Photon bremsstrahlung and diffusive broadening of a hard jet

The photon bremsstrahlung rate from a quark jet produced in deep-inelastic scattering (DIS) off a large nucleus is studied in the collinear limit. The leading medium-enhanced higher twist corrections which describe the multiple scattering of the jet in the nucleus are re-summed to all orders of twist. The propagation of the jet in the absence of further radiative energy loss is shown to be governed by a transverse momentum diffusion equation. We compute the final photon spectrum in the limit of soft photons, taking into account the leading and next-to-leading terms in the photon momentum fraction y. In this limit, the photon spectrum in a physical gauge is shown to arise from two interfering sources: one where the initial hard scattering produces an off-shell quark which immediately radiates the photon and then undergoes subsequent soft re-scattering; alternatively the quark is produced on-shell and propagates through the medium until it is driven off-shell by re-scattering and radiates the photon. Our result has a simple formal structure as a product of the photon splitting function, the quark transverse momentum distribution coming from a diffusion equation and a dimensionless factor which encodes the effect of the interferences encountered by the propagating quark over the length of the medium. The destructive nature of such interferences in the small y limit are responsible for the origin of the Landau-Pomeranchuck-Migdal (LPM) effect. Along the way we also discuss possible implications for quark jets in hot nuclear matter.Comment: 24 pages, 3 figures, Revtex

Hard collinear gluon radiation and multiple scattering in a medium

The energy loss of hard jets produced in the Deep-Inelastic scattering (DIS) off a large nucleus is considered in the collinear limit. In particular, the single gluon emission cross section due to multiple scattering in the medium is calculated. Calculations are carried out in the higher-twist scheme, which is extended to include contributions from multiple transverse scatterings on both the produced quark and the radiated gluon. The leading length enhanced parts of these power suppressed contributions are resummed. Various interferences between such diagrams lead to the Landau-Pomeranchuk-Migdal (LPM) effect. We resum the corrections from an arbitrary number of scatterings and isolate the leading contributions which are suppressed by one extra power of the hard scale $Q^{2}$. All powers of the emitted gluon forward momentum fraction $y$ are retained. We compare our results with the previous calculation of single scattering per emission in the higher-twist scheme as well as with multiple scattering resummations in other schemes. It is found that the leading ($1/Q^2$) contribution to the double differential gluon production cross section, in this approach, is equivalent to that obtained from the single scattering calculation once the transverse momentum of the final quark is integrated out. We comment on the generalization of this formalism to Monte-Carlo routines.Comment: 30 pages, 7 figures, revtex4, typos correcte

Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves

We study the long-time evolution of gravity waves on deep water exited by the stochastic external force concentrated in moderately small wave numbers. We numerically implement the primitive Euler equations for the potential flow of an ideal fluid with free surface written in canonical variables, using expansion of the Hamiltonian in powers of nonlinearity of up to fourth order terms. We show that due to nonlinear interaction processes a stationary energy spectrum close to $|k| \sim k^{-7/2}$ is formed. The observed spectrum can be interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of energy.Comment: 4 pages, 5 figure