemented with numerical gluon- and ghost-dressing functions from lattice QCD. We find that the ratio of the sigma term over the Euclidean mass is largely independent of nonperturbative interaction and vertex models for current-quark masses, $m_{u,d}(\mu) \leq m(\mu) \leq m_b(\mu)$, and equal contributions of explicit and dynamical chiral symmetry breaking occur at $m(\mu) \approx 400$~MeV. For massive solutions of the gap equation with lattice propagators this value decreases to about 200~MeV.

Inhomogeneous chiral phases away from the chiral limit

The effect of explicit chiral-symmetry breaking on inhomogeneous chiral phases is studied within a Nambu–Jona-Lasinio model with nonzero current quark mass. Generalizing an earlier result obtained in the chiral limit, we show within a Ginzburg-Landau analysis that the critical endpoint of the first-order chiral phase boundary between two homogeneous phases gets replaced by a “pseudo-Lifshitz point” when the possibility of inhomogeneous order parameters is considered. Performing a stability analysis we also show that the unstable mode along the phase boundary is in the scalar but not in the pseudoscalar channel, suggesting that modulations which contain pseudoscalar condensates, like a generalized dual chiral density wave, are disfavored against purely scalar ones. Numerically we find that the inhomogeneous phase shrinks as one moves away from the chiral limit, but survives even at significantly large values of the current quark mass.

Pion and kaon valence quark distribution functions from Dyson-Schwinger equations

Using realistic quark propagators and meson Bethe-Salpeter amplitudes based on the Dyson-Schwinger equations, we calculate the pion and kaon's valence parton distribution functions (PDF) through the modified impulse approximation. The PDFs we obtained at hadronic scale have the purely valence characteristic and exhibit both dynamical chiral symmetry breaking and SU(3) flavor symmetry breaking effects. A new calculation technique is introduced to determine the valence PDFs with precision. Through NLO DGLAP evolution, our result is compared with pion and kaon valence PDF data at experimental scale. Good agreement is found in the case of pion, while deviation emerges for kaon. We point out this situation can be resolved by incorporating gluon contributions into the mesons if the pion hosts more gluons than kaon nonperturbatively.

Novel dual chiral density wave in nuclear matter based on a parity doublet structure

We study the dual chiral density wave (DCDW) in nuclear matter using a hadronic model with the parity doublet structure. We first extend the ordinary DCDW ansatz so as to incorporate the effect of an explicit chiral symmetry breaking. Then via numerically evaluating and minimizing the effective potential, we determine the phase structure. We find, in addition to the ordinary DCDW phase where the space average of the chiral condensate vanishes, a new DCDW phase with a nonvanishing space average depending on the value of the chiral invariant mass parameter.

Electromagnetic and axial-vector form factors of the quarks and nucleon

In light of the improved precision of the experimental measurements and enormous theoretical progress, the nucleon form factors have been evaluated with an aim to understand how the static properties and dynamical behavior of nucleons emerge from the theory of strong interactions between quarks. We have analyzed the vector and axial-vector nucleon form factors ([Formula: see text] and [Formula: see text]) using the spin observables in the chiral constituent quark model ([Formula: see text]CQM) which has made a significant contribution to the unraveling of the internal structure of the nucleon in the nonperturbative regime. We have also presented a comprehensive analysis of the flavor decomposition of the form factors ([Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text]) within the framework of [Formula: see text]CQM with emphasis on the extraction of the strangeness form factors which are fundamental to determine the spin structure and test the chiral symmetry breaking effects in the nucleon. The [Formula: see text] dependence of the vector and axial-vector form factors of the nucleon has been studied using the conventional dipole form of parametrization. The results are in agreement with the available experimental data.

Simulating chiral magnetic effect and anomalous transport phenomena in the pre-equilibrium stages of heavy-ion collisions

We present a first principles approach to study the Chiral Magnetic Effect during the pre-equilibrium stage of a heavy-ion collision. We discuss the dynamics of the Chiral Magnetic Effect and Chiral Magnetic Wave based on real-time lattice simulations with dynamical (Wilson and Overlap) fermions simultaneously coupled to color and electromagnetic fields. While for light quarks we observe a dissipation-less transport of charges as in anomalous hydrodynamics, we demonstrate that for heavier quarks the effects of explicit chiral symmetry breaking lead to a significant reduction of the associated currents.

Chiral corrections to the Adler-Weisberger sum rule

The Adler-Weisberger sum rule for the nucleon axial-vector charge, $g_A$, offers a unique signature of chiral symmetry and its breaking in QCD. Its derivation relies on both algebraic aspects of chiral symmetry, which guarantee the convergence of the sum rule, and dynamical aspects of chiral symmetry breaking---as exploited using chiral perturbation theory---which allow the rigorous inclusion of explicit chiral symmetry breaking effects due to light-quark masses. The original derivations obtained the sum rule in the chiral limit and, without the benefit of chiral perturbation theory, made various attempts at extrapolating to non-vanishing pion masses. In this paper, the leading, universal, chiral corrections to the chiral-limit sum rule are obtained. Using PDG data, a recent parametrization of the pion-nucleon total cross-sections in the resonance region given by the SAID group, as well as recent Roy-Steiner equation determinations of subthreshold amplitudes, threshold parameters, and correlated low-energy constants, the Adler-Weisberger sum rule is confronted with experimental data. With uncertainty estimates associated with the cross-section parameterization, the Goldberger-Treimann discrepancy, and the truncation of the sum rule at $\mathcal{O}(M_\pi^4)$ in the chiral expansion, this work finds $g_A = 1.248 \pm 0.010 \pm \ 0.007 \pm 0.013$.

