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Variable-Flavor-Number Scheme in Analysis of Heavy-Quark Electro-Production Data

S. Alekhin, J. Blümlein, S. Klein, S. Moch

Abstract

We check the impact of the factorization scheme employed in the calculation of the heavy-quark deep-inelastic scattering (DIS) electro-production on the PDFs determined in the NNLO QCD analysis of the world inclusive neutral-current DIS data combined with the ones on the neutrino-nucleon DIS di-muon production and the fixed-target Drell-Yan process. The charm-quark DIS contribution is calculated in the general-mass variable-flavor-number (GMVFN) scheme: At asymptotically large values of the momentum transfer $Q$ it is given by the zero-mass 4-flavor scheme and at the value of $Q$ equal to the charm-quark mass it is smoothly matched with the 3-flavor scheme using the Buza-Matiounine-Smith-van Neerven prescription. The PDFs obtained in this variant of the fit are very similar to the ones obtained in the fit with a 3-flavor scheme employed. Our 5-flavor PDFs derived from the 3-flavor ones using the NNLO matching conditions are used to calculate the rates of $W^{\pm}/Z$ and $t\bar{t}$ production at the Tevatron collider and the LHC at NNLO.

Variable-Flavor-Number Scheme in Analysis of Heavy-Quark Electro-Production Data

Abstract

We check the impact of the factorization scheme employed in the calculation of the heavy-quark deep-inelastic scattering (DIS) electro-production on the PDFs determined in the NNLO QCD analysis of the world inclusive neutral-current DIS data combined with the ones on the neutrino-nucleon DIS di-muon production and the fixed-target Drell-Yan process. The charm-quark DIS contribution is calculated in the general-mass variable-flavor-number (GMVFN) scheme: At asymptotically large values of the momentum transfer it is given by the zero-mass 4-flavor scheme and at the value of equal to the charm-quark mass it is smoothly matched with the 3-flavor scheme using the Buza-Matiounine-Smith-van Neerven prescription. The PDFs obtained in this variant of the fit are very similar to the ones obtained in the fit with a 3-flavor scheme employed. Our 5-flavor PDFs derived from the 3-flavor ones using the NNLO matching conditions are used to calculate the rates of and production at the Tevatron collider and the LHC at NNLO.

Paper Structure

This paper contains 3 figures, 1 table.

Figures (3)

  • Figure 1: The values of $F_2^c(x,Q^2)$ calculated in the different schemes compared to the data by H1 H1c (squares) and ZEUS ZEUS (circles) collaborations (dotted-dashes: the 3-flavor scheme; solid lines: the BMSN prescription of the GMVFN scheme, dashes: the massless 4-flavor scheme).
  • Figure 2: The gluon (left panel) and sea (right panel) distributions at the factorization scale of $\mu=3~{\rm GeV}$ obtained in two variants of the fit. Solid lines: 3-flavor scheme, dashed lines : GMVFN scheme in the BMSN prescription.
  • Figure 3: The $1\sigma$ band for the representative set of our PDFs (shaded area) and the central values of other NNLO PDFs sets (dashes). Left panel: the 3-flavor $u$-, $d$-quarks and gluons at the scale of $\mu=2~{\rm GeV}$ compared to ones of the JR set; central panel: the 4-flavor $u$-, $d$-quarks and gluons at the scale of $\mu=2~{\rm GeV}$ compared to ones of the MSTW08 set; right panel: the 5-flavor $s$-, $c$-, and $b$-quarks at the scale of $\mu=100~{\rm GeV}$ compared to ones of the MSTW08 set.