Single top-quark production at the Tevatron and the LHC

This paper provides a review of the experimental studies of processes with a single top quark at the Tevatron proton-antiproton collider and the LHC proton-proton collider. Single top-quark production in the $t$-channel process has been measured at both colliders. The $s$-channel process has been observed at the Tevatron, and its rate has also been measured at the center-of-mass energy of 8 TeV at the LHC in spite of the comparatively harsher background contamination. LHC data also brought the observation of the associated production of a single top quark with a $W$ boson as well as with a $Z$ boson. The Cabibbo-Kobayashi-Maskawa matrix element $|V_{tb}|$ is extracted from the single top-quark production cross sections, and $t$-channel events are used to measure several properties of the top quark and set constraints on models of physics beyond the standard model. Rare final states with a single top quark are searched for, as enhancements in their production rates, if observed, would be clear signs of new physics.

Figure 1

Representative diagrams for electroweak single top-quark production in the (a) $t$-channel, (b) $s$-channel, and (c) $W$-associated production ($tW$).

Figure 2

Spectator jet pseudorapidity distribution, corresponding to the light-quark line in Fig. 1, comparing the Born level to NLO, (left) for $\eta$ at the Tevatron for top-quark (not antiquark) production. From [125]. (Right) For $|\eta |$ at the LHC for top-quark and antiquark $t$-channel production. From [239].

Figure 3

(Left) Combination discriminant distribution and (right) ${\cancel{E}}_T+\text{jets}$ analysis discriminant distribution for the CDF single top-quark observation analysis. From [5].

Figure 4

Combination discriminant distribution for the D0 single top-quark observation analysis for (a) the full range and (b) zoomed in on the signal region. From [20].

Figure 5

Representative diagrams for electroweak single top-quark $t$-channel production in (a) the $2\to 2$ mode, corresponding to the 5-flavor-number scheme and (b) the $2\to 3$ mode, corresponding to the 4-flavor-number scheme.

Figure 6

Multivariate discriminant for (left) the CDF $l+\text{jets}$ analysis for events with one $b$ tag. From [9]. (Right) The CDF ${\cancel{E}}_T+\text{jets}$ analysis for events with two tight $b$ tags. From [11].

Figure 7

Two-dimensional posterior probability density as a function of the $t$-channel and $s$-channel single top-quark production cross sections for (left) the combined CDF analysis. From [11]. (Right) The D0 analysis. From [26]. Overlaid on the D0 plot are several representative new-physics models: FCNC top-gluon interactions ([242]; [18]), a fourth-generation model ([60]), a top-flavor model ([242]), and a top pion ([199]; [242]).

Figure 8

Signal region of the multivariate discriminant (ranked by expected signal-to-background ratio) for the D0 single top-quark analysis for (a) the $t$-channel discriminant and (b) the $s$-channel discriminant. From [26].

Figure 9

Distribution of the discriminant histograms, summed over bins with similar ratios [$(s-t)/\text{background}$]. A nonlinear scale is used on the horizontal axis to better bring out the signal regions of the discriminant. From [10].

Figure 10

(Left) Posterior probability density as a function of the $t$-channel and $s$-channel cross sections. Adapted from [10]. Also shown are new-physics models: FCNC top-gluon interactions ([242]; [18]), a four-generation model ([60]), a top-flavor model ([242]), and a top pion ([199]; [242]). (Right) Summary of the Tevatron single top-quark measurements. Adapted from [10].

Figure 11

(Left) Tevatron $s$-channel discriminant with bins sorted by signal to background yields and (right) summary of Tevatron $s$-channel cross-section measurements. From [7].

Figure 12

(Left) CMS 7 TeV $t$-channel pseudorapidity distribution of the light-quark jet for muon events. From [135]. (Right) ATLAS 8 TeV $t$-channel NN discriminant distribution. From [68].

