70 research outputs found
Remarks on the U(1) axial symmetry in QCD at zero and non-zero temperature
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.Comment: Expanded version of a talk given at the ``Workshop on Quark-Gluon
Plasma and Relativistic Heavy Ions'', Frascati (Italy), January 14th-18th,
2002 (QGP2002); 61 pages, LaTeX file, + 6 PS figure
A remark on the 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'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'' ({\it 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.Comment: 24 pages (no figures), LaTeX--file. New references have been added
and commented and some other minor corrections have been performe
Eikonal propagators for the high-energy parton-parton scattering in gauge theories
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.Comment: Talk given at the ``Sixth Workshop on Non-Perturbative Quantum
Chromodynamics'', Paris (France), June 5th-9th 2001 (NPQCD 01); 8 pages,
LaTeX file, + 1 PS figur
High-energy scattering amplitudes in QCD: from Minkowskian to Euclidean space
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.Comment: Talk given at the ``26th Johns Hopkins Workshop on current problems
in particle theory: high energy reactions'', Heidelberg (Germany), 1-3 August
2002 (JHW2002); 7 pages, LaTeX file. Revised version with two errors in Eqs.
(26) and (27) correcte
Theta dependence of the vacuum energy density in chiral effective Lagrangian models at finite temperature, above
In this work, extending a previous study at zero temperature (), we
perform a systematic study of the modifications to the QCD vacuum energy
density in the finite-temperature case, above the chiral
transition at , caused by a nonzero value of the parameter , using
two different effective Lagrangian models which implement the axial
anomaly of the fundamental theory and which are both well defined also above
. In particular, we derive (and critically compare) the expressions for
the topological susceptibility and for the second cumulant
starting from the dependence of in the two
models.Comment: 23 pages; revised versio
High-energy quark-quark scattering and the eikonal approximation
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.Comment: Talk given at the ``High Energy Conference on Quantum
Chromodynamics'', Montpellier (France), July 3rd-9th 1997 (QCD 97); 6 pages,
LaTeX file, uses ``espcrc2.sty'
The topological susceptibility of QCD: from Minkowskian to Euclidean theory
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.Comment: 21 pages, LaTeX file, + 1 PS figur
Comments on high-energy total cross sections in QCD
We discuss how hadronic total cross sections at high energy depend on the
details of QCD, namely on the number of colours and the quark masses. We
find that while a "Froissart"-type behaviour is
rather general, relying only on the presence of higher-spin stable particles in
the spectrum, the value of depends quite strongly on the quark masses.
Moreover, we argue that is of order at large , and
we discuss a bound for which does not become singular in the chiral
limit, unlike the Froissart-\L ukaszuk-Martin bound.Comment: Revised version; matches published versio
Hadronic total cross sections at high energy and the QCD spectrum
We show how to obtain the leading energy dependence of hadronic total cross
sections, in the framework of the nonperturbative approach to soft high-energy
scattering based on Wilson-loop correlation functions, if certain nontrivial
analyticity assumptions are satisfied. The total cross sections turn out to be
of "Froissart" type, for . We also discuss under which conditions the coefficient is
universal, i.e., independent of the hadrons involved in the scattering process.
In the most natural scenarios for universality, can be related to the
stable spectrum of QCD, and is predicted to be , in fair agreement with experimental results. If we consider, instead, the
stable spectrum of the quenched (i.e., pure-gauge) theory, we obtain a quite
larger value , suggesting (quite
surprisingly) large unquenching effects due to the sea quarks.Comment: Revised version; 43 pages, 3 figure
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