D-meson enhancement in pp collisions at the LHC due to nonlinear gluon evolution Page: 2 of 16
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The parton distribution functions, PDFs, of the free proton are determined through
global fits obtained using the leading-order, LO, next-to-leading order, NLO, or even
next-to-next-to-leading order, NNLO, formulation of the Dokshitzer, Gribov, Lipatov,
Altarelli and Parisi, DGLAP, scale evolution equations . In particular, the HERA
data on the proton structure function F2(x, Q2)  as a function of Bjorken-x and
squared momentum transfer Q2, and, especially, the Q2 slope, 0F2(x, Q2)/OlnQ2, in
the small-x, 3 x 10-5 _ x 5 x 10-3, and small-Q2 region, 1.5 Q2 < 10 GeV2, set rather
stringent constraints on the small-x gluon distributions. The agreement of the global
fits with the measured F2(x, Q2) is, in general, very good but certain problems arise.
When the small-x and small-Q2 region is included in the DGLAP fits, they are not as
good as the excellent ones obtained at larger values of x and Q2 . In addition, some
NLO gluon distributions  become negative at small x for Q2 on the order of a few
The kernels of the DGLAP equations only describe splitting of one parton into two
or more so that the resulting equations are linear in the PDFs. This ignores the fact
that, at low Q2, the small-x gluon density may increase to the point where gluon fusion
becomes significant. These fusions generate nonlinearities in the evolution equations.
The first nonlinear corrections, the GLRMQ terms, were derived by Gribov, Levin
and Ryskin and also by Mueller and Qiu . Eventually, at even smaller x and Q2,
nonlinearities are expected to dominate the evolution to all orders. This fully nonlinear
region, where both the linear DGLAP evolution and the GLRMQ-corrected DGLAP
evolution are inapplicable, is the gluon saturation region, see e.g. Ref. .
Outside the saturation region, incorporating the nonlinearities may improve the
global fits when the small-x and Q2 regions are included. Recent work in Ref. , where
the LO DGLAP evolution equations were supplemented by the GLRMQ terms, showed
that the nonlinearly-evolved PDFs reproduce the HERA F2 measurements at x ? 3 x
10-5 and Q2 ? 1.5 GeV2  equally well or even better than the conventional LO PDFs
such as CTEQ6L . The nonlinearly-evolved gluon distributions at Q2 < 10 GeV2 and
x 0.01, however, were clearly enhanced relative to CTEQ6L and CTEQ61L . As
shown in Fig. 1 of Ref. , the enhancement arises because the nonlinear evolution is
slower than DGLAP alone. At higher x and Q2 the nonlinear and linear evolution of the
gluon distributions should become very similar to fit the same data. An enhancement
can also be expected at NLO. However, since the NLO small-x gluon distributions are
typically reduced relative to LO, at NLO the enhancement may be smaller than at
Since the same HERA data can be reproduced by linear evolution starting from
a relatively flat gluon distribution and by nonlinear evolution with clearly enhanced
small-x gluons, other observables are necessary to probe the effects of the nonlinearities.
In Ref. , charm production in pp collisions at the LHC was suggested as a promising
candidate process. Due to gluon dominance of charm production and the small values
of x and Q2 probed, x ~ 2 x 10-4 and Q2 ~ 1.69 - 6 GeV2 at midrapidity and
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Dainese, A.; Vogt, R.; Bondila, M.; Eskola, K.J. & Kolhinen, V.J. D-meson enhancement in pp collisions at the LHC due to nonlinear gluon evolution, article, August 22, 2004; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc782648/m1/2/: accessed December 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.