Isospin breaking in the vector current of the nucleon

Extraction of the nucleon's strange form factors from experimental data requires a quantitative understanding of the unavoidable contamination from isospin violation. A number of authors have addressed this issue during the past decade, and their work is reviewed here. The predictions from early models are largely consistent with recent results that rely as much as possible on input from QCD symmetries and related experimental data. The resulting bounds on isospin violation are sufficiently precise to be of value to on-going experimental and theoretical studies of the nucleon's strange form factors.Comment: 5 pages, 3 figures. Presented at the International Workshop "From Parity Violation to Hadronic Structure and more...", Milos, Greece, 16-20 May 2006. Version 2 is only to update Refs. [21] and [25

Neural Network Parameterizations of Electromagnetic Nucleon Form Factors

The electromagnetic nucleon form-factors data are studied with artificial feed forward neural networks. As a result the unbiased model-independent form-factor parametrizations are evaluated together with uncertainties. The Bayesian approach for the neural networks is adapted for chi2 error-like function and applied to the data analysis. The sequence of the feed forward neural networks with one hidden layer of units is considered. The given neural network represents a particular form-factor parametrization. The so-called evidence (the measure of how much the data favor given statistical model) is computed with the Bayesian framework and it is used to determine the best form factor parametrization.Comment: The revised version is divided into 4 sections. The discussion of the prior assumptions is added. The manuscript contains 4 new figures and 2 new tables (32 pages, 15 figures, 2 tables

Roy-Steiner equations for pion-nucleon scattering

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high-energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the $\pi\pi\to\bar NN$ partial waves into the form of a Muskhelishvili-Omn\`es problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.Comment: 106 pages, 18 figures; version published in JHE

Izvestiya mathematics

The proton is the primary building block of the visible Universe, but many of its properties—such as its charge radius and its anomalous magneticmoment—are not well understood. The root-meansquare charge radius, rp, has been determined with an accuracy of 2 per cent (at best) by electron–proton scattering experiments. The present most accurate value of rp (with an uncertainty of 1 per cent) is given by the CODATA compilation of physical constants. This value is based mainly on precision spectroscopy of atomic hydrogen and calculations of bound-state quantum electrodynamics. The accuracy of rp as deduced from electron–proton scattering limits the testing of bound-state QED in atomic hydrogen as well as the determination of the Rydberg constant (currently the most accurately measured fundamental physical constant). An attractive means to improve the accuracy in themeasurement of rp is provided bymuonic hydrogen (a proton orbited by a negative muon); its much smaller Bohr radius compared to ordinary atomic hydrogen causes enhancement of effects related to the finite size of the proton. In particular, theLamb shift (the energy difference between the 2S1/2 and 2P1/2 states) is affected by as much as 2 per cent. Here we use pulsed laser spectroscopy to measure a muonic Lamb shift of 49,881.88(76)GHz. On the basis of present calculations of fine and hyperfine splittings and QED terms, we find rp 50.84184(67) fm, which differs by 5.0 standard deviations from the CODATA value of 0.8768(69) fm. Our result implies that either the Rydberg constant has to be shifted by 2110 kHz/c (4.9 standard deviations), or the calculations of the QED effects in atomic hydrogen or muonic hydrogen atoms are insufficient