Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross sections of multi-parton processes

We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method by calculating the singular part of the one-loop helicity amplitudes of all 2 → 3 parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all 2 → 4 parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporated in existing Monte Carlo simulation programs.     

Peripherical processes in QED at high energies

In this review we consider the high energy processes in QED frames in peripherical kinematics. The key feature of this kinematics is that processes have a large cross section which do not decrease with the increasing of the initial center of mass energy. Two purposes to study peripheral processes are: the background processes with large total cross sections and the structure of jets in the fragmentation region.We describe the various QED peripherical processes in terms of Impact Factors and give the explicit expressions for the differential distributions and spin correlation effects, as well as estimates of the total cross section of peripheral processes in photon-photon, photon-lepton and lepton-lepton collisions.A special attention is paid to the small-angle Bhabha scattering process which is relevant for beam monitoring at LEP I, LEP II.Based on analytical properties of the amplitudes some relations (QED sum rules) between the high energy asymptotic of the cross sections of inelastic processes in e ⁺ e ^? collisions and higher order perturbative contributions to the electron Dirac and Pauli form-factors are derived.For practical using we present some loop momentum integrals.     

Fast computation of MadGraph amplitudes on graphics processing unit (GPU)

Continuing our previous studies on QED and QCD processes, we use the graphics processing unit (GPU) for fast calculations of helicity amplitudes for general Standard Model (SM) processes. Additional HEGET codes to handle all SM interactions are introduced, as well as the program MG2CUDA that converts arbitrary MadGraph generated HELAS amplitudes (FORTRAN) into HEGET codes in CUDA. We test all the codes by comparing amplitudes and cross sections for multi-jet processes at the LHC associated with production of single and double weak bosons, a top-quark pair, Higgs boson plus a weak boson or a top-quark pair, and multiple Higgs bosons via weak-boson fusion, where all the heavy particles are allowed to decay into light quarks and leptons with full spin correlations. All the helicity amplitudes computed by HEGET are found to agree with those computed by HELAS within the expected numerical accuracy, and the cross sections obtained by gBASES, a GPU version of the Monte Carlo integration program, agree with those obtained by BASES (FORTRAN), as well as those obtained by MadGraph. The performance of GPU was over a factor of 10 faster than CPU for all processes except those with the highest number of jets.     

Multi-parton cross sections at hadron colliders

We present an alternative method to calculate cross sections for multi-parton scattering processes in the standard model at leading order. The helicity amplitudes are computed using recursion relations in the number of particles, based on the Dyson–Schwinger equations, whereas the summation over colour and helicity configurations is performed by Monte Carlo methods. The computational cost of our algorithm grows asymptotically as 3ⁿ, where n is the number of particles involved in the process, as opposed to the n!-growth of the Feynman diagram approach. Typical results for the total cross section, the differential distributions of the invariant masses and the transverse momenta of the partons are presented and cross checked by explicit summation over colours.     

HELAS and MadGraph with goldstinos

Fortran subroutines to calculate helicity amplitudes with goldstinos, which appear as the longitudinal modes of massive gravitinos in high energy processes, are added to the HELAS (HELicity Amplitude Subroutines) library. They are coded in such a way that arbitrary amplitudes with external goldstinos can be generated automatically by MadGraph, after slight modifications. All the codes have been tested carefully by making use of the goldstino equivalence theorem and the gauge invariance of the helicity amplitudes. Hadronic total cross sections for associated gravitino productions with a gluino and a squark are also presented.     

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

As a continuation of our previous paper [Eur. Phys. J. C 23, 633 (2002)] 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 us 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. Received: 31 March 2003, Published online: 18 June 2003     

Amplitudes with different helicity configurations of noncommutative QED

The amplitudes of purely photon processes of noncommutative QED (NCQED) are derived for different helicity configurations of photons. The basic ingredient is the NCQED counterpart of the Yang–Mills recursion relations by means of Berends and Giele. The explicit solutions of recursion relations for NCQED photon current with special helicity configurations and also recursion relations for the NCQED fermion–photon current with special helicity configurations of photons (all photons have plus helicity) are presented.     

On the symmetries between neutrino and antineutrino-nucleon elastic scattering

Various symmetry relations developed between neutrino-neutron and antineutrino-proton elastic scattering cross sections are surveyed and an identity between scattering amplitudes and a symmetry between cross sections of these processes established by consideringCPT andG conjugation invariance of current matrix elements. A symmetry is obtained giving rise to a theorem on the nature of contribution of form factors to terms in the cross sections.     

