Explicit Chiral Symmetry Breaking Research Articles

Effect of charm quark on chiral phase transition in Nf=2+1+1 holographic QCD

We investigate the effect of the charm quark on the chiral phase transition of light quarks at finite temperature based on the four-flavor soft-wall holographic QCD model. In the massless limit, we find that the thermal chiral phase transition is of the second order in the four-quark-flavor system. In the case with the massive charm quark and the massless light and strange quarks, the order of the phase transition changes to the first order. This is due to the quark-flavor symmetry breaking which is associated with the violation of the U(1) axial symmetry. Once the light and strange quarks get massive, the explicit chiral symmetry breaking becomes eminent, and then the crossover phase transition is realized at the physical quark masses. We also map the order of the phase transition on a phase diagram in the quark-mass plane where the light- and strange-quark masses are degenerate but differ from the value of the charm-quark mass. This phase diagram is an extension of the conventional Columbia plot to the four-quark-flavor system. The critical exponents related to the chiral phase transition are also addressed. Published by the American Physical Society 2024

Decays of the tensor glueball in a chiral approach

Glueballs remain an experimentally undiscovered prediction of QCD. Lattice QCD predicts a spectrum of glueballs, with the tensor (JPC = 2++) glueball being the second lightest, behind the scalar glueball. From an effective hadronic model based on spontaneous and explicit chiral symmetry breaking, we compute decay ratios of the tensor glueball into various meson decay chan nels. We find the tensor glueball to primarily decay into 2 vector mesons, dom inated by ρρ and K* K*. These results are compared to experimental data of decay rates of spin 2 mesons. Based on this comparison we make statements on the eligibility of these mesons as potential tensor glueball candidates.

Light mesons and phase structures in μ B -T-eB and μ I -T-eB spaces * *Supported by the National Natural Science Foundation of China (11775165)

Light mesons are investigated in and spaces using a two-flavor NJL model and used to determine chiral symmetry restoration and the pion superfluid phase transition. In space, during the chiral symmetry restoration process, the mass of the pseudo-Goldstone mode increases, with sudden jumps. At the critical end point, the meson exhibits a sharp but continuous mass increase, with a sudden mass jump at the Mott transition. In the nearby first order chiral phase transition region, we observe two mass jumps, one induced by the Mott transition and the other by the quark mass jump. The mass of the Higgs mode σ first decreases and then increases with chiral symmetry restoration, only showing a jump at the first order chiral phase transition. We plot a chiral phase diagram in terms of the change in quark mass, the Mott transition of the pseudo-Goldstone mode , and the minimum mass of the Higgs mode σ. Owing to explicit breaking of chiral symmetry in the physical case, the chiral restoration phase boundaries on the plane from the order parameter side and meson side are different. The and σ mass jumps will be helpful to the experimental search for the chiral phase diagram and critical end point. On the plane, the competition between the pion superfluid phase transition and chiral symmetry restoration under magnetic fields is studied in terms of the Goldstone mode and pseudo-Goldstone mode . In contrast to the two mass jumps of in the first order chiral phase transition region, the meson displays several mass jumps in the chiral crossover region. At the critical end point, also has sharp but continuous mass change, with a mass jump at the Mott transition. The isospin symmetry is strict, and the pion superfluid phase transition is uniquely determined by the massless Goldstone mode . The separation of chiral restoration and the pion superfluid phase boundaries is enhanced by the external magnetic field.

Critical behaviors of the O(4) and Z(2) symmetries in the QCD phase diagram

In this work we have studied the QCD phase structure and critical dynamics related to the 3-$d$ $O(4)$ and $Z(2)$ symmetry universality classes in the two-flavor quark-meson low energy effective theory within the functional renormalization group approach. We have employed the expansion of Chebyshev polynomials to solve the flow equation for the order-parameter potential. The chiral phase transition line of $O(4)$ symmetry in the chiral limit, and the $Z(2)$ line of critical end points related to the explicit chiral symmetry breaking are depicted in the phase diagram. Various critical exponents related to the order parameter, chiral susceptibilities and correlation lengths have been calculated for the 3-$d$ $O(4)$ and $Z(2)$ universality classes in the phase diagram, respectively. We find that the critical exponents obtained in the computation, where a field-dependent mesonic nontrivial dispersion relation is taken into account, are in quantitative agreement with results from other approaches, e.g., the conformal bootstrap, Monte Carlo simulations and $d=3$ perturbation expansion, etc. Moreover, the size of the critical regime in the QCD phase diagram is found to be very small.

