Some remarks on chiral symmetry in dense matter

The restoration of chiral symmetry in quantum chromodynamics as the temperatureT and the chemical potential |μ| are increased is discussed qualitatively and using effective field theories. The latter are shown not to give reliable quantitative estimates. It is argued that a dilute gas of instantons cannot be the main dynamical agent responsible for the breakdown of chiral symmetry.     

Two dimensional gases of weight charges and SU(N) fermino theories

We analyze two dimensional gases composed of particles interacting via a Coulomb or Yakawa potential through their “non-Abelian” charges. These charges are taken to be elementary weight or root vectors of SU(N). The grand partition function of these gases is shown to be equivalent to the generating functional of sine-Gordon models with weight vectors and hence to that of SU(N) fermion models. The fermion field creates or annihilates topological solitons which have elementary weight vectors as topological quantum numbers. Then, we discuss the confinement of fermions in the SU(N) Higgs models, where instantons (Z_N vortices) constitute a Yukawa gas of weight charges. We prove that fermions are confirmed by the effects of instantons in the SU(N) Higgs models in contrast with the Abelian Higgs model.     

Interacting instantons and quantum mechanical metastability

The decay by tunneling of a quantum mechanical metastable state at finite temperature is described in terms of interacting instantons. The picture of instantons with arbitrary interaction strength is developed using complex classical paths. It is shown that there exists a temperature scale at which multi-instanton configurations “freeze”. Far below this scale the partition function of the theory is that of a gas of weakly interacting particles, while far above it the contribution of only one particle dominates. It is argued that this qualitative behavior is common to all quantum mechanical systems possessing a dilute gas regime at low temperatures.     

Perturbation theory with instantons

We develop “perturbation theory” rules for calculating the effect of instantons in a pure Yang-Mills theory with no fermions, in the “dilute gas” approximation in which the N-instanton solution is assumed to be the sum of N widely separated one-instanton solutions. These rules are then used to compute the gluon propagator and proper vertex function including all orders of the instanton interaction but only to lowest order in the gluon coupling. It is to be expected that such an approximation is valid only for momenta q larger than the physical mass μ. The result is that in this regime instantons cause variations in the propagator and vertex of the form where b is the coefficient in the expansion of the β function: β = bg³ + 3. .     

Instanton zero modes and β-functions in gauged supergravity

We prove that one loop infinities in N?3 gauged O(N) supergravities are produced only by zero modes both on de Sitter and gauge instanton backgrounds. This strongly suggests (in analogy with the super Yang-Mills case) that instantons may be used for establishing exact β-functions in supergravities. We also derive the general formula for the number of gauge instanton zero modes for arbitrary spin and find that the “magnetic moment” part of the contribution in the gauge β-function is completely due to zero modes.     

Euclidean D-branes and higher-dimensional gauge theory

We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane—that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory—is a cohomological field theory which describes the topology of the moduli space of instantons. The 7-dimensional theory is an N_T = 2 (or balanced) cohomological theory given by an action potential of Chern-Simons type. As a by-product of this method, we construct a related cohomological field theory which describes the monopole moduli space on a 7-manifold of G₂ holonomy.     

On the statistical mechanics of dense instanton gases

Instanton gases of two-dimensional?P ^n?1 and four-dimensionalSU(n) Yang-Mills theories are considered. The presumable denseness of instanton gases in these models and the corresponding statistics of instantons lead to a theormodynamic limit in which the coupling constant dependence of non-perturbative quantities is modified by a factor proportional to 1/n compared to the case of a dilute gas. As a consequence the largen limit and the infinite volume limit do not appear to commute. We present a naive droplet model for dense instanton gases which exhibits these features. Possible consequences for the large order behaviour of perturbation series are discussed.     

The role of instantons in scale-invariant gauge theories

Instanton calculations in scale-invariant gauge theories, such as QCD, have long been plaqued by divergences at large distances where strong coupling effects are important. Furthermore, Witten has argued that quantum effects may cause the instanton gas to disappear and has displayed this phenomenon in the CP^(N?1) model at large N. It is argued here that instantons can play a role in calculations involving an inherent infrared cut-off, and this is demonstrated in the CP^(N?1) model for large N at a finite temperature. Some results on finite-temperature QED are also obtained in passing.     

Yang-Mills instantons and the S-matrix

We present a scheme for calculating gauge-invariant S-matrix elements in the presence of instantons. We exploit the conformal invariance of the zero-mass field equations. The asymptotic in and out states are defined by their values on null infinity $\text{J}$. We use this method to calculate to lowest-order S-matrix elements for scalar particles and fermions in a dilute gas of SU(2) instantons and anti-instantons. The scalar particles acquire an effective mass and an effective interaction of the form $\text{exp}\text{(?(?}{}^2\text{/16π) ?}\text{?}\text{)}$, where ? is the scale of the instanton, plus other interactions which cannot be presented by a local effective lagrangian. The fermions acquire the effective lagrangian obtained by 't Hooft. In the case of a single flavour of fermions, this corresponds to a mass term.     

