We consider the thermodynamics of chiral models in the mean-field approximation and discuss the relevance of the (frequently omitted) fermion vacuum loop. Within the chiral quark-meson model and its Polyakov loop extended version, we show that the fermion vacuum fluctuations can change the order of the phase transition in the chiral limit and strongly influence physical observables. We compute the temperature-dependent effective potential and baryon number susceptibilities in these models, with and without the vacuum term, and explore the cutoff and the pion mass dependence of the susceptibilities. Finally, in the renormalized model the divergent vacuum contribution is removed using the dimensional regularization.
We study the effective chiral Lagrangian in the chiral limit from the instanton vacuum. Starting from the nonlocal effective chiral action, we derive the effective chiral Lagrangian, using the derivative expansion to order $O(p^4)$ in the chiral limit. The low energy constants, $L_1$, $L_2$, and $L_3$ are determined and compared with various models and the corresponding empirical data. The results are in a good agreement with the data. We also discuss about the upper limit of the sigma meson, based on the present results.
We study the effects of a finite quark mass in the hedgehog configuration in the two phase chiral bag model. We discuss the chiral properties, such as the fractional baryon number and the chiral Casimir energy, by using the Debye expansion for the analytical calculation and the Strutinsky's smearing method for the numerical computation. It is shown that the fractional baryon number carried by massive quarks in the vacuum is canceled by that in the meson sector. A finite term of the chiral Casimir energy is obtained with subtraction of the logarithmic divergence term.
We relate here the vacuum structure of chiral symmetry breaking to a wide class of low energy hadronic properties to examine consistency with experimental results. Phase transition of chiral symmetry breaking is described through explicit vacuum realignment. We find that for the present ansatz, vacuum structure of the light quark sector can be determined from $f_π=92$ MeV, which then yields that $Γ(π^0\rightarrow 2 γ)=8.3$ eV and, $R_{ch}=0.67$ fms, in agreement with experiments. This amounts to three independent `observations' of the vacuum structure of the light quark sector. For the calcula…
Basic chiral QCD parameters (the pion decay constant, the quark and gluon condensates, the dynamically generated quark mass, etc) as well as the vacuum energy density (up to the sign, by definition, the bag constant) have been calculated from first principles within a recently proposed zero modes enhancement (ZME) model of the true QCD vacuum. Our unique input data was chosen to be the pion decay constant in the chiral limit as given by the chiral perturbation theory at the hadronic level (CHPTh). In order to analyze our numerical results we set a scale by two different ways. In both cases we …
We discuss an interesting possibility of nontrivial, quark-mass induced chiral vacuum alignment in color-flavor locking phase of cold, dense QCD. With the simplifying assumption that the gaps for quarks are identical to those of antiquarks and the light quark masses are given by $m_u = m_d$ and $ m_s/m_d=15$, we find the true chiral vacuum can align only to one of the discrete number of directions in the continuum of chiral vacua. The alignment depends on the size of the diquark condensates, and the vacuum transitions between the discrete vacua caused by the evolution of the diquark condensate…
Using the effective potential approach for composite operators we have formulated the quantum model of the QCD vacuum. It is based on the existence and importance of the nonperturbative $q^{-4}$-type dynamical, topologically nontrivial excitations of the gluon field configuration. The QCD vacuum is found stable since the vacuum energy density has no imaginary part. Moreover, a possible ground (stationary) state of the nonperturbative Yang-Mills (quenched QCD) vacuum is discovered. The vacuum energy density at stationary state depends on a scale at which nonperturbative effects become important…
The topological susceptibility of QCD vacuum is studied in the framework of a covariant chiral quark model with non-local quark-quark interaction. The relation of the first moment of topological susceptibility χ'(0) and the 'spin crisis' problem is briefly discussed. It is shown, in particular, that one always gets the inequality χ'(0)>χ'_{OZI}.
