105 research outputs found
The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element
We calculate the two-mass QCD contributions to the massive operator matrix
element at in analytic form in Mellin
- and -space, maintaining the complete dependence on the heavy quark mass
ratio. These terms are important ingredients for the matching relations of the
variable flavor number scheme in the presence of two heavy quark flavors, such
as charm and bottom. In Mellin -space the result is given in the form of
nested harmonic, generalized harmonic, cyclotomic and binomial sums, with
arguments depending on the mass ratio. The Mellin inversion of these quantities
to -space gives rise to generalized iterated integrals with square root
valued letters in the alphabet, depending on the mass ratio as well. Numerical
results are presented.Comment: 99 pages LATEX, 2 Figure
The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme
We report on our latest results in the calculation of the two--mass
contributions to 3--loop operator matrix elements (OMEs). These OMEs are needed
to compute the corresponding contributions to the deep-inealstic scattering
structure functions and to generalize the variable flavor number scheme by
including both charm and bottom quarks. We present the results for the
non-singlet and OMEs, and compare the size of their contribution
relative to the single mass case. Results for the gluonic OME are
given in the physical case, going beyond those presented in a previous
publication where scalar diagrams were computed. We also discuss our recently
published two--mass contribution to the pure singlet OME, and present an
alternative method of calculating the corresponding diagrams.Comment: 20 pages Latex, 5 Figures, different style file
O ( α ) polarized heavy flavor corrections to deep-inelastic scattering at Q ⫠m
We calculate the quarkonic O(α) massive operator matrix elements A (N),A(N) and A,(N) for the twistâ2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region Q â« m to O(Δ) in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin space, without applying the integration-by-parts method. The result is given in terms of harmonic sums. This leads to a significant compactification of the operator matrix elements and massive Wilson coefficients in the region Q â« m derived previously in [1], which we partly confirm, and also partly correct. The results allow to determine the heavy flavor Wilson coefficients for g(x, Q) to O(α ) for all but the power suppressed terms â (m/Q) , k â„ 1. The results in momentum fraction z-space are also presented. We also discuss the small x effects in the polarized case. Numerical results are presented. We also compute the gluonic matching coefficients in the twoâmass variable flavor number scheme to O(Δ)
) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at
We calculate the quarkonic massive operator matrix elements
and
for the twist--2 operators and the associated heavy flavor Wilson coefficients
in polarized deeply inelastic scattering in the region to
in the case of the inclusive heavy flavor contributions. The
evaluation is performed in Mellin space, without applying the
integration-by-parts method. The result is given in terms of harmonic sums.
This leads to a significant compactification of the operator matrix elements
and massive Wilson coefficients in the region derived previously
in \cite{BUZA2}, which we partly confirm, and also partly correct. The results
allow to determine the heavy flavor Wilson coefficients for to
for all but the power suppressed terms . The results in momentum fraction -space are also presented. We also
discuss the small effects in the polarized case. Numerical results are
presented. We also compute the gluonic matching coefficients in the two--mass
variable flavor number scheme to .Comment: 58 pages Latex, 12 Figure
O() polarized heavy flavor corrections to deep-inelastic scattering at QâŻâ«âŻm
We calculate the quarkonic O() massive operator matrix elements and for the twistâ2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region to O() in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin space, without applying the integration-by-parts method. The result is given in terms of harmonic sums. This leads to a significant compactification of the operator matrix elements and massive Wilson coefficients in the region derived previously in [1], which we partly confirm, and also partly correct. The results allow to determine the heavy flavor Wilson coefficients for to for all but the power suppressed terms proportional to (. The results in momentum fraction z-space are also presented. We also discuss the small x effects in the polarized case. Numerical results are presented. We also compute the gluonic matching coefficients in the twoâmass variable flavor number scheme to
ViewPoint Oriented Software Development
In this paper we propose a new approach to software development which explicitly avoids the use of a single representation scheme or common schema. Instead, multiple ViewPoints are utilised to partition the domain information, the development method and the formal representations used to express software specifications. System specifications and methods are then described as configurations of related ViewPoints. This partitioning of knowledge facilitates distributed development, the use of multiple representation schemes and scalability. Furthermore, the approach is general, covering all phases of the software process from requirements to evolution. This paper motivates and systematically characterises the concept of a "ViewPoint", illustrating the concepts using a simplified example
Recent 3-Loop Heavy Flavor Corrections to Deep-Inelastic Scattering
We report on recent progress in calculating the three loop QCD corrections of
the heavy flavor contributions in deep--inelastic scattering and the massive
operator matrix elements of the variable flavor number scheme. Notably we deal
with the operator matrix elements and and
technical steps to their calculation. In particular, a new method to obtain the
inverse Mellin transform without computing the corresponding --space
expressions is discussed.Comment: Proc RADCOR 2023, 7 pages, 1 figur
The polarized three-loop anomalous dimensions from on-shell massive operator matrix elements
We calculate all contributions âTFto the polarized threeâloop anomalous dimensions in the Mâscheme using massive operator matrix elements and compare to results in the literature. This includes the com-plete anomalous dimensions Îł(2),PSqqand Îł(2)qg. We also obtain the complete twoâloop polarized anomalous dimensions in an independent calculation. While for most of the anomalous dimensions the usual direct computation methods in Mellin Nâspace can be applied since all recurrences factorize at first order, this is not the case for Îł(2)qg. Due to the necessity of deeper expansions of the master integrals in the dimensional parameter Δ=Dâ4, we had to use the method of arbitrary high moments to eliminate elliptic contributions in intermediate steps. 4000 moments were generated to determine this anomalous dimension and 2640 mo-ments turned out to be sufficient. As an aside, we also recalculate the contributions âTFto the threeâloop QCD ÎČâfunction
- âŠ