We propose to modify the saturation model of Golec-Biernat and Wüsthoff by including Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution. We find considerable improvement for the total deep inelastic cross section, in particular in the large Q 2 region. The successful description of deep inelastic scattering diffraction is preserved.The saturation model ͓1-3͔ has provided a successful description of DESY ep collider HERA deep inelastic scattering ͑DIS͒ data, in particular for the transition from the perturbative region to the nonperturbative photoproduction region. This includes both the total ␥*p cross section and the DIS diffractive cross section. Whereas the formulas are particularly appealing through their simplicity, they also have an attractive theoretical background, namely, the idea of saturation. Despite its success, the model suffers from shortcomings which should be cured. In particular, the model does not include logarithmic scaling violations; i.e., at larger values of Q 2 it does not exactly match with QCD evolution ͓Dokshitzer-Gribov-Lipatov-Altarelli-Parisi ͑DGLAP͔͒. This becomes clearly visible in the energy dependence of tot ␥*p in the region Q 2 Ͼ20 GeV 2 where the model predictions are below the data. One expects that QCD evolution should enhance the cross section in this region. It is the purpose of this paper to propose a modification of the saturation model. We attempt to preserve the success of the model in the low-Q 2 and in the transition regions, while incorporating DGLAP evolution in the large-Q 2 domain. Since the energy dependence in the large-Q 2 region is mainly due to the behavior of the dipole cross section at small dipole sizes r, our changes will affect mostly the smallr region. At the same time, particular attention will be given to DIS diffraction for which the saturation model correctly describes the energy dependence. Since the inclusive diffractive cross section mostly depends upon the large-r behavior of the dipole cross section, we attempt to leave the dipole cross section unchanged in this region. A recent attempt ͓4͔ along the same lines indicates that, in fact, diffraction provides a highly nontrivial restriction on possible modifications of the saturation model. I. THE MODELBefore we describe the modifications of the saturation model, we briefly review the main features of its original formulation. Within the dipole formulation of the ␥*p scattering,where T,L denotes the virtual photon polarization, the dipole cross section was proposed to have the formwhere R 0 (x) is the saturation scale which decreases when x→0,In order to be able to study the formal photoproduction limit, the Bjorken variable xϭx B was modified to bewhere m q is an effective quark mass, and W 2 denotes the ␥*p center-of-mass energy squared. The parameters of the model, 0 ϭ23 mb, ϭ0.29 and x 0 ϭ3ϫ10 Ϫ4 ͑for the assumed quark mass m q ϭ140 MeV) were found from a fit to small-x data ͓1͔. For alternative forms of the dipole cross section parametrization see ͓5͔.As it is well known ͓6͔, in the small-...

After a brief review of the BFKL approach to Regge processes in QCD and in supersymmetric (SUSY) gauge theories we propose a strategy for calculating the nextto-next-to-leading order corrections to the BFKL kernel. They can be obtained in terms of various cross-sections for Reggeized gluon interactions. The corresponding amplitudes can be calculated in the framework of the effective action for high energy scattering. In the case of N = 4 SUSY it is also possible to use the Bern-Dixon-Smirnov (BDS) ansatz. For this purpose the analytic properties of the BDS amplitudes at high energies are investigated, in order to verify their self-consistency. It is found that, for the number of external particles being larger than five, these amplitudes, beyond one loop, are not in agreement with the BFKL approach which predicts the existence of Regge cuts in some physical channels.

AbstractsGeomagnetic activity, the frequency and intensity of magnetic disturbance, is supposed to indicate the influence of solar corpuscular radiation on the Earth. Various schemes for measuring the fluctuations of this phenomenon are in operation, but in connection with direct ionospheric studies by radio methods it was found necessary to provide a new scheme using smaller time-units than a day or half a day. A threehour-range index/( based on the "Potsdarner erdmagnetische