Jets production in peripheral interactions of high energy leptons,quarks, photons,and gluons with the proton

The paper presents short historical reviews of the processes of lepton pairs production in peripheral interaction of leptons and ions at high energies. The orders of magnitude of the QED and QCD cross sections with the production of two and three jets are given. The technique of the analysis is described in detail based on the parameterization of Sudakov 4-momentum tasks and writing the amplitude in an explicit gaugeinvariant form. Based on this formalism the differential cross sections of QCD processes \(gp \to (ggg)p;qp \to (q\bar QQ)p;gp \to (gQ\bar Q)P\) were obtained, including the distribution on transverse momentum component of jets fragments. It was shown that the role of the contribution of “non-Abelian” nature may become dominant in a particular kinematics of the final particles. The kinematics, in which the initial particle changes the direction of movement to the opposite one, was considered in the case of heavy quark-antiquark pair production. In the appendices, the details of the calculations and the explicit form of the differential cross sections are given. Some extended comments on the frequently used cross sections of the pair production in the case of two-photon scattering are presented. In particular, the degree of the longitudinal polarization of the positron, the interaction polarized initial electron, was calculated. The method of calculating the cross sections of the 2 → 2 processes in QCD, based on the isolation of irreducible color structures and the method CALCUL of spiral amplitudes, was discussed in detail.     

Radiative corrections to helicity amplitudes forW-pair production ine + e−-annihilation

Radiative corrections toW pair production ine ⁺ e^?-annihilation are investigated. In an earlier work we discussed only the weak corrections to this process. Here we present the complete calculation including QED corrections. Full agreement with other authors is achieved. We use the helicity formalism for the projection of theS-matrix into invariant amplitudes and study the dependence of cross sections on the Higgs and top masses. Effects due to the choice of the renormalization scheme are considered.     

Scalar and Pseudo-Scalar Form Factors in Electro- and Weak-Production of Pion Near Threshold

We investigated pion production near threshold by the weak current in terms of multipole amplitudes. By exploiting the chiral Ward identity based on the QCD Lagrangian, we derived relevant multipole amplitudes in closed forms and presented their numerical results. In the amplitudes, scalar and pseudo scalar (PS) form factors, which represent the scalar and the PS quark density distributions, manifest by themselves. We applied these amplitudes to the cross sections for the weak- and electro-production near threshold. Both pion and PS form factor contributions are shown to account for the t-channel contribution in the charged pion electro-production near threshold. The asymmetry on the pion production by the neutrino and anti-neutrino is also discussed with their longitudinal and transverse cross sections.     

Description of spin-dependent observables in elastic proton-deuteron scattering on the basis of a generalized diffraction model

Spin-dependent observables of elastic proton-deuteron (pd) scattering at intermediate energies are considered on the basis of calculations within a generalized diffraction model. The generalization in question takes into account all ten helicity proton-proton (pp) and proton-neutron (pn) amplitudes constructed on the basis of a present-day partial-wave analysis and precise deuteron wave functions derived from two alternative models of nucleon-nucleon (NN) forces. Explicit relations between the invariant amplitudes of pd scattering and input NN helicity amplitudes are found. Among other things, these relations make it possible to reconstruct unknown pn amplitudes at energies above 1 GeV on the basis of data on pd scattering. The predictions of the generalized diffraction model for differential cross sections and analyzing powers are compared with the latest experimental data. Surprisingly good agreement with experimental data over a broad interval of scattering angles is found both for differential cross sections and for vector and tensor analyzing powers.     

A unified treatment of electromagnetic decays,electroproduction, and pair production in e+e− annihilation for hadrons of arbitrary spin

We gather together in a unified notation formulas for electromagnetic decay rates of resonances and cross sections for electroproduction and e⁺e^? annihilation for all those processes which can be expressed in terms of matrix elements of the electromagnetic current between single particle (or resonant) helicity states. We show in complete generality how to decompose such helicity matrix elements into form factors which are free of all kinematic singularities and constraints simultaneously at both physical thresholds, and relate them to the familiar multipole moments and to some others which have been used in data analysis. Tables are given of the form factor decomposition of the helicity matrix elements for many cases of actual and potential practical interest.     

