arXiv subjects
Publications and source records attributed to Enrico Meggiolaro.
We will discuss how the problem of high-energy hadron-hadron (dipole-dipole) scattering at low momentum transfer can be approached from the point of view of lattice QCD, by means of Monte Carlo numerical simulations.
We discuss the role of the U(1) axial symmetry for the phase structure of QCD at finite temperature. In particular, supported by recent lattice results, we analyse a scenario in which a U(1)-breaking condensate survives across the chiral transition. This scenario can be consistently reproduced using an effective Lagrangian model. The effects of the U(1) chiral condensate on the slope of the topological susceptibility in the full theory with quarks are studied. Further information on the new U(1) chiral order parameter is derived from the study (at zero temperature) of the radiative decays of the light pseudoscalar mesons in two photons.
We shall discuss about some analytic properties of the high-energy parton-parton (and hadron-hadron) scattering amplitudes in gauge theories, when going from Minkowskian to Euclidean theory, and we shall see how they can be related to the still unsolved problem of the s-dependence of the total cross-section.
This paper is organized in two parts. The first part (Sections 2-5) is dedicated to the theory at T=0 and contains a pedagogical review of some fundamental aspects related with the chiral symmetries of QCD, the U(1) problem and its solution proposed by 'tHooft, Witten and Veneziano. In the second part (Sections 6-14) we discuss the role of the U(1) axial symmetry for the phase structure of QCD at finite temperature. One expects that, above a certain critical temperature, also the U(1) axial symmetry will be restored. We will try to see if this transition has (or has not) anything to do with the usual chiral transition: various possible scenarios are discussed. In particular, we analyse a scenario in which the U(1) axial symmetry is still broken above the chiral transition. We will show that this scenario can be consistently reproduced in the full respect of the relevant QCD Ward Identities and also using an effective Lagrangian model. A new order parameter is introduced for the U(1) axial symmetry.
We discuss the role of the U(1) axial symmetry for the phase structure of QCD at finite temperature. We expect that, above a certain critical temperature, also the U(1) axial symmetry will be restored. We will try to see if this transition has (or has not) anything to do with the usual chiral transition: various possible scenarios are discussed. In particular, we analyse a scenario in which the U(1) axial symmetry is still broken above the chiral transitions. We will show that this scenario can be consistently reproduced using an effective Lagrangian model. A new order parameter is introduced for the U(1) axial symmetry.
The high-energy parton-parton scattering amplitude can be described, in the c.m.s., by the expectation value of two infinite Wilson lines, running along the classical trajectories of the two colliding particles. The above description suffers from IR divergences (typical of 3 + 1 dimensional gauge theories), which can be regularized by considering finite Wilson lines, extending in proper time from -T to T (and eventually sending T to infinity). Generalizing the results of a previous paper, we give here the general proof that the expectation value of two IR-regularized Wilson lines, forming a certain hyperbolic angle in Minkowski space-time, and the expectation value of two IR-regularized Euclidean Wilson lines, forming a certain angle in Euclidean four-space, are connected by an analytic continuation in the angular variables and in the IR cutoff T. This result can be used to evaluate the IR-regularized high-energy scattering amplitude directly in the Euclidean theory.
By a direct resummation of perturbation theory in the limit of very high energy and small transferred momentum (the so-called ``eikonal'' limit), we derive expressions for the truncated-connected quark, antiquark and gluon propagators in an external gluon field, both for scalar and fermion gauge theories. These are the basic ingredients to derive ``soft'' high-energy parton-parton scattering amplitudes, using the LSZ reduction formulae and a functional integral approach.
A nonperturbative renormalization group equation describes how the momentum dependent four-quark vertex depends on an infrared cutoff. We find a quasilocal one-particle irreducible piece generated by (anomaly-free) multi-gluon exchange. It becomes important at a cutoff scale where scalar and pseudoscalar meson-bound states are expected to play a role. This interaction remains subleading as compared to the effective one-gluon exchange contribution. The local instanton induced four-quark interaction becomes dominant at a scale around 800 MeV. In absence of a gluon mass the strong dependence of the one-gluon exchange on the transferred momentum indicates that the pointlike interactions of the Nambu-Jona-Lasinio model cannot give a very accurate description of QCD. A pointlike effective four-quark interaction becomes more realistic in case of spontaneous color symmetry breaking.
