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

Search for New Physics in Rare Top Decays: $t \bar t$ Spin Correlations and Other Observables