I'm betting on a very stern warning.
“Running onto the field at Nats Park is, according to a team official, considered to be unlawful entry, a misdemeanor according to DC Code §22-3302, which is subject to a $1,000 fine and/or up to 180 days in jail.”
http://www.welovedc.com/2010/08/15/four-protestors-arrested-at-nationals-park/
Apparently, the punishment varies from city to city, park to park?