276 research outputs found
Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d
Representations are derived for the basic scalar one-loop vertex Feynman
integrals as meromorphic functions of the space-time dimension in terms of
(generalized) hypergeometric functions and . Values at asymptotic
or exceptional kinematic points as well as expansions around the singular
points at , non-negative integers, may be derived from the
representations easily. The Feynman integrals studied here may be used as
building blocks for the calculation of one-loop and higher-loop scalar and
tensor amplitudes. From the recursion relation presented, higher n-point
functions may be obtained in a straightforward manner.Comment: 9 pages, talk presented by TR at workshop "Matter To The Deepest",
XLI International Conference on Recent Developments in Physics of Fundamental
Interactions (MTTD 2017), September 3-8, 2017, Podlesice, Poland, to appear
in the proceeding
Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations
We outline a new algorithm to solve coupled systems of differential equations
in one continuous variable (resp. coupled difference equations in one
discrete variable ) depending on a small parameter : given such a
system and given sufficiently many initial values, we can determine the first
coefficients of the Laurent-series solutions in if they are
expressible in terms of indefinite nested sums and products. This systematic
approach is based on symbolic summation algorithms in the context of difference
rings/fields and uncoupling algorithms. The proposed method gives rise to new
interesting applications in connection with integration by parts (IBP) methods.
As an illustrative example, we will demonstrate how one can calculate the
-expansion of a ladder graph with 6 massive fermion lines
General -representation for scalar one-loop Feynman integrals
A systematic study of the scalar one-loop two-, three-, and four-point
Feynman integrals is performed. We consider all cases of mass assignment and
external invariants and derive closed expressions in arbitrary space-time
dimension in terms of higher transcendental functions. The integrals play a
role as building blocks in general higher-loop or multi-leg processes. We also
perform numerical checks of the calculations using AMBRE/MB and LoopTools/FF.Comment: 5 pages Latex,Contribution to the Proceedings of QCD 15, Montpellier,
July 201
PDFs, , and quark masses from global fits
The strong coupling constant and the heavy-quark masses, ,
, are extracted simultaneosly with the parton distribution functions
(PDFs) in the updated ABM12 fit including recent data from CERN-SPS, HERA,
Tevatron, and the LHC. The values of \begin{eqnarray} \nonumber
\alpha_s(M_Z)&=&0.1147\pm0.0008~({\rm exp.)},\\ \nonumber m_c(m_c)&=&1.252\pm
0.018~({\rm exp.})~{\rm GeV},\\ \nonumber m_b(m_b)&=&3.83\pm0.12~({\rm
exp.})~{\rm GeV},\\ \nonumber m_t(m_t)&=&160.9\pm1.1~({\rm exp.})~{\rm GeV}
\end{eqnarray} are obtained with the heavy-quark mass
definition being employed throughout the analysis.Comment: 7 pages, 4 figures; preprint number correcte
A toolbox to solve coupled systems of differential and difference equations
We present algorithms to solve coupled systems of linear differential
equations, arising in the calculation of massive Feynman diagrams with local
operator insertions at 3-loop order, which do {\it not} request special choices
of bases. Here we assume that the desired solution has a power series
representation and we seek for the coefficients in closed form. In particular,
if the coefficients depend on a small parameter \ep (the dimensional
parameter), we assume that the coefficients themselves can be expanded in
formal Laurent series w.r.t.\ \ep and we try to compute the first terms in
closed form. More precisely, we have a decision algorithm which solves the
following problem: if the terms can be represented by an indefinite nested
hypergeometric sum expression (covering as special cases the harmonic sums,
cyclotomic sums, generalized harmonic sums or nested binomial sums), then we
can calculate them. If the algorithm fails, we obtain a proof that the terms
cannot be represented by the class of indefinite nested hypergeometric sum
expressions. Internally, this problem is reduced by holonomic closure
properties to solving a coupled system of linear difference equations. The
underlying method in this setting relies on decoupling algorithms, difference
ring algorithms and recurrence solving. We demonstrate by a concrete example
how this algorithm can be applied with the new Mathematica package
\texttt{SolveCoupledSystem} which is based on the packages \texttt{Sigma},
\texttt{HarmonicSums} and \texttt{OreSys}. In all applications the
representation in -space is obtained as an iterated integral representation
over general alphabets, generalizing Poincar\'{e} iterated integrals
HECTOR 1.00 - A program for the calculation of QED, QCD and electroweak corrections to ep and lN deep inelastic neutral and charged current scattering
A description of the Fortran program HECTOR for a variety of semi-analytical
calculations of radiative QED, QCD, and electroweak corrections to the
double-differential cross sections of NC and CC deep inelastic charged lepton
proton (or lepton deuteron) scattering is presented. HECTOR originates from the
substantially improved and extended earlier programs HELIOS and TERAD91. It is
mainly intended for applications at HERA or LEPxLHC, but may be used also for
muon scattering in fixed target experiments. The QED corrections may be
calculated in different sets of variables: leptonic, hadronic, mixed,
Jaquet-Blondel, double angle etc. Besides the leading logarithmic approximation
up to order O(alpha^2), exact order O(alpha) corrections and inclusive soft
photon exponentiation are taken into account. The photoproduction region is
also covered.Comment: 74 pages, LaTex, 14 figures, 7 tables, a uuencoded file containing
the latex file and figures is available from: http://www.ifh.de/theory/ or on
request from e-mail: [email protected]
Iso-spin asymmetry of quark distributions and implications for single top-quark production at the LHC
We present an improved determination of the up- and down-quark distributions
in the proton using recent data on charged lepton asymmetries from
gauge-boson production at the LHC and Tevatron. The analysis is performed in
the framework of a global fit of parton distribution functions. The fit results
are consistent with a non-zero iso-spin asymmetry of the sea, , at small values of Bjorken indicating a delayed onset of
the Regge asymptotics of a vanishing -asymmetry at
small-. We compare with up- and down-quark distributions available in the
literature and provide accurate predictions for the production of single
top-quarks at the LHC, a process which can serve as a standard candle for the
light quark flavor content of the proton.Comment: 21 pages, 13 figure
Massive three loop form factors in the planar limit
We present the color planar and complete light quark QCD contributions to the
three loop heavy quark form factors in the case of vector, axial-vector, scalar
and pseudo-scalar currents. We evaluate the master integrals applying a new
method based on differential equations for general bases, which is applicable
for any first order factorizing systems. The analytic results are expressed in
terms of harmonic polylogarithms and real-valued cyclotomic harmonic
polylogarithms.Comment: 10 pages; Proceedings of the Loops and Legs in Quantum Field Theory,
29th April 2018 - 4th May 2018, St. Goar, Germany; Report number modifie
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