Radiative return at NLO and the measurement of the hadronic cross-section in electron–positron annihilation

Electron–positron annihilation into hadrons plus an energetic photon from initial state radiation allows the hadronic cross-section to be measured over a wide range of energies. The full next-to-leading order QED corrections for the cross-section for annihilation into a real tagged photon and a virtual photon converting into hadrons are calculated where the tagged photon is radiated off the initial electron or positron. This includes virtual and soft photon corrections to the process and the emission of two real hard photons: . A Monte Carlo generator has been constructed, which incorporates these corrections and simulates the production of two charged pions or muons plus one or two photons. Predictions are presented for centre-of-mass energies between 1 and 10 GeV, corresponding to the energies of DANE, CLEO-C and B-meson factories. Received: 14 December 2001 / Published online: 5 April 2002     

Inclusive production of charged hadrons and {\rm K}^0_{\rm S} mesons in photon–photon collisions

The production of charged hadrons and mesons in the collisions of quasi-real photons has been measured using the OPAL detector at LEP. The data were taken at centre-of-mass energies of 161 and 172 GeV. The differential cross-sections as a function of the transverse momentum and the pseudorapidity of the charged hadrons and mesons have been compared to the leading order Monte Carlo simulations of PHOJET and PYTHIA and to perturbative next-to-leading order (NLO) QCD calculations. The distributions have been measured in the range GeV of the hadronic invariant mass W. By comparing the transverse momentum distribution of charged hadrons measured in interactions with -proton and meson-proton data we find evidence for hard photon interactions in addition to the purely hadronic photon interactions. Received: 4 June 1998 / Published online: 6 November 1998     

Observation of the muon inner bremsstrahlung at?LEP1

Muon bremsstrahlung photons converted in front of the DELPHI main tracker (TPC) in dimuon events at LEP1 were studied in two photon kinematic ranges: 0.2<E _γ ≤1 GeV and transverse momentum with respect to the parent muon p _T <40 MeV/c, and 1<E _γ ≤10 GeV and p _T <80 MeV/c. A good agreement of the observed photon rate with predictions from QED for the muon inner bremsstrahlung was found, contrary to the anomalous soft photon excess that has been observed recently in hadronic Z ⁰ decays. The obtained ratios of the observed signal to the predicted level of the muon bremsstrahlung are 1.06±0.12±0.07 in the photon energy range 0.2<E _γ ≤1 GeV and 1.04±0.09±0.12 in the photon energy range 1<E _γ ≤10 GeV. The bremsstrahlung dead cone is observed for the first time in the direct photon production at LEP. Deceased.     

Di-Jet production in photon-photon collisions at \sqrt{s}_{\rm ee}=161 and 172 GeV

Di-jet production is studied in collisions of quasi-real photons radiated by the LEP beams at ee centre-of-mass energies and 172 GeV. The jets are reconstructed using a cone jet finding algorithm. The angular distributions of direct and double-resolved processes are measured and compared to the predictions of leading order and next-to-leading order perturbative QCD. The jet energy profiles are also studied. The inclusive di-jet cross-section is measured as a function of and and compared to next-to-leading order perturbative QCD calculations. The inclusive di-jet cross-section as a function of is compared to the prediction of the leading order Monte Carlo generators PYTHIA and PHOJET. The Monte Carlo predictions are calculated with different parametrisations of the parton distributions of the photon. The influence of the ‘underlying event’ has been studied to reduce the model dependence of the predicted jet cross-sections from the Monte Carlo generators. Received: 15 July 1999 / Published online: 12 August 1999     

Di-jet production in γ γ collisions at LEP2

The production of two high-p _T jets in the interactions of quasi-real photons in e ⁺ e ⁻ collisions at from 189 GeV to 209 GeV is studied with data corresponding to an integrated e ⁺ e ⁻ luminosity of 550 pb⁻¹. The jets reconstructed by the k _⊥ -cluster algorithm are defined within the pseudo-rapidity range −1<η<1 and with jet transverse momentum, p _T , above 3 GeV/c. The differential di-jet cross-section is measured as a function of the mean transverse momentum of the jets and is compared to perturbative QCD calculations. Deceased     

