Decision Theory with a Hilbert Space as Possibility Space

In this paper, we propose an interpretation of the Hilbert space method used in quantum theory in the context of decision making under uncertainty. For a clear comparison we will stay as close as possible to the framework of SEU suggested by Savage (1954). We will use the Ellsberg (1961) paradox to illustrate the potential of our approach to deal with well-known paradoxa of decision theory

Effects of the Running of the QCD Coupling on the Energy Loss in the Quark-Gluon Plasma

Finite temperature modifies the running of the QCD coupling alpha_s(k,T) with resolution k. After calculating the thermal quark and gluon masses selfconsistently, we determine the quark-quark and quark-gluon cross sections in the plasma based on the running coupling. We find that the running coupling enhances these cross sections by factors of two to four depending on the temperature. We also compute the energy loss dE/dx of a high-energy quark in the plasma as a function of temperature. Our study suggests that, beside t-channel processes, inverse Compton scattering is a relevant process for a quantitative understanding of the energy loss of an incident quark in a hot plasma.Comment: 14 pages, 6 figure

Linking the Quark Meson Model with QCD at High Temperature

We model the transition of a system of quarks and gluons at high energies to a system of quarks and mesons at low energies in a consistent renormalization group approach. Flow equations interpolate between the physics of the high-temperature degrees of freedom and the low-temperature dynamics at a scale of 1 GeV. We also discuss the dependence of the equation of state on baryon density and compare our results with recent lattice gauge simulations.Comment: 11 pages, 4 figures additional discussion of the second order phase transitio

Renormalization Group Flow in large N_c

We calculate renormalization group flow equations for the linear sigma-model in large N_c approximation. The flow equations decouple and can be solved analytically. The solution is equal to a self consistent solution of the NJL model in the same approximation, which shows that flow equations are a promising method to extend the calculation to higher order in 1/N_c. Including explicit chiral symmetry breaking, the large N_c approximation describes physics reasonably well. We further compare the analytic solution to the usually used polynomial truncation and find consistency.Comment: 15 pages, 4 figures, submitted to Phys. Lett. B, added reference

The Spectrum of the Dirac Operator in the Linear Sigma Model with Quarks

We derive the spectrum of the Dirac operator for the linear sigma-model with quarks in the large N_c approximation using renormalization group flow equations. For small eigenvalues, the Banks-Casher relation and the vanishing linear term are recovered. We calculate the coefficient of the next to leading term and investigate the spectrum beyond the low energy regime.Comment: 15 pages, 6 figures, to appear in Phys. Rev.

Testing the Scale Dependence of the Scale Factor σeff\sigma_{eff} in Double Dijet Production at the LHC

The scale factor σ eff is the effective cross section used to characterize the measured rate of inclusive double dijet production in high energy hadron collisions. It is sensitive to the two-parton distributions in the hadronic projectile. In principle, the scale factor depends on the center of mass energy and on the minimal transverse energy of the jets contributing to the double dijet cross section. Here, we point out that proton-proton collisions at the LHC will provide for the first time experimental access to these scale dependences in a logarithmically wide, nominally perturbative kinematic range of minimal transverse energy between 10 GeV and 100 GeV. This constrains the dependence of two-parton distribution functions on parton momentum fractions and parton localization in impact parameter space. Novel information is to be expected about the transverse growth of hadronic distribution functions in the range of semi-hard Bjorken x (0.001 < x < 0.1) and high resolution Q^2. We discuss to what extent one can disentangle different pictures of the $x$-evolution of two-parton distributions in the transverse plane by measuring double-hard scattering events at the LHC