Proton structure corrections to hyperfine splitting in muonic hydrogen

We present the derivation of the formulas for the proton structure-dependent terms in the hyperfine splitting of muonic hydrogen. We use compatible conventions throughout the calculations to derive a consistent set of formulas that reconcile differences between our results and some specific terms in earlier work. Convention conversion corrections are explicitly presented, which reduce the calculated hyperfine splitting by about 46 ppm. We also note that using only modern fits to the proton elastic form factors gives a smaller than historical spread of Zemach radii and leads to a reduced uncertainty in the hyperfine splitting. Additionally, hyperfine splittings have an impact on the muonic hydrogen Lamb shift/proton radius measurement, however the correction we advocate has a small effect there.Comment: 6 pages, 3 figure

A generalized Kac-Ward formula

The Kac-Ward formula allows to compute the Ising partition function on a planar graph G with straight edges from the determinant of a matrix of size 2N, where N denotes the number of edges of G. In this paper, we extend this formula to any finite graph: the partition function can be written as an alternating sum of the determinants of 2^{2g} matrices of size 2N, where g is the genus of an orientable surface in which G embeds. We give two proofs of this generalized formula. The first one is purely combinatorial, while the second relies on the Fisher-Kasteleyn reduction of the Ising model to the dimer model, and on geometric techniques. As a consequence of this second proof, we also obtain the following fact: the Kac-Ward and the Fisher-Kasteleyn methods to solve the Ising model are one and the same.Comment: 23 pages, 8 figures; minor corrections in v2; to appear in J. Stat. Mech. Theory Ex

On the Deconfinement Phase Transition in the Resonance Gas

We obtain the constraints on the ruling parameters of the dense hadronic gas model at the critical temperature and propose the quasiuniversal ratios of the thermodynamic quantities. The possible appearence of thermodynamical instability in such a model is discussed.Comment: 7 pages, plain LaTeX, BI-TP 94/4

Proton structure corrections to electronic and muonic hydrogen hyperfine splitting

We present a precise determination of the polarizability and other proton structure dependent contributions to the hydrogen hyperfine splitting, based heavily on the most recent published data on proton spin dependent structure functions from the EG1 experiment at the Jefferson Laboratory. As a result, the total calculated hyperfine splitting now has a standard deviation slightly under 1 part-per-million, and is about 1 standard deviation away from the measured value. We also present results for muonic hydrogen hyperfine splitting, taking care to ensure the compatibility of the recoil and polarizability terms.Comment: 9 pages, 1 figur

Proton polarizability and the Lamb shift in muonic hydrogen

The proton structure and proton polarizability corrections to the Lamb shift of electronic hydrogen and muonic hydrogen were evaluated on the basis of modern experimental data on deep inelastic structure functions. Numerical value of proton polarizability contribution to (2P-2S) Lamb shift is equal to 4.4 GHz.Comment: 8 pages, LaTeX2.09, 2 figures, uses linedraw.st

Proton polarizability contribution to the hydrogen hyperfine splitting

The contribution of the proton polarizability to the hydrogen hyperfine splitting is evaluated on the basis of modern experimental and theoretical results on the proton polarized structure functions. The value of this correction is equal to 1.4 ppm.Comment: 11 pages, LaTeX2.09, 7 figures, uses linedraw.sty, psfig.sty, epsf.st

Muonic hydrogen ground state hyperfine splitting

Corrections of orders alpha^5, alpha^6 are calculated in the hyperfine splitting of the muonic hydrogen ground state. The nuclear structure effects are taken into account in the one- and two-loop Feynman amplitudes by means of the proton electromagnetic form factors. The modification of the hyperfine splitting part of the Breit potential due to the electron vacuum polarization is considered. Total numerical value of the 1S state hyperfine splitting 182.638 meV in the (mu p) can play the role of proper estimation for the corresponding experiment with the accuracy 30 ppm.Comment: 18 pages, Talk presented at the 11th Lomonosov Conference on Elementary Particle Physics, Moscow State University, August 200

Voting 'against all' in postcommunist Russia

Since the early 1990s voters in Russia (and most of the other post-Soviet republics) have been offered the opportunity to vote ‘against all’ parties and candidates. Increasing numbers have done so. The evidence of two post-election surveys indicates that ‘against all’ voters are younger than other voters, more urban and more highly educated. They do not reject liberal democracy, but are critical of the contemporary practice of Russian politics and find no parties that adequately reflect their views. With the ending of the ‘against all’ facility in 2006 and other changes in the Russian electoral system under the Putin presidency, levels of turnout are likely to fall further and the protest vote will seek other outlets within or outside the parliamentary system