Phenomenology of Large N c QCD

These lectures are designed to introduce the methods and results of large N _c QCD in a presentation intended for nuclear and particle physicists alike. Beginning with definitions and motivations of the approach, we demonstrate that all quark and gluon Feynman diagrams are organized into classes based on powers of 1/N _c. We then show that this result can be translated into definite statements about mesons and baryons containing arbitrary numbers of constituents. In the mesons, numerous well-known phenomenological properties follow as immediate consequences of simply counting powers of N _c, while for the baryons, quantitative large N _c analyses of masses and other properties are seen to agree with experiment, even when large N _c is set equal to its observed value of 3. Large N _c reasoning is also used to explain some simple features of nuclear interactions.     

Large N chiral dynamics

Some properties of large N chiral dynamics are discussed, using an effective Lagrangian that has been derived by Rosenzweig, Schechter, and Trahern; Di Vecchia and Veneziano; and Nath and Arnowitt.     

About the realization of chiral symmetry in QCD2

Two dimensional massless quantum chromodynamics presents many features which resemble those of the true theory. In particular the spectrum consists of mesons and baryons arranged in flavour multiplets without parity doubling. We analyze the implications of chiral symmetry, which is not spontaneously broken in two dimensions, in the spectrum and in the quark condensate. We study how parity doubling, an awaited consequence of Coleman's theorem, is avoided due to the dimensionality of space-time and confinement. We prove that a chiral phase transition is not possible in the theory.     

Tests of Large N(c) QCD from Hadronic tau Decay

We use the ALEPH Collaboration data on vector and axial-vector spectral functions to test simple duality properties of QCD in the large N(c) limit, which emerge in the approximation of a minimal hadronic ansatz of a spectrum of narrow states. These duality properties relate the short- and long-distance behaviors of specific correlation functions, which are order parameters of spontaneous chiral symmetry breaking, in a way that we find well supported by the data.     

Massless QCD and chiral symmetry breaking

It is well known that chiral symmetry is spontaneously broken in QCD. To relate this fact to non-perturbative features of the theory, like instantons, we start with a massless lagrangian and perform a non-linear chiral colored singlet transformation on the quark fields which yields (by means of Fujikawa's method) essentially two terms in the lagrangian. First a quark mass term induced by instantons and secondly a coupling between pseudoscalar mesons and the axial anomaly. Ward-Takahashi identities can be derived. To clarify the presence of this induced mass term we calculate its first perturbative part up to the two-loop level.     

Anomalies and chiral symmetry in QCD

I review some aspects of the interplay between anomalies and chiral symmetry. The quantum anomaly that breaks the U(1) axial symmetry of massless QCD leaves behind a flavor-singlet discrete chiral invariance. When the mass is turned on this residual symmetry has a close connection with the strong CP violating parameter theta. One result is that a first order transition is usually expected when the strong CP violating angle passes through pi. This symmetry can be understood either in terms of effective chiral Lagrangians or in terms of the underlying quark fields.     

The strange border of the QCD phases

We address the flavour composition along the border between the hadronic and the quark–gluon plasma phases of QCD. The ratio of strange to up and down antiquarks () produced in particle and nuclear collisions is found to increase in collisions with an initially reached energy density () up to GeV/fm. Above this value it decreases approximately linearly and reaches its asymptotic value at zero baryon chemical potential (). We demonstrate that in nuclear collisions approaches its asymptotic value at –9 GeV/fm, corresponding to –8 TeV per pair, which will be reached at the LHC. After correcting for the difference in the chemical potentials of various colliding systems, universally saturates across the QCD phase boundary, following the temperature. Recent experimental puzzles as the increase in the ratio in collisions at 40 GeV per nucleon, its different behaviour at midrapidity, the decrease of the double ratio of in nucleus–nucleus over collisions with increasing , and the increase of in over collisions at the same , are naturally explained. We study the approach of thermodynamic observables at to the transition point and extract an estimate of the critical temperature. Received: 17 April 2001 / Published online: 24 August 2001     

Topological violation of chiral symmetry in QCD

An originally massless quark flavour multiplet in QCD can be split on masses by a nonsimply connected spacetime topology if the quark flavours are associated with spin structures on the given spacetime. This mechanism is described by the example of spacetime with topology S¹ × R³ and flat metric. The possible applications are also discussed.     

The chiral phase transition in QCD

The Chiral Phase Transition in QCD is studied analytically by looking at truncations of the Schwinger-Dyson equation for the quark self-mass. We find that the usual implementation of the gluon propagator at non-zero temperature is far too simple. When the gluons are given the correct qualitative non-zero temperature behaviour, the calculation of the critical temperature changes significantly.     

Spontaneous breaking of chiral symmetry in QCD

The consistency of iso-spin (SU(3)) symmetry of the vacuum with the spontaneous breakdown of chiral symmetry without the appearance of a U(1) Goldstone boson, is investigated.     

The chiral limit of quenched lattice QCD

We investigate the low mass properties of our quenched QCD data for the range of beta values: 5.70, 6.00, 6.15 and 6.30. The chiral condensate, the ground-state meson spectrum and the scaling behaviour of various quantities are examined. A criterion for assessing at what value of the quark mass finite lattice effects become intolerable is suggested.     

First-order chiral phase transition in lattice QCD

The chiral phase transition in lattice QCD has been studied for light fermions of mass ma=0.025 on lattices of size 4⁴ and 8³×4 using the hybrid algorithm. We find evidence for a first-order chiral phase transition with a large latent heat. A comparison with 10³×6 data shows violations of asymptotic scaling for T_ch which are similar in magnitude to those observed in the pure gauge sector.     

Duality and the phases of massive gauge-invariant QCD

I discuss the phase structure of massive gauge invariant QCD (the gauged non-linear sigma model) using an operator formalism proposed by 't Hooft. The dual variables for this system are determined and the 't Hooft loop operator is constructed from these dual field variables. Its equal time commutation relations with the Wilson loop operator is explicitly verified. The system possesses two possible phases. In the semi-classical approximation (weak coupling), magnetic confinement as indicated by an area law for the expectation value of 't Hooft loops is observed. If above a certain critical coupling a condensate of vortices is formed, then the expectation value of the 't Hooft loop in the dilute vortex approximation shows a perimeter law indicating electric confinement.