1,721,036 research outputs found
On the loop-loop scattering amplitudes in Abelian and non-Abelian gauge theories
No full textThe high-energy scattering amplitude of two colour singlet quark-antiquark 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 scattering amplitude, described, in the high-energy limit, by the expectation value of two Wilson lines. We shall explicitly test this IR
finitness 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 fourth order in perturbation theory. In connection with the above-mentioned IR finitness, 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
Field strength correlators in QCD: new fits to the lattice data
No full textWe 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. (C) 1999 Published by Elsevier Science B.V. All rights reserved
SATURATION OF QCD WARD IDENTITIES ABOVE THE SU(L) X SU(L) CHIRAL TRANSITION
No full textWe show how to saturate the relevant QCD Ward identities above the SU(L) X SU(L) chiral phase transition (L being the number of light flavours), assuming, in agreement with some recent indications from lattice, that the topological susceptibility chi(YM) of the pure Yang-Mills theory is still different from zero in this region. The U(1) axial symmetry must be restored above the SU(L) X SU(L) chiral transition
The analytic continuation of the high-energy parton-parton scattering amplitude with an IR cutoff
No full textThe high-energy parton-parton scattering amplitude can be described, in the c.m.s., by the expectation value of two infinite Wilson fines, 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 --> +proportional to). 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. (C) 2002 Elsevier Science B.V. All rights reserved
Can the pomeron be derived from a Euclidean-Minkowskian duality?
No full textAfter 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
The high-energy quark-quark scattering: from Minkowskian to Euclidean theory
No full textIn this paper we consider some analytic properties of the high-energy quark-quark scattering amplitude, which, as is well known, can be described by the expectation value of two lightlike Wilson lines, running along the classical trajectories of the two colliding particles. We will show 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: the proof is given for an Abelian gauge theory (QED) in the so-called quenched approximation and for a non-Abelian gauge theory (QCD) up to the fourth order in the renormalized coupling constant in perturbation theory. This could open the possibility of evaluating the high-energy scattering amplitude directly on the lattice or using the stochastic vacuum model
The analytic continuation of the high-energy quark-quark scattering amplitude
No full textIt 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
Effects of an extra U(1) axial condensate on the radiative decay eta'-->gamma gamma at finite temperature
No full textSupported by recent lattice results, we consider a scenario in which a U(1)-breaking condensate survives across the chiral transition in QCD. This
scenario has important consequences on the pseudoscalar-meson sector, which can be studied using an effective Lagrangian model. In particular, generalizing the results obtained in a previous paper (where the zero-temperature case was
considered), we study the effects of this U(1) chiral condensate on the radiative decay eta' --> gamma gamma at finite temperature
Remark on high-energy quark-quark scattering and the eikonal approximation
No full textIn this paper we calculate the high-energy quark-quark scattering amplitude, 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. (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 ''real'' (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
High-energy quark-quark scattering and the eikonal approximation
No full textThe 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
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