140 research outputs found
) 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 ( 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)
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
The uses of Connes and Kreimer's algebraic formulation of renormalization theory
We show how, modulo the distinction between the antipode and the "twisted" or
"renormalized" antipode, Connes and Kreimer's algebraic paradigm trivializes
the proofs of equivalence of the (corrected) Dyson-Salam,
Bogoliubov-Parasiuk-Hepp and Zimmermann procedures for renormalizing Feynman
amplitudes. We discuss the outlook for a parallel simplification of
computations in quantum field theory, stemming from the same algebraic
approach.Comment: 15 pages, Latex. Minor changes, typos fixed, 2 references adde
A Tree-Loop Duality Relation at Two Loops and Beyond
The duality relation between one-loop integrals and phase-space integrals,
developed in a previous work, is extended to higher-order loops. The duality
relation is realized by a modification of the customary +i0 prescription of the
Feynman propagators, which compensates for the absence of the multiple-cut
contributions that appear in the Feynman tree theorem. We rederive the duality
theorem at one-loop order in a form that is more suitable for its iterative
extension to higher-loop orders. We explicitly show its application to two- and
three-loop scalar master integrals, and we discuss the structure of the
occurring cuts and the ensuing results in detail.Comment: 20 pages. Few typos corrected, some additional comments included,
Appendix B and one reference added. Final version as published in JHE
b-Initiated processes at the LHC: a reappraisal
Several key processes at the LHC in the standard model and beyond that
involve quarks, such as single-top, Higgs, and weak vector boson associated
production, can be described in QCD either in a 4-flavor or 5-flavor scheme. In
the former, quarks appear only in the final state and are typically
considered massive. In 5-flavor schemes, calculations include quarks in the
initial state, are simpler and allow the resummation of possibly large initial
state logarithms of the type into the
parton distribution function (PDF), being the typical scale of the
hard process. In this work we critically reconsider the rationale for using
5-flavor improved schemes at the LHC. Our motivation stems from the observation
that the effects of initial state logs are rarely very large in hadron
collisions: 4-flavor computations are pertubatively well behaved and a
substantial agreement between predictions in the two schemes is found. We
identify two distinct reasons that explain this behaviour, i.e., the
resummation of the initial state logarithms into the -PDF is relevant only
at large Bjorken and the possibly large ratios 's are
always accompanied by universal phase space suppression factors. Our study
paves the way to using both schemes for the same process so to exploit their
complementary advantages for different observables, such as employing a
5-flavor scheme to accurately predict the total cross section at NNLO and the
corresponding 4-flavor computation at NLO for fully exclusive studies.Comment: Fixed typo in Eq. (A.10) and few typos in Eq. (C.2) and (C.3
Laurent series expansion of sunrise-type diagrams using configuration space techniques
We show that configuration space techniques can be used to efficiently
calculate the complete Laurent series \eps-expansion of sunrise-type diagrams
to any loop order in D-dimensional space-time for any external momentum and for
arbitrary mass configurations. For negative powers of \eps the results are
obtained in analytical form. For positive powers of \eps including the finite
\eps^0 contribution the result is obtained numerically in terms of
low-dimensional integrals. We present general features of the calculation and
provide exemplary results up to five loop order which are compared to available
results in the literature.Comment: 20 pages, 3 eps-figures include
On the singular behaviour of scattering amplitudes in quantum field theory
We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop-tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences
On Epsilon Expansions of Four-loop Non-planar Massless Propagator Diagrams
We evaluate three typical four-loop non-planar massless propagator diagrams
in a Taylor expansion in dimensional regularization parameter
up to transcendentality weight twelve, using a recently
developed method of one of the present coauthors (R.L.). We observe only
multiple zeta values in our results.Comment: 3 pages, 1 figure, results unchanged, discussion improved, to appear
in European Physical Journal
Antenna subtraction with massive fermions at NNLO: Double real initial-final configurations
We derive the integrated forms of specific initial-final tree-level
four-parton antenna functions involving a massless initial-state parton and a
massive final-state fermion as hard radiators. These antennae are needed in the
subtraction terms required to evaluate the double real corrections to
hadronic production at the NNLO level stemming from the partonic
processes and .Comment: 24 pages, 1 figure, 1 Mathematica file attache
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