The one-loop six-dimensional hexagon integral with three massive corners

We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically. After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios. The result can be expressed as a sum of 24 terms involving only one basic function, which is a simple linear combination of logarithms, dilogarithms, and trilogarithms of uniform degree three transcendentality. Our method uses differential equations to determine the symbol of the function, and an algorithm to reconstruct the latter from its symbol. It is known that six-dimensional hexagon integrals are closely related to scattering amplitudes in N=4 super Yang-Mills theory, and we therefore expect our result to be helpful for understanding the structure of scattering amplitudes in this theory, in particular at two loops.Comment: 15 pages, 2 figure

FERMI view of the TeV blazar Markarian 421

The high energy component of the TeV blazar Markarian 421 has been extensively studied since the beginning of the 90s, when the source was first detected at gamma-rays with EGRET and the Whipple Telescope, yet the source is still far from being understood. The high sensitivity, large dynamic range, and excellent time coverage of the Fermi Large Area Telescope (LAT), all representing significant advances over previous gamma-ray observations, will play a key role in the elucidation of the physical processes underlying the high energy emission of this blazar. In this presentation we show the results from almost 6 months (4 August 2008 to 20 January 2009) of observation with LAT. We report significant flux/spectral variability on a range of time scales from weeks to days, and an energy spectrum from 0.1 GeV to 300 GeV, overlapping with the energy ranges covered by the current generation of Cherenkov Telescopes. Results on the observations of the BLLac object Markarian 421 collected in the first months of operation of the Fermi satellite have been presented. Light curves on weekly and daily timescales have been shown, as well as the results of the spectral analysis in the energy range between 100 MeV and 300 GeV, covered for the first time by a satellite experiment overlapping the lower energy observations from Cherenkov telescopes on earth. These results are still preliminary and will be enriched and completed soon by a forthcoming publication. The results shown here demonstrate the great performance of Fermi-LAT to study the gamma-emission from Mrk421 (and blazars in general) over a large dynamic range and also on short timescales, which is expected to be of key importance for the study of the emission of the source in a coordinated way with other instruments covering other energy ranges

Cosmic Ray e +/(e- + e+), p-bar/p Ratios Explained by an Injection Model Based on 2 Gamma-ray Observations

We present a model of cosmic ray (CR) injection into the Galactic space based on recent {gamma}-ray observations of supernova remnants (SNRs) and pulsar wind nebulae (PWNe) by the Fermi Large Area Telescope (Fermi) and atmospheric Cherenkov telescopes (ACTs). Steady-state (SS) injection of nuclear particles and electrons (e{sup -}) from the Galactic ensemble of SNRs, and electrons and positrons (e{sup +}) from the Galactic ensemble of PWNe are assumed, with their spectra deduced from {gamma}-ray observations and recent evolution models. The ensembles of SNRs and PWNe are assumed to share the same spatial distributions and the secondary CR production in dense molecular clouds interacting with SNRs is incorporated in the model. Propagation of CRs to Earth is calculated using GALPROP with 2 source distributions and 2 Galaxy halo sizes. We show that this observation-based model reproduces the positron fraction e{sup +}/(e{sup -} + e{sup +}) and antiproton-to-proton ratio ({bar p}/p) reported by PAMELA reasonably well without calling for new sources. Significant discrepancy is found, however, between our model and the e{sup -} + e{sup +} spectrum measured by Fermi below {approx} 20 GeV. Important quantities for Galactic CRs, including their energy injection, average lifetime, and mean gas density along their typical propagation path are also presented

Measurement of the Cosmic Ray e+ plus e- Spectrum from 20 GeV to 1 TeV with the Fermi Large Area Telescope

Designed as a high-sensitivity gamma-ray observatory, the Fermi Large Area Telescope is also an electron detector with a large acceptance exceeding 2 m{sup 2}sr at 300 GeV. Building on the gamma-ray analysis, we have developed an efficient electron detection strategy which provides sufficient background rejection for measurement of the steeply-falling electron spectrum up to 1 TeV. Our high precision data show that the electron spectrum falls with energy as E{sup -3.0} and does not exhibit prominent spectral features. Interpretations in terms of a conventional diffusive model as well as a potential local extra component are briefly discussed

