Top quark inclusive differential distributions

TL;DR

The paper investigates inclusive top-quark differential distributions at the Tevatron by combining exact NLO QCD results with all-orders soft-gluon resummation of initial-state radiation. Using a threshold-based soft-gluon framework and scheme-dependent running couplings, it demonstrates that resummed predictions yield higher cross sections than fixed-order calculations for both the transverse-momentum and rapidity distributions, with the enhancement most pronounced in the gluon-initiated channel. The authors also introduce a nonperturbative cutoff to handle infrared sensitivity and provide perturbation-improved distributions by blending exact NLO with resummed results. These findings refine theoretical predictions for top-quark production, aiding experimental analyses and mass/cross-section extractions at hadron colliders, while highlighting scheme and cutoff dependencies. Overall, the work advances understanding of soft-gluon effects in heavy-quark production near threshold and offers practical, improved predictions for Tevatron phenomenology.

Abstract

The inclusive transverse momentum and rapidity distributions for top quark production at the Fermilab Tevatron are presented both in order $α_s^3$ in QCD and using the resummation of the leading soft gluon corrections in all orders of QCD perturbation theory. The resummed results are uniformly larger than the $O(α_s^3)$ results for both distributions.

Figures (12)

• Figure 1: The top quark $p_t$ distributions $d\sigma_H^{(k)}/dp_t$ for the $q\bar{q}$ channel in the DIS scheme for a top quark mass $m=175$ GeV$/c^2$. Plotted are $d\sigma_H^{(0)}/dp_t$ (upper solid line), $d\sigma_H^{(1)}/dp_t\mid _{\rm exact}$ (lower solid line), $d\sigma_H^{(1)}/dp_t\mid _{\rm app}$ (upper dotted line), $d\sigma_H^{(2)}/dp_t\mid _{\rm app}$ (lower dotted line), and $d\sigma_H^{\rm res}/dp_t$ ($\mu_0=0.05\:m$ upper dashed line and $\mu_0=0.1\:m$ lower dashed line).
• Figure 2: The top quark $p_t$ distributions $d\sigma_H/dp_t$ for the $q\bar{q}$ channel in the DIS scheme for a top quark mass $m=175$ GeV$/c^2$. Plotted are $d\sigma_H^{(0)}/dp_t+d\sigma_H^{(1)}/dp_t\mid _{\rm exact}$ (solid line) and $d\sigma_H^{\rm imp}/dp_t$ ($\mu_0=0.05\:m$ upper dashed line and $\mu_0=0.1\:m$ lower dashed line).
• Figure 3: The top quark $p_t$ distributions $d\sigma_H^{(k)}/dp_t$ for the $gg$ channel in the $\overline{\rm MS}$ scheme for a top quark mass $m=175$ GeV$/c^2$. Plotted are $d\sigma_H^{(0)}/dp_t$ (upper solid line at large $p_t$), $d\sigma_H^{(1)}/dp_t\mid _{\rm exact}$ (lower solid line at large $p_t$), $d\sigma_H^{(1)}/dp_t\mid _{\rm app}$ (lower dotted line), $d\sigma_H^{(2)}/dp_t\mid _{\rm app}$ (upper dotted line), and $d\sigma_H^{\rm res}/dp_t$ ($\mu_0=0.2\:m$ upper dashed line and $\mu_0=0.25\:m$ lower dashed line).
• Figure 4: The top quark $p_t$ distributions $d\sigma_H/dp_t$ for the $gg$ channel in the $\overline{\rm MS}$ scheme for a top quark mass $m=175$ GeV$/c^2$. Plotted are $d\sigma_H^{(0)}/dp_t+d\sigma_H^{(1)}/dp_t\mid _{\rm exact}$ (solid line) and $d\sigma_H^{\rm imp}/dp_t$ ($\mu_0=0.2\:m$ upper dashed line and $\mu_0=0.25\:m$ lower dashed line).
• Figure 5: The top quark $p_t$ distributions $d\sigma_H^{(k)}/dp_t$ for the sum of the $q\bar{q}$ and $gg$ channels for a top quark mass $m=175$ GeV$/c^2$. Plotted are $d\sigma_H^{(0)}/dp_t$ (upper solid line), $d\sigma_H^{(1)}/dp_t\mid _{\rm exact}$ (lower solid line), $d\sigma_H^{(1)}/dp_t\mid _{\rm app}$ (upper dotted line), $d\sigma_H^{(2)}/dp_t\mid _{\rm app}$ (lower dotted line), and $d\sigma_H^{\rm res}/dp_t$ (upper and lower dashed lines).