Top quark production near threshold and the top quark mass

Abstract

We consider top-anti-top production near threshold in $e^+ e^-$ collisions, resumming Coulomb-enhanced corrections at next-to-next-to-leading order (NNLO). We also sum potentially large logarithms of the small top quark velocity at the next-to-leading logarithmic level using the renormalization group. The NNLO correction to the cross section is large, and it leads to a significant modification of the peak position and normalization. We demonstrate that an accurate top quark mass determination is feasible if one abandons the conventional pole mass scheme and if one uses a subtracted potential and the corresponding mass definition. Significant uncertainties in the normalization of the $t\bar{t}$ cross section, however, remain.

Figures (2)

• Figure 1: (a) [upper panel]: The normalized $\bar{t}t$ cross section (virtual photon contribution only) in LO (short-dashed), NLO (short-long-dashed) and NNLO (solid) as function of $E=\sqrt{s}-2 m_t$ (pole mass scheme). Parameters: $m_t=\mu_h=175\,$GeV, $\Gamma_t=1.40\,$GeV, $\alpha_s(m_Z)=0.118$. The three curves for each case refer to $\mu=\left\{15 (\hbox{upper}); 30 (\hbox{central}); 60 (\hbox{lower})\right\}\,$GeV. (b) [lower panel]: As in (a), but in the PS mass scheme with $\mu_f=20\,$GeV. Hence $E=\sqrt{s}-2 m_{t,\rm PS}(20\,\hbox{GeV})$. Other parameters as above with $m_t\to m_{t,\rm PS}(20\,\hbox{GeV})$.
• Figure 2: Dependence of the NNLO $t\bar{t}$ cross section on $\alpha_s(m_Z)$ in the PS scheme (solid) and the pole scheme (long-short-dashed). The three curves in each scheme refer to $\alpha_s(m_Z)=0.113$ (lower), $\alpha_s(m_Z)=0.118$ (middle) and $\alpha_s(m_Z)=0.123$ (upper). Recall that $E=\sqrt{s}-2 m_t$ in the pole scheme but $E=\sqrt{s}-2 m_{t,\rm PS}(20\,\hbox{GeV})$ in the PS scheme. Other parameters: $m_t=\mu_h=175\,$GeV, $\Gamma_t=1.40\,$GeV, $\mu=30\,$GeV.