Narrow Results

The implications of chiral symmetry breaking and SU(3) symmetry breaking have been studied in the chiral constituent quark model (χCQM). The role of hidden strangeness component has been investigated for the scalar matrix elements of the nucleon with an emphasis on the meson–nucleon sigma terms. The χCQM is able to give a qualitative and quantitative description of the "quark sea" generation through chiral symmetry breaking. The significant contribution of the strangeness is consistent with the recent available experimental observations.

Phase structure of the (2 + 1)-dimensional model with four-fermion interaction of spin-½ quasiparticles (electrons) both in the fermion–antifermion (or chiral) and fermion–fermion (or superconducting) channels is considered at nonzero chemical potential μ and under the influence of an in-plane, i.e. parallel to a system sheet, external magnetic field B_‖. It is shown that at sufficiently large values of μ and/or B_‖ the Cooper pairing (or superconducting) phase appears in the system at arbitrary relation between coupling constants, provided that there is an (arbitrary small) attractive interaction in the superconducting channel. In particular, at sufficiently weak attractive interaction in the chiral channel, the Cooper pairing occurs even at infinitesimal values of μ and/or B_‖. The superconducting phase of the model is always a paramagnetic one.

We propose an alternative paradigm to the conjectured Miransky scaling potentially underlying the physics describing the transition from the conformally broken to the conformally restored phase when tuning certain parameters such as the number of flavors in gauge theories. According to the new paradigm the physical scale and henceforth also the massive spectrum of the theory jump at the lower boundary of the conformal window. In particular, we propose that a theory can suddenly jump from a Quantum Chromodynamics (QCD) type spectrum, at the lower boundary of the conformal window, to a conformal one without particle interpretation. The jumping scenario, therefore, does not support a near-conformal dynamics of walking type. We will argue that jumping dynamics can occur for relevant gauge theories such as super QCD and QCD. We will also discuss the impact of jumping dynamics on the construction of models of dynamical electroweak symmetry breaking.

We examine a toy model and a cascade effect for confinement and chiral symmetry breaking which consists in several phase transitions corresponding to the formation of bound states and chiral condensates with different number of fermions for a strong group. We analyze two examples: regular quantum chromodynamics (QCD) where we calculate the “four quark” vacuum condensate and a preon composite model based on QCD at higher scales. In this context, we also determine the number of flavors at which the second chiral and confinement phase transitions occur and discuss the consequences.

A few years ago, the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green’s functions of QCD, and called effective locality. This feature of QCD is non-perturbative as it results from a full integration of the gluonic degrees of freedom. In this paper, at eikonal and quenching approximation at least, the relation of effective locality to dynamical chiral symmetry breaking is examined.

The nucleon is naturally viewed as a bipartite system of valence spin — defined by its non-vanishing chiral charge — and non-valence or sea spin. The sea spin can be traced over to give a reduced density matrix, and it is shown that the resulting entanglement entropy acts as an order parameter of chiral symmetry breaking in the nucleon. In the large-$N_c$ limit, the entanglement entropy vanishes and the valence spin accounts for all of the nucleon spin, while in the limit of maximal entanglement entropy, the nucleon loses memory of the valence spin and consequently has spin dominated by the sea. The nucleon state vector in the chiral basis, fit to low-energy data, gives a valence spin content consistent with experiment and lattice QCD determinations, and has large entanglement entropy.

While it is clear that in some kinematic regime QCD can be described by an effective (as opposed to fundamental) string theory, it is not at all clear how this string theory should be. The "natural" candidate, the bosonic string, leads to amplitudes with the usual problems related to the existence of the tachyon, the absence of the adequate Adler zero, and massless vector particles, not to mention the conformal anomaly. The supersymmetric version does not really solve most of these problems. For a long time it has been believed that the solution of at least some of these difficulties is associated to a proper identification of the vacuum, but this program has remained elusive. We show in this work how the first three problems can be avoided, by using a sigma model approach where excitations above the correct (chirally noninvariant) QCD vacuum are identified. At the leading order in a derivative expansion we recover the nonlinear sigma model of pion interactions. At the next-to-leading order the O(p⁴) Lagrangian of Gasser and Leutwyler is obtained, with values for the coefficients that match the observed values. We also discuss some issues related to the conformal anomaly.

