ONE LOOP QED VERTEX IN ANY COVARIANT GAUGE: ITS COMPLETE ANALYTIC FORM

The one loop vertex in QED is calculated in arbitrary covariant gauges as an analytic function of its momenta. The vertex is decomposed into a longitudinal part, that is fully responsible for ensuring the Ward and Ward-Takahashi identities are satisfied, and a transverse part. The transverse part is decomposed into 8 independent components each being separately free of kinematic singularities in $\bf any$ covariant gauge in a basis that modifies that proposed by Ball and Chiu. Analytic expressions for all 11 components of the ${O(\alpha)}$ vertex are given explicitly in terms of elementary functions and one Spence function. These results greatly simplify in particular kinematic regimes.Comment: 35 pages, latex, 2 figures, Complete postscript file available from: ftp://cpt1.dur.ac.uk/pub/preprints/dtp95/dtp9506/dtp9406.p

Algebraic models for the hierarchy structure of evolution equations at small x

We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the equations that include the processes of pomeron splittings. We examine the algebraic structures of the governing equation hierarchies, as well as the asymptotic behavior of their solutions in the large-rapidity limit.Comment: 12 pages, 5 figures; minor changes in the revised versio

On the anomalous dimensions of the multiple pomeron exchanges

High energy hard scattering in large $N_{c}$ limit can be described by the QCD dipole model. In this paper, single, double and triple BFKL pomeron exchange amplitudes are computed explicitly within the dipole model. Based on the calculation, the general formula $\gamma^{(k)*}_{0}=\chi^{-1}(k\chi({1/2}))$ which governs the anomalous dimension of $1\Rightarrow k$ amplitude is conjectured. As far as the unitarity problem is concerned, we find that the anomalous dimension $\gamma$ varies from graph to graph due to the DGLAP evolution. In the end, a comparison between this computation and reggeon field theory is provided.Comment: 26 pages, 7 figures. A few changes are made in Appendix

A zero-dimensional model for high-energy scattering in QCD

We investigate a zero-dimensional toy model originally introduced by Mueller and Salam which mimics high-energy scattering in QCD in the presence of both gluon saturation and gluon number fluctuations, and hence of Pomeron loops. Unlike other toy models of the reaction-diffusion type, the model studied in this paper is consistent with boost invariance and, related to that, it exhibits a mechanism for particle saturation close to that of the JIMWLK equation in QCD, namely the saturation of the emission rate due to high-density effects. Within this model, we establish the dominant high-energy behaviour of the S-matrix element for the scattering between a target obtained by evolving one particle and a projectile made with exactly n particles. Remarkably, we find that all such matrix elements approach the black disk limit S=0 at high rapidity Y, with the same exponential law: ~ exp(-Y) for all values of n. This is so because the S-matrix is dominated by rare target configurations which involve only few particles. We also find that the bulk distribution for a saturated system is of the Poisson type.Comment: 34 pages, 9 figures. Some explanations added on the frame-dependence of the relevant configurations (new section 3.3

Vacuum replicas in QCD

The properties of the vacuum are addressed in the two- and four-dimensional quark models for QCD. It is demonstrated that the two-dimensional QCD ('t Hooft model) possesses only one possible vacuum state - the solution to the mass-gap equation, which provides spontaneous breaking of the chiral symmetry (SBCS). On the contrary, the four-dimensional theory with confinement modeled by the linear potential supplied by the Coulomb OGE interaction, not only has the chirally-noninvariant ground vacuum state, but it possesses an excited vacuum replica, which also exhibits SBCS and can realize as a metastable intermediate state of hadronic systems. We discuss the influence of the latter on physical observables as well as on the possibility to probe the vacuum background fields in QCD.Comment: RevTeX4, 26 pages, 8 EPS figures, extended references, corrected some typos, to appear in Phys.Rev.

