org.jboss.resteasy.plugins.providers.sse.SseImpl#newBroadcaster() should return a new SseBroadcaster instance each time it is invoked.
If user want to have "a static or per request SseBroadcaster" it's up to him to handle it as stated by the spec:

9.4 Broadcasting

The life-cycle and scope of an SseBroadcaster is fully controlled by applications and not the JAX-RS runtime.