Quark-antiquark Condensates Research Articles

Hadronic Correlators at Finite Temperature

We consider here equal time point to point spatial correlation functions of hadronic currents at finite temperature, with respect to a structure of the QCD vacuum in terms of quark antiquark condensates. Using the temperature dependence of quark condensates from chiral perturbation theory for low temperatures and from results of lattice QCD simulations at temperatures near the critical temperature, we calculate the correlation functions in a hot medium. This analysis at finite temperature would be of relevance to the study of Quark Gluon Plasma (QGP).

Dynamical Higgs mechanism without elementary scalars: a lesson from instantons

The generation of gauge-dependent fermion vacuum condensates in Yang-Mills theory would dynamically break the gauge symmetry and thus provide an alternative to the Higgs mechanism in unified theories. We explore a simple example: instanton-induced quark pair (diquark) condensation in QCD with 2 flavors and N c colors. We do find diquark condensates in the vacuum, but only for N c = 2, where they are equivalent to the standard quark-antiquark condensate. At N c ≥ 3 diquark condensates exist as meta-stable saddle points of the instanton-induced effective QCD action and may strongly affect the properties of matter under extreme conditions. The scalar diquark excitation, which is a Goldstone boson at N c = 2, becomes unbound for N c ≥ 3.

The low energy ππ amplitude to one and two loops

The low-energy ππ amplitude is computed explicitly to two-loop accuracy in the chiral expansion. It depends only on six independent (combinations of) low-energy constants which are not fixed by chiral symmetry. Four of these constants are determined via sum rules which are evaluated using ππ scattering data at higher energies. Dependence of the low-energy phase shifts and of the threshold parameters on the remaining two constants (called α and (β) are discussed and compared to the existing data from K l4 experiments. Using generalized χPT, the constants α and β are related to fundamental QCD parameters such as the quark condensate 〈0∥ q − q∥0〉 and the quark mass ratio m s/ m ̂ . It is shown that forthcoming accurate low-energy ππ data can be used to provide, for the first time, experimental evidence in favour of or against the existence of a large quark-antiquark condensate in the QCD vacuum.

Chiral symmetry breaking and the pion wave function.

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 $\sigma$ mesons.

Finite temperature glueball-contributions in the framework of an extended nonlinear ?-model

We use an effective Lagrangian that implements aspects of chiral and conformal symmetry to compute the finite-temperature quark-antiquark condensate. The calculation is performed by means of the path integral approach, where we will take into account finite-temperature corrections up to the two loop-level by exploiting the real time formalism (RTF). To prove the validity of the RTF within the framework of the nonlinear σ-model we will first confirm the result for the finite-temperature quark condensate without glueball contributions and then will extend the computation by including a conformally extended Lagrangian density.

CHIRAL SYMMETRY BREAKING IN A PHENOMENOLOGICAL DESCRIPTION OF THE QCD VACUUM

Quark–antiquark condensation in the QCD groundstate is discussed in the framework of BCS theory. Adopting a phenomenological interaction between the quarks, the vacuum wavefunction is determined variationally. Taking these results, the properties of the vacuum and its excitations are determined. In addition the effect of instanton-type induced quark interactions is discussed.

A topological model for baryon production in jets

We present a conceptual model for baryon production in jets, inspired by the Skyrme picture of baryons as topological defects in a chiral quark-antiquark condensate. High energy collisions produce “hot” partons which split perturbatively into showers of “cool” partons which hadronize non-perturbatively. We visualize each ofthese as corresponding to a connected domain with a common orientation of the chiral condensate. Topological defects, namely baryons, are formed when there are mismatches in the orientations of adjacent field domains, rather as cosmic strings or monopoles are formed in the early Universe. Our model gives a good qualitative description of various salient features of baryon production in jets, which previously could be described only with a large number of free parameters. In particular, we give a qualitative explanation of the high baryon production rate in ɣ decays compared to the e +e − continuum. When combined with a perturbative QCD parton shower Monte Carlo it could become a basis for a fully-fledged fragmentation model.

Asymptotic constraint for chiral condensation of Coulomb gauge QCD

We study the3P0 quark-antiquark pair condensation in QCD, representing the gluon-interaction approximately by instantaneous Coulomb plus Breit potential. Particular attention is paid to non-uniqueness of the solution of the gap equation. The genuine dynamical solution can be characterized by a rapidly convergent behavior at large momentum, as was recognized in covariant formulations of Landau gauge. We impose the required behavior and make a numerical study of the chiral condensation.