We apply optimized perturbation theory to the quark-meson model at finite temperature T and quark chemical potential mu. The effective potential is calculated to one loop both in the chiral limit and at the physical point and used to study the chiral dynamics of two-flavor QCD. The critical temperature and the order of the phase transition depends heavily on whether or not one includes the bosonic and fermionic vacuum fluctuations in the effective potential. A full one-loop calculation in the chiral limit predicts a first-order transition for all values of mu. At the physical point, one finds …
In this talk it is discussed the derivation of low-frequencies part of quark determinant and partition function. As a first application, quark condensate is calculated beyond chiral limit with the account of O(m), O(1/N_c), O(1/N_c m) and O(1/N_c m ln m) corrections. It is demonstrated complete correspondence of the results to chiral perturbation theory.
In this talk, we report our present work on the chiral magnetic effect (CME) under a strong magnetic field at low temperature. To this end, we use the instanton vacuum with the finite instanton-number fluctuation Delta, which relates to the nontrivial topological charge Q_t. We compute the vacuum expectation values of the local chiral density <rho_chi>, chiral charge density <n_chi> and induced electromagnetic current <j_mu>. We observed that the longitudinal EM current is much larger than the transverse one, |j_perp/j_parallel| ~ Q_t, and the <n_chi> equals to the |<j_(3,4)>|. It also turns o…
We present in this talk a recent investigation on the magnetic susceptibility (chi) of the QCD vacuum at finite density, utilizing the nonlocal chiral quark model from the instanton vacuum. We take into account the nonzero current-quark mass (m_q) explicitly to consider the effect of explicit flavor SU(3) symmetry breaking. It turns out that, when we turn on the current-quark mass, chi becomes smaller, indicating less response to the externally induced electromagnetic field, in comparison to that for m_q=0.
Precise measurement of the $ππ$-phase shift $δ^0_0(E)$ at very low energies would provide, for the first time, the experimental evidence in favour of or against the existence of a large quark condensate in the QCD vacuum, which is standardly postulated as the mechanism of the spontaneous breakdown of chiral symmetry in QCD. The contribution of Da$ϕ$ne to this discovery could be decisive.
We present in this talk the recent investigation of the effective weak chiral Lagrangian within the framework of the instanton-induced chiral quark model. The low energy constants in leading order $g_8$ and $g_{27}$, and their ratio are determined. The momentum-dependence of the constituent quark mass turns out to improve the low energy constants to the great extent, respecting the $ΔT=1/2$ enhancement.
Using the trace anomaly relation, low-energy theorem and Witten-Veneziano formula, we have developed an analytical formalism which allows one to calculate the gluon condensate, the topological susceptibility and the mass of the $η'$ meson in the chiral limit as functions of the non-perturbative vacuum energy density. It is used for numerical evaluation of the chiral QCD topology within the QCD vacuum model consisting mainly of the quantum component given by the recently proposed zero modes enhancement (ZME) model and the classical component given by the the random instanton liquid model (RILM)…
We study the effective weak chiral Lagrangian within the framework of the instanton vacuum. We incorporate the $ΔS=1,2$ effective weak Hamiltonian into the effective low-energy QCD partition function defining the chiral symmetric quark-Goldstone boson interactions with the momentum-dependent dynamical quark mass. Employing the derivative expansion, we derive the corresponding weak effective Lagrangian in leading order with the low energy constants to be used e.g. in chiral perturbation theory. We find that the momentum-dependent dynamical quark mass plays an essential role in improving the low…
Previous work relating the flavour variation of the chiral order parameters $F_π$, $<\bar u u>$ and S-wave scattering data, based on chiral sum rules and chiral perturbation theory at order $p^4$, is extended to include $O(p^6)$ corrections. The finding of a significant decrease of these order parameters, particularly $<\bar u u>$, with the number of flavours increasing from $N_F=2$ to $N_F=3$ is confirmed, modulo an assumption on the convergence of the chiral expansion. The connection between scalar resonance physics and the phase structure of the chiral vacuum is also illustrated on the basi…
For one flavour, we observe that standard chiral random matrix models are schematic variants of the Nambu-Jona-Lasinio (NJL) models whether in vacuum or matter. The ensuing thermodynamics is that of constituent quarks, with mean-field universality in general. For two and three flavours non-standard chiral random matrix models with $U_A(1)$ breaking are suggested. For three flavours the transition is reminiscent of the isotropic-nematic transition in liquid crystals.
