NLO QCD method of the polarized SIDIS data analysis

Method of polarized semi-inclusive deep inelastic scattering (SIDIS) data analysis in the next to leading order (NLO) QCD is developed. Within the method one first directly extracts in NLO few first truncated (available to measurement) Mellin moments of the quark helicity distributions. Second, using these moments as an input to the proposed modification of the Jacobi polynomial expansion method (MJEM), one eventually reconstructs the local quark helicity distributions themselves. All numerical tests demonstrate that MJEM allows us to reproduce with the high precision the input local distributions even inside the narrow Bjorken $x$ region accessible for experiment. It is of importance that only four first input moments are sufficient to achieve a good quality of reconstruction. The application of the method to the simulated SIDIS data on the pion production is considered. The obtained results encourage one that the proposed NLO method can be successfully applied to the SIDIS data analysis. The analysis of HERMES data on pion production is performed. To this end the pion difference asymmetries are constructed from the measured by HERMES standard semi-inclusive spin asymmetries. The LO results of the valence distribution reconstruction are in a good accordance with the respective leading order SMC and HERMES results, while the NLO results are in agreement with the existing NLO parametrizations on these quantities

Conductance characteristics of current-carrying d-wave weak links

The local quasiparticle density of states in the current-carrying d-wave superconducting structures was studied theoretically. The density of states can be accessed through the conductance of the scanning tunnelling microscope. Two particular situations were considered: the current state of the homogeneous film and the weak link between two current-carrying d-wave superconductors.Comment: 4 pages, 3 figures; to appear in Low. Temp. Phy

Conformal field theory of Painlev\'e VI

Generic Painlev\'e VI tau function \tau(t) can be interpreted as four-point correlator of primary fields of arbitrary dimensions in 2D CFT with c=1. Using AGT combinatorial representation of conformal blocks and determining the corresponding structure constants, we obtain full and completely explicit expansion of \tau(t) near the singular points. After a check of this expansion, we discuss examples of conformal blocks arising from Riccati, Picard, Chazy and algebraic solutions of Painlev\'e VI.Comment: 24 pages, 1 figure; v3: added refs and minor clarifications, few typos corrected; to appear in JHE

Tracking in Antiproton Annihilation Experiments

A major ingredient of the planned new accelerator complex FAIR, to be constructed at the GSI, Darmstadt, Germany, is the availability of antiproton beams with high quality and intensity. Among the experiments which will make use of this opportunity is PANDA, a dedicated experiment to study antiproton annihilations on nucleons and nuclei. This article gives an overview on the foreseen techniques to perform charged particle tracking in the high rate environment of this experiment.Comment: 1 tar.gz file containing 5 pages paper, 3 figures in 5 files; proceedings of the TIME05 worksho

How instanton combinatorics solves Painlev\'e VI, V and III's

We elaborate on a recently conjectured relation of Painlev\'e transcendents and 2D CFT. General solutions of Painlev\'e VI, V and III are expressed in terms of $c=1$ conformal blocks and their irregular limits, AGT-related to instanton partition functions in $\mathcal{N}=2$ supersymmetric gauge theories with $N_f=0,1,2,3,4$. Resulting combinatorial series representations of Painlev\'e functions provide an efficient tool for their numerical computation at finite values of the argument. The series involve sums over bipartitions which in the simplest cases coincide with Gessel expansions of certain Toeplitz determinants. Considered applications include Fredholm determinants of classical integrable kernels, scaled gap probability in the bulk of the GUE, and all-order conformal perturbation theory expansions of correlation functions in the sine-Gordon field theory at the free-fermion point.Comment: 34 pages, 3 figures; v2: minor improvement

Energy of a knot: variational principles; Mm-energy

Let $E_f$ be the energy of some knot $\tau$ for any $f$ from certain class of functions. The problem is to find knots with extremal values of energy. We discuss the notion of the locally perturbed knot. The knot circle minimizes some energies $E_f$ and maximizes some others. So, is there any energy such that the circle neither maximizes nor minimizes this energy? Recently it was shown (A.Abrams, J.Cantarella, J.H.G.Fu, M.Ghomu, and R.Howard) that the answer is positive. We prove that nevertheless the circle is a locally extremal knot, i.e. the circle satisfies certain variational equations. We also find these equations. Finally we represent Mm-energy for a knot. The definition of this energy differs with one regarded above. Nevertheless besides its own properties Mm-energy has some similar with M\"obius energy properties.Comment: 17 pages, 6 Postscript figure