Fixed-flavor Scheme Research Articles

Q 2-evolution of parton densities at small x values. Charm contribution in the combined H1 and ZEUS F 2 data

The Bessel-inspired behavior of parton densities at small x, obtained in the case of the flat initial conditions for DGLAP evolution equations, is used in the fixed flavor scheme to analyze precise H1 and ZEUS combined data on the structure function F 2.

The effect on PDFs and [Formula: see text] due to changes in flavour scheme and higher twist contributions.

I consider the effect on MSTW partons distribution functions (PDFs) due to changes in the choices of theoretical procedure used in the fit. I first consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at all relatively small x values, the gluon distribution becoming smaller at high values of x and larger at small x, the preferred value of the coupling constant alpha _S(M_Z^2) falling, particularly at NNLO, and the fit quality deteriorates. I also consider lowering the kinematic cut on W^2 for DIS data and simultaneously introducing higher twist terms which are fit to data. This results in much smaller effects on both PDFs and alpha _S(M_Z^2) than the scheme change, except for quarks at very high x. I show that the structure function one obtains from a fixed input set of PDFs using the fixed flavour scheme and variable flavour scheme differ significantly for x sim 0.01 at high Q^2, and that this is due to the fact that in the fixed flavour scheme there is a slow convergence of large logarithmic terms of the form (alpha _Sln (Q^2/m_c^2))^n relevant for this regime. I conclude that some of the most significant differences in PDF sets are largely due to the choice of flavour scheme used.

Towards W $ b\overline b $ + j at NLO with an automatized approach to one-loop computations

We present results for the O(alpha_s) virtual corrections to q g -> W b bbar q' obtained with a new automatized approach to the evaluation of one-loop amplitudes in terms of Feynman diagrams. Together with the O(alpha_s) corrections to q q' -> W b bbar g, which can be obtained from our results by crossing symmetry, this represents the bulk of the next-to-leading order virtual QCD corrections to W b bbar + j and W b + j hadronic production, calculated in a fixed-flavor scheme with four light flavors. Furthermore, these corrections represent a well defined and independent subset of the 1-loop amplitudes needed for the NNLO calculation of W b bbar. Our approach was tested against several existing results for NLO amplitudes including selected O(alpha_s) one-loop corrections to W + 3 j hadronic production. We discuss the efficiency of our method both with respect to evaluation time and numerical stability.

3-, 4-, and 5-flavor next-to-next-to-leading order parton distribution functions from deep-inelastic-scattering data and at hadron colliders

We determine the parton distribution functions (PDFs) in a next-to-next-to-leading order QCD analysis of the inclusive neutral-current deep-inelastic-scattering (DIS) world data combined with the neutrino-nucleon DIS di-muon data and the fixed-target Drell-Yan data. The PDF evolution is performed in the ${N}_{f}=3$ fixed-flavor scheme and supplementary sets of PDFs in the 4- and 5-flavor schemes are derived from the results in the 3-flavor scheme using matching conditions. The charm-quark DIS contribution is calculated in a general-mass variable-flavor-number (GMVFN) scheme interpolating between the zero-mass 4-flavor scheme at asymptotically large values of momentum transfer ${Q}^{2}$ and the 3-flavor scheme prescription of Buza-Matiounine-Smith-van Neerven (BMSN) at the value of ${Q}^{2}={m}_{c}^{2}$. The results in the general-mass variable-flavor-number scheme are compared with those of the fixed-flavor scheme and other prescriptions used in global fits of PDFs. The strong coupling constant is measured at an accuracy of $\ensuremath{\approx}1.5%$. We obtain at next-to-next-to-leading order ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})=0.1135\ifmmode\pm\else\textpm\fi{}0.0014$ in the fixed-flavor scheme and ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})=0.1129\ifmmode\pm\else\textpm\fi{}0.0014$ applying the Buza-Matiounine-Smith-van Neerven prescription. The implications for important standard candle and hard scattering processes at hadron colliders are illustrated. Predictions for cross sections of ${W}^{\ifmmode\pm\else\textpm\fi{}}$- and $Z$-boson, the top-quark pair, and Higgs-boson production at the Tevatron and the LHC based on the 5-flavor PDFs of the present analysis are provided.

MRST partons generated in a fixed-flavour scheme

We generate fixed three- and four-light-flavour sets of partons using MRST2004 partons as input. We show that it is important to set nf=3 in the strong coupling, as well as in the splitting and coefficient functions, in order to obtain a consistent set of fixed-flavour partons. We compare the description of data using partons in both variable- and fixed-flavour-number schemes.

O( αs2) contributions to charm production in charged-current deep-inelastic lepton-hadron scattering

The most important part of the order α s 2 corrections to the charm component of the charged-current structure functions F 2 ( x, Q 2) and F 3 ( x, Q 2) has been calculated. This calculation is based on the asymptotic form of the heavy-quark coefficient functions corresponding to the higher order corrections to the W-boson-gluon fusion process. These coefficient functions, which are in principle only valid for Q 2 ⪢ m 2, can also be used to estimate the order α s 2 contributions at lower Q 2 values provided x < 0.1. It turns out that the above corrections are appreciable in the large Q 2 region and they explain the discrepancy found for the structure functions between the fixed-flavour scheme (FFS) and the variable-flavour-number scheme (VFNS). These corrections also hamper the extraction of the strange-quark density from the data obtained for the charged-current and the electromagnetic-current processes.

Scheme and scale dependence of charm production in neutrino scattering

We discuss some theoretical uncertainties in the calculation of the cross section for charm production in charged current deep inelastic neutrino scattering related to ambiguities in the treatment of terms which are singular in the limit of a vanishing charm mass. In particular we compare the so-called variable flavour scheme where these terms are absorbed in the parton distribution functions containing the charm as an active flavour, with the so-called fixed flavour scheme with no charm mass subtraction where the charm appears only in the final state of fixed-order scattering matrix elements. Using available parametrizations of parton distribution functions we find that the two schemes lead to largely differing results for separate structure functions whereas the differences cancel to a large extent in the total cross section in that kinematical region which has been measured so far.