Roberto
Ugoccioni
CENTRA - Departamento de Física
Instituto Superior Técnico
Avenida Rovisco Pais
1096 Lisboa Codex
Portugal
Research Activity
Introduction: Multiparticle Dynamics
Quantum Chromodynamics (QCD) is today well established as the theory of
strong interactions, but while the perturbative sector (the hard sector)
is well developed and successful, the non-perturbative (or soft) one, responsible,
e.g., for the confinement of quarks and gluons into hadrons, is still poorly
known. The approach I have been following in studying the soft sector of
QCD tries to obtain information through the comparison of experimental
results on charged particles to theoretical calculations on partons, thus
making the dialog between theorists and experimentalists of paramount importance.
A particular field in which this approach has been successful in the past
is that of events in which many particles are produced, ranging over all
types of reactions, from electron-positron annihilation to hadron-hadron
collisions, from heavy ions reactions to cosmic rays showers: on one hand
an enormous amount of data has been, is being and will be produced, on
the other hand calculations in QCD are becoming available and, when these
are lacking, phenomenological models are being developed. For a review,
see the Proceedings of the series of Conferences on Multiparticle Dynamics,
e.g [GLU95B]. In a more general perspective,
this area of research can be seen as an application of the methods (and
results) of statistics and of the study of complex systems, and of course
these fields can in turn benefit from the methods and results developed
in multiparticle dynamics.
Within the field of multiparticle dynamics, I have been working on the
following topics:
Phenomenological Regularities
Rapidity and multiplicity distributions have been widely studied [UGL95B]
at charged particle level (experimentally, in all types of reactions, from
nucleus-nucleus to hadron-hadron collisions to electron-positron annihilation)
and at parton level by means of Monte Carlo programs based on QCD parton
showers (Altarelli-Parisi and Konishi-Ukawa-Veneziano equations), finding
the remarkable result that, in all these cases, the multiplicity distribution
(MD) can be approximately described by the negative binomial (NB) distribution,
not only in full phase space, where conservation laws play a dominant role,
but, more important, in central intervals of rapidity, where the underlying
dynamics is exposed. In particular, the characterization of the MD by the
parameters of the "clan structure analysis" have exposed further scaling
laws and have allowed the study of differences and similarities between
different reactions. The appearance of the NB distribution does not come
as a big surprise, since it has been used in order to describe evolution
phenomena in many different fields, from the diffusion of illnesses in
epidemiology to the counting of photons in optics, to the statistical analysis
of accidents in econometrics: the common point of these apparently very
different areas of application is the non-linearity of the evolutionary
process, and the large number of items (particles, people, etc.) involved,
which makes all these fields the target of what is today known as the study
of "complex systems". Multiplicity and rapidity structures have been studied
in the full-fledged QCD parton shower model at the single jet level, in
the cases of gluon cascades and heavy quark cascades, showing the presence
of simpler structures than in the full events [GUVH90,GUVH91].
In addition, distinctive features of of events involving b-quark
production in e+e- annihilation were pointed out [GUVH91].
The experimental results by the DELPHI Collaboration at LEP which found
the NB regularity after separating 2-, 3- and 4-jet events, confirmed the
importance of the study of the single parton shower, in order to sharpen
our understanding of the single dynamical mechanism underlying all types
of reactions and leading to the NB universality [GLU92].
The study of single jets has been carried on with the aim to point out
characteristic features of multiparticle production. Multiplicity distributions
in intervals of rapidity and transverse momentum have been studied in the
QCD Parton Shower Model by means of Monte Carlo methods [BGLU93,UBGL93].
Good NB behavior was found, and the related clan structure analysis showed
that observed differences in the behavior of 2- and 3-jet samples can be
understood in terms of the relative contribution of single quark and gluon
jets. While the NB distribution fits reasonably well the data, it is now
important to study the deviations from the fits. One possible deviation
lies in the exact shape of the tail of the distribution, which can be studied
in general by analyzing the ratio of factorial cumulant moments to factorial
moments. In so doing, however, one has to be careful because the natural
fact that the experimental multiplicity distribution is truncated, due
to finite statistics, has a large importance and can indeed mask effects
of dynamical origin [UGL95,UGL95B].
Once this is taken into account, interesting results can be obtained, as
in e+e- annihilation, where the shoulder structure of charged particles
multiplicity distributions in full phase space and the quasi oscillatory
behavior of the ratio of factorial cumulants to factorial moments as a
function of the order are quantitatively reproduced within a simple parametrization
of the MD in terms of the weighted superposition of two negative binomial
distributions [GLU96,UGL96].
