Enrico Meggiolaro

Field strength correlators in full QCD

Abstract 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.

Gauge-invariant field strength correlations in QCD at zero and non-zero temperature☆

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.Abstract We determine, by numerical simulations on a lattice, the gauge-invariant two-point correlation functions of the gauge field strengths in the QCD vacuum at zero temperature, down to a distance of 0.1 fm. We also study the behaviour of the gauge-invariant field correlators in the theory at finite temperature, across the deconfinement phase transition.

Gauge-invariant field-strength correlators in pure Yang-Mills and full QCD at finite temperature

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, both for the pure-gauge SU(3) theory and for full QCD with two flavours. Quenched data agree within errors with previous determinations, but have much higher statistics. A best-fit analysis of the data has been performed, both for the quenched and the full-QCD case, showing that the electric gluon condensate drops to zero at the deconfining phase transition.

The analytic continuation of the high-energy parton–parton scattering amplitude with an IR cutoff

Abstract 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 letting T→+∞). 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.

Remark on high-energy quark-quark scattering and the eikonal approximation.

In this paper we calculate the high-energy quark-quark scattering amplitude, first in the case of scalar QCD, using Fradkin{close_quote}s approach to derive the scalar quark propagator in an external gluon field and computing it in the eikonal approximation. (This approach was also recently used by Fabbrichesi, Pettorino, Veneziano, and Vilkovisky to study the four-dimensional Planckian-energy scattering in gravity.) We then extend the results to the case of {open_quote}{open_quote}real{close_quote}{close_quote} (i.e., fermion) QCD, thus deriving again, in a rather direct way, the results previously found by Nachtmann. The Abelian case (QED) is also discussed in the Appendix. {copyright} {ital 1996 The American Physical Society.}

High-energy hadron-hadron (dipole-dipole) scattering from lattice QCD

In this paper the problem of high-energy hadron-hadron (dipole-dipole) scattering is approached (for the first time) from the point of view of lattice QCD, by means of Monte Carlo numerical simulations. In the first part, we give a brief review of how high-energy scattering amplitudes can be reconstructed, using a functional-integral approach, in terms of certain correlation functions of two Wilson loops, and we also briefly recall some relevant analyticity and crossing-symmetry properties of these loop-loop correlation functions, when going from Euclidean to Minkowskian theory. In the second part, we shall see how these (Euclidean) loop-loop correlation functions can be evaluated in lattice QCD, and we shall compare our numerical results with some nonperturbative analytical estimates that appeared in the literature, discussing, in particular, the question of the analytic continuation from Euclidean to Minkowskian theory and its relation to the still unsolved problem of the asymptotic s dependence of the hadron-hadron total cross sections.

Analyticity and crossing symmetry of the eikonal amplitudes in gauge theories

After a brief review and a more refined analysis of some relevant analyticity properties (when going from Minkowskian to Euclidean theory) of the high-energy parton-parton and hadron-hadron scattering amplitudes in gauge theories, described nonperturbatively, in the eikonal approximation, by certain correlation functions of two Wilson lines or two Wilson loops near the light cone, we shall see how these same properties lead to a nice geometrical interpretation of the crossing symmetry between quark-quark and quark-antiquark eikonal amplitudes and also between loop-loop eikonal amplitudes. This relation between Minkowskian-to-Euclidean analyticity properties and crossing symmetry is discussed in detail and explicitly tested in the first orders of perturbation theory. Some nonperturbative examples existing in the literature are also discussed.

On the loop-loop scattering amplitudes in Abelian and non-Abelian gauge theories

Abstract The high-energy elastic scattering amplitude of two colour-singlet q q ¯ pairs is governed by the correlation function of two Wilson loops, which follow the classical straight lines for quark (antiquark) trajectories. This quantity is expected to be free of IR divergences, differently from what happens for the parton–parton elastic scattering amplitude, described, in the high-energy limit, by the expectation value of two Wilson lines. We shall explicitly test this IR finiteness by a direct non-perturbative computation of the loop–loop scattering amplitudes in the (pedagogic, but surely physically interesting) case of quenched QED. The results obtained for the Abelian case will be generalized to the case of a non-Abelian gauge theory with N c colours, but stopping to the order O ( g 4 ) in perturbation theory. In connection with the above-mentioned IR finiteness, we shall also discuss some analytic properties of the loop–loop scattering amplitudes in both Abelian and non-Abelian gauge theories, when going from Minkowskian to Euclidean theory, which can be relevant to the still unsolved problem of the s -dependence of hadron–hadron total cross-sections.

Instanton effects on Wilson-loop correlators: A new comparison with numerical results from the lattice

Instanton effects on the Euclidean correlation function of two Wilson loops at an angle θ, relevant to soft high–energy dipole–dipole scattering, are calculated in the Instanton Liquid Model and compared with the existing lattice data. Moreover, the instanton–induced dipole–dipole potential is obtained from the same correlation function at θ = 0, and compared with preliminary lattice data. E–mail: matteo.giordano@df.unipi.it E–mail: enrico.meggiolaro@df.unipi.it

Can the pomeron be derived from a Euclidean–Minkowskian duality?

Abstract After a brief review, in the first part, of some relevant analyticity and crossing-symmetry properties of the correlation functions of two Wilson loops in QCD, when going from Euclidean to Minkowskian theory, in the second part we shall see how these properties can be related to the still unsolved problem of the asymptotic s -dependence of the hadron–hadron total cross sections. In particular, we critically discuss the question if (and how) a pomeron -like behaviour can be derived from this Euclidean–Minkowskian duality.