3,944 research outputs found
The Polarized Two-Loop Massive Pure Singlet Wilson Coefficient for Deep-Inelastic Scattering
We calculate the polarized massive two--loop pure singlet Wilson coefficient
contributing to the structure functions analytically in the whole
kinematic region. The Wilson coefficient contains Kummer--elliptic integrals.
We derive the representation in the asymptotic region , retaining
power corrections, and in the threshold region. The massless Wilson coefficient
is recalculated. The corresponding twist--2 corrections to the structure
function are obtained by the Wandzura--Wilczek relation. Numerical
results are presented.Comment: 22 pages Latex, 8 Figure
The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering
We calculate the massive two--loop pure singlet Wilson coefficients for heavy
quark production in the unpolarized case analytically in the whole kinematic
region and derive the threshold and asymptotic expansions. We also recalculate
the corresponding massless two--loop Wilson coefficients. The complete
expressions contain iterated integrals with elliptic letters. The contributing
alphabets enlarge the Kummer-Poincar\'e letters by a series of square-root
valued letters. A new class of iterated integrals, the Kummer-elliptic
integrals, are introduced. For the structure functions and we also
derive improved asymptotic representations adding power corrections. Numerical
results are presented.Comment: 42, pages Latex, 8 Figure
The Initial State QED Corrections to Annihilation to a Neutral Vector Boson Revisited
We calculate the non-singlet, the pure singlet contribution, and their
interference term, at due to electron-pair initial state
radiation to annihilation into a neutral vector boson in a direct
analytic computation without any approximation. The correction is represented
in terms of iterated incomplete elliptic integrals. Performing the limit we find discrepancies with the earlier results of
Ref.~\cite{Berends:1987ab} and confirm results obtained in
Ref.~\cite{Blumlein:2011mi} where the effective method of massive operator
matrix elements has been used, which works for all but the power corrections in
. In this way, we also confirm the validity of the factorization of
massive partons in the Drell-Yan process. We also add non-logarithmic terms at
which have not been considered in \cite{Berends:1987ab}. The
corrections are of central importance for precision analyzes in
annihilation into at high luminosity.Comment: 4 pages Latex, 2 Figures, several style file
Extent of regretted sexual intercourse among young teenagers in Scotland: a cross sectional survey
No abstract available
Impact of a theoretically based sex education programme (SHARE) delivered by teachers on NHS registered conceptions and terminations: final results of cluster randomised trial
<b>Objective</b>: To assess the impact of a theoretically based sex education programme (SHARE) delivered by teachers compared with conventional education in terms of conceptions and terminations registered by the NHS.
Design Follow-up of cluster randomised trial 4.5 years after intervention.
<b>Setting</b>: NHS records of women who had attended 25 secondary schools in east Scotland.
<b>Participants</b>: 4196 women (99.5% of those eligible).
<b>Intervention</b>: SHARE programme (intervention group) v existing sex education (control group).
<b>Main outcome measure</b>: NHS recorded conceptions and terminations for the achieved sample linked at age 20.
<b>Results</b>: In an "intention to treat" analysis there were no significant differences between the groups in registered conceptions per 1000 pupils (300 SHARE v 274 control; difference 26, 95% confidence interval â33 to 86) and terminations per 1000 pupils (127 v 112; difference 15, â13 to 42) between ages 16 and 20.
<b>Conclusions</b>: This specially designed sex education programme did not reduce conceptions or terminations by age 20 compared with conventional provision. The lack of effect was not due to quality of delivery. Enhancing teacher led school sex education beyond conventional provision in eastern Scotland is unlikely to reduce terminations in teenagers
Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
We calculate 3-loop master integrals for heavy quark correlators and the
3-loop QCD corrections to the -parameter. They obey non-factorizing
differential equations of second order with more than three singularities,
which cannot be factorized in Mellin- space either. The solution of the
homogeneous equations is possible in terms of convergent close integer power
series as Gau\ss{} hypergeometric functions at rational argument. In
some cases, integrals of this type can be mapped to complete elliptic integrals
at rational argument. This class of functions appears to be the next one
arising in the calculation of more complicated Feynman integrals following the
harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic
polylogarithms, square-root valued iterated integrals, and combinations
thereof, which appear in simpler cases. The inhomogeneous solution of the
corresponding differential equations can be given in terms of iterative
integrals, where the new innermost letter itself is not an iterative integral.
