A Product Formula for the Normalized Volume of Free Sums of Lattice Polytopes

The free sum is a basic geometric operation among convex polytopes. This note focuses on the relationship between the normalized volume of the free sum and that of the summands. In particular, we show that the normalized volume of the free sum of full dimensional polytopes is precisely the product of the normalized volumes of the summands.Comment: Published in the proceedings of 2017 Southern Regional Algebra Conferenc

Numerical Algebraic Geometry: A New Perspective on String and Gauge Theories

The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these short-comings. Its so-called 'embarrassing parallelizability' allows us to solve many problems and extract physical information which elude the symbolic methods. We describe the method and then use it to solve various problems arising from physics which could not be otherwise solved.Comment: 36 page

Crystal undulator experiment at IHEP

Accelerator-based sources of hard-photon radiation are a rapidly developing field. Coherent radiation of a particle beam in an undulator is a popular choice. The crystalline undulators with periodically deformed crystallographic planes offer electromagnetic fields of the order of 1000 T and could provide a period L in the sub-millimeter range. In this way, a hundred-fold gain in the energy of emitted photons would be reached, as compared to a usual undulator. The first real construction of a crystal channeling undulator was recently proposed and realised by the present collaboration. After the sine-like deformation of crystal was proven in X-ray tests, four undulators were tested for channeling in a beam of 70-GeV protons. It was observed in the experiment that the crystal cross-section is efficiently channeling high energy particles, similarly to usual crystal deflectors. The experimentally established transparence for channeling of high energy particles allows one to start a direct experiment on photon production from a positron beam in the crystalline undulator. Details of commissioning of the experimental setup in the first run with 3 GeV positron beam are presented

Production asymmetry of D-s from 600 GeV/c Sigma(-) and pi(-) beam

The production of D-S(-) relative to D-S(+) as a function of x(F) with 600 GeV/c Sigma(-) beam is measured in the interval 0.15 < x(F) < 0.7 by the SELEX (E781) experiment at Fermilab. The integrated charge asymmetries with 600 GeV/c Sigma(-) beam (0.53 +/- 0.06) and pi(-) beam (0.06 +/- 0.11) are also compared. The results show the Sigma(-) beam fragments play a role in the production of D-S(-), as suggested by the leading quark model. (C) 2003 Elsevier Science B.V. All rights reserved

First measurement of pi(-)e ->pi(-)e gamma pion virtual compton scattering

Pion virtual compton scattering (VCS) via the reaction pi(-)e-->pi(-)egamma was observed in the Fermilab E781 SELEX experiment. SELEX used a 600 GeV/c pi(-) beam incident on target atomic electrons, detecting the incident pi(-) and the final state pi(-), electron and gamma. Theoretical predictions based on chiral perturbation theory are incorporated into a Monte Carlo simulation of the experiment and are compared to the data. The number of reconstructed events (=9) and their distribution with respect to the kinematic variables (for the kinematic region studied) are in reasonable accord with the predictions. The corresponding pi(-) VCS experimental cross section is sigma=38.8+/-13 nb, in agreement with the theoretical expectation of sigma=34.7 nb

Measurement of the D-s(+/-) lifetime

We report a precise measurement of the D-s(+/-) meson lifetime. The data were taken by the SELEX experiment (E781) spectrometer using 600 GeV/c Sigma (-), pi (-) and p beams. The measurement has been done using 918 reconstructed D-s(+/-). The lifetime of the D-s(+/-) s is measured to be 472.5 +/- 17.2 +/- 6.6 fs, using K*(892)K-0(+/-) and phi pi (+/-) decay modes. The lifetime ratio of D-s(+/-) to D-0 is 1.145 +/- 0.049. (C) 2001 Elsevier Science B.V. All rights reserved