We investigate the leading-twist light-cone distribution amplitudes for the pion and kaon based on the gauge-invariant nonlocal chiral quark model from the instanton vacuum in the presence of external axial-vector currents. We find that the nonlocal contribution from the gauge invariance has much effects on the pion distribution amplitudes, while it changes mildly the kaon ones. We also study the Gegenbauer moments of the distribution amplitudes and compare them with the empirical analysis of the CLEO data.
The formulas for the temperature dependences of the non-strange and strange quark condensates are derived by taking into account the contribution of the massive resonances. Critical temperature of the chiral symmetry restoration transition is established to be 190 MeV if only meson resonances are considered, and 175 MeV if both meson and baryon resonances are taken into account.
The QCD + QED axial anomaly low-energy theorems are applied to estimate the accuracy of an instanton vacuum - based chiral quark model. The low-energy theorems give an exact relation between the matrix elements of the gluon and photon parts of the QCD + QED axial anomaly operator equation. The matrix elements between vacuum and two photon states and between vacuum and two gluon states are calculated for arbitrary N_f. It is shown that this model does satisfy the low-energy theorems with an accuracy of $\sim 17%$. We estimate also the contribution of the nonperturbative conversion of gluons int…
We study the expansion dynamics of a quark-antiquark plasma droplet from an initial state with restored chiral symmetry. The calculations are made within the linear $σ$ model scaled with an additional scalar field representing the gluon condensate. We solve numerically the classical equations of motion for the meson fields coupled to the fluid-dynamical equations for the plasma. Strong space-time oscillations of the meson fields are observed in the course of the chiral transition. A new phenomenon, the formation and collapse of vacuum bubbles, is also predicted. The particle production due to …
We discuss how the inclusion of singular gauge fields in the partition function for QCD can lead to a domain-like picture for the QCD vacuum by virtue of specific conditions on quantum fluctuations at the singularities. With a simplified model of hyperspherical domain regions with interiors of constant field strength we calculate the basic parameters of the QCD vacuum, the gluon condensate, topological susceptibility, string constant and quark condensate, and briefly discuss confinement of dynamical quarks and gluons.
We discuss the influence of fluctuations on thermodynamics near the chiral phase transition within Polyakov loop extended quark--meson model based on the functional renormalization group (FRG) method. We include the gluon fields in the FRG flow equation self-consistently on the mean-field level. We focus on the properties of the phase diagram and net-baryon number fluctuations.
Using effective potential approach for composite operators we have formulated quantum model of the QCD vacuum. It is based on the existence and importance of the nonperturbative $q^{-4}$, topologically nontrivial excitations of the gluon field configurations there. As a result of this the QCD vacuum is found stable and it has a stationary state. The value of the scale reponsible for the nonperturbative dynamics is taken from the bounds for the pion decay constant in the chiral limit. We have obtained good numerical agreement with the phenomenological values of the topological susceptibility, t…
The mesonic quantum fluctuations and their corrections on the chiral condensate and pion polarization function are investigated in the self-consistent scheme of SU(2) Nambu-Jona-Lasinio model by exactly calculating the next-to-leading order (NLO) Feynman diagrams in $1/N_c$ expansion. While the fluctuations and corrections depend strongly on the meson's three-momentum cut-off $Λ_M$, no chiral symmetry restoration is found since the cancellation between the NLO and the one-quark-loop diagram with quark mass deviated from the mean-field value.
