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We investigate a novel interplay between the decay and annihilation of a particle whose mass undergoes a large shift during a first order phase transition, leading to the particles becoming trapped in the false vacuum and enhancing their annihilation rates as the bubbles of true vacuum expand. This opens up a large region of the parameter space where annihilations can be important. We apply this scenario to baryogenesis, where we find that annihilations can be enhanced enough to generate the requires baryon asymmetry even for relatively tiny annihilation cross sections with modest CP asymmetries.

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