Chiral Condensate Research Articles (Page 1)

Abstract Exploring the mass modifications of φ mesons in nuclei provides insights into the nature of strongly interacting matter. Specifically, φ meson mass shifts can be related to the in-medium modification of the strange quark condensate. Therefore, the partial restoration of chiral symmetry can be studied by observing the mass shifts through the decay channels φ → e+e−, and φ → K+K−. In this paper, we examine the possibility of observing the φ meson mass modifications of the φ mesons in 30 GeV proton-nucleus (C, Cu, Pb) collisions, to be studied at the J-PARC E88 experiment, through the kaonic decay channel, with the off-shell Budapest Boltzmann-Uehling-Uhlenbeck (BuBUU) transport model. By applying different mean fields to the kaons, we examine their effects on the invariant mass spectra. Our simulations suggest that, although different mean fields for the kaons do affect the spectrum, there is a common observable effect primarily driven by the φ mass shift. However, due to the threshold associated with the two kaons, the signal we observe is quite different from the one expected in dilepton spectra. Therefore, to meaningfully constrain the mass shift, it will be useful to include both kaon and dilepton channels in the analysis of the experimental data.

Abstract We demonstrate that the electroweak baryogenesis can be realized in the extended Standard Model with sequential fourth generation fermions (SM4). The solution to the coupled Dyson-Schwinger equations for the fermion and Higgs masses indicates that fourth generation quarks t′ and b′ with the Yukawa couplings above the threshold $$ {g}_Q^c\approx 9.1 $$ g Q c ≈ 9.1 form condensates. This critical coupling, greater than the value $$ {g}_Y^f\approx 7 $$ g Y f ≈ 7 at the ultraviolet fixed point of the renormalization-group evolution in the SM4, implies the existence of an electroweak symmetric phase at a high energy. The t′ and b′ Yukawa couplings evolve as the energy decreases, and exceed $$ {g}_Q^c $$ g Q c at a lower scale. The Higgs potential with the dynamical symmetry breaking effect from heavy quark condensates plus the one-loop temperature-dependent correction from the heavy scalars formed by t′ and b′ quarks allow the first-order phase transition characterized by the ratio ϕ c /T c ≈ 0.9, where ϕ c is the location of the Higgs potential minimum at the critical temperature T c . Together with the baryon number violating sphaleron interaction inherent in the Standard Model and the enhanced CP violation source from fourth generation quarks, the baryon asymmetry in the Universe can be achieved.

We study the chiral condensate at finite temperature in AdS/QCD in a time-dependent background, in which the position of the black hole horizon zh changes with time, producing an increasing or decreasing temperature. Conformal invariance is broken, as in the soft-wall model, by a static quadratic dilaton. Two different scenarios are analyzed; in the first a general power-law time dependence is assumed for zh, while in the second the energy-momentum tensor at late times reproduces the one found in viscous hydrodynamics. Depending on the rate at which the system evolves, the transition shifts toward lower temperatures. If the chiral condensate is far from equilibrium at low temperatures, oscillations around its equilibrium value are observed before thermalization. A prethermalization stage is found in the chiral limit if the initial condition is set at a temperature close to the critical one. In the hydrodynamic setup the evolution of the medium is slow enough, and the chiral condensate soon matches the equilibrium curve.

Dynamical evolution of critical fluctuations with second-order baryon diffusion coupled to a chiral condensate

The Nambu-Goldstone modes on the exotic chiral condensed phase with chiral and tensor-type quark-antiquark condensates are investigated by using the two-point vertex functions. It is shown that one of the Nambu-Goldstone modes appears as a result of meson mixing. As is well known, another method to find the Nambu-Goldstone modes is given by the use of the algebraic commutation relations between broken generators and massless modes obtained through the spontaneous symmetry breaking. This method is adopted to the cases of the chiral symmetry breakings due to the tensor-type condensate and the inhomogeneous chiral condensate. The result obtained by the use of the meson two-point vertex functions is obviously reproduced in the case of the tensor-type condensate. Furthermore, we investigate the general rules for determining the broken symmetries and the Nambu-Goldstone modes algebraically. As examples, the symmetry breaking pattern and the Nambu-Goldstone modes due to the tensor-type condensate or the inhomogeneous chiral condensate are shown by adopting the general rules developed in this paper in the algebraic method. Published by the American Physical Society 2025

The exact solution of the Dirac equation for fermions coupled to an external periodic chiral condensate (chiral spiral) is used to obtain the exact formula for the Wigner function (up to the quantum loop corrections). We find that the resulting expressions for various coefficients of the Wigner function exhibit properties that cannot be reproduced within the standard semiclassical expansion. The formula for the axial vector component of the Wigner function can be conveniently used to study spin polarization effects and illustrate connections between the spin density matrix and axial current. In particular, we find that during an adiabatic change of the periodic potential into a uniform one, the polarization vector is twisted from its original direction.

