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Abstract: Medium modification of multiplicity distributions in Modified Leading Logarithmic Approximation.

We are interested in characterizing the medium effects in the multiplicity distributions within the Modified Leading
Logarithmic Approximation (MLLA).
The MLLA constitutes an interesting framework to study mean parton multiplicities and multiplicity fluctuations in QCD
jets. While the Double Logarithmic Approximation (DLA) is known to overestimate cascading processes, the MLLA allows
to make testable quantitative predictions with controllable accuracy. Results showing it works in proton-proton have been
obtained.
In our work we introduce a medium in the MLLA equations to see how the multiplicity
distributions are modified. Know the width of the distribution increases with energy, we want to find
out what happens when the jets propagate through a medium.
We start from the MLLA evolution equations for the generating functions which have been solved in
vacuum to obtain the mean multiplicity and the dispersion of the parton multiplicity distribution of quark
and gluon jets.
Expressing the generating function for the multiplicity distribution as an infinite sum in terms of the
normalized factorial moments, the first term of the sum gives the evolution equations for the mean
multiplicity. The second term provides the normalized factorial moment of order two, which is related to
the dispersion of the distribution. So, according to this, we
introduce the medium by enhancing the soft infrared parts of the kernels of
QCD equations and make the following ansatz to the quarks and gluons mean multiplicities:
$=e^\{\\gamma and We first obtain the
medium dependence of $\\gamma$ and $r$ by fixing $\\alpha_s$ and solving the equations for the generating
functions at first order. Then, inserting this result into the second order, we find the behavior
of the normalized dispersion of the multiplicity
distributions with the medium.