Figure 13

(Left) CMS 13 TeV $t$-channel NN discriminant. From [152]. (Right) ATLAS 8 TeV $t$-channel fiducial cross-section measurement compared to different signal simulations. From [68].

Figure 14

Differential distributions in $t$-channel events unfolded to parton level (left) of the transverse momentum of the top quark in the ATLAS analysis at 8 TeV. From [79]. (Right) $\cos {\theta }_{\ell }$ in the CMS analysis at 8 TeV in the muon channel. From [145].

Figure 15

Representative Feynman diagram for $W$-associated single top-quark production ($tW$) from a gluon-gluon initial state, (a) $O({\alpha }_s)$ correction that contributes to $tW$ and (b) correction with an on-shell top quark that needs to be removed.

Figure 16

(Left) Distribution of the number of reconstructed jets in the ATLAS 7 TeV $tW$ analysis. From [64]. (Right) BDT discriminant for 1-jet events in the CMS 8 TeV $tW$ analysis. From [141].

Figure 17

(Left) Constraints on the systematic uncertainties (pull, for which the nominal value is $0\pm 1\sigma$) and impact of those uncertainties on the $tW$ cross-section measurement in the ATLAS 8 TeV $tW$ analysis. From [78]. The shaded and hashed areas refer to the top axis: the shaded bands show the initial impact of that source of uncertainty on the precision of the signal strength $\mathrm{\Delta }\widehat{\mu }$; the hatched areas show the impact on the measurement of that source of uncertainty, after the profile likelihood fit at the $\pm 1\sigma$ level. The points and associated error bars show the pull of the nuisance parameters and their uncertainties and refer to the bottom axis. A mean of zero and a width of 1 would imply no constraint due to the profile likelihood fit. (Right) Differential $tW$ cross section as a function of the energy of the $b$ quark measured by ATLAS at 13 TeV. From [83].

Figure 18

Fiducial cross-section measurement in the ATLAS 8 TeV $tW$ analysis compared to theoretical predictions. From [78].

Figure 19

Number of events with a $W$ boson and a $b$ quark observed by LHCb as a function of $p_T(\mu +b)$, compared to expectations with and without a top-quark signal ($t\overline{t}+tW$) at NLO accuracy. From [221].

Figure 20

(Left) Matrix-element discriminant expressed as the probability for an observed event $X$ to be a signal event ($S$), $P(S|X)$, in the ATLAS 8 TeV $s$-channel analysis. From [74]. (Right) BDT discriminant in the CMS 8 TeV $s$-channel analysis. From [148].

Figure 21

Representative Feynman diagrams for electroweak single top-quark production in association with a $Z$ boson ($tZq$), (a) with the $Z$-boson coupling to the exchanged $W$ boson, and (b) the $Z$-boson coupling to the top quark.

Figure 22

Post-fit neural network discriminant distribution in the ATLAS search for the $tZq$ process in 13 TeV data. From [85].

Figure 23

Post-fit discriminant distribution in the CMS $tZq$ analysis at 13 TeV: (left) BDT for $1\text{−}b$-jet events, (middle) BDT for $2\text{−}b$-jet events, and (right) $W$ transverse mass distribution for $0\text{−}b$-jet events. From [158].

Figure 24

Summary of Tevatron and LHC measurements of the inclusive single top-quark production cross sections in the $t$-channel, $s$-channel, $tW$, and $tZq$ production. The measurements are compared to theoretical calculations based on NLO QCD complemented with NNLL resummation. The full theory curves as functions of the c.m. energy are calculated as in [206], [207], [208] for the $t$ channel, $s$ channel, and $tW$, and are calculated with amc@nlo (v.254) ([59]) for $tZq$. The curves for the $s$ channel and the sum of the $s$ and the $t$ channel are calculated for $p\overline{p}$ collisions up to 3 TeV and for $pp$ collisions beyond; for the $t$ channel, $tW$ and $tZq$ the curves for $pp$ and $p\overline{p}$ coincide at the considered accuracy.

