Cabibbo mixing from strong-interaction condensates

Abstract

In a scenario where the down and strange quark weak-interaction eigenstates are given a current mass, it is argued that a likely pattern of chiral symmetry breaking is one in which\(\left\langle {\bar uu} \right\rangle ,\left\langle {\bar dd} \right\rangle \) and\(\left\langle {\bar sd} \right\rangle = \left\langle {\bar ds} \right\rangle \) condensates form, the latter either instead of, or in addition to, an\(\left\langle {\bar ss} \right\rangle \) condensate. This results in a dynamical mixing contribution to the effectives-d mass matrix. Using previous estimates of quark mass ratios, the resulting Cabibbo angle is computed to be (13±4)°. A consistent solution is reached with zero Lagrangian mass for the up quark, providing a possible solution to the strongCP problem. In the absence of weak interactions,\(\left\langle {\bar sd} \right\rangle = \left\langle {\bar ds} \right\rangle = 0\), but\(\lim x \to \infty \left\langle {\bar s(x) d(x) \bar d(0) s(0)} \right\rangle \ne 0\), corresponding to a condensate of spatially noncorrelated\(\bar sd/\bar ds\) pairs, and plays a nearly identical role. Pauli-principle effects give this pair-condensed vacuum a lower energy than the usual spontaneously broken vacuum solution, and produces an allowed violation of cluster decomposition. Strangeness is not spontaneously broken, and no unwanted Goldstone bosons result.