On-Mass-Shell Renormalization of the $\langle \bar{t}t \rangle$ Contribution to the $\Delta I = 1/2$ $s \leftrightarrow d$ Self-Energy Transition

Abstract

In $\langle \bar{t}t \rangle$-scenarios for dynamical electroweak symmetry breaking, the presence of a very large t-quark condensate necessarily generates an $s \leftrightarrow d$ self-energy transition which will contribute exclusively to $\Delta I = 1/2$ strangeness-changing matrix elements. This contribution is calculated and compared to the purely perturbative contribution, which is well-known to be far too small to have an appreciable effect on $\Delta I = 1/2$ strangeness-changing matrix elements after mass-shell renormalization subtractions are taken into account. The ratio between the t-quark condensate's contribution and the standard-model perturbative contribution to the mass-shell renormalized $s \leftrightarrow d$ self-energy transition is shown to be of order $\mid m_t \langle \bar{t} t \rangle \mid / M_W ^4$, suggesting that the large t-quark condensate proposed for electroweak symmetry breaking may also be responsible for the $\Delta