Angular correlations in single-top-quark and $W_{jj}$ production at next-to-leading order

I demonstrate that the correlated angular distributions of final-state particles in both single-top-quark production and the dominant $Wjj$ backgrounds can be reliably predicted. Using these fully correlated angular distributions, I propose a set of cuts that can improve the single-top-quark discovery significance by 25%, and the signal to background ratio by a factor of 3 with very little theoretical uncertainty. Up to a subtlety in $t$-channel single-top-quark production, leading-order matrix elements are shown to be sufficient to reproduce the next-to-leading order correlated distributions.

Figure 1

Representative leading-order Feynman diagrams for (a) $t$-channel, and (b) $s$-channel production of a single top quark.

Figure 2

Decay products of the top quark and the angle ${\theta }_{\widehat{s}{e}^{+}}^t$ between the charged lepton $e^{+}$ and the spin ${\widehat{s}}_t$ of the top quark in the top-quark rest frame. It is convenient to choose the spin to be projected in the direction of the down-type quark $d$ in the event.

Figure 3

Cosine of angle ($\cos {\theta }_{e{j}_1}^t$) between the charged lepton and highest-$E_T$ light-quark jet in the top-quark rest frame of $t$-channel single-top-quark production at LO and NLO. The lepton isolation cut suppresses events at large $\cos {\theta }_{e{j}_1}^t$. A nearly angle-independent underlying contribution comes from misidentification of which jet contains the down-type quark.

Figure 4

Cosine of angle ($\cos {\theta }_{e{j}_1}$) between the charged lepton and highest-$E_T$ light-quark jet $j_1$ in the lab frame and top-quark rest frame of single-top-quark production at NLO.

Figure 5

Cosine of the angle ($\cos {\theta }_{e\overline{p}}^t$) between the charged lepton and antiproton in the top-quark rest frame of $s$-channel single-top-quark production at LO at the Fermilab Tevatron (a 1.96 TeV $p\overline{p}$ collider). The solid line corresponds to reconstructing the top-quark frame using the exact neutrino and $b$ jet from the top-quark decay. The dashed line uses the missing transverse energy and $W$ mass to fit a putative neutrino momentum. The dotted line adds the effect of using a randomly chosen $b$ jet. The rescaled NLO cross section with a randomly chosen $b$ jet is indicated by open circles.

Figure 6

Cosine of angle ($\cos {\theta }_{e{j}_1}^t$) between the charged lepton and highest-$E_T$ light-quark jet $j_1$ in the $M_{Wb}$ rest frame of $Wb\overline{b}$ (solid), and $Wjj$ (dashed) production at LO, where one of the two highest-$E_T$ jets is randomly tagged as a $b$ jet, and the other is $j_1$. The NLO cross sections are shown scaled to the LO cross sections.

Figure 7

Cosine of angle ($\cos {\theta }_{e\overline{p}}^t$) between the charged lepton and antiproton in the $M_{Wb}$ rest frame of $Wb\overline{b}$ (solid) and $Wjj$ (dashed) production at LO, where one of the two highest-$E_T$ jets is randomly tagged as a $b$ jet. The NLO cross sections are shown scaled to the LO cross sections.

Figure 8

Cosine of the angle ($\cos {\theta }_{eb}^t$) between the charged lepton and final-state $b$ quark in the top-quark rest frame. The $t$-channel and $s$-channel single-to-quark distributions are the same, since they both involve a real top-quark decay. The $Wjj$ and $Wb\overline{b}$ distributions appear similar to real top-quark decay because of the boost into the top-quark rest frame.

Figure 9

Particles in the final state of single-top-quark production in the top-quark rest frame. The angle between the charged lepton $e^{+}$ and the $b$ quark is expected to be larger than the angle between $e^{+}$ and the down-type quark $d$.