One-dimensional model for QCD at high energy

We propose a stochastic particle model in (1+1)-dimensions, with one dimension corresponding to rapidity and the other one to the transverse size of a dipole in QCD, which mimics high-energy evolution and scattering in QCD in the presence of both saturation and particle-number fluctuations, and hence of Pomeron loops. The model evolves via non-linear particle splitting, with a non-local splitting rate which is constrained by boost-invariance and multiple scattering. The splitting rate saturates at high density, so like the gluon emission rate in the JIMWLK evolution. In the mean field approximation obtained by ignoring fluctuations, the model exhibits the hallmarks of the BK equation, namely a BFKL-like evolution at low density, the formation of a traveling wave, and geometric scaling. In the full evolution including fluctuations, the geometric scaling is washed out at high energy and replaced by diffusive scaling. It is likely that the model belongs to the universality class of the reaction-diffusion process. The analysis of the model sheds new light on the Pomeron loops equations in QCD and their possible improvements.Comment: 35 pages, 4 figures, one appendi

Dylematy diagnostyczne u chorych z niedokrwistością. Zespół pustego siodła - opis przypadku

Empty sella syndrome is defined as a group of clinical symptoms developing as a result of herniation of the subarachnoid space within the sella, which is often associated with some degree of flattening of the pituitary gland. It is usually recognized incidentally during brain imaging studies performed for different indications, and in most cases this condition is asymptomatic. However, it may result in impairment of various endocrine glands, for which the pituitary gland produces its crinins. Despite the high incidence of empty sella syndrome (up to about 5% of the population) it is commonly ignored as the cause of various symptoms. We present a case of 55-year-old patient admitted to the department of internal medicine due to anaemia and progressive weakness, with recognized hypothyroidism and adrenal gland insufficiency in the course of empty sella syndrome. (Pol J Endocrinol 2010; 61 (4): 400-403)Zespół pustego siodła definiuje się jako grupę objawów klinicznych rozwijających się w wyniku wpuklania się przestrzeni podpajęczynówkowej do siodła tureckiego, co często powoduje ucisk przysadki. Zespół ten zwykle rozpoznaje się przypadkowo podczas badań obrazowych mózgu przeprowadzonych z różnych wskazań i w większości przypadków nie powoduje on żadnych objawów. Czasami jednak skutkuje on zaburzeniami czynności różnych gruczołów wydzielania wewnętrznego, spowodowanymi upośledzeniem produkcji przez przysadkę hormonów tropowych dla tych gruczołów. Mimo stosunkowo częstego występowania zespołu pustego siodła (u ok. 5% populacji), zwykle nie bierze się go pod uwagę jako możliwej przyczyny różnych symptomów. W niniejszej pracy przedstawiono przypadek 55-letniego pacjenta, przyjętego na oddział chorób wewnętrznych z powodu niedokrwistości i postępującego osłabienia, u którego rozpoznano niedoczynność tarczycy i niewydolność kory nadnerczy w przebiegu zespołu pustego siodła. (Endokrynol Pol 2010; 61 (4): 400-403

The BFKL Pomeron Calculus in zero transverse dimensions: diffractive processes and survival probability for central diffractive production

In this paper we discuss the processes of diffractive production in the framework of the BFKL Pomeron calculus in zero transverse dimension. Considering the diffractive production of a bunch of particles with not very large masses, namely, \ln\Lb M^2/m^2 \Rb \ll \frac{1}{\bas} \ln\Lb \frac{N^2_c}{\bas^2}\Rb, we found explicit formulae for calculation of the cross sections for the single and double diffractive production as well as for the value of the survival probability for the diffractive central production. These formulae include the influence of the correlations due to so called Pomeron loops on the values of all discussed observables. The comparison with the other approaches on the market is given. The main conclusion of this comparison: the Mueller-Patel-Salam-Iancu approximation gives sufficiently good descriptions and close to the exact result for elastic and diffractive cross section but considerable overshoot the value of the survival probability.Comment: 25 page

Solution for the BFKL Pomeron Calculus in zero transverse dimensions

In this paper the exact analytical solution is found for the BFKL Pomeron calculus in zero transverse dimensions, in which all Pomeron loops have been included. The comparison with the approximate methods of the solution is given, and the kinematic regions are discussed where they describe the behaviour of the scattering amplitude quite well. In particular, the semi-classical approach is considered, which reproduces the main properties of the exact solution at large values of rapidity ($Y \geq 10$). It is shown that the mean field approximation leads to a good description of the scattering amplitude only if the amplitude at low energy is rather large. However, even in this case, it does not lead to the correct asymptotic behaviour of the scattering amplitude at high energies.Comment: 37 pages,19 figures and one table, the revised versio