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Chiral Symmetry Breaking and Chiral Polarization: Tests for Finite Temperature and Many Flavors  [PDF]
Andrei Alexandru,Ivan Horváth
Physics , 2014, DOI: 10.1016/j.nuclphysb.2014.11.018
Abstract: It was recently conjectured that, in SU(3) gauge theories with fundamental quarks, valence spontaneous chiral symmetry breaking is equivalent to condensation of local dynamical chirality and appearance of chiral polarization scale $\Lambda_{ch}$. Here we consider more general association involving the low-energy layer of chirally polarized modes which, in addition to its width ($\Lambda_{ch}$), is also characterized by volume density of participating modes ($\Omega$) and the volume density of total chirality ($\Omega_{ch}$). Few possible forms of the correspondence are discussed, paying particular attention to singular cases where $\Omega$ emerges as the most versatile characteristic. The notion of finite-volume "order parameter", capturing the nature of these connections, is proposed. We study the effects of temperature (in N$_f$=0 QCD) and light quarks (in N$_f$=12), both in the regime of possible symmetry restoration, and find agreement with these ideas. In N$_f$=0 QCD, results from several volumes indicate that, at the lattice cutoff studied, the deconfinement temperature $T_c$ is strictly smaller than the overlap-valence chiral transition temperature $T_{ch}$ in real Polyakov line vacuum. Somewhat similar intermediate phase (in quark mass) is also seen in N$_f$=12. It is suggested that deconfinement in N$_f$=0 is related to indefinite convexity of absolute X-distributions.
Estimates for parameters and characteristics of the confining SU(3)-gluonic field in charged pions and kaons from leptonic decays and chiral symmetry breaking
Goncharov, Yu. P.
High Energy Physics - Phenomenology , 2008, DOI: 10.1016/j.nuclphysa.2008.08.012
Abstract: The confinement mechanism proposed earlier by the author is employed for to compute the decay constants $f_P$ corresponding to leptonic decays $P\to l^\pm+\nu_l$, $l=\mu, e$, where $P$ stands for any meson from $\pi^\pm$, $K^\pm$. For this aim the weak axial form factor of $P$-meson is nonperturbatively calculated. The study entails estimates for parameters of the confining SU(3)-gluonic field in charged pions and kaons. The corresponding estimates of the gluon concentrations, electric and magnetic colour field strengths are also adduced for the mentioned field at the scales of the mesons under consideration. Further the obtained results are applied to the problem of chiral symmetry breaking in quantum chromodynamics (QCD). It is shown that in chirally symmetric world masses of pions and kaons are fully determined by the confining SU(3)-gluonic field among (massless) $u$, $d$ and $s$ quarks and not equal to zero. Accordingly chiral symmetry is sufficiently rough approximate one holding true only when neglecting the mentioned SU(3)-gluonic field between quarks and no additional mechanism of the spontaneous chiral symmetry breaking connected to the so-called Goldstone bosons is required. Finally, a possible relation of the results obtained with a phenomenological string-like picture of confinement is discussed too.
Opening Remarks at Chiral Dynamics 2006:Experimental Tests of Chiral Symmetry Breaking
Bernstein, A. M.
High Energy Physics - Phenomenology , 2007,
Abstract: A physical introduction to the basics of chiral dynamics is presented. Emphasis is placed on experimental tests which have generally demonstrated a strong confirmation of the predictions of chiral perturbation theory, a low energy effective field theory of QCD. Special attention is paid to a few cases where discrepancies exist, requiring further work. Some desirable future tests are also recommended.
Excess of pions with chiral symmetry restoration  [PDF]
Chungsik Song,Volker Koch
Physics , 1997, DOI: 10.1016/S0370-2693(97)00575-3
Abstract: We study the effect of the chiral phase transition on pion production in hot hadronic matter. The phase of restored chiral symmetry is characterized by the appearance of the scalar $\sigma$-meson as a chiral partner of the pion as well as by the degeneracy of the vector and axial-vector mesons. We find rapid thermal and chemical equilibration of these degrees of freedom in the symmetric phase. Provided that the chiral transition temperature is not considerably high, the presence of a chirally symmetric phase will result in $\sim 1.6$ times more thermal pions in the final state.
Strangeness and Chiral Symmetry Breaking  [PDF]
Harleen Dahiya,Neetika Sharma
Physics , 2010, DOI: 10.1142/S0217732311034785
Abstract: The implications of chiral symmetry breaking and SU(3) symmetry breaking have been studied in the chiral constituent quark model ($\chi$CQM). 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 $\chi$CQM 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.