Confining configurations are introduced into the standard instanton vacuum model. This drastically improves theoretical properties of the vacuum: instanton size density $d(ρ)$ stabilizes at $ρ\sim 0.2 fm$, all chiral effects are formulated in a gauge-invariant way and quarks are confined. An interesting interplay of chiral and confining dynamics is observed; for the realistic values of parameters the Georgi-Manohar picture emerges with chiral radius $R_{ch}\sim ρ\sim 0.2 fm$ much less than confining radius $R_c\sim$ hadron radius $\sim 1 fm$. In the limit $R_{ch}\ll R_c$ the chiral mass $M_{ch…
The entanglement extended Polyakov--Nambu--Jona-Lasinio model at zero chemical potential in the presence of an external magnetic field is studied. The effect of the entanglement parametrization is analyzed, in particular, on the pseudocritical transition temperatures and on the thermodynamical properties of the model. The model predicts that the coincidence or not of both chiral and deconfinement transition temperatures, in the presence of an external magnetic field, depends on the entanglement parametrization chosen.
We investigate the chiral phase transition in the quark-meson effective model using optimised perturbation theory to one loop. Certain terms in the free energy are frequently omitted in calculations, on the assumption that their contribution is negligible. We show that this is not necessarily the case, and that the order of the phase transition, as well as the critical temperature, depends heavily on which contributions are included.
In this paper the spectrum of quark-antiquark systems, including light mesons and tachyons, is studied in the true vacuum and in the chiral invariant vacuum. The mass gap equation for the vacua and the Salpeter-RPA equation for the mesons are solved for a simple chiral invariant and confining quark model. At T=0 and in the true vacuum, the scalar and pseudoscalar, or the vector and axial vector are not degenerate, and in the chiral limit, the pseudoscalar groundstates are Goldstone bosons. At T=0 the chiral invariant vacuum is an unstable vacuum, decaying through an infinite number of scalar a…
In the framework of the instanton vacuum model we make expansion over the current mass $m$ and number of colors $N_c$ and evaluate ${\cal O}(1/N_c, m, m/N_c, m \ln m/N_c)$-corrections to the dynamical quark mass $M$, the quark condensate $<\bar qq>$, the pion mass $M_π$ and decay constant $F_π$. We found the SU(2) $χ$PT low-energy constants $\bar l_3, \bar l_4$ in a good correspondence with the phenomenology and lattice calculations.
Employing an extended three flavor version of the NJL model we discuss in detail the phase diagram of quark matter. The presence of quark as well as of diquark condensates gives raise to a rich structure of the phase diagram. We study in detail the chiral phase transition and the color superconductivity as well as color flavor locking as a function of the temperature and chemical potentials of the system.
We analyze the lowest spectral moments of the left-right two-point correlation function, using all known short-distance constraints and the recently updated ALEPH V-A spectral function from tau decays. This information is used to determine the low-energy couplings L10 and C87 of chiral perturbation theory and the lowest-dimensional contributions to the Operator Product Expansion of the left-right correlator. A detailed statistical analysis is implemented to assess the theoretical uncertainties, including violations of quark-hadron duality.
Chiral symmetry undergoes a metamorphosis at $T_c$. For $T < T_c$, the usual Noether charge, $\Qa$, is dynamically broken by the vacuum. Above $T_c$, chiral symmetry undergoes a subtle change, and the Noether charge \underline{\em morphs} into $\Qbeta$, with the thermal vacuum now becoming invariant under $\Qbeta$. This vacuum is however not invariant under the old $\Qa$ transformations. As a result, the pion remains strictly massless at high $T$. The pion propagates in the early universe with a halo. New order parameters are proposed to probe the structure of the new thermal vacuum.