Search for short-lived particles below charm threshold

We have searched for the production by virtual photons of short-lived particles that exhibit muonic decay. We used Brookhaven's 10.5 GeV/c muon beam and examined the two and three-muon final states. The sample of 158 trimuon events is due almost entirely to QED tridents. The sample of 673 dimuons can be accounted for in part by asymmetric tridents and in part by the decay of π and K mesons. We obtain an upper limit for the production of other short-lived particles of the order of Bδ < 150 pb/nucleon, where B is the branching ratio for muonic decay. From the trident sample we establish that muons obey Fermi-Dirac statistics at the level of 8 standard deviations.     

Measurement of dijet cross-sections in low {\rm Q}^2 ep collisions and the extraction of an effective parton density for the virtual photon

The triple-differential dijet cross-section, , is measured with the H1 detector at HERA as a function of the photon virtuality , the fraction of the photon's momentum carried by the parton entering the hard scattering, , and the square of the mean transverse energy, , of the two highest jets. Jets are found using a longitudinal boost-invariant clustering algorithm in the center of mass frame. The measurements cover the ranges GeV in virtuality and in inelasticity y. The results are well described by leading order QCD models which include the effects of a resolved component to the virtual photon. Models which treat the photon as point-like fail to describe the data. An effective leading order parton density for the virtual photon is extracted as a function of the photon virtuality, the probing scale and the parton momentum fraction. The and probing scale dependences of the parton density show characteristic features of photon structure, and a suppression of this structure with increasing is seen. Received: 18 December 1998 / Published online: 25 February 2000     

High-E_T inclusive jet cross sections in photoproduction at HERA

Inclusive jet differential cross sections for the reaction with quasi-real photons have been measured with the ZEUS detector at HERA. These cross sections are given for the photon-proton centre-of-mass energy interval 134 277 GeV and jet pseudorapidity in the range in the laboratory frame. The results are presented for three cone radii in the plane, . Measurements of above various jet-transverse-energy thresholds up to 25 GeV and in three ranges of W are presented and compared to next-to-leading order (NLO) QCD calculations. For jets defined with differences between data and NLO calculations are seen at high and low . The measured cross sections for jets defined with are well described by the calculations in the entire measured range of and . The inclusive jet cross section for GeV is consistent with an approximately linear variation with the cone radius R in the range between 0.5 and 1.0, and with NLO calculations. Received: 11 February 1998 / Published online: 2 July 1998     

Multi-photon production in ee collisions at \sqrt{s} = 181-209 GeV

The process is studied using data collected by the OPAL detector at LEP between the years 1997 and 2000. The data set corresponds to an integrated luminosity of 672.3 pb^-1 at centre-of-mass energies lying between 181 GeV and 209 GeV. Total and differential cross-sections are determined and found to be in good agreement with the predictions of QED. Fits to the observed angular distributions are used to set limits on parameters from several models of physics beyond the Standard Model such as cut-off parameters, contact interactions of the type , gravity in extra spatial dimensions and excited electrons. In events with three photons in the final state the mass spectrum of photon pairs is investigated. No narrow resonance is found and limits are placed on the product of the production cross-section and branching ratio. Received: 22 July 2002 / Published online: 8 November 2002     

THE VERTICAL DIFFERENTIAL MOMENTUM SPECTRUM OF THE MUON AT 3200M ABOVE SEA-LEVEL

The vertical differential momentum spectrum and the charge ratio of the cosmic ray muon, in the range(0.4—250GeV/c), has been measured by means of the magnetic spectrometer and the range-spectrometer in Yunnan station at 3200 m above the sea level. The present spectrum is in agreement with the differential spectrum of muons, measured by others at the same mountain altitude. In the 15—250GeV/c momentum range, the spectrum obtained from the present experiment is also in good agreement with the differential spectrum of the muon which has been determined by O.C. Allkofer et al. at the sea level. The charge ratio of the muon is almost constant in the range (5—100GeV/c). The average value is 1.30±0.06.     