Chiral symmetry aspects in the open charm sector

QCD sum rules serve as tools to investigate changing hadronic properties in a hot and/or dense nuclear medium. The role of chiral symmetry breaking and restoration effects in a medium can be addressed also in the heavy-light meson sector. Thus, we consider Weinberg sum rules which refer to chiral partner mesons composed of a light and a heavy quark.

Chiral symmetry breaking and confinement effects on dilepton and photon production aroundTc

Production rates of dileptons and photons from the quark-gluon (QGP) phase are calculated taking into account effects of confinement and spontaneous chiral symmetry breaking (\chi SB) not far from the transition temperature $T_c$. We find that the production rates of dileptons with large momenta and of photons originating from the QGP around $T_c$ are suppressed by the \chi SB effect. We also discuss to what extent information about details of the chiral transition, such as its characteristic temperature range and the steepness of the crossover, are reflected in these quantities.

Complex saddle points and disorder lines in QCD at finite temperature and density

The properties and consequences of complex saddle points are explored in phenomenological models of QCD at non-zero temperature and density. Such saddle points are a consequence of the sign problem, and should be considered in both theoretical calculations and lattice simulations. Although saddle points in finite-density QCD are typically in the complex plane, they are constrained by a symmetry that simplifies analysis. We model the effective potential for Polyakov loops using two different potential terms for confinement effects, and consider three different cases for quarks: very heavy quarks, massless quarks without modeling of chiral symmetry breaking effects, and light quarks with both deconfinement and chiral symmetry restoration effects included in a pair of PNJL models. In all cases, we find that a single dominant complex saddle point is required for a consistent description of the model. This saddle point is generally not far from the real axis; the most easily noticed effect is a difference between the Polyakov loop expectation values $\left\langle {\rm Tr}_{F}P\right\rangle $ and $\left\langle {\rm Tr}_{F}P^{\dagger}\right\rangle $, and that is confined to small region in the $\mu-T$ plane. In all but one case, a disorder line is found in the region of critical and/or crossover behavior. The disorder line marks the boundary between exponential decay and sinusoidally modulated exponential decay of correlation functions. Disorder line effects are potentially observable in both simulation and experiment. Precision simulations of QCD in the $\mu-T$ plane have the potential to clearly discriminate between different models of confinement.

CPviolation and chiral symmetry breaking in hot and dense quark matter in the presence of a magnetic field

We investigate chiral symmetry breaking and strong CP violation effects on the phase diagram of strongly interacting matter in presence of a constant magnetic field. The effect of magnetic field and strong CP violating term on the phase structure at finite temperature and density is studied within a three flavor Nambu-Jona-Lasinio (NJL) model including the Kobayashi-Maskawa-t'Hooft (KMT) determinant term. This is investigated using an explicit variational ansatz for ground state with quark anti-quark pairs leading to condensates both in scalar and pseudoscalar channels. Magnetic field enhances the condensate in both the channels. Inverse magnetic catalysis for CP transition at finite chemical potential is seen for zero temperature and for small magnetic fields.

Spin supercurrent, magnetization dynamics, andφ-state in spin-textured Josephson junctions

The prospect of combining the dissipationless nature of superconducting currents with the spin-polarization of magnetic materials is interesting with respect to exploring superconducting analogues of topics in spintronics. In order to accomplish this aim, it is pivotal to understand how spin-supercurrents interact dynamically with magnetization textures. We investigate the appearance of a spin-supercurrent and the resulting magnetization dynamics in a textured magnetic Josephson current by using three experimentally relevant models: i) a S/F/S junction with spin-active interfaces, ii) a S/F1/F2/F3/S Josephson junction with a ferromagnetic trilayer, and iii) a Josephson junction containing a domain wall. In all of these cases, the supercurrent is spin-polarized and exerts a spin-transfer torque on the ferromagnetic interlayers which causes magnetization dynamics. Using a scattering matrix formalism in the clean limit, we compute the Andreev-bound states and free energy of the system which is used to solve the Landau-Lifshiftz-Gilbert equation. We compute both how the inhomogeneous magnetism influences the phase-dependence of the charge supercurrent as well as the magnetization dynamics caused by the spin-supercurrent. Using a realistic experimental parameter set, we find that the supercurrent can induce magnetization switching that is controlled by the superconducting phase difference. Moreover, we demonstrate that the combined effect of chiral spin symmetry breaking and interface scattering causes the system to act as a phase battery that may supply any superconducting phase difference phi in the ground state. Such a phi junction is accompanied by an anomalous supercurrent appearing even at zero phase difference, and we demonstrate that the flow direction of this current is controlled by the chirality of the magnetization configuration.

Broken chiral symmetry on a null plane

On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincaré generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone’s theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann–Oakes–Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model.