Figure 25

Inclusive single top-quark cross sections measured at 8 TeV at the LHC, the $t$ channel vs $tW$ and the $s$ channel and $tW$ vs the $s$ channel. The SM theory predictions are calculated as in [206], [207], [208]. Also shown are example BSM scenarios: A model with CKM element $V_{ts}=0.2$ ([60]), a vectorlike fourth-generation quark with chromomagnetic couplings ([230]), a color triplet ([172]), and flavor-changing neutral current interactions of the top quark with the gluon and the charm quark ([46]).

Figure 26

Summary of ATLAS and CMS extractions of $|f_L{V}_{tb}|$ from the single top-quark cross-section measurements, using $\mathrm{NLO}+\mathrm{NNLL}$ theoretical predictions. From [243], including some preliminary results.

Figure 27

Summary of ATLAS and CMS measurements of $R_t\equiv {\sigma }_t/{\sigma }_{\overline{t}}$ at (left) 8 TeV ([139]; [79]) and (right) 13 TeV ([80]; [152]), compared with theoretical expectations at NLO obtained with hathor ([56]; [205]) and a variety of PDF sets ([191]; [51], [52]; [90]; [192]; [173]). Error bars for the different PDF sets represent the quadratic sum of the following uncertainty components: the 68% confidence level interval of the predictions of the eigenvectors in the set, the statistical uncertainty due to the finite number of iterations employed for the calculation, the uncertainty in the factorization and renormalization scales, derived varying both of them by factors of $1/2$ and 2, and the uncertainty in the top-quark mass.

Figure 28

Limits on pairs of anomalous couplings squared from the D0 combination of single top and $t\overline{t}$ anomalous coupling searches: left-handed tensor coupling vs left-handed vector coupling. From [24].

Figure 29

(Left) The definition of the polarization angles in $t$-channel single top-quark production, and (right) predicted and observed angular asymmetries. From [82].

Figure 30

Limits on anomalous couplings from the ATLAS (left) two- and (right) three-angle analyses. From [81].

Figure 31

Limits on anomalous $tWb$ couplings from the CMS analysis combining 7 and 8 TeV, projected onto two dimensions: (left) left- vs right-handed tensorial coupling, and (right) vectorial vs tensorial right-handed coupling. From [150].

Figure 32

Summary of ATLAS and CMS limits on FCNC processes, expressed in equivalent branching ratios and compared with the expectations from the SM and several new-physics models. For each FCNC process, the ATLAS limit is shown at the top and the CMS one at the bottom. From [243].

Figure 33

Observed 95% C.L. upper limit on the branching ratio of $t\to Zq$ vs the branching of $t\to \gamma q$ ($q=u$, $c$) as derived directly or indirectly by experiments at LEP, HERA, Tevatron, and the LHC: search for $e^{+}{e}^{-}\to {\gamma }^{*}/Z\to t\overline{q}/\overline{t}q$ by L3 ([39]), search for $eq\to et$ by ZEUS ([38]) and H1 ([12]), search for $t\to Zq$ decays in $t\overline{t}$ events by D0 ([22]), CDF ([2]), and search for $t\to \gamma q$ decays in $t\overline{t}$ events by CDF ([35]). From [243].

Figure 34

Dominant Feynman diagrams for the production of $tHq$ events.

Figure 35

Left: 95% C.L. upper limits on the $tHq$ cross section, divided by its expectation in the $y_t=-1$ scenario, by decay channel and combined. Right: 95% C.L. upper limits on the $tHq$ production cross section vs $\mathrm{BR}(H\to \gamma \gamma )$; the red horizontal line shows the predicted $tHq$ cross section for the SM Higgs boson with $m_H=125\mathrm{GeV}$ in the $y_t=-1$ scenario, while the black horizontal line shows the predicted $tHq$ cross section for the SM (i.e., $y_t=+1$) scenario. From [149].