OPE analysis of the nucleon scattering tensor including weak interaction and finite mass effects

We perform a systematic operator product expansion of the most general form of the nucleon scattering tensor $W_{\mu \nu}$ including electro-magnetic and weak interaction processes. Finite quark masses are taken into account and a number of higher-twist corrections are included. In this way we derive relations between the lowest moments of all 14 structure functions and matrix elements of local operators. Besides reproducing well-known results, new sum rules for parity-violating polarized structure functions and new mass correction terms are obtained.Comment: 50 pages, additional references adde

Fourier-transform spectroscopy of Sr2 and revised ground state potential

Precise potentials for the ground state X1Sigma+g and the minimum region of the excited state 2_1Sigma+u of Sr2 are derived by high resolution Fourier-transform spectroscopy of fluorescence progressions from single frequency laser excitation of Sr2 produced in a heat pipe at 950 Celsius. A change of the rotational assignment by four units compared to an earlier work (G. Gerber, R. M\"oller, and H. Schneider, J. Chem. Phys. 81, 1538 (1984)) is needed for a consistent description leading to a significant shift of the potentials towards longer inter atomic distances. The huge amount of ground state data derived for the three different isotopomers 88Sr2, 86Sr88Sr and 87Sr88Sr (almost 60% of all excisting bound rovibrational ground state levels for the isotopomer 88Sr2) fixes this assignment undoubtedly. The presented ground state potential is derived from the observed transitions for the radial region from 4 to 11 A (9 cm-1 below the asymptote) and is extended to the longe range region by the use of theoretical dispersion coefficients together with already available photoassociation data. New estimations of the scattering lengths for the complete set of isotopic combinations are derived by mass scaling with the derived potential. The data set for the excited state 2_1Sigma+u was sufficient to derive a potential energy curve around the minimum.Comment: 10 pages, 7 figures, some small corrections done especially to the potential description of the excited state (already included in the published journal version

On the Fourier transform of the characteristic functions of domains with C1C^1 -smooth boundary

We consider domains $D\subseteq\mathbb R^n$ with $C^1$ -smooth boundary and study the following question: when the Fourier transform $\hat{1_D}$ of the characteristic function $1_D$ belongs to $L^p(\mathbb R^n)$?Comment: added two references; added footnotes on pages 6 and 1

Adjointness Relations as a Criterion for Choosing an Inner Product

This is a contribution to the forthcoming book "Canonical Gravity: {}From Classical to Quantum" edited by J. Ehlers and H. Friedrich. Ashtekar's criterion for choosing an inner product in the quantisation of constrained systems is discussed. An erroneous claim in a previous paper is corrected and a cautionary example is presented.Comment: 6 pages, MPA-AR-94-

Diffractive charged meson pair production

We investigate the possibility to measure the nonforward gluon distribution function by means of diffractively produced \pi^+\pi^- and K^+K^- pairs in polarized lepton nucleon scattering. The resulting cross sections are small and are dominated by the gluonic contribution. We find relatively large spin asymmetries, both for \pi^+\pi^- and for K^+K^- pairs.Comment: 15 pages, version with changed kinematical cuts, to be pubished in Phys.Lett.

Whitney coverings and the tent spaces T1,q(γ)T^{1,q}(\gamma) for the Gaussian measure

We introduce a technique for handling Whitney decompositions in Gaussian harmonic analysis and apply it to the study of Gaussian analogues of the classical tent spaces $T^{1,q}$ of Coifman, Meyer and Stein.Comment: 13 pages, 1 figure. Revised version incorporating referee's comments. To appear in Arkiv for Matemati

Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves

This paper provides empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. The second of these conjectures relates six quantities associated to a Jacobian over the rational numbers. One of these six quantities is the size of the Shafarevich-Tate group. Unable to compute that, we computed the five other quantities and solved for the last one. In all 32 cases, the result is very close to an integer that is a power of 2. In addition, this power of 2 agrees with the size of the 2-torsion of the Shafarevich-Tate group, which we could compute