Medium-evolved fragmentation functions

TL;DR

The paper addresses the limitation of independent medium-induced emissions (Poisson/quenching-weights) in describing jet quenching by embedding medium effects directly into the parton shower via a DGLAP framework. It introduces a medium-modified splitting function $P^{tot}(z,t) = P^{vac}(z) + \Delta P(z,t)$ derived from the medium-induced gluon spectrum, and utilizes a harmonic-oscillator approximation $n(\xi) \sigma(\mathbf{r}) \simeq \tfrac{1}{2} \hat{q}(\xi) \mathbf{r}^2$ with transport coefficient $\hat{q}$ to connect medium dynamics to the shower evolution. Sudakov form factors are computed for all parton species with the medium modifications, and the medium-modified fragmentation functions (MMFFs) are evolved from an initial scale using $D^{med}(x,t_0)= D^{vac}(x,t_0)$, ensuring energy-momentum conservation at each step. The formalism reduces to the conventional vacuum DGLAP in the high virtuality/energy limit and reproduces the quenching-weights results in the appropriate limit, while yielding MMFF predictions that can be tested with LHC and RHIC jet fragmentation data and extended to finite-x effects and hadronization outside the medium.

Abstract

Medium-induced gluon radiation is usually identified as the dominant dynamical mechanism underling the {\it jet quenching} phenomenon observed in heavy-ion collisions. In its actual implementation, multiple medium-induced gluon emissions are assumed to be independent, leading, in the eikonal approximation, to a Poisson distribution. Here, we introduce a medium term in the splitting probabilities so that both medium and vacuum contributions are included on the same footing in a DGLAP approach. The improvements include energy-momentum conservation at each individual splitting, medium-modified virtuality evolution and a coherent implementation of vacuum and medium splitting probabilities. Noticeably, the usual formalism is recovered when the virtuality and the energy of the parton are very large. This leads to a similar description of the suppression observed in heavy-ion collisions with values of the transport coefficient of the same order as those obtained using the {\it quenching weights}.