348 research outputs found
Zero-jettiness beam functions at NLO
The zero-jettiness beam functions describe collinear emissions from initial state legs and appear in the factorisation theorem for cross sections in the limit of small zero-jettiness. They are an important building block for slicing schemes for colour-singlet production at hadron colliders. We report on our ongoing calculation of this quantity at next-to-next-to-next-to-leading order (NLO) in QCD, highlighting in particular the aspects of partial fraction relations and the calculation of master integrals
Zero-jettiness beam functions at NLO
The zero-jettiness beam functions describe collinear emissions from initial state legs and appear in the factorisation theorem for cross sections in the limit of small zero-jettiness. They are an important building block for slicing schemes for colour-singlet production at hadron colliders. We report on our ongoing calculation of this quantity at next-to-next-to-next-to-leading order (NLO) in QCD, highlighting in particular the aspects of partial fraction relations and the calculation of master integrals
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
Analytical and experimental methods for determining the properties of materials at very high rates of loading
In the following report, some of the properties of ALCOA 7075 T651 aluminum, when subjected to high rates of loading, are experimentally investigated by impacting two rods of the material longitudinally. One rod is accelerated to a uniform velocity with an air gun launcher. The stationary second rod is instrumented with strain gages on its lateral surface in order to determine the strain-time history following impact. A detailed description of the experimental equipment is included. Simple, one-dimensional theory is used to determine the dynamic, elastic modulus of the test material under the impact condition. Several observations regarding the behavior of the material under dynamic, plastic loading conditions are made. The importance of equipment frequency response is noted and a method is suggested for estimating the experimental error in strain measurement resulting from equipment frequency response limitations. Several other possibilities of experimental error are noted and suggestions for improvement of the experimental apparatus are given. A theoretical development for the case of the longitudinal impact of two viscoelastic rods is presented and the numerical results are summarized for the impact of two rods of a Maxwell material. Computer programs to facilitate the determination of air gun parameters and to evaluate the solutions for the viscoelastic case are included --Abstract, page ii
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
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
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
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 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
- …