I have a tomcat 7 setup with oldApp.war and newApp.war deployed on it. Both the applications share the same login credentials for users on the database.
I can acces
You can implement SSO in many different ways:
SAML 2.0 has many implementations for Identity/Service provider roles.
For an IDP implementations list I can point you to this stackoverflow post: https://stackoverflow.com/a/761774/126414
If you are planning to implement a service provider there is a nice spring extension: http://static.springsource.org/spring-security/site/extensions/saml/index.html