Off-shell effects for t-channel and s-channel single-top production at NLO in QCD

TL;DR

The paper addresses the need for precise theoretical predictions of single-top production in the $t$- and $s$-channels at NLO in QCD while including leading non-factorizable off-shell corrections beyond the narrow-width approximation.It implements an effective-theory framework that separates hard (factorizable) and soft (non-factorizable) contributions, extending previous work on $t$-channel production to include $s$-channel processes and their interference with top decay.Numerical results for the Tevatron and 7 TeV LHC show that non-factorizable corrections are generally small, but off-shell effects can be enhanced near kinematic edges; the dominant NLO effects arise from gluon-initiated channels and depend strongly on the applied cuts and channel mixing.The findings underscore the importance of spin correlations and the careful interpretation of CKM-related initial-state effects, with implications for precision top-quark mass measurements and CKM tests in high-energy collider data.

Abstract

In this work we present a calculation of both t-channel and s-channel single-top production at next-to-leading order in QCD for the Tevatron and for the LHC at a centre-of-mass energy of 7 TeV. All the cross sections and kinematical distributions presented include leading non-factorizable corrections arising from interferences of the production and decay subprocesses, extending previous results beyond the narrow-width approximation. The new off-shell effects are found to be generally small, but can be sizeable close to kinematical end-points and for specific distributions.

Figures (11)

• Figure 1: Correspondence between the expansion by regions and the effective-theory calculation: hard loops (top left) coincide with corrections to the matching coefficient of the production vertex (top right), whereas soft loops (bottom left) reproduce the effect of loop diagrams in the effective theory (bottom right).
• Figure 2: Scale dependence of the total cross section for $p \bar{p} \rightarrow J_{b}J_{l} e^+{\not} E_T$ (left) and $p \bar{p} \rightarrow J_{b} J_{\bar{b}} e^+{\not} E_T$ (right) at the Tevatron. The plot shows the LO cross section with LO (dashed blue) and NLO (solid blue) PDFs, and the NLO cross section with simultaneous variation of factorization and renormalization scale (solid red) and for fixed factorization scale (dashed red).
• Figure 3: Top invariant-mass distributions for the process $p \bar{p} \rightarrow J_{b} J_{l} e^+{\not} E_T+X$ (upper plot) and $p \bar{p} \rightarrow J_{b} J_{\bar{b}} e^+{\not} E_T+X$ (lower plot) at the Tevatron. The blue band represents the LO ET result, the red band the NLO ET result, and the green curve the NLO spin-correlated NWA prediction. For the ET results the band width is obtained by varying the factorization and renormalization scales in the interval $m_t/4 \leq \mu_R = \mu_F \leq m_t$.
• Figure 4: Kinematical distributions for $p \bar{p} \rightarrow J_{b} J_{l} e^+{\not} E_T+X$ at the Tevatron. Top: top-quark transverse mass (left) and hadronic transverse energy (right). Centre: top-quark transverse momentum (left) and top-quark pseudorapidity (right). Bottom: $e^+ \nu J_h$ invariant mass (left) and $\cos\theta_S$ (right). See the text for a precise definition of the observables and further explanations.
• Figure 5: Kinematical distributions for $p \bar{p} \rightarrow J_{b} J_{\bar{b}} e^+{\not} E_T+X$ at the Tevatron. Top: top-quark transverse mass (left) and $J_b J_{\bar{b}}$ invariant mass (right). Centre: top-quark transverse momentum (left) and top-quark rapidity (right). Bottom: $e^+ \nu_e J_{\bar{b}}$ invariant mass (left) and $\cos\theta_B$ (right). See the text for a precise definition of the observables and further explanations.