The components of the \gamma^* \gamma^* cross section

We extend our previous treatment of the p cross section based on Gribov's hypothesis to the case of photon–photon scattering. With the aid of two parameters, determined from the experimental data, we separate the interactions into two categories corresponding to short (“soft”) and long (“hard”) distance processes. The photon–photon cross section thus receives contributions from three sectors, soft–soft, hard–hard and hard–soft. The additive quark model is used to describe the soft–soft sector, pQCD the hard–hard sector, while the hard–soft sector is determined by relating it to the system. We calculate and display the behaviour of the total photon–photon cross section and its various components and polarizations for different values of energy and virtuality of the two photons, and discuss the significance of our results. Received: 12 January 2000 / Published online: 6 April 2000     

Total \gamma^{\star}\gamma^{\star} cross section and the QCD dipole picture

In the framework of the dipole picture of the BFKL pomeron we discuss two possibilities of calculating the total cross section of the virtual photons. It is shown that the dipole model reproduces the results obtained earlier from -factorization up to the selection of the scale determining the length of the QCD cascade. The choice of scale turns out to be important for the numerical outcome of the calculations. Received: 12 June 1997 / Published online: 20 February 1998     

\gamma^* \gamma^* reactions at high energies

The total hadronic cross sections at high energy are calculated as a function of energy and photon virtuality in a model combining Reggeon exchange, the quark box diagram (a fixed pole in Regge language) and soft and hard pomeron exchanges evaluated in the context of dipole-dipole scattering. Good agreement is obtained with the data for the real cross section and for the real photon structure function . However the model prediction for the cross section is too small. This is attributed to an incorrect extrapolation of the dependence of the hard pomeron adopted here. Parametrising it independently shows that the hard part of the cross section can be well represented by a simple Regge pole with intercept . Received: 19 August 1999 / Published online: 3 February 2000     

QCD saturation and $\gamma^{*}$-$\gamma^{*}$ scattering

Two photon collisions at high energy have an important theoretical advantage: the simplicity of the initial state, which gives us a unique opportunity to calculate these processes for large virtualities of both photons in the perturbative QCD approach. In this paper we study QCD saturation in two photon collisions in the framework of the Glauber-Mueller approach. The Glauber-Mueller formula is derived emphasising the impact parameter dependence (b_t) of the dipole-dipole amplitude. It is shown that non-perturbative QCD contributions are needed to describe the large b _t behaviour, and the way how to deal with them is suggested. Our approach can be viewed as the model for the saturation in which the entire impact parameter dependence is determined by the initial conditions. The unitarity bound for the total cross section, its energy dependence as well as predictions for future experiments are discussed. It is argued that the total cross section increases faster than any power of in a wide range of energy or x, namely -, where reflects the x dependence of the gluon density and is the pion mass. Received: 22 November 2002 / Revised version: 27 January 2003 / Published online: 5 May 2003 RID="a" ID="a" e-mail: kozlov@post.tau.ac.il RID="b" ID="b" e-mail: leving@post.tau.ac.il and levin@mail.desy.de     

A two-com ponent model for $\gamma^*$- p scattering at small Bjorken variable x

We extend the Golec-Biernat-Wüsthoff model for virtual photon-proton scattering to include the resolved photon component explicitly. The parameters of the resolved photon component are taken from the literature, while the parameters of the dipole-nucleon interaction are fitted to the HERA data in a selected limited range of x and Q ². A good agreement with the experimental data is obtained beyond the region of the fit.Received: 16 July 2003, Published online: 17 October 2003     

The (BFKL) Pomeron-\gamma^*-\gamma vertex for any conformal spin

To study diffractive photon production at HERA, we compute the projection of the impact-factor on the BFKL leading-order eigenfunctions for non-zero transfer. This calculation supplements former ones performed for n = 0. We provide an expression for and check that all the other components are zero. Received: 6 September 1999 / Revised version: 21 November 1999 / Published online: 17 March 2000     

Resolved \gamma^*_L in hard collisions of virtual photons: QCD effects

The manifestations of QCD effects on quark and gluon distribution functions of longitudinally polarized virtual photons involved in hard collisions are investigated. It is shown that for moderate photon virtualities and in the kinematical region accessible at HERA and LEP these effects are sizable and significantly enhance theoretical predictions based on contributions of transversally polarized virtual photon only. Received: 21 October 2000 / Published online: 23 January 2001     