We describe the physics potential of e + e − linear colliders in this report. These machines are planned to operate in the first phase at a center-of-mass energy of 500 GeV, before being scaled up to about 1 TeV. In the second phase of the operation, a final energy of about 2 TeV is expected. The machines will allow us to perform precision tests of the heavy particles in the Standard Model, the top quark and the electroweak bosons. They are ideal facilities for exploring the properties of Higgs particles, in particular in the intermediate mass range. New vector bosons and novel matter particles in extended gauge theories can be searched for and studied thoroughly. The machines provide unique opportunities for the discovery of particles in supersymmetric extensions of the Standard Model, the spectrum of Higgs particles, the supersymmetric partners of the electroweak gauge and Higgs bosons, and of the matter particles. High precision analyses of their properties and interactions will allow for extrapolations to energy scales close to the Planck scale where gravity becomes significant. In alternative scenarios, like compositeness models, novel matter particles and interactions can be discovered and investigated in the energy range above the existing colliders up to the TeV scale. Whatever scenario is realized in Nature, the discovery potential of e + e − linear colliders and the high-precision with which the properties of particles and their interactions can be analysed, define an exciting physics programme complementary to hadron machines.

A homogeneous series of monthly means of terrestrial‐magnetic activity for the years 1872 to 1930 is derived and extended backward, in annual means, to 1835. The annual variation of magnetic activity and of the relative sunspot‐numbers is discussed by means of new tests for periods. Only the semi‐annual wave in magnetic activity is recognized as physically significant. Its maxima prefer the times when the Sun is in the celestial equator, and not, as has been suggested, the times when the Sun's axis is most inclined towards the ecliptic. This view is supported by tests using the harmonic dial and the probable‐error circle, and several independent considerations. The close relations between sunspot‐numbers and terrestrial‐magnetic activity in the annual and monthly means are discussed. Some general statistical aspects are given for the treatment of the correlation between such series with after‐effects, for which both solar activity and terrestrial‐magnetic activity are typical. The homogeneity of the whole available series for relative sunspot‐numbers and for areas of sunspots and faculae is tested; some inhomogeneities are found, apart from a general lag of terrestrial‐magnetic activity that has occurred in some sunspot‐cycles. A break in the homogeneity of the international magnetic character‐figures in recent years is discovered. The individual 27‐day recurrences in terrestrial‐magnetic activity during 1906–31, and their relations to solar activity are discussed with the help of a graphical day‐by‐day record. They indicate the existence of persistent active areas on the Sun's surface, called M‐regions, which, in many cases, cannot be coordinated to such solar phenomena as are observable by direct astrophysical methods. This holds in particular for the new solar indices which are available for the years 1928–30, and which are found so closely correlated to sunspot‐numbers, that they fail to improve the correlation between solar activity and terrestrial‐magnetic activity. Observations of terrestrial‐magnetic activity yield therefore not only information about geophysical influences of such solar phenomena that may be traced in astrophysical observations, but supplement these direct observations themselves.

As a first step towards the computation of the NLO corrections to the photon impact factor in the γ * γ * → γ * γ * scattering process, we calculate the one loop corrections to the coupling of the reggeized gluon to the γ * → qq vertex. We list the results for the Feynman diagrams which contribute: all loop integrations are carried out, and the results are presented in the helicity basis of photon, quark, and antiquark.

We investigate the influence of higher twist corrections to deep inelastic structure functions in the low-Q 2 and small-x HERA region. We review the general features of the lowest-order QCD diagrams which contribute to twist-4 at small-x, in particular the sign structure of longitudinal and transverse structure functions which offers the possibility of strong cancellations in F 2 . For a numerical analysis we perform a twist analysis of the saturation model which has been very successful both in describing the structure function and the DIS diffractive cross section at HERA. As the main conclusion, twist 4 corrections are not small in F L or F T but in F 2 = F L +F T they almost cancel. This indicates the limitation on the use of the DGLAP formalism at small x and Q 2 . We point out that F L analysis needs a large twist-4 correction. We also indicate the region of validity of the twist expansion.

We propose a simple parametrization for the deep-inelastic diffractive cross section. It contains the contribution of qq production to both the longitudinal and the transverse diffractive structure functions, and of the production of qqg final states from transverse photons. We start from the hard region and perform a suitable extrapolation into the soft region. We test our model on the 1994 ZEUS and H1 data, and confront it with the H1 conjecture of a singular gluon distribution.