The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions

We consider the application of the DRA method to the case of several master integrals in a given sector. We establish a connection between the homogeneous part of dimensional recurrence and maximal unitarity cuts of the corresponding integrals: a maximally cut master integral appears to be a solution of the homogeneous part of the dimensional recurrence relation. This observation allows us to make a necessary step of the DRA method, the construction of the general solution of the homogeneous equation, which, in this case, is a coupled system of difference equations.Comment: 17 pages, 2 figure

Phase Shift in the Whitham Zone for the Gurevich-Pitaevskii Special Solution of the Korteweg-de Vries Equation

We get the leading term of the Gurevich-Pitaevskii special solution to the KdV equation in the oscillation zone without using averaging methods.Comment: 13 pages, 3 figure

Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in ϵ\epsilon

Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of dimensional regularization, $d$. The method was used to obtain analytical expressions for two missing constants in the $\epsilon$-expansion of the most complicated master integrals contributing to the three-loop massless quark and gluon form factors and thereby present the form factors in a completely analytic form. To illustrate its power we present, at transcendentality weight seven, the next order of the $\epsilon$-expansion of one of the corresponding most complicated master integrals. As a further application, we present three previously unknown terms of the expansion in $\epsilon$ of the three-loop non-planar massless propagator diagram. Only multiple $\zeta$ values at integer points are present in our result.Comment: Talk given at the International Workshop `Loops and Legs in Quantum Field Theory' (April 25--30, 2010, W\"orlitz, Germany)

Single production of doubly charged Higgs bosons at hadron colliders

We reconsider the single production of the doubly charged Higgs bosons Delta_R^{++} and Delta_L^{++} at the LHC and TEVATRON in the framework of the left-right symmetric model and the Higgs triplet model. We show that in the left-right symmetric model the production of Delta_R^{++} by Drell-Yan process via W_R exchange may give the dominant contribution. The same channel for the production of Delta_L^{++} in the Higgs triplet model is insignificant.Comment: 11 pages 5 figure

Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen

The sixth-order electron-loop vacuum-polarization contribution to the $2P_{1/2} - 2S_{1/2}$ Lamb shift of the muonic hydrogen ($\mu^{-} p^+$ bound state) has been evaluated numerically. Our result is 0.007608(1) meV. This eliminates the largest uncertainty in the theoretical calculation. Combined with the proposed precision measurement of the Lamb shift it will lead to a very precise determination of the proton charge radius.Comment: 4 pages, 5 figures the totoal LS number is change

Singly charged higgses at linear collider

We consider the production of singly charged Higgs bosons in the Higgs triplet and two Higgs doublet models. We evaluate the cross sections for the pair production and the single production of charged higgses at linear collider. The decay modes of $H^+$ and the Standard Model backgrounds are considered. We analyze the possibilities to differentiate between triplet and two Higgs doublet models.Comment: 22 pages 9 figure

Характеристики электроэнцефалограммы матери и ребенка

Cortex biopotentials of mother and baby have been measured at their physical fields shielded by a folgoizolon screen. The used screened box decreased the infrared field испытуемых by 95% and the acoustic field by 20%. A possible reaction in the form of decrease of alpha rhythm in the sensory cortex was not observed. The dynamics of the EEG amplitude, power, and rhythm frequency during the tests had individual character and was independent of the presence or absence of a screen. The result obtained may be explained by the fact that the 20% decrease of acoustic signals is insufficient for the deprivation reaction of mother and baby для реакции or other sensory modalities are important for them.Проведено измерение биопотенциалов коры головного мозга у матери и ребенка при ослаблении их физических полей экраном из фольгоизолона. Используемый экранированный бокс уменьшал инфракрасное поле испытуемых на 95%, а акустическое на 20%. Возможная реакция в виде снижения альфа-ритма в сенсорной коре не зарегистрирована. Динамика амплитуды, мощности и частоты ритмов ЭЭГ во время исследования носит индивидуальный характер и не зависит от наличия или отсутствия экрана. Полученный результат может быть связан с тем, что ослабление акустических сигналов на 20% недостаточно для реакции депривации у матери и ребенка либо для них актуальны другие сенсорные модальности

Energy of Bardeen Model Using Approximate Symmetry Method

In this paper, we investigate the energy problem in general relativity using approximate Lie symmetry methods for differential equations. This procedure is applied to Bardeen model (the regular black hole solution). Here we are forced to evaluate the third-order approximate symmetries of the orbital and geodesic equations. It is shown that energy must be re-scaled by some factor in the third-order approximation. We discuss the insights of this re-scaling factor.Comment: 14 pages, no figure, accepted for publication in Physica Script

Improved α4\alpha^4 Term of the Muon Anomalous Magnetic Moment

We have completed the evaluation of all mass-dependent $\alpha^4$ QED contributions to the muon $g-2$, or $a_\mu$, in two or more different formulations. Their numerical values have been greatly improved by an extensive computer calculation. The new value of the dominant $\alpha^4$ term $A_2^{(8)} (m_\mu / m_e)$ is 132.6823 (72), which supersedes the old value 127.50 (41). The new value of the three-mass term $A_3^{(8)} (m_\mu / m_e, m_\mu / m_\tau)$ is 0.0376 (1). The term $A_2^{(8)} (m_\mu / m_\tau)$ is crudely estimated to be about 0.005 and may be ignored for now. The total QED contribution to $a_\mu$ is $116 584 719.58 (0.02)(1.15)(0.85) \times 10^{-11}$, where 0.02 and 1.15 are uncertainties in the $\alpha^4$ and $\alpha^5$ terms and 0.85 is from the uncertainty in $\alpha$ measured by atom interferometry. This raises the Standard Model prediction by $13.9 \times 10^{-11}$, or about 1/5 of the measurement uncertainty of $a_\mu$. It is within the noise of current uncertainty ($\sim 100 \times 10^{-11}$) in the estimated hadronic contributions to $a_\mu$.Comment: Appendix A has been rewritten extensively. It includes the 4th-order calculation for illustration. Version accepted by PR