Ulrich D. Jentschura

New Limits on the Drift of Fundamental Constants from Laboratory Measurements

We have remeasured the absolute 1S-2S transition frequency nu(H) in atomic hydrogen. A comparison with the result of the previous measurement performed in 1999 sets a limit of (-29+/-57) Hz for the drift of nu(H) with respect to the ground state hyperfine splitting nu(Cs) in 133Cs. Combining this result with the recently published optical transition frequency in 199Hg+ against nu(Cs) and a microwave 87Rb and 133Cs clock comparison, we deduce separate limits on alpha/alpha=(-0.9+/-2.9) x 10(-15) yr(-1) and the fractional time variation of the ratio of Rb and Cs nuclear magnetic moments mu(Rb)/mu(Cs) equal to (-0.5+/-1.7) x 10(-15) yr(-1). The latter provides information on the temporal behavior of the constant of strong interaction.

Net-to-leading order QCD corrections for the B0B0 mixing with an extended Higgs sector

Abstract We present a calculation of the B 0 B 0 mixing including next-to-leading order (NLO) QCD corrections within the Two-Higgs Doublet Model (2HDM). The QCD corrections at NLO are contained in the factor denoted by η2 which modifies the result obtained at the lowest order of perturbation theory. In the Standard Model case, we confirm the results for η2 obtained by Buras, Jamin and Weisz [Nucl. Phys. B 347 (]990) 49]1. The factor η2 is gauge and renormalization prescription invariant and it does not depend on the infrared behaviour of the theory, which constitutes an important test of the calculations. The NLO calculations within the 2HDM enhance the LO result up to 18%, which affects the correlation between My and Vtd.

Multi-instantons and exact results I: Conjectures, WKB expansions, and instanton interactions

Abstract We consider specific quantum mechanical model problems for which perturbation theory fails to explain physical properties like the eigenvalue spectrum even qualitatively, even if the asymptotic perturbation series is augmented by resummation prescriptions to “cure” the divergence in large orders of perturbation theory. Generalizations of perturbation theory are necessary, which include instanton configurations, characterized by non-analytic factors exp(− a / g ) where a is a constant and g is the coupling. In the case of one-dimensional quantum mechanical potentials with two or more degenerate minima, the energy levels may be represented as an infinite sum of terms each of which involves a certain power of a non-analytic factor and represents itself an infinite divergent series. We attempt to provide a unified representation of related derivations previously found scattered in the literature. For the considered quantum mechanical problems, we discuss the derivation of the instanton contributions from a semi-classical calculation of the corresponding partition function in the path integral formalism. We also explain the relation with the corresponding WKB expansion of the solutions of the Schrodinger equation, or alternatively of the Fredholm determinant det( H − E ) (and some explicit calculations that verify this correspondence). We finally recall how these conjectures naturally emerge from a leading-order summation of multi-instanton contributions to the path integral representation of the partition function.

From useful algorithms for slowly convergent series to physical predictions based on divergent perturbative expansions

This review is focused on the borderline region of theoretical physics and mathematics. First, we describe numerical methods for the acceleration of the convergence of series. These provide a useful toolbox for theoretical physics which has hitherto not received the attention it actually deserves. The unifying concept for convergence acceleration methods is that in many cases, one can reach much faster convergence than by adding a particular series term by term. In some cases, it is even possible to use a divergent input series, together with a suitable sequence transformation, for the construction of numerical methods that can be applied to the calculation of special functions. This review both aims to provide some practical guidance as well as a groundwork for the study of specialized literature. As a second topic, we review some recent developments in the field of Borel resummation, which is generally recognized as one of the most versatile methods for the summation of factorially divergent (perturbation) series. Here, the focus is on algorithms which make optimal use of all information contained in a finite set of perturbative coefficients. The unifying concept for the various aspects of the Borel method investigated here is given by the singularities of the Borel transform, which introduce ambiguities from a mathematical point of view and lead to different possible physical interpretations. The two most important cases are: (i) the residues at the singularities correspond to the decay width of a resonance, and (ii) the presence of the singularities indicates the existence of nonperturbative contributions which cannot be accounted for on the basis of a Borel resummation and require generalizations toward resurgent expansions. Both of these cases are illustrated by examples.

Complete two-loop correction to the bound-electron g factor

Within a systematic approach based on dimensionally regularized nonrelativistic quantum electrodynamics, we derive a complete result for the two-loop correction to order ({alpha}/{pi}){sup 2}(Z{alpha}){sup 4} for the g factor of an electron bound in an nS state of a hydrogenlike ion. The results obtained significantly improve the accuracy of the theoretical predictions for the hydrogenlike carbon and oxygen ions and influence the value of the electron mass inferred from g-factor measurements.

Multi-instantons and exact results II: Specific cases, higher-order effects, and numerical calculations

Abstract In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton contributions to the partition function, using the formalism introduced in the first part of the treatise [Ann. Phys. (N. Y.) (previous issue) (2004)]. The following potentials are considered: (i) asymmetric potentials with degenerate minima, (ii) the periodic cosine potential, (iii) anharmonic oscillators with radial symmetry, and (iv) a specific potential which bears an analogy with the Fokker–Planck equation. The latter potential has the peculiar property that the perturbation series for the ground-state energy vanishes to all orders and is thus formally convergent (the ground-state energy, however, is non-zero and positive). For the potentials (ii), (iii), and (iv), we calculate the perturbative B-function as well as the instanton A-function to fourth order in g. We also consider the double-well potential in detail, and present some higher-order analytic as well as numerical calculations to verify explicitly the related conjectures up to the order of three instantons. Strategies analogous to those outlined here could result in new conjectures for problems where our present understanding is more limited.

Isotope shift in the dielectronic recombination of three-electron ANd57+.

Isotope shifts in dielectronic recombination spectra were studied for Li-like (A)Nd(57+) ions with A=142 and A=150. From the displacement of resonance positions energy shifts deltaE(142 150)(2s-2p(1/2))=40.2(3)(6) meV [(stat)(sys)] and deltaE(142 150)(2s-2p(3/2))=42.3(12)(20) meV of 2s-2p(j) transitions were deduced. An evaluation of these values within a full QED treatment yields a change in the mean-square charge radius of (142 150)deltar(2)=-1.36(1)(3) fm(2). The approach is conceptually new and combines the advantage of a simple atomic structure with high sensitivity to nuclear size.

Calculation of the Electron Self Energy for Low Nuclear Charge

We present a nonperturbative numerical evaluation of the one-photon electron self-energy for hydrogenlike ions with low nuclear charge numbers

A problematic set of two-loop self-energy corrections

Z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

Higher-order binding corrections to the Lamb shift of 2{ital P} states

to 5. Our calculation for the