The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We analyze the case when the coherence lengths of two consecutive splitting processes overlap, which is important for understanding corrections to standard treatments of the LPM effect in QCD. Previous authors have analyzed this problem in the case of overlapping double bremsstrahlung where at least one of the bremsstrahlung gluons is soft. Here we show how to generalize to include the case where both splittings are hard. A number of techniques must be developed, and so in this paper we simplify by (i) restricting attention to a subset of the interference effects, which we call the "crossed" diagrams, and (ii) working in the large-N c limit. We first develop some general formulas that could in principle be implemented numerically (with substantial difficulty). To make more analytic progress, we then focus on the case of a thick, homogeneous medium and make the multiple scattering approximation (also known as theq or harmonic approximation) appropriate at high energy. We show that the differential rate dΓ/dx dy for overlapping double bremsstrahlung of gluons with momentum fractions x and y can then be reduced to the calculation of a 1-dimensional integral, which we perform numerically.

CMS is a general purpose experiment, designed to study the physics of pp collisions at 14 TeV at the Large Hadron Collider (LHC). It currently involves more than 2000 physicists from more than 150 institutes and 37 countries. The LHC will provide extraordinary opportunities for particle physics based on its unprecedented collision energy and luminosity when it begins operation in 2007.The principal aim of this report is to present the strategy of CMS to explore the rich physics programme offered by the LHC. This volume demonstrates the physics capability of the CMS experiment. The prime goals of CMS are to explore physics at the TeV scale and to study the mechanism of electroweak symmetry breaking-through the discovery of the Higgs particle or otherwise. To carry out this task, CMS must be prepared to search for new particles, such as the Higgs boson or supersymmetric partners of the Standard Model particles, from the start-up of the LHC since new physics at the TeV scale may manifest itself with modest data samples of the order of a few fb −1 or less. The analysis tools that have been developed are applied to study in great detail and with all the methodology of performing an analysis on CMS data specific benchmark processes upon which to gauge the performance of CMS. These processes cover several Higgs boson decay channels, the production and decay of new particles such as Z and supersymmetric particles, B s production and processes in heavy ion collisions. The simulation of these benchmark processes includes subtle effects such as possible detector miscalibration and misalignment. Besides these benchmark processes, the physics reach of CMS is studied for a large number of signatures arising in the Standard Model and also in theories beyond the Standard Model for integrated luminosities ranging from 1 fb −1 to 30 fb −1 . The Standard Model processes include QCD, B-physics, diffraction, detailed studies of the top quark properties, and electroweak physics topics such as the W and Z 0 boson properties. The production and decay of the Higgs particle is studied for many observable decays, and the precision with which the Higgs boson properties can be derived is determined. About ten different supersymmetry benchmark points are analysed using full simulation. The CMS discovery reach is evaluated in the SUSY parameter space covering a large variety of decay signatures.

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. In this paper, we continue analysis of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-gluon approximations. In particular, this paper analyzes the subtle problem of how to precisely separate overlapping double splitting (e.g. overlapping double bremsstrahlung) from the case of consecutive, independent bremsstrahlung (which is the case that would be implemented in a Monte Carlo simulation based solely on single splitting rates). As an example of the method, we consider the rate of real double gluon bremsstrahlung from an initial gluon with various simplifying assumptions (thick media;q approximation; large N c ; and neglect for the moment of processes involving 4-gluon vertices) and explicitly compute the correction ∆ dΓ/dx dy due to overlapping formation times.

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-emission approximations. Previous work has computed overlap effects for double splitting g → gg → ggg. To make use of those results, one also needs calculations of related virtual loop corrections to single splitting g → gg in order to cancel severe (power-law) infrared (IR) divergences. This paper provides calculations of nearly all such processes involving gluons and discusses how to organize the results to demonstrate the cancellation. In the soft emission limit, our results reproduce the known double-log behavior of earlier authors who worked in leading-log approximation. We also present a first (albeit numerical and not yet analytic) investigation of sub-leading, single IR logarithms. Ultraviolet divergences appearing in our calculations correctly renormalize the coupling αs in the usual LPM result for leading-order g → gg.

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. Of recent interest is the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD). In previous papers, we have developed methods for computing such corrections without making soft-gluon approximations. However, our methods require consistent treatment of canceling ultraviolet (UV) divergences associated with coincident emission times, even for processes with tree-level amplitudes. In this paper, we show how to use dimensional regularization to properly handle the UV contributions. We also present a simple diagnostic test that any consistent UV regularization method for this problem needs to pass.

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-emission approximations. In this particular paper, we show (i) how the "instantaneous" interactions of Light-Cone Perturbation Theory must be included in the calculation to account for effects of longitudinally-polarized gauge bosons in intermediate states, and (ii) how to compute virtual corrections to LPM emission rates, which will be necessary in order to make infrared-safe calculations of the characteristics of inmedium QCD showering of high-energy partons. In order to develop these topics in as simple a context as possible, we will focus in the current paper not on QCD but on large-N f QED, where N f is the number of electron flavors. Contents

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. In this paper, we continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-gluon approximations. In particular, this paper completes the calculation of the rate for real double gluon bremsstrahlung from an initial gluon with various simplifying assumptions (thick media; $\hat q$ approximation; and large $N_c$) by now including processes involving 4-gluon vertices.Comment: 35 pages, 17 figures [changes from v1: minor typo fixes and minor referencing updates

This report presents the capabilities of the CMS experiment to explore the rich heavy-ion physics programme offered by the CERN Large Hadron Collider (LHC). The collisions of lead nuclei at energies √ s N N = 5.5 TeV, will probe quark and gluon matter at unprecedented values of energy density. The prime goal of this research is to study the fundamental theory of the strong interaction -Quantum Chromodynamics (QCD) -in extreme conditions of temperature, density and parton momentum fraction (low-x).This report covers in detail the potential of CMS to carry out a series of representative Pb-Pb measurements. These include "bulk" observables, (charged hadron multiplicity, low p T inclusive hadron identified spectra and elliptic flow) which provide information on the collective properties of the system, as well as perturbative probes such as quarkonia, heavy-quarks, jets and high p T hadrons which yield "tomographic" information of the hottest and densest phases of the reaction.