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Initial Conditions for Modified DGLAP Evolution of the Modified Fragmentation Functions in Nuclear Medium

Initial conditions are required to solve medium modified DGLAP (mDGLAP) evolution equations for modified fragmentation functions due to multiple scatterings and parton energy loss. Such initial conditions should in principle include energy loss for partons at scale $Q_0$ above which mDGLAP evolution equations can be applied. Several models for the initial condition motivated by induced gluon bremsstrahlung in perturbative QCD are used to calculate the modified fragmentation functions in nuclear medium and to extract the jet transport parameter $\hat q$ from fits to experimental data in deeply inelastic scattering (DIS) off nuclei. The model with a Poisson convolution of multiple gluon emissions is found to provide the overall best $χ^2$/d.o.f. fit to the HERMES data and gives a value of $\hat q_0 \approx 0.020 \pm 0.005$ GeV$^2$/fm at the center of a large nucleus.