The three-loop Adler DD-function for N=1{\cal N}=1 SQCD regularized by dimensional reduction

The three-loop Adler $D$-function for ${\cal N}=1$ SQCD in the \overline{\mbox{DR}} scheme is calculated starting from the three-loop result recently obtained with the higher covariant derivative regularization. For this purpose, for the theory regularized by higher derivatives we find a subtraction scheme in which the Green functions coincide with the ones obtained with the dimensional reduction and the modified minimal subtraction prescription for the renormalization of the SQCD coupling constant and of the matter superfields. Also we calculate the $D$-function in the \overline{\mbox{DR}} scheme for all renormalization constants (including the one for the electromagnetic coupling constant which appears due to the SQCD corrections). It is shown that the results do not satisfy the NSVZ-like equation relating the $D$-function to the anomalous dimension of the matter superfields. However, the NSVZ-like scheme can be constructed with the help of a properly tuned finite renormalization. It is also demonstrated that the three-loop $D$-function defined in terms of the bare couplings with the dimensional reduction does not satisfy the NSVZ-like equation for an arbitrary renormalization prescription. We also investigate a possibility to present the results in the form of the $\beta$-expansion and the scheme dependence of this expansion.Comment: 25 pages, 2 figures, 1 table, improved conclusion, version accepted for publication in JHE

Hausdorff dimension of some groups acting on the binary tree

Based on the work of Abercrombie, Barnea and Shalev gave an explicit formula for the Hausdorff dimension of a group acting on a rooted tree. We focus here on the binary tree T. Abert and Virag showed that there exist finitely generated (but not necessarily level-transitive) subgroups of AutT of arbitrary dimension in [0,1]. In this article we explicitly compute the Hausdorff dimension of the level-transitive spinal groups. We then show examples of 3-generated spinal groups which have transcendental Hausdroff dimension, and exhibit a construction of 2-generated groups whose Hausdorff dimension is 1.Comment: 10 pages; full revision; simplified some proof

Alpha-nucleus potential for alpha-decay and sub-barrier fusion

The set of parameters for alpha-nucleus potential is derived by using the data for both the alpha-decay half-lives and the fusion cross-sections around the barrier for reactions alpha+40Ca, alpha+59Co, alpha+208Pb. The alpha-decay half-lives are obtained in the framework of a cluster model using the WKB approximation. The evaluated alpha-decay half-lives and the fusion cross-sections agreed well with the data. Fusion reactions between alpha-particle and heavy nuclei can be used for both the formation of very heavy nuclei and spectroscopic studies of the formed compound nuclei.Comment: 10 pages, 5 figure

BitTorrent is Apt for Geophysical Data Collection and Distribution

This article covers a nouveau idea of how to collect and handle geophysical data with a peer-to-peer network in near real-time. The text covers a brief introduction to the cause, the technology, and the particular case of collecting data from GNSS stations. We describe the proof-of-concept implementation that has been tested. The test was conducted with an experimental GNSS station and a data aggregation facility. In the test, original raw GNSS signal measurements were transferred to the data aggregation center and subsequently to the consumer. Our implementation utilized BitTorrent to communicate and transfer data. The solution could be used to establish the majority of data aggregation centers activities to provide fast, reliable, and transparent real-time data handling experience to the scientific community.Comment: 13 pages, 2 figure

Does the Borexino experiment have enough resolution to detect the neutrino flavor day-night asymmetry?

The Earth's density distribution can be approximately considered piecewise continuous at the scale of two-flavor oscillations of neutrinos with energies about 1 MeV. This quite general assumption appears to be enough to analytically calculate the day-night asymmetry factor. Using the explicit time averaging procedure, we show that, within the leading-order approximation, this factor is determined by the electron density immediately before the detector, i.e. in the Earth's crust. Within the approximation chosen, the resulting asymmetry factor does not depend either on the properties of the inner Earth's layers or on the substance and the dimensions of the detector. For beryllium neutrinos, we arrive at the asymmetry factor estimation of about $-4 \times 10^{-4}$, which is at least one order of magnitude beyond the present experimental resolution, including that of the Borexino experiment.Comment: 16 pages, 3 figures; Talk given at the 17th International Seminar on High Energy Physics "QUARKS'2012" (Yaroslavl, Russia, June 4-10, 2012); to appear in the Proceedings volum