Comparison of phase space slicing and dipole subtraction methods for \gamma^* \rightarrow Q\bar{Q}

We compare the phase space slicing and dipole subtraction methods in the computation of the inclusive and differential next-to-leading order cross sections for heavy quark production in the simple process . For the phase space slicing method we study the effects of improvement terms that remove restrictions on the slicing parameter . For the dipole method our comparison is a first check on some of its counterterms involving massive quarks, derived recently. In our comparison we address issues such as numerical accuracy and efficiency. Received: 15 October 2001 / Published online: 25 January 2002     

Total ionization cross section in electron-hydrogen scattering

The total ionization cross section in electron-hydrogen scattering in the energy range 20.4–68.0 eV has been calculated by a method in which the initial state of the system is treated by a distorted wave polarized orbital method and the final state is described by (1) a product of two unscreened Coulomb functions and (2) a product of a plane wave and a Coulomb function. The corresponding two sets of results using a plane wave in the incident channel have also been reported. The present results where both the electrons are represented by Coulomb waves are in closer agreement than other theoretical predictions With measured values.     

Measuring the FSR-inclusive $\pi^+\pi^-$ cross section

Final state radiation (FSR) in pion pair production cannot be calculated reliably because of the composite structure of the pions. However, FSR corrections have to be taken into account for a precise evaluation of the hadronic contribution to g-2 of the muon. The role of FSR in both energy scan and radiative return experiments is discussed. It is shown how FSR influences the pion form factor extraction from experimental data and, as a consequence, the evaluation of . In fact the FSR corrections should be included to reach the precision we are aiming at. We argue that for an extraction of the desired FSR-inclusive cross section a photon-inclusive scan measurement of the ”” cross section is needed. For exclusive scan and radiative return measurements in contrast we have to rely on ad hoc FSR models if we want to obtain either or the FSR-exclusive cross section . We thus advocate to consider seriously precise photon-inclusive energy scan measurements at present and future low energy e ⁺ e ^- -facilities. Then together with radiative return measurements from DANE and BABAR and forthcoming scan measurements at VEPP-2000 we have a good chance to substantially improve the evaluation of in the future. Received: 2 January 2003 / Published online: 24 March 2003     

Total cross section for photon-nucleon interaction in the energy range $$\sqrt \mathcal{S} = 40 - 250 GeV$$

Results obtained by directly measuring the total cross section for photon-nucleon interaction through recording photoproduction processes at the Baksan underground scintillation telescope of the Institute for Nuclear Research (Russian Academy of Sciences, Moscow) are presented. The effect of a faster growth of photon-hadron cross sections in relation to hadron-hadron cross sections is confirmed in the energy range \(\sqrt \mathcal{S} = 40 - 130 GeV\). It is shown that an increase in the number of additive quarks in photon-hadronization products may be one of the reasons behind this effect. Experimental data on the cross sections for photon-nucleon and photon-photon interactions are subjected to a comparative analysis, and the status of the results obtained from direct and indirect cross-section measurements in the high-energy region is discussed.     

Total cross section of two-photon production of hadrons

The total cross section for hadrons was measured as a function of the invariant massW of the system (1.25 to 4.25 GeV) at thee ⁺ e ^–-collider VEPP-4 with the detector MD-1. For the first time the data were obtained by detecting both scattered leptons with almost zero emission angles. The mean squared four momentum transfer q ² is –0.005 GeV², the rmsW resolution is 100–250 MeV. The data on the mean charged multiplicity n _C are well described by the function n _C =(1.62 ±0.37)+(1.83±0.45)·ln(W(GeV)). TheW dependence of the total cross section is consistent with the theoretical prediction (nb)=240+270/W(GeV).     

Total photoproduction cross section at very high energy

In this paper we apply to the photoproduction total cross section a model we have proposed for purely hadronic processes and which is based on QCD mini-jets and soft gluon re-summation. We compare the predictions of our model with the HERA data as well as with other models. For cosmic rays, our model predicts substantially higher cross sections at TeV energies than models based on factorization, but lower than models based on mini-jets alone, without soft gluons. We discuss the origin of this difference.