You need some form of connector - it's impossible to "integrate" two systems that don't have a connector without creating something.
Either you need to add something to salesforce to run the data exchange over REST, or the other way around - add something into JIRA that can talk to Salesforce (note that the JIRA addon that provides Salesforce integration is that route)
There's no need to have anything in-between them, they can talk directly to each other, but you need to find or write something to actually do that.
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