Neutrino processes in the K⁰ condensed phase of color flavor locked quark matter

We study weak interactions involving Goldstone bosons in the neutral kaon condensed phase of color flavor locked quark matter. We calculate the rates for the dominant processes that contribute to the neutrino mean free path and to neutrino production. A light K⁺ state, with a mass m_K⁺∝(Δ/μ)(Δ/m_s)(m_d-m_u), where μ and Δ are the quark chemical potential and superconducting gap respectively, is shown to play an important role. We identify unique characteristics of weak interaction rates in this novel phase and discuss how they might influence neutrino emission in core collapse supernova and neutron stars.