Toward high-precision values of the self energy of non-S states in hydrogen and hydrogen-like ions

The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between 20 and 110 are given for a large number of states. The self-energy is the largest contribution of Quantum Electrodynamics (QED) to the energy levels of these atomic systems. These results greatly expand the number of levels for which the self energy is known with a controlled and high precision. Applications include the adjustment of the Rydberg constant and atomic calculations that take into account QED effects.Comment: Minor changes since previous versio

Recoil correction to the bound-electron g factor in H-like atoms to all orders in αZ\alpha Z

The nuclear recoil correction to the bound-electron g factor in H-like atoms is calculated to first order in $m/M$ and to all orders in $\alpha Z$. The calculation is performed in the range Z=1-100. A large contribution of terms of order $(\alpha Z)^5$ and higher is found. Even for hydrogen, the higher-order correction exceeds the $(\alpha Z)^4$ term, while for uranium it is above the leading $(\alpha Z)^2$ correction.Comment: 6 pages, 3 tables, 1 figur

Three-flavor atmospheric neutrino anomaly

We investigate the indications of flavor oscillations that come from the anomalous flavor composition of the atmospheric neutrino flux observed in some underground experiments. We study the information coming from the neutrino-induced $\mu$-like and $e$-like events both in the sub-GeV energy range (Kamiokande, IMB, Fr{\'e}jus, and NUSEX experiments) and in the multi-GeV energy range (Kamiokande experiment). First we analyze all the data in the limits of pure $\nu_\mu\leftrightarrow\nu_\tau$ and $\nu_\mu\leftrightarrow\nu_e$ oscillations. We obtain that $\nu_\mu\leftrightarrow\nu_e$ oscillations provide a better fit, in particular to the multi-GeV data. Then we perform a three-flavor analysis in the hypothesis of dominance of one neutrino square mass difference, $m^2$, implying that the neutrino mixing is parametrized by two angles, $(\psi,\,\phi)\in[0,\,\pi/2]$. We explore the space $(m^2,\,\psi,\,\phi)$ exhaustively, and find the regions favored by the oscillation hypothesis. The results are displayed in a form suited to the comparison with other flavor oscillation searches at accelerator, reactor, and solar $\nu$ experiments. In the analysis, we pay particular attention to the earth matter effects, to the correlation of the uncertainties, and to the symmetry properties of the oscillation probability.Comment: 25 pages (RevTeX) + 12 figures, requires epsfig.sty. All the figures are bitmapped. Postscript figures with full resolution are available at ftp://ftp.sns.ias.edu/pub/lisi/atmpaper

Solving Medium-Density Subset Sum Problems in Expected Polynomial Time: An Enumeration Approach

The subset sum problem (SSP) can be briefly stated as: given a target integer $E$ and a set $A$ containing $n$ positive integer $a_j$, find a subset of $A$ summing to $E$. The \textit{density} $d$ of an SSP instance is defined by the ratio of $n$ to $m$, where $m$ is the logarithm of the largest integer within $A$. Based on the structural and statistical properties of subset sums, we present an improved enumeration scheme for SSP, and implement it as a complete and exact algorithm (EnumPlus). The algorithm always equivalently reduces an instance to be low-density, and then solve it by enumeration. Through this approach, we show the possibility to design a sole algorithm that can efficiently solve arbitrary density instance in a uniform way. Furthermore, our algorithm has considerable performance advantage over previous algorithms. Firstly, it extends the density scope, in which SSP can be solved in expected polynomial time. Specifically, It solves SSP in expected $O(n\log{n})$ time when density $d \geq c\cdot \sqrt{n}/\log{n}$, while the previously best density scope is $d \geq c\cdot n/(\log{n})^{2}$. In addition, the overall expected time and space requirement in the average case are proven to be $O(n^5\log n)$ and $O(n^5)$ respectively. Secondly, in the worst case, it slightly improves the previously best time complexity of exact algorithms for SSP. Specifically, the worst-case time complexity of our algorithm is proved to be $O((n-6)2^{n/2}+n)$, while the previously best result is $O(n2^{n/2})$.Comment: 11 pages, 1 figur

