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We present the mini-proceedings of the workshop on ``Parton fragmentation in the vacuum and in the medium held at the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*, Trento) in February 2008. The workshop gathered both theorists and experimentalists to discuss the current status of investigations of quark and gluon fragmentation into hadrons at different accelerator facilities (LEP, B-factories, JLab, HERA, RHIC, and Tevatron) as well as preparations for extension of these studies at the LHC. The main physics topics covered were: (i) light-quark and gluon fragmentation in the vacuum including theoretical (global fits analyses and MLLA) and experimental (data from e+e-, p-p, e-p collisions) aspects, (ii) strange and heavy-quark fragmentation, (iii) parton fragmentation in cold QCD matter (nuclear DIS), and (iv) medium-modified fragmentation in hot and dense QCD matter (high-energy nucleus-nucleus collisions). These mini-proceedings consist of an introduction and short summaries of the talks presented at the meeting.
We discuss a general diagrammatic description of n-point functions in the QCD instanton vacuum that resums planar diagrams, enforces gauge invariance and spontaneously broken chiral symmetry. We use these diagrammatic rules to derive the pion and kao
We map the spectrum of $1to 2$ parton splittings inside a medium characterized by a transport coefficient $hat q$ onto the kinematical Lund plane, taking into account the finite formation time of the process. We discuss the distinct regimes arising i
We present a quantum-mechanical description of quark-hadron fragmentation in a nuclear environment. It employs the path-integral formulation of quantum mechanics, which takes care of all phases and interferences, and which contains all relevant time
We calculate in this paper the perturbative gluon transverse momentum dependent parton distribution functions (TMDPDFs) and fragmentation functions (TMDFFs) using the exponential regulator for rapidity divergences. We obtain results for both unpolari
We revisit the calculation of perturbative quark transverse momentum dependent parton distribution functions and fragmentation functions using the exponential regulator for rapidity divergences. We show that the exponential regulator provides a consi