While logged in as sysadmin, create a stored proc that includes "WITH EXECUTE AS OWNER". In that proc, have the command:
EXEC msdb..sp_start_job @job_name = @job_name, ...
Then GRANT the role(s)/user(s) execute authority on that stored proc.
SQL DBA,SQL Server MVP(07, 08, 09) A socialist is someone who will give you the shirt off *someone else's* back.