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Quark mass effects in QCD jets

Germán Rodrigo

TL;DR

The paper addresses how bottom-quark mass effects influence QCD jet observables in $Z\to$ three-jet decays by performing a complete $O(\alpha_s^2)$ calculation with massive quarks across several jet algorithms. It discusses the distinction between pole and running masses, their scale evolution, and the potential to extract $m_b$ from LEP data using mass-sensitive observables, while ensuring IR cancellations and highlighting the running of $m_b$ from low energy to the $M_Z$ scale. The main contributions are the first NLO computation of massive three-jet rates, the demonstration that massless results are recovered in the appropriate limit, and the analysis showing how mass effects depend on $y_c$ and the chosen jet algorithm. This work provides a pathway to determining the bottom-quark mass and its running from LEP measurements, though connection to hadronization remains an important future step.

Abstract

We present the calculation of the decay width of the Z-boson into three jets including complete quark mass effects to second order in the strong coupling constant. The study is done for different jet clustering algorithms such as EM, JADE, E and DURHAM. Because three-jet observables are very sensitive to the quark mass we consider the possibility of extracting the bottom quark mass from LEP data.

Quark mass effects in QCD jets

TL;DR

The paper addresses how bottom-quark mass effects influence QCD jet observables in three-jet decays by performing a complete calculation with massive quarks across several jet algorithms. It discusses the distinction between pole and running masses, their scale evolution, and the potential to extract from LEP data using mass-sensitive observables, while ensuring IR cancellations and highlighting the running of from low energy to the scale. The main contributions are the first NLO computation of massive three-jet rates, the demonstration that massless results are recovered in the appropriate limit, and the analysis showing how mass effects depend on and the chosen jet algorithm. This work provides a pathway to determining the bottom-quark mass and its running from LEP measurements, though connection to hadronization remains an important future step.

Abstract

We present the calculation of the decay width of the Z-boson into three jets including complete quark mass effects to second order in the strong coupling constant. The study is done for different jet clustering algorithms such as EM, JADE, E and DURHAM. Because three-jet observables are very sensitive to the quark mass we consider the possibility of extracting the bottom quark mass from LEP data.

Paper Structure

This paper contains 4 sections, 6 equations, 5 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. THREE JETS OBSERVABLES AT LO
  3. THREE JETS OBSERVABLES AT NLO
  4. CONCLUSIONS

Figures (5)

  • Figure 1: Running of the bottom quark mass from low energies to the $M_Z$ scale. Upper line is the run of $\bar{m}_b(\bar{m}_b)=4.39(GeV)$ with $\alpha_{\rm{S}} (M_Z)=0.112$. Bottom line is the run of $\bar{m}_b(\bar{m}_b)=4.27(GeV)$ with $\alpha_{\rm{S}} (M_Z)=0.124$. Second picture is the difference of both, our estimate for the propagated error.
  • Figure 2: Feynman diagrams contributing to the three-jets decay rate of $Z\rightarrow b\bar{b}$ at order $\alpha_{\rm{S}}$.
  • Figure 3: Feynman diagrams contributing to the three-jets decay rate of $Z\rightarrow b\bar{b}$ at order $\alpha_{\rm{S}}^2$. Self-energies in external legs have not been shown.
  • Figure 4: NLO vector contribution to the three-jet decay rate of $Z\rightarrow b\bar{b}$ for bottom quark masses from $1$ to $5(GeV)$ and fixed $y_c$ in the JADE algorithm. Big circle is the massless case.
  • Figure 5: NLO vector contribution to the three-jet decay rate of $Z\rightarrow b\bar{b}$ for bottom quark masses from $1$ to $5(GeV)$ and fixed $y_c$ in the E algorithm. Big circle is the massless case.