A new class of iterative integrals is introduced containing letters in which
(multiple) definite integrals appear as factors. For the elliptic case, we also
derive the solution in terms of integrals over modular functions and also
modular forms, using -product and series representations implied by Jacobi's
functions and Dedekind's -function. The corresponding
representations can be traced back to polynomials out of Lambert--Eisenstein
series, having representations also as elliptic polylogarithms, a -factorial
, logarithms and polylogarithms of and their -integrals.
Due to the specific form of the physical variable for different
processes, different representations do usually appear. Numerical results are
also presented.Comment: 68 pages LATEX, 10 Figure
Tumbleweeds and airborne gravitational noise sources for LIGO
Gravitational-wave detectors are sensitive not only to astrophysical
gravitational waves, but also to the fluctuating Newtonian gravitational forces
of moving masses in the ground and air around the detector. This paper studies
the gravitational effects of density perturbations in the atmosphere, and from
massive airborne objects near the detector. These effects were previously
considered by Saulson; in this paper I revisit these phenomena, considering
transient atmospheric shocks, and the effects of sound waves or objects
colliding with the ground or buildings around the test masses. I also consider
temperature perturbations advected past the detector as a source of
gravitational noise. I find that the gravitational noise background is below
the expected noise floor even of advanced interferometric detectors, although
only by an order of magnitude for temperature perturbations carried along
turbulent streamlines. I also find that transient shockwaves in the atmosphere
could potentially produce large spurious signals, with signal-to-noise ratios
in the hundreds in an advanced interferometric detector. These signals could be
vetoed by means of acoustic sensors outside of the buildings. Massive
wind-borne objects such as tumbleweeds could also produce gravitational signals
with signal-to-noise ratios in the hundreds if they collide with the
interferometer buildings, so it may be necessary to build fences preventing
such objects from approaching within about 30m of the test masses.Comment: 15 pages, 10 PostScript figures, uses REVTeX4.cls and epsfig.st
Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations
Various of the single scale quantities in massless and massive QCD up to
3-loop order can be expressed by iterative integrals over certain classes of
alphabets, from the harmonic polylogarithms to root-valued alphabets. Examples
are the anomalous dimensions to 3-loop order, the massless Wilson coefficients
and also different massive operator matrix elements. Starting at 3-loop order,
however, also other letters appear in the case of massive operator matrix
elements, the so called iterative non-iterative integrals, which are related to
solutions based on complete elliptic integrals or any other special function
with an integral representation that is definite but not a Volterra-type
integral. After outlining the formalism leading to iterative non-iterative
integrals,we present examples for both of these cases with the 3-loop anomalous
dimension and the structure of the principle solution in
the iterative non-interative case of the 3-loop QCD corrections to the
-parameter.Comment: 13 pages LATEX, 2 Figure
3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering
A survey is given on the status of 3-loop heavy flavor corrections to
deep-inelastic structure functions at large enough virtualities .Comment: 13 pages Latex, 8 Figures, Contribution to the Proceedings of EPS
2015 Wie
Revisiting the Initial State QED Corrections to Annihilation into a Neutral Boson
At colliders the QED--initial state radiation forms a large part
of the radiative corrections. Their precise and fast evaluation is an essential
asset for the experiments at LEP, the ILC and the FCC-ee, operating at high
luminosity. A long standing problem in the analytic calculation of the
initial state corrections concerns a discrepancy which has been
observed between the result of Berends et al. (1988) \cite{Berends:1987ab} in
the limit and the result by Bl{\"u}mlein et al. (2011)
\cite{Blumlein:2011mi} using massive operator matrix elements deriving this
limit directly. In order to resolve this important issue we recalculated this
process by integrating directly over the phase space without any approximation.
For parts of the corrections we find exact solutions of the cross section in
terms of iterated integrals over square root valued letters representing
incomplete elliptic integrals and iterations over them. The expansion in the
limit reveals errors in the constant term of the
former calculation and yields agreement with the calculation based on massive
operator matrix elements, which has impact on the experimental analysis
programs. This finding also explicitly proofs the factorization of massive
initial state particles in the high energy limit including the terms of
for this process.Comment: 9 pages LAE
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