QCD in Infrared Region and Spontaneous Breaking of the Chiral Symmetry  [PDF]
Mirzayusuf Musakhanov
Physics , 2012,
Abstract: The spontaneous breaking of chiral symmetry (SBCS) is one of the most important phenomena of hadron physics. It defines the properties of all the light mesons and baryons. The Chiral Perturbation Theory (ChPT) encodes QCD hadronic correlators at low-energy region in the terms the low-energy constants (LEC) -- the expansion parameters on light quark current masses $m$ and external momenta $p$. The LEC's can be extracted from the phenomenology or from QCD lattice calculations. On the other hand, QCD instanton vacuum/instanton liquid model provides a very natural nonperturbative explanation of the SBCS. It provides a consistent framework for description of the pions and thus may be used for evaluation of the LEC. Our aim is to calculate the vacuum properties and the LEC's within instanton vacuum model and confront with phenomenology and lattice results.
Chiral Symmetry Breaking in QCD  [PDF]
Yu. A. Simonov
Physics , 2004,
Abstract: Chiral Symmetry Breaking (CSB) is derived in QCD starting from the QCD Lagrangian and using Field Correlators Method (FCM). The kernel in the resulting equations responsible for CSB is directly connected to confinement, and therefore both phenomena occur and vanish together as supported by lattice data. Chiral Lagrangian and quark-meson Lagrangian are derived with explicit coefficients and compared to standard expressions. Spectrum of Nambu-Goldstone mesons and their radial excitations is calculated in good agreement with experiment.
Chiral symmetry breaking and monopoles  [PDF]
Adriano Di Giacomo,Masayasu Hasegawa,Fabrizio Pucci
Physics , 2015,
Abstract: To understand the relation between the chiral symmetry breaking and monopoles, the chiral condensate which is the order parameter of the chiral symmetry breaking is calculated in the $\overline{\mbox{MS}}$ scheme at 2 [GeV]. First, we add one pair of monopoles, varying the monopole charges $m_{c}$ from zero to four, to SU(3) quenched configurations by a monopole creation operator. The low-lying eigenvalues of the Overlap Dirac operator are computed from the gauge links of the normal configurations and the configurations with additional monopoles. Next, we compare the distributions of the nearest-neighbor spacing of the low-lying eigenvalues with the prediction of the random matrix theory. The low-lying eigenvalues not depending on the scale parameter $\Sigma$ are compared to the prediction of the random matrix theory. The results show the consistency with the random matrix theory. Thus, the additional monopoles do not affect the low-lying eigenvalues. Moreover, we discover that the additional monopoles increase the scale parameter $\Sigma$. We then evaluate the chiral condensate in the $\overline{\mbox{MS}}$ scheme at 2 [GeV] from the scale parameter $\Sigma$ and the renormalization constant $Z_{S}$. The final results clearly show that the chiral condensate linearly decreases by increasing the monopole charges.
Chiral Symmetry Breaking by Instantons  [PDF]
Dmitri Diakonov
Physics , 1996,
Abstract: This is a review of the QCD instanton vacuum. After introducing instantons and their physical meaning, I show that the number of instantons in the vacuum fluctuates in accordance with the QCD trace anomaly. The main properties of the instanton ensemble are given. Chiral symmetry breaking by instantons is explained in three different though mathematically equivalent ways. In particular, a derivation of the Nambu--Jona-Lasinio-type model from instantons is presented, and the effective chiral lagrangian to which QCD is reduced at low momenta, is given. I end up by discussing possible confinement mechanisms.
Chiral Symmetry Breaking in Graphene  [PDF]
Gordon W. Semenoff
Physics , 2011, DOI: 10.1088/0031-8949/2012/T146/014016
Abstract: The question of whether the Coulomb interaction is strong enough to break the sublattice symmetry of un-doped graphene is discussed. We formulate a strong coupling expansion where the ground state of the Coulomb Hamiltonian is found exactly and the kinetic hopping Hamiltonian is treated as a perturbation. We argue that many of the properties of the resulting system would be shared by graphene with a Hubbard model interaction. In particular, the best candidate sublattice symmetry breaking ground state is an antiferromagnetic Mott insulator. We discuss the results of some numerical simulations which indicate that the Coulomb interaction is indeed subcritical. We also point out the curious fact that, if the electron did not have spin degeneracy, the tendency to break chiral symmetry would be much greater and even relatively weak Coulomb interactions would likely gap the spectrum.
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