For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently ...‘simple’ numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in
d
=4−2
ε
dimensions. One method uses Mellin–Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A.V. Smirnov and V.A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop
ε
-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sector_decomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin–Barnes representations and sector decompositions, is compared. The computational packages are publicly available.
Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop N-point corrections are needed. We study here the tensor reduction for Feynman integrals with N⩾6. A ...general, recursive solution by Binoth et al. expresses N-point Feynman integrals of rank R in terms of (N−1)-point Feynman integrals of rank (R−1) (for N⩾6). We show that the coefficients can be obtained analytically from suitable representations of the metric tensor. Contractions of the tensor integrals with external momenta can be efficiently expressed as well. We consider our approach particularly well suited for automatization.
ZFITTER is a Fortran program for the calculation of fermion pair production and radiative corrections at high energy
e
+
e
−
colliders; it is also suitable for other applications where electroweak ...radiative corrections appear.
ZFITTER is based on a semi-analytical approach to the calculation of radiative corrections in the Standard Model. We present a summary of new features of the
ZFITTER program version 6.42 compared to version 6.21. The most important additions are: (i) some higher-order QED corrections to fermion pair production, (ii) electroweak one-loop corrections to atomic parity violation, (iii) electroweak one-loop corrections to
ν
¯
e
ν
e
production, (iv) electroweak two-loop corrections to the
W boson mass and the effective weak mixing angle.
Title of program:
ZFITTER version 6.42 (18 May 2005)
Catalogue identifier:ADMJ_v2_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/ADMJ_v2_0
Authors of original program: D. Bardin, P. Christova, M. Jack, L. Kalinovskaya, A. Olshevski, S. Riemann, T. Riemann
Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland
Reference for
ZFITTER version 6.21:
D. Bardin et al., Comput. Phys. Comm. 133 (2001) 229–395
Operating system:
UNIX/LINUX, program tested under, e.g.,
HP-UX and
PC/Linux
Programming language used:
FORTRAN 77
High speed storage required: <2 MB
No. of lines in distributed program, including test data, etc.:29 164
No. of bytes in distributed program, including test data, etc.:185 824
Distribution format:tar.gz
Does the new version supersede the previous version:Yes
Nature of the physical problem: Fermion pair production is an important reaction for precision tests of the Standard Model, at LEP/SLC and future linear colliders at higher energies. For this purpose, QED, electroweak and QCD radiative corrections have to be calculated with high precision, including higher order effects. Multi parameter fits used to extract model parameters from experimental measurements require a program of sufficient flexibility and high calculational speed.
ZFITTER combines these two aspects by employing analytical integrations of matrix elements and at most one-dimensional numerical integration, as well as a variety of flags defining the physics content used. The calculated predictions are typically at the per mille precision level, sometimes better.
Method of solution: Numerical integration of analytical formulae.
Reasons for new version:Addition of substantial material into the code: covering of more reactions; more accurate description of existing reactions.
Summary of revisions:New parts for predicting atomic parity violation and for neutrino pair production; more accurate higher order QED corrections for fermion pair production; two-loop corrections to the predictions of
W mass and of the weak mixing angle.
Restrictions on the complexity of the problem: Fermion pair production is described below the top quark pair production threshold. Photonic corrections are taken into account with simple cuts on photon energy, or the energies and acollinearity of the two fermions, and
one fermion production angle. The treatment of Bhabha scattering is less advanced.
Typical running time: On a Pentium IV PC installation (2.8 GHz) using g77 under Linux 2.4.21, approximately 23 s are needed to run the standard test of subroutine
ZFTEST. This result is for a
default/recommended setting of the input parameters, with
all corrections in the Standard Model switched
on.
ZFTEST computes 12 cross-sections and cross-section asymmetries for 8 energies with 5 interfaces, i.e. about 360 cross-sections in 23 s.
A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In ...this Letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with external momenta. This is based on sums over signed minors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently.
Background
It is unknown how often Dutch patient decision aids are used during kidney failure treatment modality education and what their impact is on shared decision‐making.
Objectives
We determined ...the use of Three Good Questions, ‘Overviews of options’, and Dutch Kidney Guide by kidney healthcare professionals. Also, we determined patient‐experienced shared decision‐making. Finally, we determined whether the experience of shared decision‐making among patients changed after a training workshop for healthcare professionals.
Design
Quality improvement study.
Participants
Healthcare professionals answered questionnaires regarding education/patient decision aids. Patients with estimated glomerular filtration rate <20 mL/min/1.73 m2 completed shared decision‐making questionnaires. Data were analysed with one‐way analysis of variance and linear regression.
Results
Of 117 healthcare professionals, 56% applied shared decision‐making by discussing Three Good Questions (28%), ‘Overviews of options’ (31%–33%) and Kidney Guide (51%). Of 182 patients, 61%–85% was satisfied with their education. Of worst scoring hospitals regarding shared decision‐making, only 50% used ‘Overviews of options’/Kidney Guide. Of best scoring hospitals 100% used them, needed less conversations (p = 0.05), provided information about all treatment options and more often provided information at home. After the workshop, patients' shared decision‐making scores remained unchanged.
Conclusions
The use of specifically developed patient decision aids during kidney failure treatment modality education is limited. Hospitals that did use them had higher shared decision‐making scores. However, the degree of shared decision‐making experienced by patients remained unchanged after healthcare professionals were trained on shared decision‐making and the implementation of patient decision aids.
We perform a new, recursive reduction of one-loop
n-point rank
R tensor Feynman integrals in short:
(
n
,
R
)
-integrals for
n
⩽
6
with
R
⩽
n
by representing
(
n
,
R
)
-integrals in terms of
(
n
,
R
...−
1
)
- and
(
n
−
1
,
R
−
1
)
-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, a recursive reduction for the tensors is found. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories.
The SANC system is used for systematic calculations of various processes within the Standard Model in the one-loop approximation. QED, electroweak, and QCD corrections are computed to a number of ...processes being of interest for modern and future high-energy experiments. Several applications for the LHC physics program are presented. Development of the system and the general problems and perspectives for future improvement of the theoretical precision are discussed.
Virtual fermionic
N
f
= 1 and
N
f
= 2 contributions to Bhabha scattering are combined with realistic real corrections at next-to-next-to-leading order in QED. The virtual corrections are determined ...by the package
bha_nnlo_hf
, and real corrections with the Monte Carlo generators B
hagen
-1P
h
, H
elac
-P
hegas
and E
khara
. Numerical results are discussed at the energies of and with realistic cuts used at the Φ factory DANE, at the
B
factories PEP-II and KEK, and at the charm/τ factory BEPC II. We compare these complete calculations with the approximate ones realized in the generator B
aba
Y
aga
@NLO used at meson factories to evaluate their luminosities. For realistic reference event selections we find agreement for the NNLO leptonic and hadronic corrections within 0.07% or better and conclude that they are well accounted for in the generator by comparison with the present experimental accuracy.
The luminosity measurement at the projected International Linear e+e- Collider ILC is planned to be performed with forward Bhabha scattering with an accuracy of the order of 10-4. A theoretical ...prediction of the differential cross-section has to include one-loop weak corrections, with leading higher order terms, and the complete two-loop QED corrections. Here, we present the weak part and the virtual one-loop photonic corrections. For the photonic corrections, the expansions in ε=(4-d)/2 are derived with inclusion of the terms of order ε in order to match the two-loop accuracy. For the photonic box master integral in d dimensions we compare several different methods of evaluation.
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