Reconstructing Generalized Exponential Laws by Self-Similar Exponential Approximants

We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power series. Comparison with the standard Pad\'e approximants shows that, in general, the self-similar exponential approximants provide significantly better reconstructions.Comment: Revtex file, 21 pages, 21 figure

Effective action for Einstein-Maxwell theory at order RF**4

We use a recently derived integral representation of the one-loop effective action in Einstein-Maxwell theory for an explicit calculation of the part of the effective action containing the information on the low energy limit of the five-point amplitudes involving one graviton, four photons and either a scalar or spinor loop. All available identities are used to get the result into a relatively compact form.Comment: 13 pages, no figure

Two-loop amplitudes with nested sums: Fermionic contributions to e+ e- --> q qbar g

We present the calculation of the nf-contributions to the two-loop amplitude for e+ e- --> q qbar g and give results for the full one-loop amplitude to order eps^2 in the dimensional regularization parameter. Our results agree with those recently obtained by Garland et al.. The calculation makes extensive use of an efficient method based on nested sums to calculate two-loop integrals with arbitrary powers of the propagators. The use of nested sums leads in a natural way to multiple polylogarithms with simple arguments, which allow a straightforward analytic continuation.Comment: 31 pages, a file "coefficients.h" with the results in FORM format is include

Single-valued harmonic polylogarithms and the multi-Regge limit

We argue that the natural functions for describing the multi-Regge limit of six-gluon scattering in planar N=4 super Yang-Mills theory are the single-valued harmonic polylogarithmic functions introduced by Brown. These functions depend on a single complex variable and its conjugate, (w,w*). Using these functions, and formulas due to Fadin, Lipatov and Prygarin, we determine the six-gluon MHV remainder function in the leading-logarithmic approximation (LLA) in this limit through ten loops, and the next-to-LLA (NLLA) terms through nine loops. In separate work, we have determined the symbol of the four-loop remainder function for general kinematics, up to 113 constants. Taking its multi-Regge limit and matching to our four-loop LLA and NLLA results, we fix all but one of the constants that survive in this limit. The multi-Regge limit factorizes in the variables (\nu,n) which are related to (w,w*) by a Fourier-Mellin transform. We can transform the single-valued harmonic polylogarithms to functions of (\nu,n) that incorporate harmonic sums, systematically through transcendental weight six. Combining this information with the four-loop results, we determine the eigenvalues of the BFKL kernel in the adjoint representation to NNLLA accuracy, and the MHV product of impact factors to NNNLLA accuracy, up to constants representing beyond-the-symbol terms and the one symbol-level constant. Remarkably, only derivatives of the polygamma function enter these results. Finally, the LLA approximation to the six-gluon NMHV amplitude is evaluated through ten loops.Comment: 71 pages, 2 figures, plus 10 ancillary files containing analytic expressions in Mathematica format. V2: Typos corrected and references added. V3: Typos corrected; assumption about single-Reggeon exchange made explici

QED Effective Action at Finite Temperature: Two-Loop Dominance

We calculate the two-loop effective action of QED for arbitrary constant electromagnetic fields at finite temperature T in the limit of T much smaller than the electron mass. It is shown that in this regime the two-loop contribution always exceeds the influence of the one-loop part due to the thermal excitation of the internal photon. As an application, we study light propagation and photon splitting in the presence of a magnetic background field at low temperature. We furthermore discover a thermally induced contribution to pair production in electric fields.Comment: 34 pages, 4 figures, LaTe

Performance of the ARIANNA Hexagonal Radio Array

Installation of the ARIANNA Hexagonal Radio Array (HRA) on the Ross Ice Shelf of Antarctica has been completed. This detector serves as a pilot program to the ARIANNA neutrino telescope, which aims to measure the diffuse flux of very high energy neutrinos by observing the radio pulse generated by neutrino-induced charged particle showers in the ice. All HRA stations ran reliably and took data during the entire 2014-2015 austral summer season. A new radio signal direction reconstruction procedure is described, and is observed to have a resolution better than a degree. The reconstruction is used in a preliminary search for potential neutrino candidate events in the data from one of the newly installed detector stations. Three cuts are used to separate radio backgrounds from neutrino signals. The cuts are found to filter out all data recorded by the station during the season while preserving 85.4% of simulated neutrino events that trigger the station. This efficiency is similar to that found in analyses of previous HRA data taking seasons.Comment: Proceedings from the 34th ICRC2015, http://icrc2015.nl/ . 8 pages, 6 figure

Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics

We study the gauge covariance of the massive fermion propagator in three as well as four dimensional Quantum Electrodynamics (QED). Starting from its value at the lowest order in perturbation theory, we evaluate a non-perturbative expression for it by means of its Landau-Khalatnikov-Fradkin (LKF) transformation. We compare the perturbative expansion of our findings with the known one loop results and observe perfect agreement upto a gauge parameter independent term, a difference permitted by the structure of the LKF transformations.Comment: 9 pages, no figures, uses revte

Probing For New Physics and Detecting non linear vacuum QED effects using gravitational wave interferometer antennas

Low energy non linear QED effects in vacuum have been predicted since 1936 and have been subject of research for many decades. Two main schemes have been proposed for such a 'first' detection: measurements of ellipticity acquired by a linearly polarized beam of light passing through a magnetic field and direct light-light scattering. The study of the propagation of light through an external field can also be used to probe for new physics such as the existence of axion-like particles and millicharged particles. Their existence in nature would cause the index of refraction of vacuum to be different from unity in the presence of an external field and dependent of the polarization direction of the light propagating. The major achievement of reaching the project sensitivities in gravitational wave interferometers such as LIGO an VIRGO has opened the possibility of using such instruments for the detection of QED corrections in electrodynamics and for probing new physics at very low energies. In this paper we discuss the difference between direct birefringence measurements and index of refraction measurements. We propose an almost parasitic implementation of an external magnetic field along the arms of the VIRGO interferometer and discuss the advantage of this choice in comparison to a previously proposed configuration based on shorter prototype interferometers which we believe is inadequate. Considering the design sensitivity in the strain, for the near future VIRGO+ interferometer, of $h<2\cdot10^{-23} \frac{1}{\sqrt{\rm Hz}}$ in the range 40 Hz $- 400$ Hz leads to a variable dipole magnet configuration at a frequency above 20 Hz such that $B^{2}D \ge 13000$ T$^{2}$m/$\sqrt{\rm Hz}$ for a `first' vacuum non linear QED detection

Inhibition decorrelates visual feature representations in the inner retina

The retina extracts visual features for transmission to the brain. Different types of bipolar cell split the photoreceptor input into parallel channels and provide the excitatory drive for downstream visual circuits. Mouse bipolar cell types have been described at great anatomical and genetic detail, but a similarly deep understanding of their functional diversity is lacking. Here, by imaging light-driven glutamate release from more than 13,000 bipolar cell axon terminals in the intact retina, we show that bipolar cell functional diversity is generated by the interplay of dendritic excitatory inputs and axonal inhibitory inputs. The resulting centre and surround components of bipolar cell receptive fields interact to decorrelate bipolar cell output in the spatial and temporal domains. Our findings highlight the importance of inhibitory circuits in generating functionally diverse excitatory pathways and suggest that decorrelation of parallel visual pathways begins as early as the second synapse of the mouse visual system