Monte Carlo models: Quo vadimus? Page: 5 of 10
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5
is similar to the initial state saturation [30]. A phenomenological implementation of the
initial state saturation is shown [32] to give a similar result as the two-component model.
Another independent constraint is the rapidity dependence of dNch/dr//(Ngrt). PHOBOS
preliminary [3] data are consistent with HIJING model.
3. Interplay between soft and hard processes
The centrality dependences of soft and hard processes not only manifest themselves in
the total charged multiplicity but also in the hadron PT spectra. Incoherent hard parton
scattering should dominate the hadron spectra at high PT while coherent soft interactions
contribute mainly to the low PT region. This leads to some nontrivial nuclear dependence
of hadron PT spectra. A good Monte Carlo model should be able to simulate this nuclear
dependence.
In a schematic Glauber model of multiple parton scattering, one can calculate the
produced parton spectra [33] in p + A collisions:
E d-A N d-NN 9A1/3 dxi- d3
A d3A E d3 + 167r2 >i f/Nx(,) Ek iN kN - koiN + jNO N , (5)
AdP p 1ro i E
where h4N is the differential cross section for parton-nucleon scattering i+N -> j+X, and
fi/N(xi) is the parton distribution in a nucleon. The effective parton-nucleon total cross
section is defined as oiN (pi = z Zj f E hjN (pi, pj and the differential nucleon-nucleon
cross section for parton production as Edo- N743 - /f xtf,/N(xi)1N(pi, p). We have
taken a nucleus to be a hard sphere of radius rA = r0A1/3.
In the above equation, the first term corresponds to the incoherent sum of single par-
ton scatterings in a nucleus. The second term gives the nuclear modification of the
parton spectrum due to multiple parton scattering inside a nucleus. This term con-
tains contributions from both the double parton scattering and the negative absorptive
correction. For a schematic study, let us assume that all partons are identical and
the differential parton-nucleon cross sections have a simple regularized power-law form
h4N- h(pT) = C/(pT+ pj)". The parameter po can be considered as the scale separating
soft and hard processes. One can then calculate the nuclear modification factor of the
parton spectra,
EdNA d3p
AEdUNN/d3p'
which is shown in Fig. 3 for three different values of n as a function of pT/po. Relative
to the additive model of incoherent hard scattering, the spectra are enhanced at large PT
(RA > 1) for hard processes due to multiple scattering. For soft processes at low PT, the
absorptive correction is large and the second term in Eq. (5) becomes negative, leading
to the suppression of hadron spectra (RA < 1). The transition between suppression and
enhancement occurs at around the scale po that separates soft and hard processes. If we
analyze the hadron spectra in pp(p) collisions as shown in Fig. 4, one can indeed see the
two underlying components: one in power-law form that dominates spectra at high PT
and another in exponential form for low PT hadrons. The transition between these two
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Wang, Xin-Nian. Monte Carlo models: Quo vadimus?, article, January 1, 2001; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc743080/m1/5/: accessed April 30, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.