51 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 Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
We present the two-loop QCD helicity amplitudes for quark-quark and
quark-antiquark scattering. These amplitudes are relevant for
next-to-next-to-leading order corrections to (polarized) jet production at
hadron colliders. We give the results in the `t Hooft-Veltman and
four-dimensional helicity (FDH) variants of dimensional regularization and
present the scheme dependence of the results. We verify that the finite
remainder, after subtracting the divergences using Catani's formula, are in
agreement with previous results. We also provide the amplitudes for
gluino-gluino scattering in pure N=1 supersymmetric Yang-Mills theory. We
describe ambiguities in continuing the Dirac algebra to D dimensions, including
ones which violate fermion helicity conservation. The finite remainders after
subtracting the divergences using Catani's formula, which enter into physical
quantities, are free of these ambiguities. We show that in the FDH scheme, for
gluino-gluino scattering, the finite remainders satisfy the expected
supersymmetry Ward identities.Comment: arXiv admin note: substantial text overlap with arXiv:hep-ph/030416
Large scale analytic calculations in quantum field theories
We present a survey on the mathematical structure of zero- and single scale
quantities and the associated calculation methods and function spaces in higher
order perturbative calculations in relativistic renormalizable quantum field
theories.Comment: 25 pages Latex, 1 style fil
Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory
We present the two-loop QCD helicity amplitudes for quark-gluon scattering,
and for quark-antiquark annihilation into two gluons. These amplitudes are
relevant for next-to-next-to-leading order corrections to (polarized) jet
production at hadron colliders. We give the results in the `t Hooft-Veltman and
four-dimensional helicity (FDH) variants of dimensional regularization. The
transition rules for converting the amplitudes between the different variants
are much more intricate than for the previously discussed case of gluon-gluon
scattering. Summing our two-loop expressions over helicities and colors, and
converting to conventional dimensional regularization, gives results in
complete agreement with those of Anastasiou, Glover, Oleari and Tejeda-Yeomans.
We describe the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric
Yang-Mills theory, obtained from the QCD amplitudes by modifying the color
representation and multiplicities, and verify supersymmetry Ward identities in
the FDH scheme.Comment: 77 pages. v2: corrected errors in eqs. (3.7) and (3.8) for one-loop
assembly; remaining results unaffecte
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
Universal Higher Order Singlet QED Corrections to Unpolarized Lepton Scattering
We calculate the universal flavor-singlet radiative QED corrections to
unpolarized lepton scattering applicable to general differential scattering
cross sections, involving charged fermions or photons in initial or final
states. The radiators are derived to in analytic
form. Numerical illustrations are given.Comment: 31 pages, 3 figures, 1 style fil
Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter
We continue the study of the construction of analytical coefficients of the
epsilon-expansion of hypergeometric functions and their connection with Feynman
diagrams. In this paper, we show the following results:
Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth
(see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions.
Theorem B: The epsilon expansion of a hypergeometric function with one
half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the
harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are
ratios of polynomials. Some extra materials are available via the www at this
http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected
and a few references added; v3: few references added
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.
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