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NNLO Logarithmic Expansions and Precise Determinations of the Neutral Currents near the Z Resonance at the LHC: The Drell-Yan case

Alessandro Cafarella, Claudio Coriano, Marco Guzzi

Abstract

We present a comparative study of the invariant mass and rapidity distributions in Drell-Yan lepton pair production, with particular emphasis on the role played by the QCD evolution. We focus our study around the Z resonance ($50 <Q < 200$ GeV) and perform a general analysis of the factorization/renormalization scale dependence of the cross sections, with the two scales included both in the evolution and in the hard scatterings. We also present the variations of the cross sections due to the errors on the parton distributions (pdf's) and an analysis of the corresponding $K$-factors. Predictions from several sets of pdf's, evolved by MRST and Alekhin are compared with those generated using \textsc{Candia}, a NNLO evolution program that implements the theory of the logarithmic expansions, developed in a previous work. These expansions allow to select truncated solutions of varying accuracy using the method of the $x$-space iterates. The evolved parton distributions are in good agreement with other approaches. The study can be generalized for high precision searches of extra neutral gauge interactions at the LHC.

NNLO Logarithmic Expansions and Precise Determinations of the Neutral Currents near the Z Resonance at the LHC: The Drell-Yan case

Abstract

We present a comparative study of the invariant mass and rapidity distributions in Drell-Yan lepton pair production, with particular emphasis on the role played by the QCD evolution. We focus our study around the Z resonance ( GeV) and perform a general analysis of the factorization/renormalization scale dependence of the cross sections, with the two scales included both in the evolution and in the hard scatterings. We also present the variations of the cross sections due to the errors on the parton distributions (pdf's) and an analysis of the corresponding -factors. Predictions from several sets of pdf's, evolved by MRST and Alekhin are compared with those generated using \textsc{Candia}, a NNLO evolution program that implements the theory of the logarithmic expansions, developed in a previous work. These expansions allow to select truncated solutions of varying accuracy using the method of the -space iterates. The evolved parton distributions are in good agreement with other approaches. The study can be generalized for high precision searches of extra neutral gauge interactions at the LHC.

Paper Structure

This paper contains 23 sections, 87 equations, 16 figures, 30 tables.

Table of Contents

  1. Introduction
  2. Comparison with the previous literature
  3. Our approach
  4. Initial sets
  5. A classification of the possible solutions
  6. The two forms of the evolution
  7. The logarithmic expansions for the form-1 of the evolution
  8. Exact Solutions in the nonsinglet case at NNLO
  9. The Singlet Case
  10. Relating the $U$-ansatz to the logarithmic expansion
  11. Resummation and the exact solution
  12. The treatment of the renormalization scale dependence and the implementation
  13. The cross section and the parton luminosities
  14. Numerical Analysis: Comparison with the Les Houches and the MRST Models
  15. Comparisons with the Les Houches benchmarks
  16. ...and 8 more sections

Figures (16)

  • Figure 1: Plot of the percentage differences between the asymptotic Drell-Yan cross section and those obtained using expansions of the pdf's of a fixed order $\kappa$, shown as a function of $\kappa$ for the NLO and NNLO cases. We have used the MRST parametric input with $\mu_0=1$ GeV and $Q=M_{Z}$. The evolution is based on Candia.
  • Figure 2: Asymptotic and truncated pdf's for the valence up-quark and for the gluons at NLO and NNLO with $\mu_R=\mu_F=100$ GeV. We have selected the Les Houches input and a fixed number of flavors, $N_{f}=4$. The small range for $x$ has been chosen to resolve among the various predictions.
  • Figure 3: Various $K$-factors obtained with the evolution performed by Candia and MRST.
  • Figure 4: Cross Sections in the region of the peak of the Z boson at LO, NLO, and NNLO obtained using the luminosities evolved respectively by Alekhin and MRST
  • Figure 5: Cross Sections in the region of the Z with a zoom in the peak region.
  • ...and 11 more figures