Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pade resummation method, with an additional improvement due to utilization of the leading renormalon poles (for a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317, p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pade approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results enhanced; one section and one appendix added and some minor changes and additions; to appear in phys. rev.

The spectrum features of UHECRs below and surrounding GZK

The energy spectrum of UHECRs is discussed on the basis of the Yakutsk array database analysis. In the region E=0.1 to 30 EeV the showers are detected under trigger-500, while at energies above 30 EeV the whole acceptance area for trigger-1000 is used in order to utilize all the data available in the region of GZK cutoff.Comment: Invited talk at CRIS2004: GZK and surroundings, Catania, Italy, 31.05.04. To appear in Nucl. Phys. B Proc. Supp

Classical approach in quantum physics

The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a semiclassical spectrum of hydrogen atom in crossed electric and magnetic fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's approach to Stark problem, long-lived excited states of a helium atom recently discovered with the help of Poincar$\acute{\mathrm{e}}$ section, inelastic transitions in slow and fast electron-atom and ion-atom collisions - is reviewed. Further, a classical representation in quantum theory is discussed. In this representation the quantum states are treating as an ensemble of classical states. This approach opens the way to an accurate description of the initial and final states in classical trajectory Monte Carlo (CTMC) method and a purely classical explanation of tunneling phenomenon. The general aspects of the structure of the semiclassical series such as renormgroup symmetry, criterion of accuracy and so on are reviewed as well. In conclusion, the relation between quantum theory, classical physics and measurement is discussed.Comment: This review paper was rejected from J.Phys.A with referee's comment "The author has made many worthwhile contributions to semiclassical physics, but this article does not meet the standard for a topical review"

Spin asymmetry A_1^d and the spin-dependent structure function g_1^d of the deuteron at low values of x and Q^2

We present a precise measurement of the deuteron longitudinal spin asymmetry A_1^d and of the deuteron spin-dependent structure function g_1^d at Q^2 < 1 GeV^2 and 4*10^-5 < x < 2.5*10^-2 based on the data collected by the COMPASS experiment at CERN during the years 2002 and 2003. The statistical precision is tenfold better than that of the previous measurement in this region. The measured A_1^d and g_1^d are found to be consistent with zero in the whole range of x.Comment: 17 pages, 10 figure

Gluon polarization in the nucleon from quasi-real photoproduction of high-pT hadron pairs

We present a determination of the gluon polarization Delta G/G in the nucleon, based on the helicity asymmetry of quasi-real photoproduction events, Q^2<1(GeV/c)^2, with a pair of large transverse-momentum hadrons in the final state. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarized muon beam scattered on a polarized 6-LiD target. The helicity asymmetry for the selected events is = 0.002 +- 0.019(stat.) +- 0.003(syst.). From this value, we obtain in a leading-order QCD analysis Delta G/G=0.024 +- 0.089(stat.) +- 0.057(syst.) at x_g = 0.095 and mu^2 =~ 3 (GeV}/c)^2.Comment: 10 pages, 3 figure

The COMPASS Experiment at CERN

The COMPASS experiment makes use of the CERN SPS high-intensitymuon and hadron beams for the investigation of the nucleon spin structure and the spectroscopy of hadrons. One or more outgoing particles are detected in coincidence with the incoming muon or hadron. A large polarized target inside a superconducting solenoid is used for the measurements with the muon beam. Outgoing particles are detected by a two-stage, large angle and large momentum range spectrometer. The setup is built using several types of tracking detectors, according to the expected incident rate, required space resolution and the solid angle to be covered. Particle identification is achieved using a RICH counter and both hadron and electromagnetic calorimeters. The setup has been successfully operated from 2002 onwards using a muon beam. Data with a hadron beam were also collected in 2004. This article describes the main features and performances of the spectrometer in 2004; a short summary of the 2006 upgrade is also given.Comment: 84 papes, 74 figure

The Deuteron Spin-dependent Structure Function g1d and its First Moment

We present a measurement of the deuteron spin-dependent structure function g1d based on the data collected by the COMPASS experiment at CERN during the years 2002-2004. The data provide an accurate evaluation for Gamma_1^d, the first moment of g1d(x), and for the matrix element of the singlet axial current, a0. The results of QCD fits in the next to leading order (NLO) on all g1 deep inelastic scattering data are also presented. They provide two solutions with the gluon spin distribution function Delta G positive or negative, which describe the data equally well. In both cases, at Q^2 = 3 (GeV/c)^2 the first moment of Delta G is found to be of the order of 0.2 - 0.3 in absolute value.Comment: fits redone using MRST2004 instead of MRSV1998 for G(x), correlation matrix adde

A new measurement of the Collins and Sivers asymmetries on a transversely polarised deuteron target

New high precision measurements of the Collins and Sivers asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarised 6LiD target are presented. The data were taken in 2003 and 2004 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV/c. Both the Collins and Sivers asymmetries turn out to be compatible with zero, within the present statistical errors, which are more than a factor of 2 smaller than those of the published COMPASS results from the 2002 data. The final results from the 2002, 2003 and 2004 runs are compared with naive expectations and with existing model calculations.Comment: 40 pages, 28 figure

Measurement of the Spin Structure of the Deuteron in the DIS Region

We present a new measurement of the longitudinal spin asymmetry A_1^d and the spin-dependent structure function g_1^d of the deuteron in the range 1 GeV^2 < Q^2 < 100 GeV^2 and 0.004< x <0.7. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarised muon beam and a large polarised 6-LiD target. The results are in agreement with those from previous experiments and improve considerably the statistical accuracy in the region 0.004 < x < 0.03.Comment: 10 pages, 6 figures, subm. to PLB, revised: author list, Fig. 4, details adde

Search for the Phi(1860) Pentaquark at COMPASS

Narrow Xi-pi+- and Xi-bar+pi+- resonances produced by quasi-real photons have been searched for by the COMPASS experiment at CERN. The study was stimulated by the recent observation of an exotic baryonic state decaying into Xi-pi-, at a mass of 1862 MeV, interpreted as a pentaquark. While the ordinary hyperon states Xi(1530)^0 and Xi-bar(1530)^0 are clearly seen, no exotic baryon is observed in the data taken in 2002 and 2003.Comment: 10 pages, 5 figure