Quantum Chromodynamics (QCD) at long distances can be described by the chiral Lagrangian. On the other hand there is overwhelming evidence that QCD and all non-Abelian theories admit an effective string description. Here we review a derivation of the (intrinsic) parity-even chiral Lagrangian by requiring that the propagation of the QCD string takes place on a background where chiral symmetry is spontaneously broken. Requiring conformal invariance leads to the equation of motion of the chiral Lagrangian. We then proceed to coupling the string degrees of freedom to external gauge fields and we recover in this way the covariant equations of motion of the gauge-invariant chiral Lagrangian at . We consider next the parity-odd part (Wess–Zumino–Witten) action and argue that this requires the introduction of the spin degrees of freedom (absent in the usual effective action treatment). We manage to reproduce the Wess–Zumino–Witten term in two dimensions (2D) in an unambiguous way. In 4D the situation is considerably more involved. We outline the modification of boundary interaction that is necessary to induce the parity-odd part of the chiral Lagrangian.

We apply Bogolubov approach to QCD with two light quarks to demonstrate a spontaneous generation of an effective interaction, leading to the Nambu–Jona-Lasinio model. The resulting theory contains two parameters: average low-energy value of α_s and current light quark mass m₀. All other low-energy parameters: the pion decay constant, mass of the π-meson, mass of the σ-meson and its width, the constituent quark mass, and the quark condensate are expressed in terms of the two input parameters in satisfactory correspondence to experimental data and chiral phenomenology. For example, in the approximation being used we have for α_s = 0.67 and m₀ = 20 MeV: f_π = 93 MeV, m_π = 135 MeV, m_σ = 492 MeV, Γ_σ = 574 MeV, m_q = 295 MeV, .

The research activity in the field of hadronic atoms performed at Laboratori Nazionali di Frascati by an International Collaboration is reviewed. The results already obtained for Kaonic Hydrogen are presented and the future programs are discussed.

With precision X-ray spectroscopy of kaonic hydrogen at the DAΦNE electron-positron collider at Laboratori Nazionali di Frascati the chiral symmetry breaking scenario in the strangeness sector will be investigated by studying the K^-p s-wave interaction at threshold. This is possible by observing the strong interaction induced shift and width of the 1s state in kaonic hydrogen atoms. The results of the first measurement at LNF with DEAR (DAΦNE Exotic Atom Research) will be given and the new SIDDHARTA (Silicon Drift Detector for Hadronic Atom Research with Timing Application) project will be described, which is aiming at a substantial improvement of the preceding DEAR result.

It is well known that chiral symmetry breaking (χSB) in QCD with N_f = 2 light quark flavors can be described by orthogonal groups as O(4) → O(3), due to local isomorphisms. Here we discuss the question how specific this property is. We consider generalized forms of χSB involving an arbitrary number of light flavors of continuum or lattice fermions, in various representations. We search systematically for isomorphic descriptions by nonunitary, compact Lie groups. It turns out that there are a few alternative options in terms of orthogonal groups, while we did not find any description entirely based on symplectic or exceptional Lie groups. If we adapt such an alternative as the symmetry breaking pattern for a generalized Higgs mechanism, we may consider a Higgs particle composed of bound fermions and trace back the mass generation to χSB. In fact, some of the patterns that we encounter appear in technicolor models. In particular if one observes a Higgs mechanism that can be expressed in terms of orthogonal groups, we specify in which cases it could also represent some kind of χSB of techniquarks.

The properties of two-flavored massless Nambu–Jona-Lasinio (NJL) model in (1+1)-dimensional R¹ × S¹ space–time with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials μ_I, μ. The consideration is performed in the large N_c limit, where N_c is the number of colored quarks. It is shown that at L = ∞ (L is the length of the circumference S¹) the charged pion condensation (PC) phase with zero quark number density is realized at arbitrary nonzero μ_I and for rather small values of μ. However, at arbitrary finite values of L the phase portrait of the model contains the charged PC phase with nonzero quark number density (in the case of periodic boundary conditions for quark fields). Hence, finite sizes of the system can serve as a factor promoting the appearance of the charged PC phase in quark matter with nonzero baryon densities. In contrast, the phase with chiral symmetry breaking may exist only at rather large values of L.

