Narrow resonance in an open channel

We discuss the possibility that a very narrow resonance will exist in a multiresonance system above the threshold of an open decay channel. We show that its width varies as the square of the commutator of the mass and width matrices near the vanishing point of this commutator. A hypothetical example of such an effect, relevant to narrow-resonance searches in e⁺e^- annihilation, is discussed.