Tuning FORM with large calculations

Some recent additions to FORM are discussed. In particular large file support and the tablebases are presented.Comment: 5 pages, LaTeX. Talk given at RADCOR02, Kloster Ban

Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language

The traditional split-up into a low level language and a high level language in the design of computer algebra systems may become obsolete with the advent of more versatile computer languages. We describe GiNaC, a special-purpose system that deliberately denies the need for such a distinction. It is entirely written in C++ and the user can interact with it directly in that language. It was designed to provide efficient handling of multivariate polynomials, algebras and special functions that are needed for loop calculations in theoretical quantum field theory. It also bears some potential to become a more general purpose symbolic package

First Results with a new Method for calculating 2-loop Box-Functions

We describe a first attempt to calculate scalar 2-loop box-functions with arbitrary internal masses, applying a novel method proposed in hep-ph/9407234. Four of the eight integrals are accessible to integration by means of the residue theorem, leaving a rational function in the remaining variables. The result of the procedure is a three- or sometimes two-dimensional integral representation over a finite volume that can be further evaluated using numerical methods.Comment: 10 pages, LaTeX2e, 11 eps-figures, needs epsfig.st

First Time-dependent Study of H2 and H3+ Ortho-Para Chemistry in the Diffuse Interstellar Medium: Observations Meet Theoretical Predictions

The chemistry in the diffuse interstellar medium initiates the gradual increase of molecular complexity during the life cycle of matter. A key molecule that enables build-up of new molecular bonds and new molecules via proton-donation is H3+. Its evolution is tightly related to molecular hydrogen and thought to be well understood. However, recent observations of ortho and para lines of H2 and H3+ in the diffuse ISM showed a puzzling discrepancy in nuclear spin excitation temperatures and populations between these two key species. H3+, unlike H2, seems to be out of thermal equilibrium, contrary to the predictions of modern astrochemical models. We conduct the first time-dependent modeling of the para-fractions of H2 and H3+ in the diffuse ISM and compare our results to a set of line-of-sight observations, including new measurements presented in this study. We isolate a set of key reactions for H3+ and find that the destruction of the lowest rotational states of H3+ by dissociative recombination largely control its ortho/para ratio. A plausible agreement with observations cannot be achieved unless a ratio larger than 1:5 for the destruction of (1,1)- and (1,0)-states of H3+ is assumed. Additionally, an increased CR ionization rate to 10(-15) 1/s further improves the fit whereas variations of other individual physical parameters, such as density and chemical age, have only a minor effect on the predicted ortho/para ratios. Thus our study calls for new laboratory measurements of the dissociative recombination rate and branching ratio of the key ion H3+ under interstellar conditions.Comment: 27 pages, 6 figures, 3 table

Simulated void galaxies in the standard cold dark matter model

We analyze a (120 h^{-1} Mpc)^3 adaptive mesh refinement hydrodynamic simulation that contains a higher-resolution 31 x 31 x 35 h^{-3} Mpc subvolume centered on a ~30 Mpc diameter void. Our detailed ~1 kpc resolution allows us to identify 1300 galaxies within this void to a limiting halo mass of ~10^{10} M_sun. Nearly 1000 galaxies are found to be in underdense regions, with 300 galaxies residing in regions less than half the mean density of the simulation volume. We construct mock observations of the stellar and gas properties of these systems, and reproduce the range of colors and luminosities observed in the SDSS for nearby (z < 0.03) galaxies. We find no trends with density for the most luminous (M_r -16), though they are less reliably resolved, typically appear bluer, with higher rates of star formation and specific star formation and lower mean stellar ages than galaxies in average density environments. We find a significant population of low luminosity (M_r ~ -14) dwarf galaxies that is preferentially located in low density regions and specifically in the void center. This population may help to reduce, but not remove, the discrepancy between the predicted and observed number of void galaxies.Comment: 23 pages, 14 figures, submitted to Ap

Spectroscopy and dissociative recombination of the lowest rotational states of H3+

The dissociative recombination of the lowest rotational states of H3+ has been investigated at the storage ring TSR using a cryogenic 22-pole radiofrequency ion trap as injector. The H3+ was cooled with buffer gas at ~15 K to the lowest rotational levels, (J,G)=(1,0) and (1,1), which belong to the ortho and para proton-spin symmetry, respectively. The rate coefficients and dissociation dynamics of H3+(J,G) populations produced with normal- and para-H2 were measured and compared to the rate and dynamics of a hot H3+ beam from a Penning source. The production of cold H3+ rotational populations was separately studied by rovibrational laser spectroscopy using chemical probing with argon around 55 K. First results indicate a ~20% relative increase of the para contribution when using para-H2 as parent gas. The H3+ rate coefficient observed for the para-H2 source gas, however, is quite similar to the H3+ rate for the normal-H2 source gas. The recombination dynamics confirm that for both source gases, only small populations of rotationally excited levels are present. The distribution of 3-body fragmentation geometries displays a broad part of various triangular shapes with an enhancement of ~12% for events with symmetric near-linear configurations. No large dependences on internal state or collision energy are found.Comment: 10 pages, 9 figures, to be published in Journal of Physics: Conference Proceeding

Characterizing spiral arm and interarm star formation

Interarm star formation contributes significantly to a galaxy's star formation budget, and provides an opportunity to study stellar birthplaces unperturbed by spiral arm dynamics. Using optical integral field spectroscopy of the nearby galaxy NGC 628 with VLT/MUSE, we construct Halpha maps including detailed corrections for dust extinction and stellar absorption to identify 391 HII regions at 35pc resolution over 12 kpc^2. Using tracers sensitive to the underlying gravitational potential, we associate HII regions with either arm (271) or interarm (120) environments. Using our full spectral coverage of each region, we find that most HII region physical properties (luminosity, size, metallicity, ionization parameter) are independent of environment. We calculate the fraction of Halpha luminosity due to the diffuse ionized gas (DIG) background contaminating each HII region, and find the DIG surface brightness to be higher within HII regions compared to the surroundings, and slightly higher within arm HII regions. Use of the temperature sensitive [SII]/Halpha line ratio map instead of the Halpha surface brightness to identify HII region boundaries does not change this result. Using the dust attenuation as a tracer of the gas, we find depletion times consistent with previous work (2 x 10^9 yr) with no differences between the arm and interarm, however this is very sensitive to the DIG correction. Unlike molecular clouds, which can be dynamically affected by the galactic environment, we see fairly consistent HII region properties in both arm and interarm environments. This suggests either a difference in arm star formation and feedback, or a decoupling of dense star forming clumps from the more extended surrounding molecular gas.Comment: 10 pages, 4 figures, 1 table, accepted for publication in Ap

On the Invariance of Residues of Feynman Graphs

We use simple iterated one-loop graphs in massless Yukawa theory and QED to pose the following question: what are the symmetries of the residues of a graph under a permutation of places to insert subdivergences. The investigation confirms partial invariance of the residue under such permutations: the highest weight transcendental is invariant under such a permutation. For QED this result is gauge invariant, ie the permutation invariance holds for any gauge. Computations are done making use of the Hopf algebra structure of graphs and employing GiNaC to automate the calculations.Comment: 24 pages, latex generated figures. Minor changes in revised versio