To provide reliable quantitative predictions for hot and dense QCD matter, a holographic model must be calibrated to match first-principles lattice results at vanishing baryon chemical potential. The equation of state from two leading lattice groups, HotQCD and the Wuppertal-Budapest (WB) collaboration, exhibits notable differences at high temperatures. We revisit the Einstein-Maxwell-dilaton (EMD) holographic model for hot QCD with 2+1 flavors and physical quark masses, fitting the lattice QCD data from the WB collaboration. In particular, using the parameterization for the scalar potential and gauge coupling from our previous work [Phys. Rev. D 106 (2022) L121902], we achieve quantitative agreement between the equation of state, chiral condensates, and state-of-the-art lattice results. Furthermore, higher-order baryon number susceptibilities are consistent with those for 2+1+1 flavor QCD. In particular, the critical endpoint (CEP) obtained from the WB collaboration data closely matches that from the combination of HotQCD and WB datasets, highlighting the robustness of the CEP location. Our holographic prediction for the location of the CEP also aligns with recent Bayesian analysis of multiple EMD models and an effective potential approach to QCD from gap equations.

The properties of quantum chromodynamics (QCD) matter at finite isospin densities are investigated employing holographic hard-wall and soft-wall anti–de Sitter (AdS)/QCD models. It is confirmed that at high enough isospin densities, charged pions start to condense and the pion superfluid phase appears in the system. It is shown that the chiral condensate and the pion condensate can be transformed to each other and form a chiral circle in the superfluid phase. We derived the equation of state (EoS) for pionic matter, calculated the normalized trace anomaly Δ and (ε−3p)/mπ4, and analyzed the sound speed and adiabatic index. Additionally, we provided data on the mass-radius relation and tidal deformability of pion stars. The results indicate that the holographic models align well with lattice QCD concerning isospin density, axial-vector condensation, EoS, and trace anomaly, though discrepancies in sound speed and adiabatic index emerge at higher isospin chemical potentials. The holographic models closely match the leading-order results from chiral perturbation theory (χPT) in certain observables, suggesting that they may effectively capture aspects of χPT dynamics within a five-dimensional framework under the probe approximation. Published by the American Physical Society 2025

We consider the chiral phase transition relevant for QCD matter at finite temperature but with vanishing baryon density. Presumably, the chiral phase transition is of second order for two-flavor QCD in the chiral limit [F. Cuteri , On the order of the QCD chiral phase transition for different numbers of quark flavours, .]. Near the transition temperature, we apply the Schwinger-Keldysh formalism and construct a low-energy effective field theory for the system, in which fluctuations and dissipations are systematically captured. The dynamical variables involve the chiral charge densities and order parameter (chiral condensate). Via the holographic Schwinger-Keldysh technique, the effective action is further confirmed within a modified anti–de Sitter QCD model. With higher-order terms suitably neglected, the stochastic equations derived from the effective field theory resemble those of model F in the Hohenberg-Halperin classification. Within the effective field theory, we briefly discuss the spontaneous breaking of chiral symmetry and Goldstone modes. Published by the American Physical Society 2025

We argue that the Standard Model is accompanied by a new pseudoscalar degree of freedom, ηw meson, which cancels the topological susceptibility of the electroweak vacuum and gets its mass from this effect. The prediction is based on the analyticity properties of the Chern-Simons correlator combined with the basic features of gravity. Depending on the quality level of the U(1)B+L symmetry, the ηw emerges as a B+L pseudo-Goldstone boson or as a Stückelberg 2-form of the electroweak gauge redundancy. An intriguing scenario of the first category is the emergence of ηw in the form of the phase of a U(1)B+L-violating fermion condensate triggered by the instantons, somewhat similar to the η′ meson in QCD. Regardless of its origin, the presence of the ηw meson in the theory appears to be a matter of consistency. Published by the American Physical Society 2025