Figure 10

Cosine of the angle ($\cos {\theta }_{e{j}_1}^t$) between the charged lepton and final-state jet $j_1$ in the top-quark rest frame, before and after the cut $\cos {\theta }_{eb}^t<\cos {\theta }_{e{j}_1}^t$. The $t$-channel and $s$-channel single-to-quark distributions are the same after cuts. The $Wjj$ and $Wb\overline{b}$ distributions go from approximately flat to very similar to the $t$-channel distribution before cuts.

Figure 11

Effect of the cut $a<b$ on an initially flat distribution $b$ for two cases: (left) completely flat distributions, (right) a falling distribution for $a$ (similar to the actual $\cos {\theta }_{eb}^t$). The resulting shape for $b$ is an integral over $a$ and is only modestly sensitive to the detailed shape of $a$.

Figure 12

Correlated angular distributions of the final-state particles in the top-quark rest frame of $t$-channel single-top-quark production at NLO (top) and the difference between NLO and LO (bottom). This is a two-dimensional projection between $\cos {\theta }_{e{j}_1}^t$, where $e$ is the charged lepton and $j_1$ is tagged as the highest-$E_T$ light-quark jet, and $\cos {\theta }_{b{j}_1}^t$, where $b$ is the $b$ jet from the top-quark decay.

Figure 13

Correlated angular distributions of the final-state particles in the top-quark rest frame of $t$-channel single-top-quark production at NLO (top), and the difference between NLO and LO (bottom). Same as Fig. 12 but projecting on $\cos {\theta }_{e{j}_1}^t$ and $\cos {\theta }_{eb}^t$.

Figure 14

Correlated angular distributions of the final-state particles in the top-quark rest frame of $t$-channel single-top-quark production at NLO (top), and the difference between NLO and LO (bottom). Same as Fig. 12 but projecting on $\cos {\theta }_{eb}^t$ and $\cos {\theta }_{b{j}_1}^t$.

Figure 15

Correlated angular distributions of the final-state particles in the top-quark rest frame of $s$-channel single-top-quark production at NLO. Labels are the same as in Fig. 12.

Figure 16

Correlated angular distributions of the final-state particles in the top-quark rest frame of $s$-channel single-top-quark production at NLO. Same as Fig. 15 but projecting on $\cos {\theta }_{e{j}_1}^t$ and $\cos {\theta }_{eb}^t$.

Figure 17

Correlated angular distributions of the final-state particles in the top-quark rest frame of $s$-channel single-top-quark production at NLO. Same as Fig. 15 but projecting on $\cos {\theta }_{eb}^t$ and $\cos {\theta }_{b{j}_1}^t$.

Figure 18

Correlated angular distributions of the final-state particles in the reconstructed top-quark rest frame of $Wjj$ production at NLO. Labels are the same as in Fig. 12.

Figure 19

Correlated angular distributions of the final-state particles in the reconstructed top-quark rest frame of $Wjj$ production at NLO. Same as Fig. 18 but projecting on $\cos {\theta }_{e{j}_1}^t$ and $\cos {\theta }_{eb}^t$.

Figure 20

Correlated angular distributions of the final-state particles in the reconstructed top-quark rest frame of $Wjj$ production at NLO. Same as Fig. 18 but projecting on $\cos {\theta }_{eb}^t$ and $\cos {\theta }_{b{j}_1}^t$.

Figure 21

Correlated angular distributions of the final-state particles in the top-quark rest frame of $s$-channel single-top-quark production at NLO. Same as Fig. 15 but projecting on $\cos {\theta }_{e\overline{p}}^t$ and $\cos {\theta }_{e{j}_1}^t$, where $\overline{p}$ is the incoming antiproton.

Figure 22

Correlated angular distributions of the final-state particles in the reconstructed top-quark rest frame of $Wjj$ production at NLO. Labels are the same as in Fig. 21.

Figure 23

Invariant mass of the identified $b$ jet and highest-$E_T$ jet $j_1$ from $t$- and $s$-channel single-top-quark, $Wjj$, and $Wb\overline{b}$ production.