Thermalization of Hadrons via Hagedorn States

Hagedorn states are characterized by being very massive hadron-like resonances and by not being limited to quantum numbers of known hadrons. To generate such a zoo of different Hagedorn states, a covariantly formulated bootstrap equation is solved by ensuring energy conservation and conservation of baryon number $B$, strangeness $S$ and electric charge $Q$. The numerical solution of this equation provides Hagedorn spectra, which enable to obtain the decay width for Hagedorn states needed in cascading decay simulations. A single (heavy) Hagedorn state cascades by various two-body decay channels subsequently into final stable hadrons. All final hadronic observables like masses, spectral functions and decay branching ratios for hadronic feed down are taken from the hadronic transport model UrQMD. Strikingly, the final energy spectra of resulting hadrons are exponential showing a thermal-like distribution with the characteristic Hagedorn temperature

Development of UHF measurements

Collector gauge and orbitron gauge for ultrahigh vacuum measurement

Equilibration of hadrons in HICs via Hagedorn States

Hagedorn states (HS) are a tool to model the hadronization process which occurs in the phase transition region between the quark gluon plasma (QGP) and the hadron resonance gas (HRG). These states are believed to appear near the Hagedorn temperature $T_H$ which in our understanding equals the critical temperature $T_c$. A covariantly formulated bootstrap equation is solved to generate the zoo of these particles characterized baryon number $B$, strangeness $S$ and electric charge $Q$. These hadron-like resonances are characterized by being very massive and by not being limited to quantum numbers of known hadrons. All hadronic properties like masses, spectral functions etc.are taken from the hadronic transport model Ultra Relativistic Quantum Molecular Dynamics (UrQMD). Decay chains of single Hagedorn states provide a well description of experimentally observed multiplicity ratios of strange and multi-strange particles. In addition, the final energy spectra of resulting hadrons show a thermal-like distribution with the characteristic Hagedorn temperature $T_H$. Box calculations including these Hagedorn states are performed. Indeed, the time scales leading to equilibration of the system are drastically reduced down to 2...5 fm/c.Comment: To appear in the proceedings of the 15th International Conference on Strangeness in Quark Matter (SQM2015), Dubna, Russian Federation, 6-11 July 201

Fast Dynamical Evolution of Hadron Resonance Gas via Hagedorn States

Hagedorn states are the key to understand how all hadrons observed in high energy heavy ion collisions seem to reach thermal equilibrium so quickly. An assembly of Hagedorn states is formed in elementary hadronic or heavy ion collisions at hadronization. Microscopic simulations within the transport model UrQMD allow to study the time evolution of such a pure non-equilibrated Hagedorn state gas towards a thermally equilibrated Hadron Resonance Gas by using dynamics, which unlike strings, fully respect detailed balance. Propagation, repopulation, rescatterings and decays of Hagedorn states provide the yields of all hadrons up to a mass of m=2.5 GeV. Ratios of feed down corrected hadron multiplicities are compared to corresponding experimental data from the ALICE collaboration at LHC. The quick thermalization within t=1-2 fm\c of the emerging Hadron Resonance Gas exposes Hagedorn states as a tool to understand hadronization.Comment: 5 pages, 7 figures, 1 tabl

Particle Ratios and the QCD Critical Temperature

We show how the measured particle ratios at RHIC can be used to provide non-trivial information about the critical temperature of the QCD phase transition. This is obtained by including the effects of highly massive Hagedorn resonances on statistical models, which are used to describe hadronic yields. Hagedorn states are relevant close to $T_c$ and have been shown to decrease $\eta/s$ to the KSS limit and allow for quick chemical equilibrium times in dynamical calculations of hadrons. The inclusion of Hagedorn states creates a dependence of the thermal fits on the Hagedorn temperature, $T_H$, which is assumed to be equal to $T_c$, and leads to an overall improvement of thermal fits. We find that for Au+Au collisions at RHIC at $\sqrt{s_{NN}}=200$ GeV the best square fit measure, $\chi^2$, occurs at $T_c \sim 176$ MeV and produces a chemical freeze-out temperature of 170.4 MeV and a baryon chemical potential of 27.8 MeV.Comment: 6 pages, 2 figures, talk presented at the International Conference on Strangeness in Quark Matter, Buzios, Rio de Janeiro, Brazil, Sept. 27 - oct. 2, 200

Thermalization through Hagedorn states - the importance of multiparticle collisions

Quick chemical equilibration times of hadrons within a hadron gas are explained dynamically using Hagedorn states, which drive particles into equilibrium close to the critical temperature. Within this scheme master equations are employed for the chemical equilibration of various hadronic particles like (strange) baryon and antibaryons. A comparison of the Hagedorn model to recent lattice results is made and it is found that for both Tc =176 MeV and Tc=196 MeV, the hadrons can reach chemical equilibrium almost immediately, well before the chemical freeze-out temperatures found in thermal fits for a hadron gas without Hagedorn states.Comment: 8 pages, 3 figures, talk presented at the International Conference on Strangeness in Quark Matter, Buzios, Rio de Janeiro, Brazil, Sept. 27 - Oct. 2, 200

Predicting Phenotypic Diversity and the Underlying Quantitative Molecular Transitions

During development, signaling networks control the formation of multicellular patterns. To what extent quantitative fluctuations in these complex networks may affect multicellular phenotype remains unclear. Here, we describe a computational approach to predict and analyze the phenotypic diversity that is accessible to a developmental signaling network. Applying this framework to vulval development in C. elegans, we demonstrate that quantitative changes in the regulatory network can render ~500 multicellular phenotypes. This phenotypic capacity is an order-of-magnitude below the theoretical upper limit for this system but yet is large enough to demonstrate that the system is not restricted to a select few outcomes. Using metrics to gauge the robustness of these phenotypes to parameter perturbations, we identify a select subset of novel phenotypes that are the most promising for experimental validation. In addition, our model calculations provide a layout of these phenotypes in network parameter space. Analyzing this landscape of multicellular phenotypes yielded two significant insights. First, we show that experimentally well-established mutant phenotypes may be rendered using non-canonical network perturbations. Second, we show that the predicted multicellular patterns include not only those observed in C. elegans, but also those occurring exclusively in other species of the Caenorhabditis genus. This result demonstrates that quantitative diversification of a common regulatory network is indeed demonstrably sufficient to generate the phenotypic differences observed across three major species within the Caenorhabditis genus. Using our computational framework, we systematically identify the quantitative changes that may have occurred in the regulatory network during the evolution of these species. Our model predictions show that significant phenotypic diversity may be sampled through quantitative variations in the regulatory network without overhauling the core network architecture. Furthermore, by comparing the predicted landscape of phenotypes to multicellular patterns that have been experimentally observed across multiple species, we systematically trace the quantitative regulatory changes that may have occurred during the evolution of the Caenorhabditis genus