We present a search for a new particle T′ decaying to a top quark via T′→t+X, where X goes undetected. We use a data sample corresponding to 5.7fb-1 of integrated luminosity of pp̄ collisions with √s=1.96TeV, collected at Fermilab Tevatron by the CDF II detector. Our search for pair production of T′ is focused on the hadronic decay channel, pp̄→T′T ̄′→tt̄+XX̄→bqq̄b̄ qq̄+XX̄. We interpret our results in terms of a model where T ′ is an exotic fourth generation quark and X is a dark matter particle. The data are consistent with standard model expectations. We set a limit on the generic production of T′T̄′→tt̄+XX̄, excluding the fourth generation exotic quarks T′ at 95% confidence level up to m T′=400GeV/c2 for mX≤70GeV/c2. © 2011 American Physical Society.