1. A computer program product for implementing process identifier (PID) based cache information transfer, the computer program product comprising: a tangible, non-transitory storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for performing a method comprising: sending, by a first core of a processor, a PID associated with a cache miss in a first local cache of the first core to a second cache of the processor; determining that the PID associated with the cache miss is listed in a PID table of the second cache; based on the PID being listed in the PID table of the second cache, determining a plurality of entries in a cache directory of the second cache that are associated with the PID; and pushing cache information associated with each of the determined plurality of entries in the cache directory from the second cache to the first local cache.