Calculated Electron Fluxes at Airplane Altitudes

A precision measurement of atmospheric electron fluxes has been performed on a Japanese commercial airliner (Enomoto, {\it et al.}, 1991). We have performed a monte carlo calculation of the cosmic ray secondary electron fluxes expected in this experiment. The monte carlo uses the hadronic portion of our neutrino flux cascade program combined with the electromagnetic cascade portion of the CERN library program GEANT. Our results give good agreement with the data, provided we boost the overall normalization of the primary cosmic ray flux by 12\% over the normalization used in the neutrino flux calculation.Comment: in REVTEX, 12 pages + 4 figures available upon reques

Soft Contributions to Hard Pion Photoproduction

Hard, or high transverse momentum, pion photoproduction can be a tool for probing the parton structure of the beam and target. We estimate the soft contributions to this process, with an eye toward delineating the region where perturbatively calculable processes dominate. Our soft process estimate is based on vector meson dominance and data based parameterizations of semiexclusive hadronic cross sections. We find that soft processes dominate in single pion photoproduction somewhat past 2 GeV transverse momentum at a few times 10 GeV incoming energy. The recent polarization asymmetry data is consistent with the perturbative asymmetry being diluted by polarization insensitive soft processes. Determining the polarized gluon distribution using hard pion photoproduction appears feasible with a few hundred GeV incoming energy (in the target rest frame).Comment: 6 pages, 5 figure

Two-Loop Effects and Current Status of the 4He+ Lamb Shift

We report on recent progress in the treatment of two-loop binding corrections to the Lamb shift, with a special emphasis on S and P states. We use these and other results in order to infer an updated theoretical value of the Lamb shift in 4He+.Comment: 11 pages, nrc1 style; paper presented at PSAS (2006), Venic

Unconventional superstring derived E6_{\bf 6} models and neutrino phenomenology

Conventional superstring derived E$_6$ models can accommodate small neutrino masses if a discrete symmetry is imposed which forbids tree level Dirac neutrino masses but allows for radiative mass generation. Since the only possible symmetries of this kind are known to be generation dependent, we explore the possibility that the three sets of light states in each generation do not have the same assignments with respect to the 27 of $E_6$, leading to non universal gauge interactions under the additional $U(1)'$ factors for the known fermions. We argue that models realising such a scenario are viable, with their structure being constrained mainly by the requirement of the absence of flavor changing neutral currents in the Higgs sector. Moreover, in contrast to the standard case, rank 6 models are not disfavoured with respect to rank 5. By requiring the number of light neutral states to be minimal, these models have an almost unique pattern of neutrino masses and mixings. We construct a model based on the unconventional assignment scenario in which (with a natural choice of the parameters) m_{\nut}\sim O(10)eV is generated at one loop, m_{\num} is generated at two loops and lies in a range interesting for the solar neutrino problem, and \nue remains massless. In addition, since baryon and lepton number are conserved, there is no proton decay in the model. To illustrate the non-standard phenomenology implied by our scheme we also discuss a second scenario in which an attempt for solving the solar neutrino puzzle with matter enhanced oscillations and practically massless neutrinos can be formulated, and in which peculiar effects for the \num --> \nut conversion of the upward-going atmospheric neutrinos could arise as well.Comment: Plain Tex, 33 pages, 3 PostScript figures (uses epsf.tex). Modified file-format. No changes in the tex

Charged Scalar Particles and τ\tau Leptonic Decay

Charged scalar particles introduced in some extensions of the standard model can induce $\tau$ leptonic decay at tree level. We find that with some charged SU(2)-singlet scalar particles, like ones introduced in Zee-type models, $\tau$ leptonic decay width is always smaller than what is predicted by the standard model, therefore they may offer a natural solution to $\tau$ decay puzzle. To be more specific, we examine some Zee-type models in detail to see if at the same time they are acceptable in particle physics, cosmology and astrophysics. It is shown that $\tau$ decay data do put some constrains on these models.Comment: ICTP Report No. IC/93/31, 12 pages, Latex, one figure is not included, it is available upon deman