Differential distributions for single top quark production at the LHeC

We present a phenomenological study of the single top (anti)quark production with leptonic decays at the Large Hadron Electron Collider at next-to-leading order (NLO) in QCD. We focus on various differential distributions in a fiducial region. The NLO corrections can reduce the fiducial cross section by 14%. We find that the NLO predictions exhibit strong stability under scale variations for most observables considered, while the scale variations at leading order dominate in the theoretical uncertainties. We propose a method of determining the top quark mass using the measurement of the average transverse momentum of the charged lepton. The scale variations at the NLO induce a theoretical uncertainty of about 1.3 GeV of the extracted top quark mass. The statistical error of the extracted top quark mass amounts to 1.1 GeV. We also investigate the impact of the QCD corrections and the scale variations in searches for the anomalous $Wtb$ couplings.

Figure 1

LO Feynman diagrams for the single top quark production with leptonic decays at the LHeC. We also include the subprocess that has an indistinguishable final state as the single top quark production.

Figure 2

One-loop Feynman diagrams for the single top quark production with leptonic decays at the LHeC with a $\overline{b}$ quark in the initial state.

Figure 3

Real emission Feynman diagrams for the single top quark production with leptonic decays at the LHeC with a $\overline{b}$ quark in the initial state.

Figure 4

Real emission Feynman diagrams for the single top quark production with leptonic decays at the LHeC with a gluon in the initial state.

Figure 5

The dependence of the fiducial cross section on the factorization and renormalization scales (${\mu }_F={\mu }_R$).

Figure 6

Transverse momentum and pseudorapidity distributions of the charged lepton with fiducial cuts applied at LO and NLO with a nominal scale choice of $m_t/2$ and alternative scale choices of $m_t/4$ and $m_t$. The middle panel shows the ratio of the NLO predictions to LO predictions ($d{\sigma }_{\mathrm{NLO}}/d{\sigma }_{\mathrm{LO}}$) with each scale choice. The lower plot shows the PDF uncertainties and scale variations at both LO and NLO.

Figure 7

Similar to Fig. 6 but for the transverse momentum and pseudorapidity distributions of the b-jet.

Figure 8

Similar to Fig. 6 but for the invariant mass distributions of the charged lepton and b-jet system ($M_{{\ell }^{-}b}$).

Figure 9

Similar to Fig. 6 but for the distribution of the missing transverse momentum ($P_{T,\mathrm{miss}}=|P_{T,{\nu }_{{\ell }^{-}}}+P_{T,{\overline{\nu }}_e}|$) distribution.

Figure 10

Similar to Fig. 6 for the distributions of helicity angles of the visible-particles-reconstructed top quark and the truth top quark.

Figure 11

Transverse momentum distribution of the charged lepton with the fiducial cuts applied for different choices of the top quark mass at NLO in QCD.

Figure 12

Projection of the top quark mass measurement with a hypothetical value of 172.5 GeV. The diagonal line is the NLO prediction on $⟨p_{T,{\ell }^{-}}⟩$ as a function of the top quark mass. The diagonal band represents the scale variations of $⟨p_{T,{\ell }^{-}}⟩$ at NLO. The horizontal band represents the estimated statistical error of $⟨p_{T,{\ell }^{-}}⟩$. Vertical lines indicate various uncertainties of the extracted top quark mass.