(Reuters) - Cory Booker, the New Jersey mayor who is a rising star in the Democratic party, filed documents on Friday revealing his intention to run for the U.S. Senate in 2014, possibly setting up a primary challenge against 88-year-old Democratic incumbent Frank Lautenberg Booker, the 43-year-old mayor of Newark, announced in December he would "explore the possibility" of running for Senate. Lautenberg has yet to announce his intentions. His press office did not return a call seeking comment on Booker's filing with the U.S. Federal Election Commission. ...