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