These two components are to be associated with two-jet and multi-jet production,
i.e., they are the result of hard gluon radiation.
Parton Showers and Models thereof
The results on phenomenological regularities demand an analytical calculations
in limited regions of phase space: the objective difficulty of carrying
them out within perturbative QCD suggests the alternative of building a
phenomenological model for a single jet. Indeed a Simplified Parton Shower
model (SPS) was developed [UG92,GU92,U92]
in order to examine more deeply the single jet structure from a theoretical
point of view: this model contains, in a correct kinematical framework,
the essentials of QCD, in this case the triple gluon vertex, and describes
a simplified parton shower evolving in virtuality and rapidity. A solution
was attempted both analytically and, when necessary, numerically through
a Monte Carlo implementation: the NB regularity was found in final parton
multiplicity distributions both in full phase space and in limited regions
of phase space [UG92,GLU92,GU92,U92].
As mentioned above, the idea of "clans" as group of particles of common
ancestry, introduced by Van Hove and Giovannini in order to clarify and
investigate NB regularity, has shown further regularities in the data which
are qualitatively reproduced by the SPS model. It is interesting now to
ask whether this idea is limited to a statistical concept or if it can
work as an approximate description of parton showers; in order to answer
to this question, a generalized version of the SPS model (called GSPS)
has been introduced [UGL94B,UGL94]
by considering clans as genuine elementary subprocesses, i.e, as intermediate
partons sources independently produced (so that all correlations are exhausted
within a clan). From the point of view of parton cascading this amounts
to allow local violations of the energy-momentum conservation law (conserved
globally in a statistical sense). The results have been obtained analytically
for the behaviour of clan parameters in intervals of rapidity and are in
qualitative agreement with the experimental results and Monte Carlo calculations
mentioned in the previous section [UGL94,LGU95,GLU96,UGL96].
Very recently in Lund a new approximation to QCD parton showers has been
developed. It consists in a discretization of the phase space in which
gluons are emitted in the framework of the QCD dipole model. One of the
main consequences of this discretization is that a finite number of gluons
are produced, and that the cut-off for the parton shower is part of the
whole scheme. Another consequence is the possibility to compute analitically
all inclusive distribution, at least in full phase space. An application
to rapidity intervals is discussed in [U96],
together with results on multiplicities and fluctuations that are very
close to the effects seen.
Correlations and Fluctuations
Properties of hierarchical correlation function (in which correlations
of order n can be expressed in terms of 2-particle correlations)
can be expressed in terms of the probability of producing no particles
in restricted regions of phase space (the "void probability"). A void function
can be defined from the void probability and the average number of particles
produced; scaling of this function with energy and rapidity turns out to
be the necessary and sufficient condition for characterizing the hierarchical
structure for cumulants [LGU93,UGL94].
The connection of the void probability with infinitely divisible distributions
leads in a natural way to a generalized concept of clan, whose average
number uniquely determines the void probability. Exploring the consequences
of these results by assuming that NB regularity holds in the real world,
the void probability was shown to provide [GLU94,LGU93]
a possible tool for distinguishing quark- and gluon-jets in small central
rapidity bins.
Rapidity Gaps
Events which produce no charged particles in a central region of rapidity
can be produced either by "exotic" mechanisms (colour singlet exchange)
or by fluctuations in the more common colour octet exchange, in which the
void probability is related to the clan parametrization in a simple way;
it is then possible to apply the knowledge obtained from the study of multiplicity
distributions in order to discriminate quantitatively exotic events from
the background, and/or to study the different behaviour of the probability
of voids in the two cases [LGU95,GLU95].
Bose-Einstein Effect
In my diploma thesis I studied the effects of second order interference
(intensity correlations, also known as Bose--Einstein correlations) in
optics and astronomy (where it was first introduced by Hanbury-Brown and
Twiss, and is known as HBT effect), and in particle physics (studied first
by Goldhaber, Goldhaber, Lee and Pais). This quantum-mechanical phenomenon
enhances the probability for identical bosons (photons, pions, kaons...)
to be emitted with small relative four-momentum. From the magnitude of
the effect it is possible to determine both the space-time dimensions of
the source of particles, and the "degree of coherence" of the emitting
spots within the source itself. BE interference has received continued
attention both at theoretical and experimental level in all types of reaction,
as extensively discussed, e.g., in the series of conferences on Multiparticle
Dynamics; in this context in particular it was shown that BE correlations
are the main source of correlations in small cells of phase space (a phenomenon
which was dubbed "intermittency"). For the future, heavy ion collisions
experiment will produce thousand of particles in a single event, and the
use of BE interferometry will be one important tool in the study of the
complex phenomena expected in this kind of reactions.