113 research outputs found
Numerical Implementation of Harmonic Polylogarithms to Weight w = 8
We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic
polylogarithms up to w = 8 at an absolute accuracy of
or better. Using algebraic and argument relations the numerical representation
can be limited to the range . We provide replacement
files to map all harmonic polylogarithms to a basis and the usual range of
arguments to the above interval analytically. We also
briefly comment on a numerical implementation of real valued cyclotomic
harmonic polylogarithms.Comment: 19 pages LATEX, 3 Figures, ancillary dat
3-loop Massive Contributions to the DIS Operator Matrix Element
Contributions to heavy flavour transition matrix elements in the variable
flavour number scheme are considered at 3-loop order. In particular a
calculation of the diagrams with two equal masses that contribute to the
massive operator matrix element is performed. In the Mellin
space result one finds finite nested binomial sums. In -space these sums
correspond to iterated integrals over an alphabet containing also square-root
valued letters.Comment: 4 pages, Contribution to the Proceedings of QCD '14, Montpellier,
July 201
3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering with Two Heavy Quark Lines
We consider gluonic contributions to the heavy flavor Wilson coefficients at
3-loop order in QCD with two heavy quark lines in the asymptotic region . Here we report on the complete result in the case of two equal
masses for the massive operator matrix element ,
which contributes to the corresponding heavy flavor transition matrix element
in the variable flavor number scheme. Nested finite binomial sums and iterated
integrals over square-root valued alphabets emerge in the result for this
quantity in and -space, respectively. We also present results for the
case of two unequal masses for the flavor non-singlet OMEs and on the scalar
integrals ic case of , which were calculated without a further
approximation. The graphs can be expressed by finite nested binomial sums over
generalized harmonic sums, the alphabet of which contains rational letters in
the ratio .Comment: 10 pages LATEX, 1 Figure, Proceedings of Loops and Legs in Quantum
Field Theory, Weimar April 201
The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function and Transversity
We calculate the massive flavor non-singlet Wilson coefficient for the heavy
flavor contributions to the structure function in the asymptotic
region and the associated operator matrix element to 3-loop order in Quantum Chromodynamics at general values of the
Mellin variable . This matrix element is associated to the vector current
and axial vector current for the even and the odd moments , respectively. We
also calculate the corresponding operator matrix elements for transversity,
compute the contributions to the 3-loop anomalous dimensions to and
compare to results in the literature. The 3-loop matching of the flavor
non-singlet distribution in the variable flavor number scheme is derived. All
results can be expressed in terms of nested harmonic sums in space and
harmonic polylogarithms in -space. Numerical results are presented for the
non-singlet charm quark contribution to .Comment: 82 pages, 3 style files, 33 Figure
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
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
Recent progress on the calculation of three-loop heavy flavor Wilson coefficients in deep-inelastic scattering
We report on our latest results in the calculation of the three-loop heavy
flavor contributions to the Wilson coefficients in deep-inelastic scattering in
the asymptotic region . We discuss the different methods used to
compute the required operator matrix elements and the corresponding Feynman
integrals. These methods very recently allowed us to obtain a series of new
operator matrix elements and Wilson coefficients like the flavor non-singlet
and pure singlet Wilson coefficients.Comment: 11 pages Latex, 2 Figures, Proc. of Loops and Legs in Quantum Field
Theory, April 2014, Weimar, German
New Results on Massive 3-Loop Wilson Coefficients in Deep-Inelastic Scattering
We present recent results on newly calculated 2- and 3-loop contributions to
the heavy quark parts of the structure functions in deep-inelastic scattering
due to charm and bottom.Comment: Contribution to the Proc. of Loops and Legs 2016, PoS, in prin
3-loop heavy flavor Wilson coefficients in deep-inelastic scattering
We present our most recent results on the calculation of the heavy flavor
contributions to deep-inelastic scattering at 3-loop order in the large
limit, where the heavy flavor Wilson coefficients are known to factorize into
light flavor Wilson coefficients and massive operator matrix elements. We
describe the different techniques employed for the calculation and show the
results in the case of the heavy flavor non-singlet and pure singlet
contributions to the structure function .Comment: 4 pages Latex, 2 style files, 4 Figures, Contribution to the
Proceedings of QCD '14, Montpellier, Jult 201
Charm in Deep-Inelastic Scattering
We show how to extend systematically the FONLL scheme for inclusion of heavy quark mass effects in DIS to account for the possible effects of an intrinsic charm component in the nucleon. We show that when there is no intrinsic charm, FONLL is equivalent to S-ACOT to any order in perturbation theory, while when an intrinsic charm component is included FONLL is identical to ACOT, again to all orders in perturbation theory. We discuss in detail the inclusion of top and bottom quarks to construct a variable flavour number scheme, and give explicit expressions for the construction of the structure functions , and to NNLO
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