442 research outputs found
Betriebswirthschaftlich-technische Fragen moderner Landwirthschaft. 1, Dünger und Düngen
http://www.ester.ee/record=b3581103*es
The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function and the Anomalous Dimension
The pure singlet asymptotic heavy flavor corrections to 3-loop order for the
deep-inelastic scattering structure function and the corresponding
transition matrix element in the variable flavor number
scheme are computed. In Mellin- space these inclusive quantities depend on
generalized harmonic sums. We also recalculate the complete 3-loop pure singlet
anomalous dimension for the first time. Numerical results for the Wilson
coefficients, the operator matrix element and the contribution to the structure
function are presented.Comment: 85 pages Latex, 14 Figures, 2 style file
The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer
We calculate the massive flavor non-singlet Wilson coefficient for the heavy
flavor contributions to the polarized structure function in the
asymptotic region to 3-loop order in Quantum Chromodynamics at
general values of the Mellin variable and the momentum fraction , and
derive heavy flavor corrections to the Bjorken sum-rule. Numerical results are
presented for the charm quark contribution. Results on the structure function
in the twist-2 approximation are also given.Comment: 29 pages, 8 Figure
Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results
We present recent analytic results for the 3-loop corrections to the massive
operator matrix element for further color factors. These results
have been obtained using the method of arbitrarily large moments. We also give
an overview on the results which were obtained solving all difference and
differential equations for the corresponding master integrals that factorize at
first order.Comment: 11 pages Latex, To appear in the Proceedings of: QCDEV2017, JLAB,
Newport News, VA, USA, May 22-26, 2017; Po
Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra
Three loop ladder and -topology diagrams contributing to the massive
operator matrix element are calculated. The corresponding objects can
all be expressed in terms of nested sums and recurrences depending on the
Mellin variable and the dimensional parameter . Given these
representations, the desired Laurent series expansions in can be
obtained with the help of our computer algebra toolbox. Here we rely on
generalized hypergeometric functions and Mellin-Barnes representations, on
difference ring algorithms for symbolic summation, on an optimized version of
the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on
new methods to calculate Laurent series solutions of coupled systems of
differential equations. The solutions can be computed for general coefficient
matrices directly for any basis also performing the expansion in the
dimensional parameter in case it is expressible in terms of indefinite nested
product-sum expressions. This structural result is based on new results of our
difference ring theory. In the cases discussed we deal with iterative sum- and
integral-solutions over general alphabets. The final results are expressed in
terms of special sums, forming quasi-shuffle algebras, such as nested harmonic
sums, generalized harmonic sums, and nested binomially weighted (cyclotomic)
sums. Analytic continuations to complex values of are possible through the
recursion relations obeyed by these quantities and their analytic asymptotic
expansions. The latter lead to a host of new constants beyond the multiple zeta
values, the infinite generalized harmonic and cyclotomic sums in the case of
-topologies.Comment: 110 pages Latex, 4 Figure
The O(\alpha_s^3) Heavy Flavor Contributions to the Charged Current Structure Function xF_3(x,Q^2) at Large Momentum Transfer
We calculate the massive Wilson coefficients for the heavy flavor
contributions to the non-singlet charged current deep-inelastic scattering
structure function in the asymptotic
region to 3-loop order in Quantum Chromodynamics (QCD) at general
values of the Mellin variable and the momentum fraction . Besides the
heavy quark pair production also the single heavy flavor excitation contributes. Numerical results are presented for the charm quark
contributions and consequences on the Gross-Llewellyn Smith sum rule are
discussed.Comment: 30 pages, 6 figures. arXiv admin note: text overlap with
arXiv:1504.0821
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
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