A metastable phase has important physical implications, since it may form vacuum bubbles detectable experimentally, whereas an unstable vacuum instantly explodes. It is well known, due to chiral symmetry breaking, there are at least two very different QCD vacua. At T=0 and in the true vacuum, the scalar and pseudoscalar, or the vector and axial vector are not degenerate, and in the chiral limit, the pseudoscalar ground states are Goldstone bosons. At T=0 the chiral invariant vacuum is an unstable vacuum, decaying through an infinite number of scalar and pseudoscalar tachyons. Moreover QCD vacu…
We consider here chiral symmetry breaking through nontrivial vacuum structure with quark antiquark condensates. We then relate the condensate function to the wave function of pion as a Goldstone mode. This simultaneously yields the pion also as a quark antiquark bound state as a localised zero mode in vacuum. We illustrate the above with Nambu Jona-Lasinio model to calculate different pionic properties in terms of the vacuum structure for breaking of exact or approximate chiral symmetry, as well as the condensate fluctuations giving rise to $σ$ mesons.
We study the QCD vacuum orientation angles in correlation with the strong CP phases. A vacuum alignment equation of the dynamical chiral symmetry breaking is derived based on the anomalous Ward identity. It is emphasized that a chiral rotation of the quark field causes a change of the vacuum orientation and a change in the definition of the light pseudoscalar generators. As an illustration of the idea, $\h\rightarrow 2\p$ decays are carefully studied in different chiral frames. Contrary to the claim in Ref.[7], the $θ$-term does not directly contribute to the CP-violating processes.
I consider parity violation of the chiral symmetry broken vacuum. It is shown that the parity of the true vacuum in the chiral symmetry breaking model is violated. I propose new mechanism of massive neutrino, which the neutrinos have mass in terms of the chiral symmetry breaking. In this mechanism, it may give us new understanding why almost neutrinos have left chirality. Further, NJL model is proposed as alternative phenomenological model of neutrinos.
Using the trace anomaly and low energy relations, as well as the Witten-Veneziano formula for the mass of the $η'$ meson, we have developed a formalism which makes it possible to express the gluon condensate, the topological susceptibility and the mass of the $η'$ meson as a functions of the truly nonperturbative vacuum energy density which is one of the most important characteristics of the QCD true ground state. It was directly applied to the numerical evaluation of the chiral QCD vacuum topological structure within its quantum zero momentum modes enhancement model. A rather good agreement w…
We investigate chiral symmetry breaking in strong magnetic fields at finite temperature and densities in a 3 flavor Nambu Jona Lasinio (NJL) model including the Kobayashi Maskawa t-Hooft (KMT) determinant term, using an explicit structure for the ground state in terms of quark antiquark condensates. The mass gap equations are solved self consistently and are used to compute the thermodynamic potential. We also derive the equation of state for strange quark matter in the presence of strong magnetic fields which could be relevant for proto-neutron stars. ~
We consider chiral symmetry breaking through nontrivial vacuum structure with an explicit construct for the vacuum with quark antiquark condensates in QCD with Coulomb gauge for different phenomenological potentials. The dimensional parameter for the condensate function gets related to $<{\bar ψ}ψ>$ of Shifman, Vainshtein and Zakharov. We then relate the condensate function to the wave function of pion as a Goldstone mode. This simultaneously yields the pion also as a quark antiquark bound state as a localised zero mode of vacuum. We then calculate different pionic properties using the wave fu…
A qualitative mechanism for the emergence of domain structured background gluon fields due to singularities in gauge field configurations is considered, and a model displaying a type of mean field approximation to the QCD partition function based on this mechanism is formulated. Estimation of the vacuum parameters (gluon condensate, topological susceptibility, string constant and quark condensate) indicates that domain-like structures lead to an area law for the Wilson loop, nonzero topological susceptibility and spontaneous breakdown of chiral symmetry. Gluon and ghost propagators in the pres…
