37 research outputs found
Integrals Over Polytopes, Multiple Zeta Values and Polylogarithms, and Euler's Constant
Let be the triangle with vertices (1,0), (0,1), (1,1). We study certain
integrals over , one of which was computed by Euler. We give expressions for
them both as a linear combination of multiple zeta values, and as a polynomial
in single zeta values. We obtain asymptotic expansions of the integrals, and of
sums of certain multiple zeta values with constant weight. We also give related
expressions for Euler's constant. In the final section, we evaluate more
general integrals -- one is a Chen (Drinfeld-Kontsevich) iterated integral --
over some polytopes that are higher-dimensional analogs of . This leads to a
relation between certain multiple polylogarithm values and multiple zeta
values.Comment: 19 pages, to appear in Mat Zametki. Ver 2.: Added Remark 3 on a Chen
(Drinfeld-Kontsevich) iterated integral; simplified Proposition 2; gave
reference for (19); corrected [16]; fixed typ
Two-Loop Correction to Bhabha Scattering
We present the two-loop virtual QED corrections to e^+ e^- to mu^+ mu^- and
Bhabha scattering in dimensional regularization. The results are expressed in
terms of polylogarithms. The form of the infrared divergences agrees with
previous expectations. These results are a crucial ingredient in the complete
next-to-next-to-leading order QED corrections to these processes. A future
application will be to reduce theoretical uncertainties associated with
luminosity measurements at e^+ e^- colliders. The calculation also tests
methods that may be applied to analogous QCD processes.Comment: Latex, 22 pages, 1 figur
Harmonic Sums and Mellin Transforms up to two-loop Order
A systematic study is performed on the finite harmonic sums up to level four.
These sums form the general basis for the Mellin transforms of all individual
functions of the momentum fraction emerging in the quantities of
massless QED and QCD up to two--loop order, as the unpolarized and polarized
splitting functions, coefficient functions, and hard scattering cross sections
for space and time-like momentum transfer. The finite harmonic sums are
calculated explicitly in the linear representation. Algebraic relations
connecting these sums are derived to obtain representations based on a reduced
set of basic functions. The Mellin transforms of all the corresponding Nielsen
functions are calculated.Comment: 44 pages Latex, contract number adde
phi photo-production from Li, C, Al, and Cu nuclei at Egamma=1.5 - 2.4 GeV
The photo-production of mesons from Li, C, Al, and Cu at forward
angles has been measured at =1.5--2.4 GeV. The number of events for
incoherent phi photo-production is found to have a target mass number
dependence of in the kinematical region of
. The total cross section of the -nucleon interaction,
, has been estimated as mb using the
-dependence of the photo-production yield and a Glauber-type multiple
scattering theory. This value is much larger than in free
space, suggesting that the properties might change in the nuclear
medium.Comment: 12 pages 4 figures, submitted to Phys. Lett.