We consider the impact of isospin violation on the analysis of K-> pi pi
decays. We scrutinize, in particular, the phenomenological role played by the
additional weak amplitude, of |Delta I|=5/2 in character, incurred by the
presence of isospin violation. We show that Watson's theorem is appropriate in
O(m_d-m_u), so that the inferred pi-pi phase shift at sqrt{s}=m_K determines
the strong phase difference between the I=0 and I=2 amplitudes in K-> pi pi
decay. We find the magnitude of the |Delta I|=5/2 amplitude thus implied by the
empirical branching ratios to be larger than expected from estimates of
isospin-violating strong and electromagnetic effects. We effect a new
determination of the octet and 27-plet coupling constants with
strong-interaction isospin violation and with electromagnetic effects, as
computed by Cirigliano, Donoghue, and Golowich, and find that we are unable to
resolve the difficulty. Exploring the role of |Delta I|=5/2 transitions in the
CP-violating observable epsilon'/epsilon, we determine that the presence of a
|Delta I|=5/2 amplitude impacts the empirical determination of omega, the ratio
of the real parts of the |Delta I|=3/2 to |Delta I|=1/2 amplitudes, and that it
generates a decrease in the estimation of epsilon'/epsilon.Comment: 29 pages, 1 ps fig, refs. added, to appear in Phys. Rev.