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Heavy-quark contributions to the DIS structure functions $F_4$ and $F_5$ at NLO in the ACOT scheme

Edoardo Spezzano, Tomas Jezo, Michael Klasen, Peter Risse, Ingo Schienbein

Abstract

We compute the contributions of heavy quarks to the deep-inelastic scattering structure functions $F_4$ and $F_5$ at next-to-leading order of perturbative QCD in the ACOT scheme. Both analytic results including the details of the calculation as well as numerical results for the neutral and charged current cases are presented. Our study thus lays the groundwork for future measurements of these two structure functions in experiments such as the SHiP experiment.

Heavy-quark contributions to the DIS structure functions $F_4$ and $F_5$ at NLO in the ACOT scheme

Abstract

We compute the contributions of heavy quarks to the deep-inelastic scattering structure functions and at next-to-leading order of perturbative QCD in the ACOT scheme. Both analytic results including the details of the calculation as well as numerical results for the neutral and charged current cases are presented. Our study thus lays the groundwork for future measurements of these two structure functions in experiments such as the SHiP experiment.

Paper Structure

This paper contains 17 sections, 2 theorems, 111 equations, 6 figures.

Table of Contents

  1. Introduction
  2. DIS with massive leptons
  3. Quark scattering
  4. Real contribution
  5. Virtual contribution
  6. Combined contributions
  7. Wilson coefficients and NLO contribution
  8. Boson-gluon fusion
  9. Structure functions in the ACOT scheme
  10. Numerical implementation and results
  11. Neutral-current results
  12. Charged-current results
  13. Conclusions
  14. Collinear frame
  15. F2 QS
  16. ...and 2 more sections

Key Result

Lemma 1

The convolution of a plus distribution with weight $s(z)$ over $[\chi, 1]$ satisfies:

Figures (6)

  • Figure 1: Feynman diagrams relevant for the real contribution at next-to-leading order to the quark scattering process. The emitted gluon is denoted by $g$.
  • Figure 2: Feynman diagram (triangle vertex correction) relevant for the virtual contribution at next-to-leading order to the quark scattering process.
  • Figure 3: Feynman diagrams relevant for the real contribution at next-to-leading order to the boson-gluon fusion process.
  • Figure 4: The total structure functions $xF_4$ (left) and $xF_5$ (right) for $Z$ exchange at NLO for various $Q^2$ values. The LO contributions are given by the dashed lines. The bottom panel shows the NLO over LO ratio on a logarithmic scale for $F_4$ and on a linear scale for $F_5$. Note the difference in the scales between $F_4$ and $F_5$ for both the absolute and ratio plots.
  • Figure 5: Same as \ref{['fig:NCF4F5_NLO_LO']} but for CC. We show $xF_4$ in the top row and $xF_5$ in the bottom row for $W^-$ exchange in the left column and $W^+$ exchange in the right column.
  • ...and 1 more figures

Theorems & Definitions (4)

  • Lemma 1: Convolution Identity
  • proof
  • Lemma 2: Product Rule
  • proof