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Quark-mass effects for jet production in e^+ e^- collisions at the next-to-leading order: results and applications

German Rodrigo, Mikhail Bilenky, Arcadi Santamaria

TL;DR

This work delivers a complete next-to-leading order QCD calculation of heavy-quark three-jet production in $e^+e^-$ collisions at the $Z$ peak, incorporating full mass effects. It employs phase-space slicing to manage infrared divergences and analyzes four jet-clustering algorithms (E, EM, JADE, DURHAM) to compute finite observables $R_3^{b\ell}$ and $D_2^{b\ell}$, which can be used to extract the bottom mass $m_b(m_Z)$ and probe mass running. The paper provides detailed results, including the $H_V(y_c,r_b)$ and $H_A(y_c,r_b)$ functions at NLO, extensive checks against massless limits, and fits for mass-dependent coefficients, with a clear demonstration that running-mass formulations improve stability. Overall, it establishes a practical framework for precision bottom-quark mass determination from $Z$-pole data and contributes to tests of QCD universality and Yukawa-running effects in the SM.

Abstract

We present a detailed description of our calculation of next-to-leading order QCD corrections to heavy quark production in e^+ e^- collisions including mass effects. In particular, we study the observables $R_3^{b\ql}$ and $D_2^{b\ql}$ in the E, EM, JADE and DURHAM jet-clustering algorithms and show how one can use these observables to obtain $m_b(m_Z)$ from data at the $Z$ peak.

Quark-mass effects for jet production in e^+ e^- collisions at the next-to-leading order: results and applications

TL;DR

This work delivers a complete next-to-leading order QCD calculation of heavy-quark three-jet production in collisions at the peak, incorporating full mass effects. It employs phase-space slicing to manage infrared divergences and analyzes four jet-clustering algorithms (E, EM, JADE, DURHAM) to compute finite observables and , which can be used to extract the bottom mass and probe mass running. The paper provides detailed results, including the and functions at NLO, extensive checks against massless limits, and fits for mass-dependent coefficients, with a clear demonstration that running-mass formulations improve stability. Overall, it establishes a practical framework for precision bottom-quark mass determination from -pole data and contributes to tests of QCD universality and Yukawa-running effects in the SM.

Abstract

We present a detailed description of our calculation of next-to-leading order QCD corrections to heavy quark production in e^+ e^- collisions including mass effects. In particular, we study the observables and in the E, EM, JADE and DURHAM jet-clustering algorithms and show how one can use these observables to obtain from data at the peak.

Paper Structure

This paper contains 23 sections, 84 equations, 12 figures, 12 tables.

Table of Contents

  1. Introduction
  2. The decay $Z \rightarrow 3 jets$ with heavy quarks at the leading order
  3. Decay into two and three jets and jet-clustering algorithms
  4. $Z \rightarrow 3 jets$ at tree level
  5. Three-jet ratios at next-to-leading order: overview of the calculation
  6. Three-parton contributions
  7. Classification of diagrams
  8. Renormalization counterterms
  9. Infrared divergent contributions
  10. Four-parton contributions
  11. Classification of Diagrams
  12. Emission of two real gluons
  13. Emission of four quarks
  14. Infrared divergent contributions
  15. Results and applications: $R_3^{b\ell}$, $D_2^{b\ell}$ and $m_b(m_Z)$ from data at the $Z$ peak
  16. ...and 8 more sections

Figures (12)

  • Figure 1: Tree-level diagrams contributing to $Z\rightarrow b\bar{b}g$.
  • Figure 2: Radiative corrections to the process $Z\rightarrow b\bar{b}g$. Diagrams $V1$ to $V12$ contribute at $O(\alpha_s^2)$ through their interference with the lowest order bremsstrahlung diagrams $Ta$ and $Tb$.
  • Figure 3: Selfenergy diagrams. Graphs involving ghosts and similar in structure to $S5$ and $S6$ have not been shown.
  • Figure 4: Bubble classification relating virtual and real contributions at $O(\alpha_s^2)$ according to their divergent structure. Again we do not show diagrams similar to Class D with ghosts in the loop.
  • Figure 5: Feynman diagrams contributing to the process $Z\rightarrow b\bar{b}gg$.
  • ...and 7 more figures