Gluon distributions in real and virtual photon and the photon structure function

Gluon distributions in real and virtual photons are calculated using evolution equations in the NLO approximation. The quark distributions in the photon determined on the basis of the QCD sum rule approach in [1] are taken as an input. It is shown that gluon distribution in the photon can be reliably determined up tox=0.03÷0.05, much lower than the corresponding values in the case of quark distributions. Two variants of the calculations are considered: (1) it is assumed that there are no intrinsic gluons in the photon at some low normalization pointQ ²=Q ₀ ² ∼1GeV²; (2) it is assumed that gluonic content of the photon at lowQ ₀ ² is described by gluonic content of vector mesonsρ, ω, ϕ. The gluon distributions in these two variants appear to be different. This fact permits one to clarify the origin of nonperturbative gluonic content of the photon by comparing the results with experiment. Structure functionsF ₂(x) for real and virtual photon are calculated and it is shown that in the regionx≥0.2 where QCD approach is valid, there is a good agreement with experiment.     

Predictions for high-energy real and virtual photon–photon scattering from color dipole BFKL–Regge factorization

High-energy virtual photon–virtual photon scattering can be viewed as an interaction of small size color dipoles from the beam and target photons, which makes scattering at high energies (LEP, LEP200 and NLC) an indispensable probe of the short distance properties of the QCD pomeron exchange. Based on the color dipole representation, we investigate the consequences for the scattering of the incorporation of asymptotic freedom into the BFKL equation which makes the QCD pomeron a series of isolated poles in the angular momentum plane. The emerging color dipole BFKL–Regge factorization allows us to relate in a model-independent way the contributions of each BFKL pole to scattering and DIS off protons. Numerical predictions based on our early works on the color dipole BFKL phenomenology of DIS on protons are in good agreement with the experimental data on the photon structure function and the most recent data on the cross section from the OPAL and L3 experiments at LEP200. We discuss the role of non-perturbative dynamics and predict a pronounced effect of the Regge-factorization breaking due to large unfactorizable non-perturbative corrections to the perturbative vacuum exchange. We comment on the salient features of the BFKL–Regge expansion for scattering including the issue of the decoupling of subleading BFKL poles and the soft plus rightmost hard BFKL pole dominance. Received: 9 January 2001 / Revised version: 25 September 2001 / Published online: 7 December 2001     

Factorization scheme and parton distributions in the polarized virtual photon target

We investigate spin-dependent parton distributions in the polarized virtual photon target in perturbative QCD up to the next-to-leading order (NLO). In the case , where is the mass squared of the probe (target) photon, the parton distributions can be predicted completely up to NLO, but they are factorization-scheme dependent. We analyze the parton distributions in six different factorization schemes and discuss their scheme dependence. We study, in particular, the QCD and QED axial anomaly effects on the first moments of the parton distributions to see the interplay between the axial anomalies and factorization schemes. We also show that the factorization-scheme dependence is characterized by the large-x behaviors of the quark distributions in the virtual photon. The gluon distribution is predicted to be the same up to NLO among the six factorization schemes examined. In particular, the first moment of the gluon distribution is found to be factorization-scheme independent up to NLO. Received: 24 January 2001 / Published online: 18 May 2001     

Real and virtual photon contributions to inelasticep scattering

We investigate direct and resolved photon contributions to hardep scattering at high energies. Some terms of the direct contribution are already included in the resolved photon one, described in terms of the photon structure functions. A suitable subtraction mechanism has to be found in order to avoid double counting. Inelasticep scattering requires the knowledge of photon structure functions over a wide range in photon virtuality, in particular from approximately zero up to almost 10⁵ GeV² at HERA. We analyse the real and virtual photon structure function and we comment on the structure of the photon in the intermediate region of low virtuality. We finally describe howep cross sections can be obtained as functions of the virtuality of the exchanged photon.     

A new method to test virtual photon spectra

Millisecond isomers in¹⁴⁶Tb,¹⁴⁸Ho and¹⁵⁰Tm, observed in⁶⁰Ni reactions on³⁹Y,⁹⁰Zr, and⁹²Mo targets, are interpreted as (πh_11/2 vh_11/2 ^?1) 10⁺ isomers predicted by the shell model. Their decays are characterized.     

Three photon virtual annihilation contributions to positronium hyperfine structure

Three photon virtual annihilation contributions to the positronium hyperfine interval are calculated to order α⁶m(α⁴R_∞). The result is obtained in analytic form and leads to the small value of -0.91 MHz for the contribution to the ground state energy difference from this source.     

Spin-dependent processes involving a real photon

We calculate the helicity difference quark and gluon distributions in a polarized real photon using the Altarelli-Parisi equations. The corresponding helicity difference fragmentation functions to produce a real photon are dealt with in the same way. Both sets of results are presented in the form of simple parametrizations and the former used to investigate spin-spin asymmetries in the photoproduction of two high transverse momentum jets. These asymmetries are classed as “four jet” or “three jet” depending on whether any photon fragments are present in the final state along the beam axis. We find that the four-jet asymmetry should provide an experimental test for the presence of the anomalous polarized photon structure function while the three-jet asymmetry should provide new information about the spin structure of a polarized proton and in particular its gluon component.     

Transition from bloch equations to rate equations for multiple photon excitation of polyatomic molecules

A novel form of phenomenological optical Bloch equations, with density matrix elements depending both on the number of laser quanta in the pumped molecular vibrational mode and on the number of quanta dumped into the thermal bath formed by the remaining vibrational modes, is used to derive rate equations for multiple photon excitation of polyatomic molecules.     