A model for the chiral phase transition in QCD

We study the temperature dependence of chiral symmetry breaking in Coulomb gauge QCD with massless quarks and an instantaneous approximation for the gluon interaction. The latter is modelled with a simple temperature dependent running coupling constant, which takes into account the known theoretical constraints on the QCD gluon propagator. The ensuing gap equation for the quark-antiquark condensate is solved numerically. We find the predictions of the model to come out quite reasonably, considering the simplicity of our model interaction. The results strongly suggest that the chiral symmetry restoration transition is second order.

Quantum-field theory and the dynamical generation of quark masses

The dynamical generation of quark masses is discussed in terms of quark–antiquark, gluon–gluon, and quark–antiquark– gluon condensates. The quark–antiquark condensate is shown to contribute in a gauge-invariant manner to the dynamical quark mass. Arguments are put forward to suggest that the other condensates contribute only to the wave-function renormalization of the quark field and not to the magnitude of the dynamical quark mass.

Structure of axionic domain walls.

The structure of axionic domain walls is investigated using the low-energy effective theory of axions and pions. We derive the spatial dependence of the phases of the Peccei-Quinn scalar field and the QCD quark-antiquark condensates inside an axionic domain wall. Thence an accurate estimate of the wall surface energy density is obtained. The equations of motion for axions, photons, leptons, and baryons in the neighborhood of axionic domain walls are written down and estimates are given for the wall reflection and transmission coefficients of these particles. Finally, we discuss the energy dissipation by axionic domain walls oscillating in the early universe due to the reflection of particles in the primordial soup.

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.

Phase structure for one-plaquette lattice quantum chromodynamics with fermions in a1Ntopological expansion

A generalized $\frac{1}{N}$ expansion for a $\mathrm{U}({N}_{c})$ gauge theory with a global $\mathrm{U}({N}_{f})$ flavor symmetry is investigated in the limit of both ${N}_{c}$ and ${N}_{f}$ large with the ratio $\ensuremath{\zeta}\ensuremath{\equiv}\frac{{N}_{f}}{{N}_{c}}$ held fixed utilizing a large-$N$ semiclassical treatment. The phase diagram in this $\frac{1}{N}$ topological expansion limit is obtained exactly for a single-plaquette lattice system; novel phase structure is found due to quark-antiquark condensation.

Chiral symmetry breaking parameters from QCD sum rules

Abstract We obtain new QCD sum rules by considering vacuum expectation values of two-point functions, taking all the five quark bilinears into account. These sum rules are employed to extract values of different chiral symmetry breaking parameters in QCD theory. We find masses of light quarks, m = 1 2 (m u +m d ) = 8.4 ± 1.2 MeV , m s = 205 ± 65 MeV . Further, we obtain corrections to certain soft pion (kaon) PCAC relations and the violation of SU(3) flavour symmetry by the non-strange and strange quark-antiquark vacuum condensate.

Baryon sum rules and chiral symmetry breaking

In an SVZ-type approach sum rules for baryonic currents have been investigated, without radiative QCD corrections but with the inclusion of non-perturbative terms due to the non-vanishing vacuum expectation value of the quark-antiquark condensate. We give upper bounds for baryon masses, which allow a choice of optimal interpolating operators for low-lying baryon states. The results show that the mentioned vacuum expectation value not only sets the scale for parity splitting but also for the masses of the baryons directly. The alternative way of explicit symmetry breaking by quark masses has also been investigated in the same technical framework.

Alternative patterns of chiral symmetry breaking in QCD

We consider the particle spectrum that QCD with n flavors of massless quarks would have if a quark-quark condensate formed in the color triplet channel, rather than a quark-antiquark condensate in the color singlet channel. We find observable massless fermions which carry baryon number ±1. We also consider an arbitrary number of colors, and find similar results when the number of colors is odd. Our results always satisfy 't Hooft's anomaly constraints.

QCD sum rules for “baryonic currents”

By saturating QCD sum rules for “baryonic currents” with the low lying states we obtain relations between baryon masses and the vacuum expectation value of the quark-antiquark condensate.