download report - Sapienza

Scientific Report 2007-2009
Theoretical physics
T5. Properties of hadron collisions at high energy
The high energy frontier in particle physics is presently
investigated by the experiments beginning to take data
at the CERN Large Hadron Collider and by the Auger
experiment, looking at the air showers produced by the
highest energy cosmic rays. It is therefore of considerable
interest to study the evolution with energy of the
cross sections in hadron–hadron collisions and the properties
of multiparticle production in these interactions.
Given the composite nature of hadrons, it is natural to
interpret the hadronic data in terms of elementary interactions
between quarks and gluons; this is however a difficult
task, which goes beyond the limits of perturbative
QCD. A possible approach is provided by the so–called
”mini–jet” eikonal models, that however in their original
formulation did not include properly an important class
of events, those due to inelastic diffraction. Following
the old suggestion by Good and Walker based on an optical
analogy, diffractive events can be introduced via a
multichannel eikonal model, as it has been done already
by several authors.
In our recent work [1] we addressed the problem of
determining the effects of fluctuations of the partonic
configurations in the colliding hadrons, and of investigating
the relation between these fluctuations and the
abundance of inelastic diffractive events. We suggested
to describe the fluctuations in the number of elementary
interactions at a given impact parameter in terms
of a single function, and gave a simple parameterization
for it. In the limit of negligible fluctuations the model
coincides with the naïve mini–jet model of Durand and
Pi. Such model does not include the inelastic diffraction,
that is certainly present as it appears from Fig. 1.
Moreover, this model requires the proton transverse dimension
to increase with energy, in order to fit the data
for total and elastic cross sections from center-of-mass
energy √ s ∼ 60 GeV (ISR) up to √ s ∼ 1800 GeV (Fermilab
Tevatron).
To describe at the same time total, elastic and diffractive
cross sections we are forced to increase the variance
of the fluctuations distribution, and in this way we
were able to obtain reasonably accurate description of
the data with transverse dimensions of the proton that
stay constant with energy. The transverse radius turns
out to be smaller than the electromagnetic one, suggesting
that soft gluons have an impact parameter distribution
narrower than valence quarks. The inclusion of
fluctuations has also the consequence that the number of
elementary interactions in an inelastic collision is larger
(and more rapidly increasing) than in other models: this
is a possibility that should be compared with data after
including our formulae in a full Montecarlo code.
Figure 2: The points are measurements of the pp and pp
total cross sections. The red [dashed] lines represent the fit
of σ tot(s) suggested in the Particle Data Group .
Two different, somehow extreme forms of the energy
dependence of the parameters have been used to extrapolate
to higher energies ( √ s ∼ 14 TeV for LHC and
E p = 10 19 or 10 20 eV for cosmic rays), giving rise to the
blue [thick] and black [thin] curves in the figures. As it
can be seen, the uncertainty in predicting the total cross
section is still rather large.
Further investigations along these lines will be
prompted by the upcoming data from the LHC experiments.
References
1. P. Lipari et al., Phys. Rev. D 80, 074014 (2009).
Authors
P. Lipari 1 , M. Lusignoli
Figure 1: The points are measurements of the single diffraction
pp and pp cross sections.
Sapienza Università di Roma 28 Dipartimento di Fisica