Single-Top-Quark Production via W-Gluon Fusion at Next-to-Leading Order

TL;DR

The paper provides the first complete and consistent next-to-leading-order calculation of single-top-quark production via $W$-gluon fusion, using the $\overline{\rm MS}$ factorization scheme with a perturbatively derived $b$-quark distribution. It reveals two independent NLO corrections, $1/\ln(m_t^2/m_b^2)$ and $\alpha_s$, which are numerically comparable and addresses the proper treatment of collinear logarithms through a structure-function approach. By carefully selecting scales for light- and heavy-quark distributions and validating against prior scheme choices, the authors obtain stabilized cross sections with reduced theoretical uncertainties at Tevatron and LHC, highlighting the channel’s viability for measuring $V_{tb}$ and probing new physics. The work also quantifies large corrections at HERA and underscores the importance of PDF uncertainties in precision predictions for heavy-quark initiated processes.

Abstract

Single-top-quark production via W-gluon fusion at hadron colliders provides an opportunity to directly probe the charged-current interaction of the top quark. We calculate the next-to-leading-order corrections to this process at the Fermilab Tevatron, the CERN Large Hadron Collider, and DESY HERA. Using a b-quark distribution function to sum collinear logarithms, we show that there are two independent corrections, of order 1/[ln(m_t^2/m_b^2)] and alpha_s. This observation is generic to processes involving a perturbatively derived heavy-quark distribution function at an energy scale large compared with the heavy-quark mass.

Figures (9)

• Figure 1: Single-top-quark production via $W$-gluon fusion.
• Figure 2: (a) Leading-order process for single-top-quark production, using a $b$ distribution function. (b) Correction to the leading-order process from an initial gluon. (c) Subtracting the collinear region from (b), corresponding to a gluon splitting into a $b\bar{b}$ pair. (b) and (c) taken together constitute a correction of order $1/\ln (m_t^2/m_b^2)$ to the leading-order process in (a).
• Figure 3: Order $\alpha_s$ correction to the heavy-quark vertex in the leading-order process $qb \to q^\prime t$. (c) represents the subtraction of the collinear region from (b).
• Figure 4: Order $\alpha_s$ correction to the light-quark vertex in the leading-order process $qb \to q^\prime t$.
• Figure 5: The ratio of the $b$ distribution function to the gluon distribution function, times $2\pi/\alpha_s(\mu^2)$, versus the factorization scale $\mu$, for various fixed values of $x$. The curves are approximately linear when $\mu$ is plotted on a logarithmic scale, indicating that $b(x,\mu^2) \propto [\alpha_s(\mu^2)/2\pi] \ln (\mu^2/m_b^2) g(x,\mu^2)$, as suggested by the approximation of Eq. (\ref{['b']}).