## 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.