Search for new physics in rare top decays: $t\overline{t}$ spin correlations and other observables

In this paper we study new-physics contributions to the top-quark decay $t\to b\overline{b}c$. We search for ways of detecting such new physics via measurements at the LHC. As top quarks are mainly produced at the LHC in $t\overline{t}$ production via gluon fusion, we analyze the process $gg\to t\overline{t}\to (b\overline{b}c)(\overline{b}\ell \overline{\nu })$. We find six observables that can be used to reveal the presence of new physics in $t\to b\overline{b}c$. Three are invariant mass-squared distributions involving two of the final-state particles in the top decay, and three are angular correlations between the final-state quarks coming from the $t$ decay and the ${\ell }^{-}$ coming from the $\overline{t}$ decay. The angular correlations are related to the $t\overline{t}$ spin correlation.

Figure 1

Kinematics for the process $gg\to t\overline{t}\to (b\overline{b}c)(\overline{b}\ell \overline{\nu })$ [12]. ${\mathrm{\Omega }}_1^{**}$ denotes the direction of ${\overrightarrow{p}}_1^{**}$ in the rest frame of $M_2$, relative to the direction of ${\overrightarrow{p}}_1^{*}+{\overrightarrow{p}}_2^{*}$, where $M_2^2=(p_1+p_2{)}^2$. Similarly, ${\mathrm{\Omega }}_2^{*}$ denotes the direction of $({\overrightarrow{p}}_1^{*}+{\overrightarrow{p}}_2^{*})$ in the $t$ rest frame, relative to the direction of ${\overrightarrow{p}}_t$ in the $t\overline{t}$ rest frame. ${\mathrm{\Omega }}_t$ denotes the direction of ${\overrightarrow{p}}_t$ relative to ${\overrightarrow{q}}_1$, also in the $t\overline{t}$ rest frame. The solid angles ${\mathrm{\Omega }}_4^{**}$ and ${\mathrm{\Omega }}_5^{*}$ are defined analogously to ${\mathrm{\Omega }}_1^{**}$ and ${\mathrm{\Omega }}_2^{*}$, respectively, and $M_5^2=(p_4+p_5{)}^2$.

Figure 2

A comparison of the normalized $d\sigma /d{\zeta }_{bc}^2$ distribution obtained using madgraph 5 with that of Eq. (14). This is done for the SM and for the NP scenario in which $X_{RR}^S=X_{RR}^V=X_{RR}^T=1+i$, with all other NP parameters set to zero (labeled here as NP-RR).

Figure 3

A comparison of the normalized $d\sigma /d\cos {\theta }_{\overline{b}}^{*}d\cos {\theta }_{\ell }^{*}$ angular distribution obtained using madgraph 5 with that of Eq. (15). This is done for the SM and for the NP scenario in which $X_{RR}^S=X_{RR}^V=X_{RR}^T=1+i$ (labeled here as NP-RR).

Figure 4

Feynman diagrams for $gg\to t\overline{t}$. The $t$ subsequently decays to $b\overline{b}c$.

Figure 5

Feynman diagrams for (a) $gg\to t\overline{t}\to (b\overline{b}c)\overline{t}$ and (b) $gg\to t\overline{t}\to (b\overline{b}c)(\overline{b}\ell \overline{\nu })$. The subscripts $i,j,\dots ,n$ are color indices. All NP effects are assumed to be contained in $\overline{B}$; $gg\to t\overline{t}$ and $\overline{t}\to \overline{b}\ell \overline{\nu }$ are assumed to be SM-like.