Geant4 is a toolkit for simulating the passage of particles through matter. It includes a complete range of functionality including tracking, geometry, physics models and hits. The physics processes offered cover a comprehensive range, including electromagnetic, hadronic and optical processes, a large set of long-lived particles, materials and elements, over a wide energy range starting, in some cases, from View the MathML source and extending in others to the TeV energy range. It has been designed and constructed to expose the physics models utilised, to handle complex geometries, and to enable its easy adaptation for optimal use in different sets of applications. The toolkit is the result of a worldwide collaboration of physicists and software engineers. It has been created exploiting software engineering and object-oriented technology and implemented in the C++ programming language. It has been used in applications in particle physics, nuclear physics, accelerator design, space engineering and medical physics

Nuclei can be described satisfactorily in a nonlinear chiral SU(3)-framework, even with standard potentials of the linear $\sigma$-model. The condensate value of the strange scalar meson is found to be important for the properties of nuclei even without adding hyperons. By neglecting terms which couple the strange to the nonstrange condensate one can reduce the model to a Walecka model structure embedded in SU(3). We discuss inherent problems with chiral SU(3) models regarding hyperon optical potentials.Comment: 25 pages, RevTe

We study dense nuclear matter and the chiral phase transition in a SU(2) parity doublet model at zero temperature. The model is defined by adding the chiral partner of the nucleon, the N', to the linear sigma model, treating the mass of the N' as an unknown free parameter. The parity doublet model gives a reasonable description of the properties of cold nuclear matter, and avoids unphysical behaviour present in the standard SU(2) linear sigma model. If the N' is identified as the N'(1535), the parity doublet model shows a first order phase transition to a chirally restored phase at large densities, ρ ≈ 10ρ0, defining the transition by the degeneracy of the masses of the nucleon and the N'. If the mass of the N' is chosen to be 1.2 GeV, then the critical density of the chiral phase transition is lowered to three times normal nuclear matter density, and for physical values of the pion mass, the first order transition turns into a smooth crossover.

We study the effect of dense quarks in a SU (N ) matrix model of deconfinement. For three or more colors, the quark contribution to the loop potential is complex. After adding the charge conjugate loop, the measure of the matrix integral is real, but not positive definite. In a matrix model, quarks act like a background Z(N ) field; at nonzero density, the background field also has an imaginary part, proportional to the imaginary part of the loop. Consequently, while the expectation values of the loop and its complex conjugate are both real, they are not equal. These results suggest a possible approach to the fermion sign problem in lattice QCD. PACS numbers:At nonzero temperature, numerical simulations in lattice QCD have provided fundamental insight into the transition from a hadronic, to a deconfined, chirally symmetric plasma [1]. At nonzero quark density, however, at present simulations are stymied by the "fermion sign problem" [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. Even in the limit of high temperature, and small chemical potential, only approximate methods can be used [18,19,20,21,22,23].In this paper we consider deconfinement in a mean field approximation to a model of thermal Wilson lines [24,25], which is a matrix model [26,27,28,29,30,31,32,33,34,35,36,37]. In Sec. I we discuss general features of SU (N ) matrix models at nonzero quark density [27]. In sec. II, this is briefly contrasted with the (trivial) case of a U (1) model [5]. Numerical results for three colors are presented in Sec. III. In Sec. IV, we conclude with some remarks about some methods which might be of use for dense quarks in lattice QCD. I. SU (N ) MATRIX MODELIn a gauge theory at nonzero temperature, a basic quantity is the thermal Wilson line, L = P exp(ig A 0 dτ ), where g is the gauge coupling, A 0 is the timelike component of the vector potential, and the integral over the imaginary time, τ , runs from 0 to 1/T , where T is the temperature [24]. An effective theory of thermal Wilson lines, interacting with static magnetic fields, can be constructed, and is valid in describing correlations over spatial distances ≫ 1/T [26,28,29,30,31,32,33,35,36,37].Over large distances, we use a mean field approximation to this effective theory. This gives an integral over a single Wilson line, L, with the partition function that of a matrix model:L is an SU (N ) matrix, satisfying L † L = 1 and det L = 1. Under gauge transformations Ω, it transforms as L → Ω † LΩ, so that gauge invariant quantities are formed by taking traces of L. These are Polyakov loops. In the matrix model, the effects of gluons and quarks are represented by potentials, V gl (L) and V qk (L), which are (gauge invariant) functions of the Wilson line. The effects of fluctuations, which are not included in the matrix model, can also be included in a systematic fashion [33,38].The pure glue theory is invariant under a global symmetry of Z(N ) , and so this must be a symmetry of the gluon loop potential, V gl (L). The simplest form for the gluon loop potential is a type of...