91 research outputs found
Application of the DRA method to the calculation of the four-loop QED-type tadpoles
We apply the DRA method to the calculation of the four-loop `QED-type'
tadpoles. For arbitrary space-time dimensionality D the results have the form
of multiple convergent sums. We use these results to obtain the
epsilon-expansion of the integrals around D=3 and D=4.Comment: References added, some typos corrected. Results unchange
Analytic Results for Massless Three-Loop Form Factors
We evaluate, exactly in d, the master integrals contributing to massless
three-loop QCD form factors. The calculation is based on a combination of a
method recently suggested by one of the authors (R.L.) with other techniques:
sector decomposition implemented in FIESTA, the method of Mellin--Barnes
representation, and the PSLQ algorithm. Using our results for the master
integrals we obtain analytical expressions for two missing constants in the
ep-expansion of the two most complicated master integrals and present the form
factors in a completely analytic form.Comment: minor revisions, to appear in JHE
The Quark Beam Function at NNLL
In hard collisions at a hadron collider the most appropriate description of
the initial state depends on what is measured in the final state. Parton
distribution functions (PDFs) evolved to the hard collision scale Q are
appropriate for inclusive observables, but not for measurements with a specific
number of hard jets, leptons, and photons. Here the incoming protons are probed
and lose their identity to an incoming jet at a scale \mu_B << Q, and the
initial state is described by universal beam functions. We discuss the
field-theoretic treatment of beam functions, and show that the beam function
has the same RG evolution as the jet function to all orders in perturbation
theory. In contrast to PDF evolution, the beam function evolution does not mix
quarks and gluons and changes the virtuality of the colliding parton at fixed
momentum fraction. At \mu_B, the incoming jet can be described perturbatively,
and we give a detailed derivation of the one-loop matching of the quark beam
function onto quark and gluon PDFs. We compute the associated NLO Wilson
coefficients and explicitly verify the cancellation of IR singularities. As an
application, we give an expression for the next-to-next-to-leading logarithmic
order (NNLL) resummed Drell-Yan beam thrust cross section.Comment: 54 pages, 9 figures; v2: notation simplified in a few places, typos
fixed; v3: journal versio
Parton Fragmentation within an Identified Jet at NNLL
The fragmentation of a light parton i to a jet containing a light energetic
hadron h, where the momentum fraction of this hadron as well as the invariant
mass of the jet is measured, is described by "fragmenting jet functions". We
calculate the one-loop matching coefficients J_{ij} that relate the fragmenting
jet functions G_i^h to the standard, unpolarized fragmentation functions D_j^h
for quark and gluon jets. We perform this calculation using various IR
regulators and show explicitly how the IR divergences cancel in the matching.
We derive the relationship between the coefficients J_{ij} and the quark and
gluon jet functions. This provides a cross-check of our results. As an
application we study the process e+ e- to X pi+ on the Upsilon(4S) resonance
where we measure the momentum fraction of the pi+ and restrict to the dijet
limit by imposing a cut on thrust T. In our analysis we sum the logarithms of
tau=1-T in the cross section to next-to-next-to-leading-logarithmic accuracy
(NNLL). We find that including contributions up to NNLL (or NLO) can have a
large impact on extracting fragmentation functions from e+ e- to dijet + h.Comment: expanded introduction, typos fixed, journal versio
QCD: The Theory of Strong Interactions
This Chapter is devoted to a concise introduction to Quantum Chromo-Dynamics (QCD), the theory of strong interactions. We start with a general introduction where a broad overview of the strong interactions is presented
Five-loop renormalisation of QCD in covariant gauges
We present the complete set of vertex, wave function and charge
renormalisation constants in QCD in a general simple gauge group and with the
complete dependence on the covariant gauge parameter in the minimal
subtraction scheme of conventional dimensional regularisation. Our results
confirm all already known results, which were obtained in the Feynman gauge,
and allow the extraction of other useful gauges such as the Landau gauge. We
use these results to extract the Landau gauge five-loop anomalous dimensions of
the composite operator as well as the Landau gauge scheme independent
gluon, ghost and fermion propagators at five loops.Comment: 17 pages; FORM and Mathematica result files available with the
source; corrected minor typos, added references, journal ref, 1 remark, 1
note and 1 additional result fil
Higgs boson gluon-fusion production beyond threshold in N3LO QCD
In this article, we compute the gluon fusion Higgs boson cross-section at
N3LO through the second term in the threshold expansion. This calculation
constitutes a major milestone towards the full N3LO cross section. Our result
has the best formal accuracy in the threshold expansion currently available,
and includes contributions from collinear regions besides subleading
corrections from soft and hard regions, as well as certain logarithmically
enhanced contributions for general kinematics. We use our results to perform a
critical appraisal of the validity of the threshold approximation at N3LO in
perturbative QCD
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