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NRQCD Analysis of Bottomonium Production at the Tevatron

Eric Braaten, Sean Fleming, Adam K. Leibovich

TL;DR

This work reanalyzes Tevatron bottomonium production within NRQCD factorization, extracting color-octet and color-singlet matrix elements from Run IB data on $\Upsilon(nS)$ and $\chi_b(nP)$ while accounting for feeddown. The authors use these matrix elements to predict spin-triplet and spin-singlet bottomonium production, notably predicting sizable direct $\eta_b(1S)$ production and proposing $\eta_b\to J/\psi J/\psi$ as a viable Run II discovery channel. A major limitation is the lack of soft-gluon resummation at small $p_T$, which introduces large uncertainties and deviates from data below $p_T=8$ GeV; the paper calls for combining LO and NLO calculations to obtain smooth distributions and more reliable predictions. Overall, the analysis provides updated NRQCD matrix elements and concrete predictions for $\eta_b$ and $h_b$ production at the Tevatron, with implications for Run II experimental searches.

Abstract

Recent data from the CDF collaboration on the production of spin-triplet bottomonium states at the Tevatron p \bar p collider are analyzed within the NRQCD factorization formalism. The color-singlet matrix elements are determined from electromagnetic decays and from potential models. The color-octet matrix elements are determined by fitting the CDF data on the cross sections for Upsilon(1S), Upsilon(2S), and Upsilon(3S) at large p_T and the fractions of Upsilon(1S) coming from chi_b(1P) and chi_b(2P). We use the resulting matrix elements to predict the cross sections at the Tevatron for the spin-singlet states eta_b(nS) and h_b(nP). We argue that eta_b(1S) should be observable in Run II through the decay eta_b -> J/psi + J/psi.

NRQCD Analysis of Bottomonium Production at the Tevatron

TL;DR

This work reanalyzes Tevatron bottomonium production within NRQCD factorization, extracting color-octet and color-singlet matrix elements from Run IB data on and while accounting for feeddown. The authors use these matrix elements to predict spin-triplet and spin-singlet bottomonium production, notably predicting sizable direct production and proposing as a viable Run II discovery channel. A major limitation is the lack of soft-gluon resummation at small , which introduces large uncertainties and deviates from data below GeV; the paper calls for combining LO and NLO calculations to obtain smooth distributions and more reliable predictions. Overall, the analysis provides updated NRQCD matrix elements and concrete predictions for and production at the Tevatron, with implications for Run II experimental searches.

Abstract

Recent data from the CDF collaboration on the production of spin-triplet bottomonium states at the Tevatron p \bar p collider are analyzed within the NRQCD factorization formalism. The color-singlet matrix elements are determined from electromagnetic decays and from potential models. The color-octet matrix elements are determined by fitting the CDF data on the cross sections for Upsilon(1S), Upsilon(2S), and Upsilon(3S) at large p_T and the fractions of Upsilon(1S) coming from chi_b(1P) and chi_b(2P). We use the resulting matrix elements to predict the cross sections at the Tevatron for the spin-singlet states eta_b(nS) and h_b(nP). We argue that eta_b(1S) should be observable in Run II through the decay eta_b -> J/psi + J/psi.

Paper Structure

This paper contains 11 sections, 18 equations, 3 figures, 7 tables.

Table of Contents

  1. Introduction
  2. NRQCD Matrix Elements
  3. Parton Differential Cross Sections
  4. Color-singlet Matrix Elements
  5. Color-octet Matrix Elements
  6. Inclusive Matrix Elements for S-waves
  7. Direct Matrix Elements for P-waves
  8. Direct Matrix Elements for S-waves
  9. Inclusive Cross Sections for Spin-triplet States
  10. Direct Cross Sections for Spin-singlet States
  11. Discussion

Figures (3)

  • Figure 1: Inclusive cross section for $\Upsilon(1S)$ at $y = 0$ in Run I multiplied by its branching fraction $B$ into $\mu^+ \mu^-$ as a function of $p_T$: CDF data, NRQCD fit (solid line) with statistical error bars (dotted lines), and color-singlet model prediction (dashed line).
  • Figure 2: Inclusive cross section for $\Upsilon(2S)$ at $y = 0$ in Run I multiplied by its branching fraction $B$ into $\mu^+ \mu^-$ as a function of $p_T$: CDF data, NRQCD fit, and color-singlet model prediction.
  • Figure 3: Inclusive cross section for $\Upsilon(3S)$ at Run I multiplied by its branching fraction $B$ into $\mu^+ \mu^-$ as a function of $p_T$: CDF data, NRQCD fit, and color-singlet model prediction.