A test of virtual photon theory

In order to extract a photodisintegration cross section in the c.m. system from an electrodisintegration cross section measured in the lab system, one has to assume that the electrons are mostly scattered forward and that the monopole contributions are negligible. To test the validity of these approximations, we assumed a square well potential for the initial and final states and calculated the photodisintegration cross section exactly within this model. These results were then compared with the results one would obtain using the virtual photon theory approximations for electron energies of 0–300 MeV and excitation energies up to 40 MeV. In comparing the two results, we are able to show how and why the virtual photon theory approximations fail in certain kinematical regions.     

Recent result from the A2 real photon facility at MAMI

The upgraded MAMI C accelerator is delivering electrons with an energy of 1558 MeV routinely. The A2 collaboration is doing experiments with energy marked polarised real photons produced via ＂Bremsstrahlung＂. Recent results from the GDH-experiment using a longitudinal polarised frozen spin target in combination with the DAPHNE detector and from the Crystal Ball experiment at MAMI are presented.     

Recent result from the A2 real photon facility at MAMI

The upgraded MAMI C accelerator is delivering electrons with an energy of 1558 MeV rou-tinely. The A2 collaboration is doing experiments with energy marked polarised real photons produced via "Bremsstrahlung". Recent results from the GDH-experiment using a longitudinal polarised frozen spin target in combination with the DAPHNE detector and from the Crystal Ball experiment at MAMI are presented.     

Dots in rods as polarized single photon sources

We report the evidence of a polarized single photon flux from a colloidal nanoparticle. We analyze, by time and polarization resolved spectroscopy measurements, the polarization behavior of a single CdSe/CdS core/shell dot in rod, achieving a polarization ratio at room temperature of ∼75% and a lifetime of the excited state of ∼11 ns.     

Nonlocal structures: Bilocal photon

As a starting point, it is postulated that all particles and fields are built from a single primitive field, which must then be a massless fermion with a spin of one-half. Two helicities are embodied in a spin of one-half. The vacuum is an open Fermi sea whose height is a wave number . Elementary particles are structures having the form of standing-wave systems floating on the vacuum sea, with the height providing both the scale of inner structural size and the mass unit for the elementary particle mass spectrum. A bilocal photon starts with a function describing two primitive quanta with parallel spin and opposite spin. A centroid-time wave equation then couples-in an infinite set of orthogonal functions. The introduction of an operatorQ permits the reduction of the infinite secular determinant to a finite six-by-six determinant. Solutions (for the infinite expansion) are obtained describing photons with right-handed and left-handed polarizations. Superpositions of these give linearly polarized photons. Electric and magnetic field vectors, satisfying the vacuum Maxwell equations, are obtained from a bilocal Hertz vector given by = (2/³ c)(/t _r)_r(1,2), where (1,2) is the bilocal wave function, and t_r and r are the relative time and relative position variables.     

Moments of the virtual photon structure function

The photon structure function is a useful testing ground for QCD. It is perturbatively computable apart from a contribution from what is usually called the hadronic component of the photon. There have been many proposals concerning this nonperturbative part of the real photon structure function. By studying moments of the virtual photon structure function, we explore the extent to which proposed nonperturbative contributions can be identified experimentally.     

Understanding interference experiments with polarized light through photon trajectories

Bohmian mechanics allows to visualize and understand the quantum-mechanical behavior of massive particles in terms of trajectories. As shown by Bialynicki-Birula, Electromagnetism also admits a hydrodynamical formulation when the existence of a wave function for photons (properly defined) is assumed. This formulation thus provides an alternative interpretation of optical phenomena in terms of photon trajectories, whose flow yields a pictorial view of the evolution of the electromagnetic energy density in configuration space. This trajectory-based theoretical framework is considered here to study and analyze the outcome from Young-type diffraction experiments within the context of the Arago-Fresnel laws. More specifically, photon trajectories in the region behind the two slits are obtained in the case where the slits are illuminated by a polarized monochromatic plane wave. Expressions to determine electromagnetic energy flow lines and photon trajectories within this scenario are provided, as well as a procedure to compute them in the particular case of gratings totally transparent inside the slits and completely absorbing outside them. As is shown, the electromagnetic energy flow lines obtained allow to monitor at each point of space the behavior of the electromagnetic energy flow and, therefore, to evaluate the effects caused on it by the presence (right behind each slit) of polarizers with the same or different polarization axes. This leads to a trajectory-based picture of the Arago-Fresnel laws for the interference of polarized light.     

Splitting of a polarized photon by an unpolarized electron

The process of splitting of a polarized photon of a plane electromagnetic wave into two polarized photons by an unpolarized electron is examined. The degree of circular and linear polarization of the photon radiated is studied in detail.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 133–138, August, 1978.The authors are grateful to Professor V. G. Bagrov for discussing the research.     

Current tensor with heavy photon for double hard photon emission by a longitudinally polarized electron

The electron current tensor for the scattering of a heavy photon on a longitudinally polarized electron with the emission of two hard real photons is considered. The contributions of collinear and semicollinear kinematics are computed. The result allows one to calculate the corresponding contribution to the second-order radiative correction to the deep inelastic scattering or electron-positron annihilation cross sections with next-to-leading-order accuracy. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 12, 845–850 (25 June 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.