Low-rank properties in the hybrid finite element-boundary integral method

C

An effective theory for jet propagation in dense QCD matter: jet broadening and medium-induced bremsstrahlung

Two effects, jet broadening and gluon bremsstrahlung induced by the propagation of a highly energetic quark in dense QCD matter, are reconsidered from effective theory point of view. We modify the standard Soft Collinear Effective Theory (SCET) Lagrangian to include Glauber modes, which are needed to implement the interactions between the medium and the collinear fields. We derive the Feynman rules for this Lagrangian and show that it is invariant under soft and collinear gauge transformations. We find that the newly constructed theory SCET$_{\rm G}$ recovers exactly the general result for the transverse momentum broadening of jets. In the limit where the radiated gluons are significantly less energetic than the parent quark, we obtain a jet energy-loss kernel identical to the one discussed in the reaction operator approach to parton propagation in matter. In the framework of SCET$_{\rm G}$ we present results for the fully-differential bremsstrahlung spectrum for both the incoherent and the Landau-Pomeranchunk-Migdal suppressed regimes beyond the soft-gluon approximation. Gauge invariance of the physics results is demonstrated explicitly by performing the calculations in both the light-cone and covariant $R_{\xi}$ gauges. We also show how the process-dependent medium-induced radiative corrections factorize from the jet production cross section on the example of the quark jets considered here.Comment: 52 pages, 15 pdf figures, as published in JHE

Improved convergence of scattering calculations in the oscillator representation

The Schr\"odinger equation for two and tree-body problems is solved for scattering states in a hybrid representation where solutions are expanded in the eigenstates of the harmonic oscillator in the interaction region and on a finite difference grid in the near-- and far--field. The two representations are coupled through a high--order asymptotic formula that takes into account the function values and the third derivative in the classical turning points. For various examples the convergence is analyzed for various physics problems that use an expansion in a large number of oscillator states. The results show significant improvement over the JM-ECS method [Bidasyuk et al, Phys. Rev. C 82, 064603 (2010)]

Transport with three-particle interaction

Starting from a point - like two - and three - particle interaction the kinetic equation is derived. While the drift term of the kinetic equation turns out to be determined by the known Skyrme mean field the collision integral appears in two - and three - particle parts. The cross section results from the same microscopic footing and is naturally density dependent due to the three - particle force. By this way no hybrid model for drift and cross section is needed for nuclear transport. Besides the mean field correlation energy the resulting equation of state has also a two - and three - particle correlation energy which are both calculated analytically for the ground state. These energies contribute to the equation of state and lead to an occurrence of a maximum at 3 times nuclear density in the total energy.Comment: typos correction