In this paper, we consider hard-wall anti–de Sitter/quantum chromodynamics (AdS/QCD) models extended by a string-theory inspired Chern-Simons action in terms of a superconnection involving a bifundamental scalar field which corresponds to the open-string tachyon of brane-antibrane configurations and which is naturally identified with the holographic dual of the quark condensate in chiral symmetry breaking. This realizes both the axial and chiral anomalies of QCD with a Witten-Veneziano mechanism for the η′ mass in addition to current quark masses, but somewhat differently than in the Katz-Schwartz AdS/QCD model used previously by us to evaluate pseudoscalar and axial vector transition form factors and their contribution to the hadronic light-by-light (HLBL) piece of the muon g−2. Compared to the Katz-Schwartz model, we obtain a significantly more realistic description of axial-vector mesons with regard to f1−f1′ mixing and equivalent photon rates. Moreover, predictions of the f1→e+e− branching ratios are found to be in line with a recent phenomenological study. However, pseudoscalar transition form factors compare less well with experiment; in particular the π0 transition form factor turns out to be overestimated at moderate nonzero virtuality. For the combined HLBL contribution to the muon g−2 from the towers of axial vector mesons and excited pseudoscalars we obtain, however, a result very close to that of the Katz-Schwartz model.

We revisit the problem of constructing a color superconducting phase in bottom-up holography. We introduce a model that describes the five-dimensional dynamics of a scalar field dual to a chiral symmetry breaking condensate, which is coupled to the RR 4-form. The coupling is given by a topological WZ term, which is elegantly responsible both for scalar condensation at high density, and color Higgsing in the condensed phase. This construction realizes both properties at finite density and Higgsing fraction.

We investigate how a magnetic background field influences the location and the nature of the Roberge-Weiss (RW) finite temperature transition for Nf=2+1 quantum chromodynamics (QCD) with physical quark masses. To that purpose, we perform numerical simulations of the finite temperature theory, discretized through stout staggered quarks and the tree-level improved Symanzik pure gauge action, considering two different values of the Euclidean temporal extent in lattice units, Nt=6, 8. The RW transition temperature TRW decreases with eB, in particular it follows closely the behavior of the pseudocritical QCD crossover temperature Tpc, so that TRW(eB)−Tpc(eB) is practically constant, within errors, for magnetic fields up to eB∼1 GeV2; consistent results are found from the drop of the chiral condensate, which signals chiral symmetry restoration, leading also to the phenomenon of inverse magnetic catalysis above the transition. Moreover, we find that the magnetic field turns the RW transition from second order to first order, with a tricritical magnetic field in-between 1 and 2.4 GeV2, i.e., for magnetic fields substantially lower than those for which the standard QCD transition turns to first order. Published by the American Physical Society 2025

We study the effects of helical magnetic fields on chiral symmetry breaking within the AdS/QCD framework using the D3/D7-brane model. By analyzing the brane embeddings, we obtain three types of massless solutions, corresponding to three phases with different behavior in the dual field theory. From the study of quark condensates, free energy, and electric currents, we find that helical magnetic fields can counteract uniform-field-induced symmetry breaking, driving the system towards symmetry restoration. We also find an effect analog to the chiral magnetic effect whereby the current is parallel to the magnetic field. We further study the massive case, and find that the helical configuration is less effective in erasing the first order phase transition that is present in the case of a constant magnetic field.

Stability of chiral magnon condensates in collinear antiferromagnetic insulators

We investigate properties of the quark–antiquark mesons at zero and finite temperature in the framework of a solvable chirally symmetric quark model. The interquark linearly rising interaction is reminiscent of that derived in Coulomb gauge QCD, with the string tension being the only model parameter. We demonstrate that while the confining interaction induces spontaneous breaking of chiral symmetry at T=0, it gets restored at a temperature Tch≃90 MeV for the string tension fixed to provide the phenomenological value of the quark condensate. This temperature is similar to Tch≃130 MeV observed on the lattice in the chiral limit for Nc=3. The physical mechanism responsible for chiral symmetry restoration in the confining regime is Pauli blocking of the quark levels, required for the existence of a nonvanishing quark condensate, by thermal excitations of the quarks and antiquarks. Thus, above the chiral restoration temperature, meson-like states are chirally symmetric and approximately chiral spin symmetric. A crucial property of the confined meson-like light-light states above Tch is their size that exceeds drastically that in the chirally broken phase below Tch. Heavy-heavy mesons nearly preserve their size irrespective of the temperature. Furthermore, the root-mean-square radius of the states with J=0,1 diverges in the chiral limit. This unexpected property must be a key to understanding unusual features of the hot QCD matter as observed at RHIC and LHC. Consequently, the confining but chirally symmetric matter above Tch can be considered as a dense system of very large and strongly overlapping meson-like states (“strings”).

