Threshold effects in the decay of heavy b ' and t ' quarks

A sequential fourth generation is still viable, but the t' and b' quarks are constrained to be not too far apart in mass. The t'{\to}bW and b'{\to}tW decay channels are still being pursued at the Tevatron, which would soon be surpassed by the LHC. We use a convolution method with up to five-body final state to study t' and b' decays. We show how the two decay branches for m_{b'} below the tW threshold, b'{\to}tW^* and t^*W, merge with b'{\to}tW above the threshold. We then consider the heavy-to-heavy transitions b'{\to}t^{\prime(*)}W^{(*)} (or t'{\to}b^{\prime(*)}W^{(*)}), as they are not suppressed by quark mixing. We find that, because of the threshold sensitivity of the branching fraction of t'{\to}b'W^* (or b'{\to}t'W^*), it is possible to measure the strength of the CKM mixing element V_{t'b} (or V_{tb'}), especially when it is rather small. We urge the experiments to pursue and separate the t'{\to}b'W^* (or b'{\to}t'W^*) decay in their search program.