A short review is presented of the spontaneous violation of chiral symmetry in QCD vacuum. It is demonstrated, that this phenomenon is the origin of baryon masses in QCD. The value of nucleon mass is calculated as well as the masses of hyperons and some baryonic resonances and expressed mainly through the values of quark condensates -- $<0\mid \bar{q} q \mid 0>, ~q=u,d,s$ -- the vacuum expectation values (v.e.v.) of quark field. The concept of vacuum expectation values induced by external fields is introduced. It is demonstrated that such v.e.v. induced by static electromagnetic field results …
We show how a scheme of rewriting a divergent momentum integral can conciliate results obtained with the Nambu--Jona-Lasinio model and recent lattice results for the chiral transition in the presence of a chiral imbalance in quark matter. Purely vacuum contributions are separated from medium-dependent regularized momentum integrals in such a way that one is left with ultraviolet divergent momentum integrals that depend on vacuum quantities only. The scheme is applicable to other commonly used effective models to study quark matter with a chiral imbalance, it allows us to identify the source of…
A model for the QCD vacuum based on domain-like background gluon fields has previously been developed and demonstrated to exhibit confinement of quarks and strong correlation of the local chirality of quark modes and duality of the background gluon field. On the boundary of the j-th domain, quark fluctuations satisfy chirality violating boundary conditions parametrized by a chiral angle $α_j$ which is treated as a collective variable. The dependence of the free energy of an ensemble of $N\to\infty$ domains on $\{α_j, j=1... N\}$ is studied. For one massless flavour there are only two degenerat…
In a series of articles it was recently claimed that the quantum chromodynamic (QCD) condensates are not the properties of the vacuum but of the hadrons and are confined inside them. We point out that this claim is incompatible with the chiral Lagrangian and Bose-Einstein statistics of the Goldstone bosons (pions) in chiral limit and conclude that the quark condensate must be the property of the QCD vacuum.
We consider here chiral symmetry breaking in quantum chromodynamics arising from gluon condensates in vacuum. Through coherent states of gluons simulating a mean field type of approximation, we show that the off-shell gluon condensates of vacuum generate a mass-like contribution for the quarks, giving rise to chiral symmetry breaking. We next note that spontaneous breaking of global chiral symmetry links the four component quark field operator to the pion wave function. This in turn yields many hadronic properties in the light quark sector in agreement with experiments, leading to the conclusi…
The BP-FTW effective action is a good laboratory to study the nature of chiral symmetry at high $T$. It is invariant under a new Noether charge, $\Qbeta$. By explicit quantization, performed to order $\Tprime$ we show that the thermal vacuum is annihilated by $\Qbeta$, so that the new chiral symmetry is not broken spontaneously at high $T$. This high $T$ Noether charge is, however, different from the usual zero temperature chirality, $\Q$. Our quantization also shows that the thermal vacuum is not annihilated by $\Q$, so that the old chiral symmetry remains broken at high $T$. The thermal vacu…
In recent years, significant progress was reached in understanding of vacuum and hadronic structure. We review recent works on the {\it point-to-point correlation functions}, comparing those obtained from phenomenology, ``instanton liquid" models and on the lattice. The second topic is physics of chiral symmetry restoration, which may lead to observable hadron modification and unusual event-per-event fluctuations. We discuss collective flow and phenomena related with a remarkable ``softness" of the equation of state near the phase transition, as well as phenomena at small $p_t$. We also descri…
A new zero modes enhancement (ZME) model of the true QCD vacuum is breifly described. It makes possible to analytically investigate and calculate numerically low-energy QCD structure from first principles. Expressions of basic chiral QCD parameters (the pion decay constant, the quark and gluon condensates, the dynamically generated quark mass, etc) as well as the vacuum energy density (up to the sign, by definition, the bag constant), suitable for numerical calculations, have been derived. Solution to the Schwinger-Dyson (SD) equation for the quark propagator in the infrared (IR) domain on the…
The existence of a Goldstone boson is demonstrated in chiral random matrix theory. After determining the effective coupling and calculating the scalar and pseudoscalar propagators, a random phase approximation summation reveals the massless pion and massive sigma modes expected whenever chiral symmetry is spontaneously broken.