Measurement of doubly differential collision cross-sections for double-photon Compton scattering of 0.662 MeV gamma rays

The doubly differential collision cross-sections of the double-photon Compton process have been measured experimentally for 0.662 MeV incident gamma photons. The measurements are carried out using a single gamma detector, a technique avoiding the use of the complicated slow–fast coincidence set-up used till now for observing this higher order QED process. The energy spectra of detected photons are observed as a long tail to the single-photon Compton line on the lower side of the full energy peak in the recorded scattered energy spectrum. The measured values of the cross-section for different independent energy levels of one of the two final photons are of the same magnitude but show deviation from the corresponding values obtained from the theory. However, the present measurements are first of its kind and in view of the nature and order of deviations, the agreement of measured values with theory is quite satisfactory.     

Measurement of isolated prompt photon production in photon-photon collisions at $\sqrt{s_{\rm ee}} = 183$-209 GeV

For the first time at LEP the production of prompt photons is studied in the collisions of quasi-real photons using the OPAL data taken at centre-of-mass energies between 183 GeV and 209 GeV. The total inclusive production cross-section for isolated prompt photons in the kinematic range of transverse momentum GeV and pseudorapidity is determined to be . Differential cross-sections are compared to the predictions of a next-to-leading-order (NLO) calculation.Received: 6 May 2003, Published online: 4 November 2003     

Total hadronic cross-section of photon-photon interactions at LEP

The total hadronic cross-section for the interaction of real photons, hadrons, is measured for centre-of-mass energies GeV. The cross-section is extracted from a measurement of the process hadrons, using a luminosity function for the photon flux together with form factors for extrapolating to real photons ( GeV). The data were taken with the OPAL detector at LEP at centre-of-mass energies , 172$ and 183 GeV. The cross-section is compared with Regge factorisation and with the energy dependence observed in p and pp interactions. The data are also compared to models which predict a faster rise of compared to p and pp interactions due to additional hard interactions not present in hadronic collisions. Received: 3 June 1999 / Published online: 6 April 2000     

On refractive processes in strong laser field quantum electrodynamics

Refractive processes in strong-field QED are pure quantum processes, which involve only external photons and the background electromagnetic field. We show analytically that such processes occurring in a plane-wave field and involving external real photons are all characterized by a surprisingly modest net exchange of energy and momentum with the laser field, corresponding to a few laser photons, even in the limit of ultra-relativistic laser intensities. We obtain this result by a direct calculation of the transition matrix element of an arbitrary refractive QED process and accounting exactly for the background plane-wave field. A simple physical explanation of this modest net exchange of laser photons is provided, based on the fact that the laser field couples with the external photons only indirectly through virtual electron–positron pairs. For stronger and stronger laser fields, the pairs cover a shorter and shorter distance before they annihilate again, such that the laser can transfer to them an energy corresponding to only a few photons. These results can be relevant for the future experiments aiming to test strong-field QED at present and next-generation facilities.     

A measurement of the photonuclear interactions of 180 GeV muons in iron

The energy spectrum and the cross section of photonuclear interactions of 180 GeV muons in iron were measured at the CERN SPS using prototype modules of the ATLAS hadron calorimeter. The differential cross section for a muon fractional energy loss was measured in the range 0.1&lt;v&lt;1. The integrated cross section is cm²g^-1 in agreement with the theoretical prediction of cm²g^-1. The best adjustment of the data to the theory is achieved for the value of of the photon-nucleon cross section for photons with energies in the range from 18 to 180 GeV. Received: 22 January 2003 / Published online: 5 May 2003     