We extend our prior results on the worldline computation of the axial vector-vector-vector (AVV) triangle anomaly in polarized deeply inelastic scattering (DIS) to the finite mass case by computing in addition the pseudoscalar-vector-vector (PVV) triangle graph. For the well-studied QED case, we show explicitly how the off-forward AVV pole exactly cancels an identical PVV pole. We then demonstrate the dramatic difference in QCD due to the chiral condensate, which qualitatively modifies anomalous Ward identities. As in the massless case, the anomaly pole in QCD is canceled by the dynamics of a primordial isosinglet pseudoscalar η¯-meson, whose Wess-Zumino-Witten coupling to the topological charge density shifts the pole to the physical η′ mass, with the finite quark mass contribution differing by O(10%) from the Witten-Veneziano formula. We obtain a compact analytic expression for the finite mass corrections to Shore and Veneziano’s result that the proton’s net quark helicity ΔΣ∝χQCD′|m=0(0), the forward slope of the topological susceptibility in the chiral limit, and show they are of the order of a few percentages. Our prior prediction that the polarized DIS structure function g1 is quenched by sphaleronlike topological transitions at small x is unaffected by quark mass effects. Our results illustrate how worldline computations of anomalous processes, in synergy with lattice computations and nonet chiral perturbation theory, can uncover novel nonperturbative features of QCD at the Electron-Ion Collider. Published by the American Physical Society 2025

We investigate the effects of temperature T and external magnetic fields eB on the chiral condensates and screening masses of neutral pseudoscalar mesons, including π0, K0, and ηss¯0, in (2+1)-flavor lattice QCD with physical quark masses. The chiral condensates are intrinsically connected to the screening masses via Ward-Takahashi identities, with the latter characterizing the inverse of the spatial correlation length in the pseudoscalar channel. Using highly improved staggered quark (HISQ), we perform simulations on lattices with temporal extents Nτ=8, 12, 16 and an aspect ratio of 4, covering five temperatures from 145 MeV to 166 MeV. For each temperature, eight magnetic field strengths are simulated, reaching up to eB∼0.8 GeV2. These simulations allow us to provide continuum estimates for the chiral condensates and screening masses. We observe intricate behavior in the light (ud), strange-light (ds), and strange (s) quark condensates as functions of the magnetic field and temperature, reflecting the competition between magnetic catalysis and inverse magnetic catalysis effects. This complex behavior is also mirrored in the screening masses of the neutral pseudoscalar mesons. Notably, the screening masses of π0 and K0 exhibit a nonmonotonic dependence on eB, closely following the variations in their corresponding chiral condensates. Meanwhile, the screening mass of ηss¯0 decreases monotonically with increasing eB. These findings provide valuable insights for understanding the behavior of QCD in a thermomagnetic medium and can serve as benchmarks for low-energy QCD models and effective theories.

We investigate the time evolution of the quark condensate toward a chiral symmetry broken phase in hot and dense quark matter using a field-theoretic quark model with nonlocal chiral-invariant four-fermion coupling. By purposely selecting a parameter set in which inhomogeneous phases are energetically disfavored, we nonetheless observe the emergence of metastable patterned configurations that appear to persist for remarkably long timescales. These findings suggest that even when not fully stable, inhomogeneous phases may play a significant role in the dynamics of chiral symmetry breaking and restoration. To gain deeper insight into these phenomena, we also analyze the impact of the dimensionality of coordinate space on both the formation and stability of inhomogeneous chiral condensates.

The Schwinger model with two massive fermions is a nontrivial theory for which no analytical solution is known. The strong coupling limit of the theory allows for different semiclassical approximations to extract properties of its low-lying spectrum. In particular, analytical results exist for the fermion condensate, the fermion mass dependence of the pseudoscalar meson mass or its decay constant. These approximations, nonetheless, are not able to quantitatively predict isospin breaking effects in the light spectrum, for example. In this paper we use lattice simulations to test various analytical predictions and study isospin breaking effects from nondegenerate quark masses. We also introduce a low-energy effective field theory based on a nonlinear σ model with a dilaton field, which leads to the correct fermion mass dependence of the pion mass, the correct σ-to-π mass ratio and a prediction of the isospin breaking effects, which we test numerically. Published by the American Physical Society 2025