We study the nontrivial solutions of the Quantum Chromodynamics (QCD) fermionic gap equation (FGE) including the contribution of dynamically massive gluons and the confining propagator proposed by Cornwall. Without the confining propagator, in the case of nonrunning gluon mass (m_g), we found the multivacuum solutions (replicas) reported in the literature and we were able to define limits on m_g for dynamical chiral symmetry breaking (CSB). On the other side, when considering the running in the gluon mass the vacuum replicas are absent in the limits on m_g where the chiral symmetry is broken. In the pure confining sector, the multivacuum states are always absent so it is said that only one stable solution for the gap equation is found as claimed in previous analysis using different approaches. Finally, in the case of the complete gap equation i.e. with both contributions, the vacuum replicas are also absent in both cases; with constant and with running gluon mass.

We study the phase diagram of an $SU(N)$ gauge theory in terms of the number of colors $N$ and flavors $N_f$ with emphasis on the confinement and chiral symmetry breaking phases. We argue that as opposed to SUSY QCD there is a small region in the $(N,N_f)$ plane where the theory has the chiral symmetry broken but it is unconfined. The possibility of a new phase with strong confinement and chiral symmetry breaking is suggested.

We propose a Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies in the context of composite Higgs bosons. Standard model fermions are represented by algebraic spinors of six-dimensional binary Clifford algebra, while ternary Clifford algebra-related flavor projection operators control allowable flavor-mixing interactions. There are three composite electroweak Higgs bosons resulted from top quark, tau neutrino, and tau lepton condensations. Each of the three condensations gives rise to masses of four different fermions. The fermion mass hierarchies within these three groups are determined by four-fermion condensations, which break two global chiral symmetries. The four-fermion condensations induce axion-like pseudo-Nambu–Goldstone bosons and can be dark matter candidates. In addition to the 125 GeV Higgs boson observed at the Large Hadron Collider, we anticipate detection of tau neutrino composite Higgs boson via the charm quark decay channel.

The near-zero modes of the Dirac operator are connected to spontaneous breaking of chiral symmetry in QCD (SBCS) via the Banks–Casher relation. At the same time, the distribution of the near-zero modes is well described by the Random Matrix Theory (RMT) with the Gaussian Unitary Ensemble (GUE). Then, it has become a standard lore that a randomness, as observed through distributions of the near-zero modes of the Dirac operator, is a consequence of SBCS. The higher-lying modes of the Dirac operator are not affected by SBCS and are sensitive to confinement physics and related $SU{(2)}_{\mathrm{\text{CS}}}$ and $SU(2N_F)$ symmetries. We study the distribution of the near-zero and higher-lying eigenmodes of the overlap Dirac operator within $N_F=2$ dynamical simulations. We find that both the distributions of the near-zero and higher-lying modes are perfectly described by GUE of RMT. This means that randomness, while consistent with SBCS, is not a consequence of SBCS and is linked to the confining chromo-electric field.

We study the hydrodynamics of the nuclear matter of two flavors of light quarks with spontaneous chiral symmetry breaking based on the Poisson bracket method. The effects of mass are included and the full hydrodynamic equation for pions is given. The in-medium dispersion relation of pions in the neutron rich background state and the possibility of the phase transition to pion condensation are also discussed.

Paradigm shift in gauge topology, from instantons to their constituents — instanton-dyons — has recently lead to very significant advances. Unlike instantons, these objects have three different set of charges, therefore allowing to explain and to tie together several important phenomena: confinement, chiral symmetry breaking and magnetic screening.

A possibility of a pseudovector-type quark–antiquark condensed phase, which leads to a quark spin polarized phase, in the quark matter is investigated taking account of the vacuum effects leading to the chiral symmetry breaking by using the Nambu–Jona–Lasinio model. Also, possible Nambu–Goldstone modes on the pseudovector-type quark–antiquark condensate and the tensor-type quark–antiquark condensate, which also leads to the quark spin polarized phase, are investigated.