2,764 research outputs found
The Gluon Beam Function at Two Loops
The virtuality-dependent beam function is a universal ingredient in the
resummation for observables probing the virtuality of incoming partons,
including N-jettiness and beam thrust. We compute the gluon beam function at
two-loop order. Together with our previous results for the two-loop quark beam
function, this completes the full set of virtuality-dependent beam functions at
next-to-next-to-leading order (NNLO). Our results are required to account for
all collinear ISR effects to the N-jettiness event shape through N^3LL order.
We present numerical results for both the quark and gluon beam functions up to
NNLO and N^3LL order. Numerically, the NNLO matching corrections are important.
They reduce the residual matching scale dependence in the resummed beam
function by about a factor of two.Comment: 21 pages, 6 figures; v2: journal versio
The Quark Beam Function at Two Loops
In differential measurements at a hadron collider, collinear initial-state
radiation is described by process-independent beam functions. They are the
field-theoretic analog of initial-state parton showers. Depending on the
measured observable they are differential in the virtuality and/or transverse
momentum of the colliding partons in addition to the usual longitudinal
momentum fraction. Perturbatively, the beam functions can be calculated by
matching them onto standard quark and gluon parton distribution functions. We
calculate the inclusive virtuality-dependent quark beam function at NNLO, which
is relevant for any observables probing the virtuality of the incoming partons,
including N-jettiness and beam thrust. For such observables, our results are an
important ingredient in the resummation of large logarithms at N3LL order, and
provide all contributions enhanced by collinear t-channel singularities at NNLO
for quark-initiated processes in analytic form. We perform the calculation in
both Feynman and axial gauge and use two different methods to evaluate the
discontinuity of the two-loop Feynman diagrams, providing nontrivial checks of
the calculation. As part of our results we reproduce the known two-loop QCD
splitting functions and confirm at two loops that the virtuality-dependent beam
and final-state jet functions have the same anomalous dimension.Comment: 27 pages, 3 figures; v2: journal versio
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Developing good practice in the provision of outdoor education in the early years
This study is an investigation into the relationship between children's use of the outdoor environment and the early years curriculum. An action research approach was used in which cycles of observation, reflection and intervention led to deeper understandings about children's learning and the way it can be facilitated through the use of outdoor learning experiences. The findings highlight the potential an outdoor space can offer children as a base for learning and demonstrate how learning outdoors enables children to develop dispositions which are vital for their future achievements. I set the research in the historical context by drawing on the work of people in the past who have influenced the development of early years education and whose work is still relevant today. The research process has included a major action research cycle through which the outdoor environment of the setting was developed from a small nursery garden to a full forest school experience using the schools grounds and beyond
Critical Percolation in High Dimensions
We present Monte Carlo estimates for site and bond percolation thresholds in
simple hypercubic lattices with 4 to 13 dimensions. For d<6 they are
preliminary, for d >= 6 they are between 20 to 10^4 times more precise than the
best previous estimates. This was achieved by three ingredients: (i) simple and
fast hashing which allowed us to simulate clusters of millions of sites on
computers with less than 500 MB memory; (ii) a histogram method which allowed
us to obtain information for several p values from a single simulation; and
(iii) a new variance reduction technique which is especially efficient at high
dimensions where it reduces error bars by a factor up to approximately 30 and
more. Based on these data we propose a new scaling law for finite cluster size
corrections.Comment: 5 pages including figures, RevTe
N-jettiness Subtractions for NNLO QCD Calculations
We present a subtraction method utilizing the N-jettiness observable, Tau_N,
to perform QCD calculations for arbitrary processes at next-to-next-to-leading
order (NNLO). Our method employs soft-collinear effective theory (SCET) to
determine the IR singular contributions of N-jet cross sections for Tau_N -> 0,
and uses these to construct suitable Tau_N-subtractions. The construction is
systematic and economic, due to being based on a physical observable. The
resulting NNLO calculation is fully differential and in a form directly
suitable for combining with resummation and parton showers. We explain in
detail the application to processes with an arbitrary number of massless
partons at lepton and hadron colliders together with the required external
inputs in the form of QCD amplitudes and lower-order calculations. We provide
explicit expressions for the Tau_N-subtractions at NLO and NNLO. The required
ingredients are fully known at NLO, and at NNLO for processes with two external
QCD partons. The remaining NNLO ingredient for three or more external partons
can be obtained numerically with existing NNLO techniques. As an example, we
employ our method to obtain the NNLO rapidity spectrum for Drell-Yan and
gluon-fusion Higgs production. We discuss aspects of numerical accuracy and
convergence and the practical implementation. We also discuss and comment on
possible extensions, such as more-differential subtractions, necessary steps
for going to N3LO, and the treatment of massive quarks.Comment: 51 pages, 10 figures, v2: journal versio
What is Double Parton Scattering?
Processes such as double Drell-Yan and same-sign WW production have
contributions from double parton scattering, which are not well-defined because
of a delta(z_\perp=0) singularity that is generated by QCD evolution. We study
the single and double parton contributions to these processes, and show how to
handle the singularity using factorization and operator renormalization. We
compute the QCD evolution of double parton distribution functions (PDFs) due to
mixing with single PDFs. The modified evolution of dPDFs at z_\perp=0,
including generalized dPDFs for the non-forward case, is given in the appendix.
We include a brief discussion of the experimental interpretation of dPDFs and
how they can probe flavor, spin and color correlations of partons in hadrons.Comment: 7 pages, 12 figures; v2: appendix fixed and extended, journal versio
Local availability and long-range trade: the worked stone assemblage
Inter disciplinary study of major excavation assemblage from Norse settlement site in Orkney. Combines methodological and typological developments with scientific discussion
Heuristic Spike Sorting Tuner (HSST), a framework to determine optimal parameter selection for a generic spike sorting algorithm
Extracellular microelectrodes frequently record neural activity from more than one neuron in the vicinity of the electrode. The process of labeling each recorded spike waveform with the identity of its source neuron is called spike sorting and is often approached from an abstracted statistical perspective. However, these approaches do not consider neurophysiological realities and may ignore important features that could improve the accuracy of these methods. Further, standard algorithms typically require selection of at least one free parameter, which can have significant effects on the quality of the output. We describe a Heuristic Spike Sorting Tuner (HSST) that determines the optimal choice of the free parameters for a given spike sorting algorithm based on the neurophysiological qualification of unit isolation and signal discrimination. A set of heuristic metrics are used to score the output of a spike sorting algorithm over a range of free parameters resulting in optimal sorting quality. We demonstrate that these metrics can be used to tune parameters in several spike sorting algorithms. The HSST algorithm shows robustness to variations in signal to noise ratio, number and relative size of units per channel. Moreover, the HSST algorithm is computationally efficient, operates unsupervised, and is parallelizable for batch processing
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