Elastic electroproduction of \rho mesons at HERA

The elastic electroproduction of mesons is studied at HERA with the H1 detector for a photon virtuality in the range and for a hadronic centre of mass energy in the range GeV. The shape of the () mass distribution in the resonance region is measured as a function of . The full set of spin density matrix elements is determined, and evidence is found for a helicity flip amplitude at the level of of the non-flip amplitudes. Measurements are presented of the dependence of the cross section on , W and t (the four-momentum transfer squared to the proton). They suggest that, especially at large , the cross section develops a stronger W dependence than that expected from the behaviour of elastic and total hadron–hadron cross sections. Received: 22 February 1999 / Published online: 25 February 2000     

Model independent fitting to theZ line shape

An improved model independent formula to fit theZ line shape parameters is presented. The accuracy of the QED radiative corrections used in the formula is estimated, as is the absolute accuracy of the formula itself. The precision of the formula is compared with existing fitting formulae, in terms of cross sections produced and in terms of theZ parameters returned from a fit. The errors which the LEP-SLC experiments can expect to achieve on theZ parameters are examined as a function of total integrated luminosity. The formula presented here can fit theZ parameters with high accuracy: below 1 MeV for theZ mass, the order of 1 MeV for total width, and below 0.04% for the hadronic and leptonic peak cross sections. Such biases will remain much below the expected experimental uncertainties from LEP and SLC.     

Cross sections for charmonia dissociation in collisions with pions, rhos and kaons

We calculate the unpolarized cross sections for dissociation reactions of charmonia in collisions with π,ρ and K in a potential that is derived from QCD.The reactions are governed by the quark-interchange processes.The mesonic quark-antiquark relative-motion wave functions are determined by the central spinindependent terms of the potential.The numerical wave functions and cross sections are parametrized.The difference of transition amplitudes in the prior form and in the post form is explored by deriving and examining the transition amplitudes of the one-gluon-exchange spin-spin term of the potential in the two forms.We find that the post-prior discrepancy in meson-meson elastic scattering that is governed by quark-interchange processes depends on the difierence of quark or antiquark masses and of quark-antiquark spatial distributions ofthe two mesons.     

Signature and unitary in the multi-Regge model

In a previous paper it was shown how factorisation and signature properties for production processes arose from a well-defined set of singularities in complex angular momentum and helicity. These arose for Feynman diagrams without crossed channel singularities. In this paper we show how the general case gives rise to a sum of terms of this form. We also show how these precise singularities are crucial to prevent the occurence of terms in inclusive pionisation cross sections which are much greater than the canonical pomeron terms.     

Reproducing kernel Hilbert spaces and extremal problems for scattering of particles with arbitrary spins

In this paper each helicity amplitude of the two-body scattering of particles with arbitrary spins is considered as an element of a special class of Hilbert spacesH ^[u]. This space, which is called reproducing kernel Hilbert space (RKHS) has many special properties that appear to make it a natural space of functions to associate with the scattering helicity amplitudes. Some of the special properties of the RKHS are developed and then used to characterization of reproducing kernel (RK) ofH ^[u] as the solution to certain extremal problems. Then, it was shown that the optimal scattering state from the RKHS of the helicity amplitudes is analogous to the coherent state from the RKHS of the wave functions. The essential characteristic features of the scattering of particles with arbitrary spins in the optimal state dominance limit are established. An important alternative to the partial wave helicity analysis in terms of a fundamental set of optimal states is presented.     

Angular correlation for nuclear muon capture

Formulae for the capture rates, gamma-neutrino correlations, and angular distributions of recoil in muon capture processes J_i J_f by an unpolarized nucleus for J_i ≦ 3 and J_f ≦ 5/2, with and without change of parity of nuclear levels, are given explicitely in terms of the multipole amplitudes. Relation of helicity amplitudes for muonic atom decay to the multipole amplitudes and to amplitudes introduced by other authors is presented. The derivation is based on kinematics only, and the formulae are strictly valid for the muon capture by any nuclei. The formulae are convenient for model calculations of partial transitions with realistic nuclear and muon wave functions and for the phenomenological analysis of a weak interaction.     

SINGLE BREMSSTRAHLUNG PROCESSES IN QUANTUM GRAVITY

We investigate single bremsstxahlung processes in gauge theories involving massless scalars and fermions interacting with photons and gravitons.As in QED and SU(N),we find that the cross sections are very simple and can be factorized in two parts:a generalized infrared factor and a factor which is related to the lowest order elastic process.