We illustrate two new theoretical conditions under which a two-body decay of a resonance violates time reversal invariance. As a consequence, we deduce two different kinds of tests of time reversal violation for such decays. The tests proposed may help detecting possible signals of physics beyond the Standard Model. In particular, they are sensitive to contributions of spontaneous CP violation. Moreover one of the two conditions found receives favourable indications from known decays and, for some strong decays, it implies selection rules to be tested experimentally.
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