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Application of the Principle of Maximum Conformality to the Top-Quark Forward-Backward Asymmetry at the Tevatron

Stanley J. Brodsky, Xing-Gang Wu

TL;DR

This work shows that applying the Principle of Maximum Conformality (PMC) to NNLO $t\bar{t}$ production yields renormalization-scale and scheme-independent predictions with improved perturbative convergence. Extending PMC to the top-quark forward-backward asymmetry, the authors obtain larger asymmetries (e.g., $A_{FB}^{t\bar{t},{\rm PMC}}\approx 12.7\%$, $A_{FB}^{p\bar{p},{\rm PMC}}\approx 8.39\%$, and $A_{FB}^{t\bar{t},{\rm PMC}}(M_{t\bar{t}}>450\,\text{GeV})\approx 35.0\%$) that are closer to Tevatron measurements. The total cross-section becomes nearly insensitive to the initial scale, indicating a renormalization-group-consistent framework and reducing the discrepancy between SM predictions and data. Overall, PMC provides a practical method to reduce theoretical uncertainties in high-energy QCD top-quark observables, diminishing the parameter space for new physics interpretations.

Abstract

The renormalization scale uncertainty can be eliminated by the Principle of Maximum Conformality (PMC) in a systematic scheme-independent way. Applying the PMC for the $t\bar{t}$-pair hadroproduction at the NNLO level, we have found that the total cross-sections $σ_{t\bar{t}}$ at both the Tevatron and LHC remain almost unchanged when taking very disparate initial scales $μ^{\rm init}_R$ equal to $m_t$, $10\,m_t$, $20\,m_t$ and $\sqrt{s}$, which is consistent with renormalization group invariance. As an important new application, we apply PMC scale-setting to study the top-quark forward-backward asymmetry. We observe that the more convergent perturbative series after PMC scale-setting leads to a more accurate top-quark forward-backward asymmetry. The resulting PMC prediction on the asymmetry is also free from the initial renormalization scale-dependence. Because the NLO PMC scale has a dip behavior for the $(q\bar{q})$-channel at small subprocess collision energies, the importance of this channel to the asymmetry is increased. We observe that the asymmetries $A_{FB}^{t\bar{t}}$ and $A_{FB}^{p\bar{p}}$ at the Tevatron will be increased by 42% in comparison to the previous estimates obtained by using conventional scale-setting; i.e. we obtain $A_{FB}^{t\bar{t},{\rm PMC}} \simeq 12.5%$ and $A_{FB}^{p\bar{p},{\rm PMC}} \simeq 8.28%$. Moreover, we obtain $A_{FB}^{t\bar{t},{\rm PMC}}(M_{t\bar{t}}>450 \;{\rm GeV}) \simeq 35.0%$. These predictions have a $1σ$-deviation from the present CDF and D0 measurements; the large discrepancies of the top-quark forward-backward asymmetry between the Standard Model estimate and the CDF and D0 data are thus greatly reduced.

Application of the Principle of Maximum Conformality to the Top-Quark Forward-Backward Asymmetry at the Tevatron

TL;DR

This work shows that applying the Principle of Maximum Conformality (PMC) to NNLO production yields renormalization-scale and scheme-independent predictions with improved perturbative convergence. Extending PMC to the top-quark forward-backward asymmetry, the authors obtain larger asymmetries (e.g., , , and ) that are closer to Tevatron measurements. The total cross-section becomes nearly insensitive to the initial scale, indicating a renormalization-group-consistent framework and reducing the discrepancy between SM predictions and data. Overall, PMC provides a practical method to reduce theoretical uncertainties in high-energy QCD top-quark observables, diminishing the parameter space for new physics interpretations.

Abstract

The renormalization scale uncertainty can be eliminated by the Principle of Maximum Conformality (PMC) in a systematic scheme-independent way. Applying the PMC for the -pair hadroproduction at the NNLO level, we have found that the total cross-sections at both the Tevatron and LHC remain almost unchanged when taking very disparate initial scales equal to , , and , which is consistent with renormalization group invariance. As an important new application, we apply PMC scale-setting to study the top-quark forward-backward asymmetry. We observe that the more convergent perturbative series after PMC scale-setting leads to a more accurate top-quark forward-backward asymmetry. The resulting PMC prediction on the asymmetry is also free from the initial renormalization scale-dependence. Because the NLO PMC scale has a dip behavior for the -channel at small subprocess collision energies, the importance of this channel to the asymmetry is increased. We observe that the asymmetries and at the Tevatron will be increased by 42% in comparison to the previous estimates obtained by using conventional scale-setting; i.e. we obtain and . Moreover, we obtain . These predictions have a -deviation from the present CDF and D0 measurements; the large discrepancies of the top-quark forward-backward asymmetry between the Standard Model estimate and the CDF and D0 data are thus greatly reduced.

Paper Structure

This paper contains 6 sections, 18 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. The forward-backward asymmetry
  3. Phenomenological applications
  4. The PMC prediction of $A_{FB}^{t\bar{t}}(M_{t\bar{t}}>450\; {\rm GeV})$
  5. Initial renormalization scale dependence
  6. summary

Figures (6)

  • Figure 4: PMC scales for the dominant asymmetry $(q\bar{q})$-channel versus the sub-process collision energy $\sqrt{s}$ for the top quark pair production up to $1.96$ TeV, where we have set the initial renormalization scale $\mu^{\rm init}_r=m_t=172.9$ GeV.
  • Figure 5: PMC coefficients of the dominant asymmetric $(q\bar{q})$-channel versus the subprocess collision energy $\sqrt{s}$, which determine the dip behavior of the NLO PMC scale $\mu^{\rm PMC, NLO}_R$. $\mu^{\rm init}_R=m_t=172.9$ GeV.
  • Figure 6: Dominant cut diagrams for the $n_f$-terms at the $\alpha^4$-order of the $(q\bar{q})$-channel, which are responsible for the smaller effective NLO PMC scale $\overline{\mu}^{\rm PMC, NLO}_R$, where the solid circles stand for the light quark loops.
  • Figure 7: Comparison of the PMC prediction with the CDF data cdf2 for the $t\bar{t}$-pair forward-backward asymmetry for the whole phase space. The upper diagram is for $A_{FB}^{t\bar{t}}$ in the $t\bar{t}$-rest frame and the lower diagram is for $A_{FB}^{p\bar{p}}$ in the laboratory frame. The Hollik and Pagani's results (HP) qedc2 using conventional scale setting are presented for a comparison. The result for D0 data d0 shows a similar behavior.
  • Figure 8: The PMC prediction of $A_{FB}^{t\bar{t}}(M_{t\bar{t}}>450\; {\rm GeV})$ and the corresponding CDF data cdf2 for the $t\bar{t}$-pair forward-backward asymmetry for $M_{t\bar{t}}>450$ GeV. The Hollik and Pagani's results (HP) qedc2 using conventional scale setting are presented for a comparison.
  • ...and 1 more figures