Index summation in real time statistical field theory

We have written a Mathematica program that calculates the integrand corresponding to any amplitude in the closed-time-path formulation of real time statistical field theory. The program is designed so that it can be used by someone with no previous experience with Mathematica. It performs the contractions over the tensor indices that appear in real time statistical field theory and gives the result in the 1-2, Keldysh or RA basis. The program treats all fields as scalars, but the result can be applied to theories with dirac and lorentz structure by making simple adjustments. As an example, we have used the program to calculate the ward identity for the QED 3-point function, the QED 4-point function for two photons and two fermions, and the QED 5-point function for three photons and two fermions. In real time statistical field theory, there are seven 3-point functions, 15 4-point functions and 31 5-point functions. We produce a table that gives the results for all of these functions. In addition, we give a simple general expression for the KMS conditions between n-point green functions and vertex functions, in both the Keldysh and RA bases. PACS 11.10.Wx; 11.15.-q     

Unpolarized azimuthal asymmetries in SIDIS at COMPASS

The study of the spin structure of the nucleon and of the effects due to the quarks transverse momentum are part of the scientific program of COMPASS, a fixed target experiment at the CERN SPS. The azimuthal modulations which appear in the cross-section of SIDIS off unpolarised targets give insight on the intrinsic momentum structure of the nucleon and on the possible correlation between transverse spin and transverse momentum of the quarks. We present the results for the amplitudes of the cos(?), cos(2?), and sin(?) modulatuions (where ? is the azimuthal hadron angle in the gamma-nucleon system) obtained from the COMPASS data collected with a 160 GeV/c positive muon beam impinging on a deuteron target. The amplitudes are measured for both positive and negative hadrons, and the results on the dependence of the relevant kinematical variables obtained after a multi dimensional analysis are also presented.     

Measurement of prompt photons with associated jets in photoproduction at HERA

The photoproduction of prompt photons, together with an accompanying jet, has been studied in ep collisions at a centre-of-mass energy of 318 GeV with the ZEUS detector at HERA using an integrated luminosity of 77 pb^-1. Cross sections were measured for the transverse energy of the photon and the jet larger than 5 and 6 GeV, respectively. The differential γ+jet cross sections were reconstructed as functions of the transverse energy, pseudorapidity and x_γ ^obs, the fraction of the incoming photon momentum taken by the photon-jet system. Predictions based on leading-logarithm parton-shower Monte Carlo models and next-to-leading-order (NLO) QCD generally underestimate the cross sections for the transverse energies of prompt photons below 7 GeV, while the k_T-factorisation QCD calculation agrees with the data better. When the minimum transverse energy of prompt photons is increased to 7 GeV, both NLO QCD and the k_T-factorisation calculations are in good agreement with the data.     

Measurement of the hadronic cross-section for the scattering of two virtual photons at LEP

The interaction of virtual photons is investigated using the reaction hadrons based on data taken by the OPAL experiment at centre-of-mass energies GeV, for GeV and at an average of 17.9 GeV. The measured cross-sections are compared to predictions of the Quark Parton Model (QPM), to the Leading Order QCD Monte Carlo model PHOJET, to the NLO prediction for the reaction , and to BFKL calculations. PHOJET, NLO , and QPM describe the data reasonably well, whereas the cross-section predicted by a Leading Order BFKL calculation is too large. Received: 3 September 2001 / Published online: 5 April 2002     

Exact results in QED

We consider several applications of the simplest nonlinear QED phenomena described by the light-by-light (LBL) scattering tensor. Among the relevant processes we present the splitting of high energy photon in a Coulomb field, calculate the asymptotics of differential photon photon elastic scattering. We show that LBL mechanism of the four photon mode of neutral pion decay have a dominant role compared, for instance, with the quark loop Feynman amplitude contribution. The mechanisms of creation of two and three gluon jets at colliding electro-positron beams is analyzed. We calculate also the contribution of LBL mechanism to the ortho-positronium decay width. One Of the important application is the analytic calculation of the QED contribution to the anomalous magnetic moment of the muon arising from LBL mechanism realized through electron positron loops, which is enhanced by the logarithm of the ratio of muon to electron masses. The modification of the QED kernel, which takes into account the QED polarization operator is used to extract the pure strong interaction contribution. We consider as well the problem of the Coulomb law modification. At second part of review we consider Moeller scattering process and RC to it. We show that RC are in agreement with renormalization group approach and could be taken into account in form of Drell-Yan process cross-section.