The assumption of linear confinement leads to a proportionality of the energy–momentum and space–time pictures of fragmentation for a simple system in the Lund string model. The hadronization of more complicated systems is more difficult to describe, and in the past only the energy–momentum picture has been implemented. In this article also the space–time picture is worked out, for open and closed multiparton topologies, for junction systems, and for massive quarks. Some first results are presented, for toy systems but in particular for LHC events. The density of hadron production is quantified under different conditions. The (not unexpected) conclusion is that this density can become quite high, and thereby motivate the observed collective behaviour in high-multiplicity collisions. The new framework, made available as part of the Pythia event generator, offers a starting point for future model building in a number of respects, such as hadronic rescattering.

We show that the σ/f0(500) state with finite-temperature T corrections to its spectral properties included, plays an essential role for the description of the scalar susceptibility χS, signaling chiral symmetry restoration. First, we use the O(4) Linear Sigma Model as a testbed to derive the connection between χS and the σ propagator and to check the validity and reliability of the approach where χS is saturated by the σ/f0(500) inverse self-energy, which we calculate at finite T to one loop. A more accurate phenomenological description is achieved by considering the saturation approach as given by the thermal f0(500) state generated in Unitarized Chiral Perturbation Theory. Such approach allows to describe fairly well recent lattice data within the uncertainty range given by the UChPT parameters. Finally, we compare the UChPT saturated description with one based on the Hadron Resonance Gas, for which the hadron mass dependences are extracted from recent theoretical analysis. Several fits to lattice data are performed, which confirm the validity of the thermal f0(500) saturated approach and hence the importance of that thermal state for chiral symmetry restoration.

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