The On-Orbit Calibrations for the Fermi Large Area Telescope

The Large Area Telescope (LAT) on-board the Fermi Gamma-ray Space Telescope began its on-orbit operations on June 23, 2008. Calibrations, defined in a generic sense, correspond to synchronization of trigger signals, optimization of delays for latching data, determination of detector thresholds, gains and responses, evaluation of the perimeter of the South Atlantic Anomaly (SAA), measurements of live time, of absolute time, and internal and spacecraft boresight alignments. Here we describe on-orbit calibration results obtained using known astrophysical sources, galactic cosmic rays, and charge injection into the front-end electronics of each detector. Instrument response functions will be described in a separate publication. This paper demonstrates the stability of calibrations and describes minor changes observed since launch. These results have been used to calibrate the LAT datasets to be publicly released in August 2009

Pulsed Gamma-Rays From the Millisecond Pulsar J0030+0451 with the Fermi Large Area Telescope

We report the discovery of gamma-ray pulsations from the nearby isolated millisecond pulsar PSR J0030+0451 with the Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope (formerly GLAST). This discovery makes PSR J0030+0451 the second millisecond pulsar to be detected in gamma-rays after PSR J0218+4232, observed by the EGRET instrument on the Compton Gamma Ray Observatory. The spin-down power {dot E} = 3.5 x 10{sup 33} ergs s{sup -1} is an order of magnitude lower than the empirical lower bound of previously known gamma-ray pulsars. The emission profile is characterized by two narrow peaks, respectively 0.07 {+-} 0.01 and 0.08 {+-} 0.02 wide, separated by 0.44 {+-} 0.02 in phase. The first gamma-ray peak falls 0.15 {+-} 0.01 after the main radio peak. The pulse shape is similar to that of the 'normal' gamma-ray pulsars. An exponentially cut-off power-law fit of the emission spectrum leads to an integral photon flux above 100 MeV of (6.76 {+-} 1.05 {+-} 1.35) x 10{sup -8} cm{sup -2} s{sup -1} with cut-off energy (1.7 {+-} 0.4 {+-} 0.5) GeV. Based on its parallax distance of (300 {+-} 90) pc, we obtain a gamma-ray efficiency L{sub {gamma}}/{dot E} {approx_equal} 15% for the conversion of spin-down energy rate into gamma-ray radiation, assuming isotropic emission

Fermi LAT Observation of Diffuse Gamma-Rays Produced through Interactions Between Local Interstellar Matter and High Energy Cosmic Rays

Observations by the Large Area Telescope (LAT) on the Fermi mission of diffuse {gamma}-rays in a mid-latitude region in the third quadrant (Galactic longitude l from 200{sup o} to 260{sup o} and latitude |b| from 22{sup o} to 60{sup o}) are reported. The region contains no known large molecular cloud and most of the atomic hydrogen is within 1 kpc of the solar system. The contributions of {gamma}-ray point sources and inverse Compton scattering are estimated and subtracted. The residual {gamma}-ray intensity exhibits a linear correlation with the atomic gas column density in energy from 100 MeV to 10 GeV. The measured integrated {gamma}-ray emissivity is (1.63 {+-} 0.05) x 10{sup -26} photons s{sup -1}sr{sup -1} H-atom{sup -1} and (0.66 {+-} 0.02) x 10{sup -26} photons s{sup -1}sr{sup -1} H-atom{sup -1} above 100 MeV and above 300 MeV, respectively, with an additional systematic error of {approx}10%. The differential emissivity from 100 MeV to 10 GeV agrees with calculations based on cosmic ray spectra consistent with those directly measured, at the 10% level. The results obtained indicate that cosmic ray nuclei spectra within 1 kpc from the solar system in regions studied are close to the local interstellar spectra inferred from direct measurements at the Earth within {approx}10%