Chiral Symmetry Breaking Condensates Research Articles

Influence of vector interactions on the favored shape of inhomogeneous chiral condensates

We update a previous study of the effects of vector interactions in the Nambu--Jona-Lasinio model on the formation of inhomogeneous chiral symmetry breaking condensates. In particular, by properly considering a spatially modulated vector mean-field associated with the quark number density of the system we show that, as the value of the vector coupling increases, a chiral density wave modulation can become thermodynamically favored over a real sinusoidal modulation. This behavior is found both via a Ginzburg-Landau analysis close to the Lifshitz point, as well as with a full numerical diagonalization of the mean-field Dirac Hamiltonian at vanishing temperature.

The impact of chirally odd condensates on the rho meson

Based on QCD sum rules we explore the consequences of a scenario for the ρ meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. This clean-cut scenario causes a lowering of the ρ spectral moment by about 120 MeV. The complementarity of mass shift and broadening is discussed. A simple parametrization of the ρ spectral function leads to a width of about 280 MeV if no shift of the peak position is assumed.

Generalized Weinberg Sum Rules in Deconstructed QCD

Recently, Son and Stephanov have considered an "open moose" as a possible dual model of a QCD-like theory of chiral symmetry breaking. In this note we demonstrate that although the Weinberg sum rules are satisfied in any such model, the relevant sums converge very slowly and in a manner unlike QCD. Further, we show that such a model satisfies a set of generalized sum rules. These sum rules can be understood by looking at the operator product expansion for the correlation function of chiral currents, and correspond to the absence of low-dimension gauge-invariant chiral symmetry breaking condensates. These results imply that, regardless of the couplings and F-constants chosen, the open moose is not the dual of any QCD-like theory of chiral symmetry breaking. We also show that the generalized sum rules can be "solved", leading to a compact expression for the difference of vector- and axial-current correlation functions. This expression allows for a simple formula for the S parameter (L_10), which implies that S is always positive and of order one in any (unitary) open linear moose model. Therefore the S parameter is positive and order one in any "Higgsless model" based on the continuum limit of a linear moose regardless of the warping or position-dependent gauge-coupling chosen.

Mapping the QCD phase diagram

The QCD vacuum in which we live, which has the familiar hadrons as its excitations, is but one phase of QCD, and far from the simplest one at that. One way to better understand this phase and the nonperturbative dynamics of QCD more generally is to study other phases and the transitions between phases. We are engaged in a voyage of exploration, mapping the QCD phase diagram as a function of temperature T and baryon number chemical potential μ. Because of asymptotic freedom, the high temperature and high baryon density phases of QCD are more simply and more appropriately described in terms of quarks and gluons as degrees of freedom, rather than hadrons. The chiral symmetry breaking condensate which characterizes the vacuum phase melts away. At high densities, quarks form Cooper pairs and new condensates develop. The formation of such superconducting phases [1–4] requires only weak attractive interactions; these phases may nevertheless break chiral symmetry [5] and have excitations which are indistinguishable from those in a confined phase [5–8]. These cold dense quark matter phases may arise in the centers of neutron stars; mapping this region of the phase diagram will require an interplay between theory and neutron star phenomenology. The goal of the experimental heavy ion physics program is to explore and map the higher temperature regions of the diagram. Recent theoretical developments suggest that a key qualitative feature, namely a critical point which in a sense defines the landscape to be mapped, may be within reach of discovery and analysis by the CERN SPS, if data is taken at several different energies [9,10]. The discovery of the critical point would in a stroke transform the map of the QCD phase diagram which we sketch below from one based only on reasonable inference from universality, lattice gauge theory and models into one with a solid experimental basis.

CHIRAL SYMMETRY BREAKING AS A CONSEQUENCE OF NONTRIVIAL SPATIAL TOPOLOGY

A singular configuration of external static magnetic field in the form of a pointlike vortex polarizes the vacuum of quantized massless spinor field in (2+1)-dimensional space–time. This results in an analogue of the Bohm–Aharonov effect: the chiral symmetry breaking condensate, energy density and current emerge in the vacuum even in the case when the spatial region of nonvanishing external field strength is excluded. The dependence of the vacuum characteristics both on the value of the vortex flux and on the choice of the boundary condition at the location of the vortex is determined.

The stability of the chiral vacuum

The gap equation for the chiral symmetry breaking condensate is analysed in Coulomb gauge, making an instantaneous approximation to the gluon interaction. In this approximation we may use a phenomenological potential for the interaction. By looking at the asymptotic behaviour of the gap function for confining and non-confining potentials at the expectation value of the hamiltonian between quasi-particle states in a linearised approximation, it is shown that the chiral vacuum is unstable for confining potentials and stable for non-confining potentials.

Chiral symmetry breaking condensates from baryonic sum rules

We analyse baryonic sum rules in order to determine chiral symmetry breaking condensates. We especially investigate the influence of the choice of the interpolating field and of the factorization hypothesis for the four quark condensate. Our results are consistent with those obtained from pseudoscalar sum rules and PCAC.

Generalizations of Dashen's formula in supersymmetric QCD

In supersymmetric QCD there are two formulae for the masses and the decay constans of pseudo-Goldstone bosons. The first one, the direct analogue of Dashen's formula, relates the “pion” mass-squared matrix to the quark-antiquark condensate, while the second one, recently obtained by Veneziano, relates the mass matrix to a chiral symmetry breaking condensate of squark fields. These formulae are established using superfield chiral Ward identities and special properties of a class of composite operators.