We present a $U(4)_R \times U(4)_L$ chirally symmetric model, which in addition to scalar and pseudoscalar mesons also includes vector and axial-vector mesons. A part from the three new parameters pertaining to the charm degree of freedom, the parameters of the model are fixed from the $N_f=3$ flavor sector. We calculate open charmed meson masses and the weak decay constants of nonstrange open charm $D$ and strange open charm $D_S$. We also evaluate the (OZI-dominant) strong decays of open charmed mesons. The results are turn out to be in quantitative agreement with experimental data.
The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial-vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in th…
We analyze the chiral symmetries of flavored quantum chromodynamics in two dimensions and show the existence of chiral condensates within the path-integral approach. The massless and massive cases are discussed as well, for arbitrary finite and infinite number of colors. Our results put forward the question of topological issues when matter is in the fundamental representation of the gauge group.
Due to its light mass of order Lambda_QCD, the strange quark can play a special role in Chiral Symmetry Breaking (ChSB): differences in the pattern of ChSB in the limits N_f=2 (m_u,m_d->0, m_s physical) and N_f=3 (m_u,m_d,m_s->0) may arise due to vacuum fluctuations of s-bar s pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p^4) low-energy constants L_4 and L_6. In case of large fluctuations, we show that the customary treatment of SU(3)xSU(3) chiral expansions generate instabilities upsetting their convergence. We develop a systematic …
We construct the grand partition function of the system of massive Dirac fermions in a uniform magnetic field from Landau levels, through which all thermodynamic quantities can be obtained. Making use of the Abel-Plana formula, these thermodynamic quantities can be expanded as power series with respect to the dimensionless variable $b=2eB/T^{2}$. The zero-field magnetic susceptibility is expanded at zero mass, and the leading order term is logarithmic. We also calculate scalar, vector current, axial vector current and energy-momentum tensor of the system through ensemble average approach. Mass…
Basic chiral QCD parameters (the pion decay constant, the quark and gluon condensates, the dynamically generated quark mass, etc) as well as the vacuum energy density have been calculated from first principles within a recently proposed dynamical equations approach to QCD at low energies. The zero modes enhancement (ZME) model of quark confinement and dynamical chiral symmetry breaking (DCSB) based on the solution to the Schwinger-Dyson (SD) equation for the quark propagator in the infrared (IR) domain was used for this purpose. There are only two independent quantities by means of which calcu…
An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral $SU_{\mathrm L}(N_f)\times SU_{\mathrm R}(N_f)$ and $U_{\mathrm A}(1)$ symmetries. Hadronization formalism based on this ensemble leads to manifestly defined quantum effective meson action. Strong, electromagnetic and weak interactions of mesons are represented in the action in terms of nonlocal …
The recent measurements of azimuthal single spin asymmetries by the HERMES collaboration has opened up new possibility to measure chiral-odd distribution functions through semi-inclusive deep-inelastic scatterings. Here, predictions are given for the twist-2 and twist-3 chiral-odd distribution functions of the nucleon within the framework of the chiral quark soliton model, with full inclusion of the vacuum polarization effects as well as the subleading $1/N_c$ corrections. The importance of the vacuum polarization effects is demonstrated by showing that the so-called Soffer inequality holds no…
The scalar susceptibility (chi_s) of QCD, which represents the response of the chiral condensate to a small perturbation of explicit chiral-symmetry breaking, is investigated within the nonlocal chiral quark model (NLchiQM) based on the instanton vacuum configuration for N_f = 2. We also take into account 1/N_c meson-loop (ML) corrections including scalar and pseudoscalar mesons. It turns out that the chiral condensate is modified to a large extend by the ML corrections in the vicinity of m = 0, whereas its effect becomes weak beyond m ~ 100 MeV. As numerical results, we find that chi_s = -0.3…
