New method for calculating helicity amplitudes of jet-like QED processes for high-energy colliders II. Processes with lepton pair production

As continuation of our previous paper we further develop our new method for calculating helicity amplitudes of jet-like QED processes described by tree diagrams, applying it to lepton pair production. This method consists in replacing spinor structures for real and weakly virtual intermediate leptons by simple transition vertices. New vertices are introduced for the pair production case, and previous bremsstrahlung vertices are generalized to include virtual photons inside the considered jet. We present a diagrammatic approach that allows to write down in an efficient way the leading helicity amplitudes, at tree level. The obtained compact amplitudes are particularly suitable for numerical calculations in jet-like kinematics. Several examples with up to four particles in a jet are discussed in detail.Comment: 11 pages, 11 figures, Latex, Springer-Latex macros include

New method for calculating helicity amplitudes of jet--like QED processes for high--energy colliders I. Bremsstrahlung processes

Inelastic QED processes, the cross sections of which do not drop with increasing energy, play an important role at high-energy colliders. Such reactions have the form of two-jet processes with the exchange of a virtual photon in the t-channel. We consider them in the region of small scattering angles $m/E \lesssim \theta \ll 1$, which yields the dominant contribution to their total cross sections. A new effective method is presented and applied to QED processes with emission of real photons to calculate the helicity amplitudes of these processes. Its basic idea is similar to the well-known equivalent-lepton method. Compact analytical expressions for those amplitudes up to $e^8$ are derived omitting only terms of the order of $m^2/E^2, \theta^2$, $\theta m/E$ and higher order. The helicity amplitudes are presented in a compact form in which large compensating terms are already cancelled. Some common properties for all jet-like processes are found and we discuss their origin.Comment: 17 pages, LATEX (svjour style files included

A new possibility to monitor collisions of relativistic heavy ions at LHC and RHIC

We consider the radiation of particles of one bunch in the collective field of the oncoming bunch, called coherent bremsstrahlung (CBS). The main characteristics of CBS for LHC (in the Pb-Pb mode) and for RHIC are calculated. At LHC about $3.9 10^8 dE_\gamma/E_\gamma$ photons per second are expected for photon energies $E_\gamma \stackrel{<} {\sim} E_c= 93$ eV. It seems that CBS can be a potential tool for optimizing collisions and for measuring beam parameters. The bunch length can be found from the critical energy of the CBS spectrum; the transverse bunch size is related to the photon rate. A specific dependence of photon rate on the impact parameter between the beams allows for a fast control over the beam displacement.Comment: 9 pages + 4 figures, latex with poscript figures uuencode

Charge asymmetry of pions in the process e−e+→e−e+π+π−e^-e^+\to e^-e^+\pi^+\pi^-

The study of the charge asymmetry of produced particles allows to investigate the interference of different production mechanisms and to determine new features of the corresponding amplitudes. In the process $e^- e^+ \to e^- e^+ \pi^+ \pi^-$ the two-pion system is produced via two mechanisms: two-photon (C-even state) and bremsstrahlung (C-odd state) production. We study the charge asymmetry of pions in a differential in the pion momenta cross section originating from an interference between these two mechanisms. At low effective mass of dipions this asymmetry is directly related to the s- and p-phases of elastic $\pi\pi$ scattering. At higher energies it can give new information about the $f_0$ meson family, $f_2(1270)$ meson, etc. The asymmetry is expressed via the pion form factor $F_\pi$ and helicity amplitudes $M_{ab}$ for the subprocess $\gamma^*\gamma\to \pi^+\pi^-$ as $\sum G_{ab}{\rm Re}(F_\pi^*M_{ab})$ where we have calculated analytically the coefficients $G_{ab}$ for the region giving the main contribution to the effect. Several distributions of pions are presented performing a numerical analysis in a model with point-like pions. In the region near the dipion threshold the asymmetry is of the order of 1%. We show that with suitable cuts the signal to background ratio can be increased up to about 10%.Comment: 16 pages, 10 figures, LaTeX, style files for EPJC include

Photoemission study of the spin-density wave state in thin films of Cr

Angle-resolved photoemission (PE) was used to characterize the spin-density wave (SDW) state in thin films of Cr grown on W(110). The PE data were analysed using results of local spin density approximation layer-Korringa-Kohn-Rostoker calculations. It is shown that the incommensurate SDW can be monitored and important parameters of SDW-related interactions, such as coupling strength and energy of collective magnetic excitations, can be determined from the dispersion of the renormalized electronic bands close to the Fermi energy. The developed approach can readily be applied to other SDW systems including magnetic multilayer structures.Comment: 4 figure

Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach

We develop a general approach to the nonequilibrium dynamics of quantum impurity systems for arbitrary coupling strength. The numerical renormalization group is used to generate a complete basis set necessary for the correct description of the time evolution. We benchmark our method with the exact analytical solution for the resonant-level model. As a first application, we investigate the equilibration of a quantum dot subject to a sudden change of the gate voltage and external magnetic field. Two distinct relaxation times are identified for the spin and charge dynamics.Comment: 5 pages, 5 figure