In this paper we consider soft high-energy parton-parton scattering processes in gauge theories, i.e., elastic scattering processes involving partons at very high squared energies in the center of mass and small squared transferred momentum. By a direct resummation of perturbation theory in the limit we are considering, we derive expressions for the truncated-connected quark (antiquark) propagator in an external gluon field, as well as for the residue at the pole of the full unrenormalized propagator, both for scalar and fermion gauge theories. These are the basic ingredients to derive high-energy parton-parton scattering amplitudes, using the LSZ reduction formulae and a functional integral approach. The above procedure is also extended to include the case in which at least one of the partons is a gluon. The meaning and the validity of the results are discussed.
We study the asymptotic short-distance behaviour as well as the asymptotic large-distance behaviour of the gauge-invariant quark-antiquark nonlocal condensates in QCD. A comparison of some analytical results with the available lattice data is performed.
We discuss the results obtained by fitting the lattice data of the gauge-invariant field strength correlators in QCD with some particular functions which are commonly used in the literature in some phenomenological approaches to high-energy hadron-hadron scattering. A comparison is done with the results obtained in the original fits to the lattice data.
We show how the topological susceptibility in the Minkowskian theory of QCD is related to the corresponding quantity in the Euclidean theory, which is measured on the lattice. We discuss both the zero-temperature case (T = 0) and the finite-temperature case (T > 0). It is shown that the two quantities are equal when T = 0, while the relation between them is much less trivial when T > 0. The possible existence of ``Kogut-Susskind poles'' in the matrix elements of the topological charge density between states with equal four-momenta turns out to invalidate the equality of these two quantities in a strict sense. However, an equality relation is recovered after one re-defines the Minkowskian topological susceptibility by using a proper infrared regularization.
We determine, by numerical simulations on a lattice, the gauge-invariant two-point correlation functions of the gauge field strengths in the QCD vacuum with four flavours of dynamical staggered fermions.
The high-energy quark-quark scattering amplitude is calculated first in the case of scalar QCD, using Fradkin's approach to derive the scalar quark propagator in an external gluon field and computing it in the eikonal approximation. The results are then extended to the case of ``real'' (i.e., fermion) QCD. The high-energy quark-quark scattering amplitude turns out to be described by the expectation value of two lightlike Wilson lines, running along the classical trajectories of the two colliding particles. Interesting analytic properties of the high-energy quark-quark scattering amplitude can be derived, going from Minkowskian to Euclidean theory: they could open the possibility of evaluating the high-energy scattering amplitude directly on the lattice.
We study, by numerical simulations on a lattice, the behaviour of the gauge-invariant two-point correlation functions of the gauge field strengths in the QCD vacuum with dynamical fermions.
It is known that the high-energy quark-quark scattering amplitude can be described by the expectation value of two lightlike Wilson lines, running along the classical trajectories of the two colliding particles. Generalizing the results of a previous paper, we give here the general proof that the expectation value of two infinite Wilson lines, forming a certain hyperbolic angle in Minkowski space-time, and the expectation value of two infinite Euclidean Wilson lines, forming a certain angle in Euclidean four-space, are connected by an analytic continuation in the angular variables. This result could be used to evaluate the high-energy scattering amplitude directly on the lattice.
We study, by numerical simulations on a lattice, the behaviour of the gauge--invariant field strength correlators in QCD both at zero temperature, down to a distance of 0.1 fm, and at finite temperature, across the deconfinement phase transition.
We study by numerical simulations on a lattice the behaviour of the gauge--invariant two--point correlation functions of the gauge field strengths across the deconfinement phase transition.