Highp T hadrons as leading particles in jets produced at the ISR

The density of charged particles near a single highp _T trigger particle in proton-proton collisions has been studied with the SFM detector at the CERN-ISR. It is shown that:—the secondaries cluster in a jet-like manner about the trigger particle; —the momentum distributions in this trigger jet can be unambiguously separated from the spectator background distributions;—the momentum distributions in this trigger jet can be unambiguously separated from the spectator background distributions;—the momentum component transverse to the jet direction is exponentially damped;—the width of the transverse distributions increases with the momentum component along the jet;—the fractional longitudinal momentum density depends strongly on the trigger transverse momentum and scales with \(x_T = {{2p_T } \mathord{\left/ {\vphantom {{2p_T } {\sqrt s }}} \right. \kern-0em} {\sqrt s }}\) . All these findings support the hard constituent scattering origin of highp _T hadrons.     

Structure of higher order corrections to the Lipatov asymptotic form

High orders of perturbation theory can be calculated by the Lipatov method, whereby they are determined by saddle-point configurations, or instantons, of the corresponding functional integrals. For most field theories, the Lipatov asymptotic form has the functional form ca ^NΓ(N+b) (N is the order of perturbation theory) and the relative corrections to it are series in powers of 1/N. It is shown that this series diverges factorially and its high-order coefficients can be calculated using a procedure similar to the Lipatov one: the Kth expansion coefficient has the form const[ln(S ₁/S ₀)]^?K Γ(K+(r ₁? r ₀)/2), where S ₀ and S ₁ are the values of the action for the first and second instantons of this particular field theory, and r ₀ and r ₁ are the corresponding number of zeroth-order modes; the instantons satisfy the same equation as in the Lipatov method and are assumed to be renumbered in order of their increasing action. This result is universal and is valid in any field theory for which the Lipatov asymptotic form is as specified above.     

Towards a semi-classical approximation of the non-linear σ-model

We consider the contribution of instantons of arbitrary topological charge to the expectation value of any observable in the CP¹ model defined on the sphere S².We replace the integration over one of the parameters of the instantons by an integration over the group of isospin transformations and carry it out explicitly by using the isospin invariance. This allows us to express the result as the expectation value of an observable of a neutral gas of 2 species of particles, computed in the grand canonical ensemble. The interactions are complicated and involve multi-body forces (2 × k, k being the topological charge).     

Chiral and UA(1) phase transitions in QCD: an analysis of the I=0 pseudoscalars

We study chiral and U_A(1) phase transition in the dilute gas approximation. A comprehensive analysis of the mass and mixing angel of η and η^′ reveals that in the transition of the quark-gluon-plasma droplets to the hadrons, besides the chiral phase transition, the U_A(1) phase transition also plays a significant and non-trivial role.     

Strong coupling versus large N in σ-models

We show that the lattice CP^(N?1) model does not have a phase transition at N = ∞, of the type proposed for SU(N) gauge theories, despite having instantons. It does, however, have non-commuting large-N and strong coupling expansions. This rather unique situation is associated with the screening properties of the model.     

The hadronisation of a quark-gluon plasma

We consider two scenarios for the expansion of a quark-gluon plasma. If the evolution is slow enough, the system can remain in equilibrium throughout its entire history up to the freeze-out of a hadron gas; for a very rapid expansion, it may break up into hadrons before or at the confinement transition, without ever going through an equilibrium hadron phase. We compare hadron production rates in the two approaches and show that for a hadronisation temperatureT?200 MeV and baryonic chemical potential μ _B ?500 MeV, their predictions essentially coincide. Present data on strange particle production lead to values in this range and hence cannot provide a distinction between the two scenarios. Pion, nucleon and non-strange meson production seem to require a considerably lower freeze-out temperature and baryonic chemical potential. In the hadron gas picture, this is in accord with the difference in mean free path of the different hadrons in the medium; it suggests a sequential freeze-out, in which strange hadrons stop interacting earlier than non-strange hadrons. In the quark-gluon plasma break-up, the hadronic final state fails to provide the high entropy per baryon observed in non-strange hadron production. The break-up moreover leads to a decrease of the entropy per baryon; hence it must be conceptually modified before it can be considered as a viable hadronisation mechanism.     

Correlation with large transverse momentum photons and the gluon structure function

The inclusive two-particle cross section for the production of largep _T photons and opposite side charged hadrons in proton-proton collisions is examined in detail in the framework of QCD. The model, with the parametrization as in our previous work, agrees with the measured single photon spectra. Quantitative predictions are made for two-particle distributions to be measured at the ISR. The contributions due to the photon bremsstrahlung and the effects coming from the intrinsic constituent motion are estimated. It is shown that indeed the direct subprocess gluon+quark→photon+quark gives the dominant contribution in the experimentally relevant region of phase space, and that direct information about the gluon structure function can be obtained from such measurements.     

Analysis of transverse momentum and event shape invN scattering

The transverse momentum distributions of hadrons produced in neutrino-nucleon charged current interactions and their dependence onW are analysed in detail. It is found that the components of the transverse momentum in the event plane and normal to it increase withW at about the same rate throughout the availableW range. A comparison withe ⁺ e ^? data is made. Studies of the energy flow and angular distributions in the events classified as planar do not show clear evidence for high energy, wide angle gluon radiation, in contrast to the conclusion of a previous analysis of similar neutrino data.