The role of the UA(1) breaking term in dynamical chiral symmetry breaking of chiral effective theories

Abstract The spontaneous breaking of chiral symmetry is examined by chiral effective theories, such as the linear $\sigma$ model and the Nambu–Jona-Lasinio (NJL) model. We discuss the properties of the sigma meson regarded as the quantum fluctuation of the chiral condensate when the chiral symmetry is spontaneously broken, mainly by the U$_{A}$(1) anomaly. We derive a mass relation among the SU(3) flavor singlet mesons, $\eta_{0}$ and $\sigma_{0}$, in the linear $\sigma$ model to be satisfied for the anomaly-driven symmetry breaking in the chiral limit, and find that it is also supported in the NJL model. With the explicit breaking of chiral symmetry, we show that both of the chiral effective models reproducing the observed physical quantities suggest that the $\sigma_{0}$ meson should have a mass smaller than $\sim$800 MeV when anomaly-driven symmetry breaking takes place.

Proper-time method for unequal masses

The result of removing of heavy non-equal mass particles from the theory can be described, at low energy, by the effective action, which is a series in inverse-square powers of the mass. We propose a new efficient tool to calculate the leading terms of this series based on the Schwinger proper-time method. Unequal masses give rise to a large number of effective vertices describing the explicit flavor symmetry breaking effects with well-defined coupling constants. Our method is pertinent to the theory with explicit and spontaneous chiral symmetry breaking, chiral gauge theory, standard and beyond standard model effective field theory, the theory of critical phenomena, cosmology, etc.

Inhomogeneous phases in the quark-meson model with explicit chiral-symmetry breaking

We investigate the existence of inhomogeneous chiral phases in the quark-meson model with explicit chiral-symmetry breaking. We find that the inhomogeneous region shrinks with increasing pion masses but survives for the physical value of mπ. The instability towards inhomogeneous matter occurs in the scalar channel, while pseudoscalar modes are disfavored.

Inverse mass hierarchy of light scalar mesons driven by anomaly-induced flavor breaking

Abstract We propose a novel mechanism to reproduce the observed mass hierarchy for scalar mesons lighter than 1 GeV (called the inverse hierarchy), regarding them as mesons made of a quark and an anti-quark ($q\bar{q}$ mesons). The source is provided by the SU(3) flavor-symmetry breaking induced by the U(1) axial anomaly. In particular, the anomaly term including the explicit chiral symmetry breaking plays a significant role in the light scalar meson spectrum. To be concrete, we construct a linear sigma model for scalar mesons of $q\bar{q}$ type together with their pseudoscalar chiral partners, including an anomaly-induced explicit chiral symmetry-breaking term. We find that, due to the proposed mechanism, the inverse hierarchy, i.e., $m\left[ a_0 (980) \right] \simeq m\left[ f_0 (980) \right] > m \left[ K_0^\ast (700) \right] > m \left[ f_0(500) \right]$, is indeed realized. Consequently, the quark content of $f_0 (500)$ is dominated by the isoscalar $\bar uu+ \bar dd$ component, and $f_0 (980)$ by the strange quark bilinear one, $s\bar{s}$.

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.

η′ and η mesons at high T when the UA(1) and chiral symmetry breaking are tied

The approach to the eta'-eta complex employing chirally well-behaved quark-antiquark bound states and incorporating the non-Abelian axial anomaly of QCD through the generalization of the Witten-Veneziano relation, is extended to finite temperatures. Employing the chiral condensate has led to a sharp chiral and U_A(1) symmetry restoration, but with the condensates of quarks with realistic explicit chiral symmetry breaking, which exhibit a smooth, crossover chiral symmetry restoration in qualitative agreement with lattice QCD results, we get a crossover U_A(1) transition, with smooth and gradual melting of anomalous mass contributions. This way we obtain a substantial drop of the eta' mass around the chiral transition temperature, but no eta mass drop. This is consistent with the present empirical evidence.

A charged particle veto detector for kaonic deuterium measurements at DAΦNE

The antikaon-nucleon interaction close to threshold provides crucial information on the interplay between spontaneous and explicit chiral symmetry breaking in low-energy QCD. In this context, the importance of kaonic deuterium x-ray spectroscopy has been well recognized, but no experimental results have yet been obtained due to the difficulty of the measurement. To measure the shift and width of the kaonic deuterium 1s state with an accuracy of 30 eV and 75 eV, respectively, an apparatus is under construction at the Laboratori Nazionali di Frascati. A detailed Monte Carlo simulation has shown that an increase of the signal to background ratio by a factor of ten will be required compared to the successfully performed kaonic hydrogen measurement (SIDDHARTA). Three pillars are essential for the newly developed experimental apparatus: a large area x-ray detector system (consisting of Silicon Drift Detectors), a lightweight cryogenic target system and a veto system, consisting of an outer veto detector (Veto-1) for active shielding and an inner veto detector (Veto-2) for charged particle suppression. For both veto systems, an excellent time resolution is required to distinguish kaons stopping in gas from direct kaon stops in the entrance window or side wall of the target. First test measurements on the Veto-2 system were performed. An average time resolution of (54 ± 2) ps and detection efficiencies of ~ 99 % were achieved.

