Particles In Intermediate States Research Articles

Mathematical aspects of the nuclear glory phenomenon: from backward focusing to Chebyshev polynomials

The angular dependence of the cumulative particles production off nuclei near the kinematical boundary for multistep process is defined by characteristic polynomials in angular variables, describing spatial momenta of the particles in intermediate states. Physical argumentation, exploring the small phase space method, leads to the appearance of equations for the polynomials in cos(θ/N), where θ is the polar angle defining the momentum of final (cumulative) particle, the integer N being the number of interactions. The recurrent relations between polynomials with different N and their factorization properties are derived, the connection of these polynomials with known in mathematics Chebyshev polynomials of 2-d kind is established. As a result, differential cross section of the cumulative particle production has characteristic behaviour near the strictly backward direction (θ ∼ π, the backward focusing effect). Such behaviour takes place for any multiplicity of the interaction, beginning with n = 3, elastic or inelastic (with resonance excitations in intermediate states) and can be called the nuclear glory phenomenon.

Constraining compressed supersymmetry using leptonic signatures

Abstract We study the impact of the multi-lepton searches at the LHC on supersymmetric models with compressed mass spectra. For such models the acceptances of the usual search strategies are significantly reduced due to requirement of large effective mass and $ E_T^{\mathrm{miss}} $ . On the other hand, lepton searches do have much lower thresholds for $ E_T^{\mathrm{miss}} $ and p T of the final state objects. Therefore, if a model with a compressed mass spectrum allows for multi-lepton final states, one could derive constraints using multi-lepton searches. For a class of simplified models we study the exclusion limits using ATLAS multi-lepton search analyses for the final states containing 2-4 electrons or muons with a total integrated luminosity of 1-2 fb−1 at $ \sqrt{s}=7\,\mathrm{TeV} $ . We also modify those analyses by imposing additional cuts, so that their sensitivity to compressed supersymmetric models increase. Using the original and modified analyses, we show that the exclusion limits can be competitive with jet plus $ E_T^{\mathrm{miss}} $ searches, providing exclusion limits up to gluino masses of 1 TeV. We also analyse the efficiencies for several classes of events coming from different intermediate state particles. This allows us to assess exclusion limits in similar class of models with different cross sections and branching ratios without requiring a Monte Carlo simulation.

Probing CP violation with kinematic reconstruction at the LHC

AbstractWe discuss the potential of observing effects of CP‐violation phases in squark decay chains at the LHC [1]. As the CP‐odd observable, we use the asymmetry composed by triple products of final state momenta. There are good prospects of observing these effects using the method of kinematic reconstruction for the final and intermediate state particles. We also discuss the main experimental factors and the expected sensitivity.

FACTORIZATION EFFECTS IN A MODEL OF UNSTABLE PARTICLES

The effects of factorization are considered within the framework of the model of unstable particles with a smeared mass. It is shown that two-particle cross-section and three-particle decay width can be described by the universal factorized formulae for an unstable particles of an arbitrary spin in an intermediate state. The exact factorization is caused by the specific structure of the model unstable-particle propagators. This result is generalized to complicated scattering and decay-chain processes with unstable particles in intermediate states. We analyze applicability of the method and evaluate its accuracy.

Three-body Coulomb Green function and the reactions with charged particles at low energies

It has been shown that the inclusion of all possible Coulomb rescatterings of three charged particles in intermediate state results in an infinite series of diagrams which have a pole located at the same place as the pole of the pole diagram. The contribution of the pole terms of such infinite series has explicitly been singled out and summed-up. Renormalization of the pole diagram amplitude due to all the possible Coulomb rescatterings of particles in intermediate state has been found. The result obtained means that the three-body Coulomb Green function entering the expression for the reaction amplitude may be written in the form of the renormalized free Green function plus the residue which behaves as in the case of short-range interactions.

Theoretical Difficulties with the Regge-Eikonal Model

Dynamical models are used to discuss the theoretical justification of the Regge-eikonal formula for scattering amplitudes. A generalized ladder-diagram model with Reggeon exchange replacing single-particle exchange yields the eikonal result only if the Reggeon amplitude has no mass-shell dependence, since the intermediate-state particles are far from their mass shells at high energy. This result is contrasted with a nonperturbative model of a Regge-pole amplitude which has strong mass-shell dependence. Next, a theory in which the coupling of the Reggeons to the external particles is nonplanar is examined. The double-Reggeon-exchange amplitude does not satisfy the eikonal representation. The perturbation-theory model of Cicuta and Sugar is shown to break down if higher-order corrections to the residue function are calculated. The conclusion of the paper is that there does not exist any theoretical justification for considering the Regge-eikonal model to be a valid description of high-energy scattering.

Spectral Representations in Perturbation Theory. I. Vertex Function

The vertex operator is examined in lowest order perturbation theory. It is found that, as a function of the invariant momentum transfer ${q}^{2}={\mathrm{q}}^{2}\ensuremath{-}{{q}_{0}}^{2}$, it is analytic in a cut plane with the branch point on the negative real axis. A spectral representation (dispersion relation) may therefore be inferred. The threshold of the spectrum depends on the masses of all fields involved unless certain inequalities hold between the masses of the incident and outgoing particles on one hand and the particles in intermediate states on the other; in that case the threshold depends only on the intermediate masses.

Bound State Corrections in Two-Body Systems

Available expressions for two-body equations contain an interaction kernel which treats particles in intermediate states as free. In situations where the binding is important, such as the calculation of low-energy electrodynamic corrections, a more accurate treatment is necessary. A satisfactory formalism is developed for systems in which an instantaneous interaction is responsible for the binding. The procedure may then be used to evaluate the effects of small retarded perturbations. It consists of summing those binding interactions which occur during the retarded perturbations and which never should have been expanded as "small" effects. The result is expressed in terms of the two-body Green's function of the instantaneously interacting system. This function occurs to describe the propagation of the two particles in the intermediate state. The relative time coordinate does not appear explicitly in the formulas. The method is applied to the calculation of the hyperfine structure of positronium. The infrared divergences which occurred in a previous investigation of this effect are eliminated by the new approach.