7,577 research outputs found
A Variable-Flavour Number Scheme for NNLO
At NNLO it is particularly important to have a Variable-Flavour Number Scheme
(VFNS) to deal with heavy quarks because there are major problems with both the
zero mass variable-flavour number scheme and the fixed-flavour number scheme. I
illustrate these problems and present a general formulation of a
Variable-Flavour Number Scheme (VFNS)for heavy quarks that is explicitly
implemented up to NNLO in the strong coupling constant alpha_S, and may be used
in NNLO global fits for parton distributions. The procedure combines elements
of the ACOT(chi) scheme and the Thorne-Roberts scheme. Despite the fact that at
NNLO the parton distributions are discontinuous as one changes the number of
active quark flavours, all physical quantities are continuous at flavour
transitions and the comparison with data is successful.Comment: 17 pages, 5 figures included as .ps files, uses axodraw. One
additional explanatory sentence after eq. (25). Correction of typos and
updated references. To be published in Phys. Rev.
A Variable Flavour Number Scheme at NNLO
I present a formulation of a Variable Flavour Number Scheme for heavy quarks
that is implemented up to NNLO in the strong coupling constant and may be used
in NNLO global fits for parton distributions.Comment: 4 pages, 6 figures included as .ps files. To appear in proceedings of
DIS05, XIII International Workshop on Deep Inelastic Scatterin
A Complete Leading-Order, Renormalization-Scheme-Consistent Calculation of Small--x Structure functions, Including Leading-ln(1/x) Terms
We present calculations of the structure functions F_2(x,Q^2) and F_L(x,Q^2),
concentrating on small x. After discussing the standard expansion of the
structure functions in powers of \alpha_s(Q^2) we consider a leading-order
expansion in ln(1/x) and finally an expansion which is leading order in both
ln(1/x) and \alpha_s(Q^2), and which we argue is the only really correct
expansion scheme. Ordering the calculation in a renormalization-scheme-
consistent manner, there is no factorization scheme dependence, as there should
not be in calculations of physical quantities. The calculational method
naturally leads to the ``physical anomalous dimensions'' of Catani, but imposes
stronger constraints than just the use of these effective anomalous dimensions.
In particular, a relationship between the small-x forms of the inputs
F_2(x,Q_0^2) and F_L(x,Q_0^2) is predicted. Analysis of a wide range of data
for F_2(x,Q^2) is performed, and a very good global fit obtained, particularly
for data at small x. The fit allows a prediction for F_L(x,Q^2) to be produced,
which is smaller than those produced by the usual NLO-in-\alpha_s(Q^2) fits to
F_2(x,Q^2) and different in shape.Comment: 106 pages, 4 figures as ps files, includes a variation of harmac.
Corrections to some typos in references, and form of some references changed,
in particular hep-ph(ex) numbers included for papers not yet published. No
changes to body of tex
The role of uncertainties in parton distribution functions
I consider the uncertainties in parton distributions and the consequences for
hadronic cross-sections. There is ever-increasing sophistication in the
relationship between the uncertainties of the distributions and the errors on
the experimental data used to extract them. However, I demonstrate that this
uncertainty is frequently subsumed by that due to the choice of data used in
fits, and more surprisingly by the precise details of the theoretical framework
used. Variations in heavy flavour prescriptions provide striking examples.Comment: 10 pages, 15 figures as .ps or .eps files, invited talk at
PHYSTAT-LHC Workshop on Statistical Issues for LHC Physics, June 200
Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs
We investigate the Monte Carlo approach to propagation of experimental
uncertainties within the context of the established "MSTW 2008" global analysis
of parton distribution functions (PDFs) of the proton at next-to-leading order
in the strong coupling. We show that the Monte Carlo approach using replicas of
the original data gives PDF uncertainties in good agreement with the usual
Hessian approach using the standard Delta(chi^2) = 1 criterion, then we explore
potential parameterisation bias by increasing the number of free parameters,
concluding that any parameterisation bias is likely to be small, with the
exception of the valence-quark distributions at low momentum fractions x. We
motivate the need for a larger tolerance, Delta(chi^2) > 1, by making fits to
restricted data sets and idealised consistent or inconsistent pseudodata.
Instead of using data replicas, we alternatively produce PDF sets randomly
distributed according to the covariance matrix of fit parameters including
appropriate tolerance values, then we demonstrate a simpler method to produce
an arbitrary number of random predictions on-the-fly from the existing
eigenvector PDF sets. Finally, as a simple example application, we use Bayesian
reweighting to study the effect of recent LHC data on the lepton charge
asymmetry from W boson decays.Comment: 37 pages, 17 figures. v2: version published in JHEP. Supplementary
material at http://mstwpdf.hepforge.org/random
Parton Distributions
I discuss our current understanding of parton distributions. I begin with the
underlying theoretical framework, and the way in which different data sets
constrain different partons, highlighting recent developments. The methods of
examining the uncertainties on the distributions and those physical quantities
dependent on them is analysed. Finally I look at the evidence that additional
theoretical corrections beyond NLO perturbative QCD may be necessary, what type
of corrections are indicated and the impact these may have on the
uncertainties.Comment: Invited talk at "XXI International Symposium on Lepton and Photon
Interactions at High Energies," (Fermilab, Chicago, August 2003). 12 pages,
21 figure
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