Heavy Quark Pair Production near Threshold with Potential Non-Relativistic QCD

TL;DR

The paper develops a Renormalization-Group Improved pNRQCD framework to treat heavy-quark pair production near threshold, delivering NNLO accuracy with complete NNLL resummation of logarithms for both t tbar production and heavy quarkonium decays. It demonstrates that resummation stabilizes the cross section normalization and peak position and explores threshold-mass schemes (PS, RS, RS') to control renormalon effects, applying the formalism to both top and bottom sectors. While NNLL improves scale dependence and perturbative convergence, especially for the top case, residual hard-scale sensitivity and convergence issues persist in certain bottomonium observables, indicating the need for full NNNLO alongside NNLL. The work highlights practical implications for precision top mass determinations and bottom quark studies, and emphasizes the continued development required for fully robust heavy-quark threshold predictions.

Abstract

We study the effect of the resummation of logarithms for t\bar{t} production near threshold and inclusive electromagnetic decays of heavy quarkonium. This analysis is complete at next-to-next-to-leading order and includes the full resummation of logarithms at next-to-leading-logarithmic accuracy and some partial contributions at next-to-next-to-leading logarithmic accuracy. Compared with fixed-order computations at next-to-next-to-leading order the scale dependence and convergence of the perturbative series is greatly improved for both the position of the peak and the normalization of the total cross section. Nevertheless, we identify a possible source of large scale dependence in the result. At present we estimate the remaining theoretical uncertainty of the normalization of the total cross section to be of the order of 10% and for the position of the peak of the order of 100 MeV.

Figures (9)

• Figure 1: Threshold scan for $t\bar{t}$ using the PS mass, $m_{\rm PS}(20\, {\rm GeV})=175$ GeV. The upper panel shows the fixed order results, LO, NLO and NNLO, whereas in the lower panel the RGI results LL, NLL and NNLL are displayed. The soft scale is varied from $\mu_s$=30 GeV to $\mu_s$=80 GeV.
• Figure 2: The normalization of the peak of the RGI threshold cross section as a function of the soft scale $\mu_s$. The vertical dashed lines show the limits of variation used in Figure \ref{['fig:scan1']}.
• Figure 3: The position of the peak of the RGI threshold cross section as a function of the soft scale $\mu_s$. The vertical dashed lines show the limits of variation used in Figure \ref{['fig:scan1']}.
• Figure 4: Dependence of the $t\bar{t}$ threshold scan on the hard scale $\mu_h$, using the PS mass. At NNLL (NLL) the lower (upper) curve corresponds to $\mu_h=250$ GeV, whereas the upper (lower) curve corresponds to $\mu_h=100$ GeV.
• Figure 5: Effects of the QED corrections to the $t\bar{t}$ threshold scan. The hard ans soft sales are chosen as $\mu_h=m_{\rm PS}=175$ GeV and $\mu_s=40$ GeV.