Thermodynamical properties of strongly interacting matter in a model with explicit chiral symmetry breaking interactions

We analyse the effects of the light and strange current quark masses on the phase diagram of QCD at finite temperature and vanishing baryonic chemical potential, computing the speed of sound, the trace anomaly of the energy momentum tensor and the fluctuations and correlations of the conserved charges associated to baryonic, electric and strangeness numbers. The framework is a known extension of the three flavor Nambu Jona Lasinio model, which includes the full set of explicit chiral symmetry breaking interactions (ESB) up to the same order in large $N_c$ counting as the 't Hooft flavor mixing terms and eight quark interactions. It is shown that the ESB terms are relevant for the description of a soft region in the system's speed of sound and overall slope behavior of the observables computed. At the same time the role of the 8q interactions gets highlighted. The model extension with the Polyakov loop is considered and the results are compared to lattice QCD data.

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.

Lattice Supersymmetry and Order-Disorder Coexistence in the Tricritical Ising Model.

We introduce and analyze a quantum spin or Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the scaling limit but also manifests itself on the lattice. Namely, we find explicit lattice expressions for the supersymmetry generators and currents. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. These confirm the coexistence between two (topologically) ordered ground states and a disordered one in the gapped phase. Deforming the model by including explicit chiral symmetry breaking, we find the phases persist up to an unusual chiral phase transition where the supersymmetry becomes exact even on the lattice.

A New Silicon Drift Detector For Kaonic Deuterium Measurements: On behalf of the E57 collaboration at J-PARC

The interaction of antikaons with nucleons and nuclei in the lowenergy regime is a very active research field in hadron physics. Specially, the antikaon-nucleon interaction close to threshold provides crucial information on the interplay between spontaneous and explicit chiral symmetry breaking in low-energy QCD and touching one of the fundamental problems in hadron physic today - the still unsolved question of how hadron masses are generated. To study this problem, we have developed a new X–ray detector system and constructed an experimental apparatus to measure the kaonic deuterium 1s ground state shift and width with an accuracy of 60 eV and 140 eV, respectively.

Linear sigma model for multiflavor gauge theories

We consider a linear sigma model describing $2N_f^2$ bosons ($\sigma$, ${\bf a_0}$, $\eta '$ and ${\bf \pi}$) as an approximate effective theory for a $SU(3)$ local gauge theory with $N_f$ Dirac fermions in the fundamental representation. The model has a renormalizable $U(N_f)_L\bigotimes U(N_f)_R$ invariant part, which has an approximate $O(2N_f^2)$ symmetry, and two additional terms, one describing the effects of a $SU(N_f)_V$ invariant mass term and the other the effects of the axial anomaly. We calculate the spectrum for arbitrary $N_f$. Using preliminary and published lattice results from the LatKMI collaboration, we found combinations of the masses that vary slowly with the explicit chiral symmetry breaking and $N_f$. This suggests that the anomaly term plays a leading role in the mass spectrum and that simple formulas such as $M_\sigma^2\simeq (2/N_f-C_\sigma)M_{\eta '}^2$ should apply in the chiral limit. Lattice measurements of $M_{\eta '}^2$ and of approximate constants such as $C_\sigma$ could help locating the boundary of the conformal window. We show that our calculation can be adapted for arbitrary representations of the gauge group and in particular to the minimal model with two sextets, where similar patterns are likely to apply.

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.

Spin 1 Low-lying Meson Spectra and the Subtle Link to the Spin 0 Mesons

An NJL-type three-flavor quark model with a complete set of explicit chiral symmetry breaking terms is extended to include vector and axial vector effective interaction terms. The bosonized Lagrangian is written up to quadratic order in the bosonic fields and the role of the new interactions is analysed in detail. The model's parameters are fitted to yield reasonable values to the four low-lying spin 0 and spin 1 meson nonets' masses.

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 $g_A = 1.248 \pm 0.010 \pm \ 0.007 \pm 0.013$.