The relationship between Product Owner, Business Analyst and Tester

In an Agile/Scrum team the Product Owner manages the Product Backlog, a Business Analyst may help further elaborate the backlog. Acceptance Criteria is "one of the" or the output of that elaboration. A Tester may futher define the Acceptance Criteria and write test scripts to verify it. What is the relationship between the three roles? Inseparable, acquaintance or in a love triangle?

My thoughts spring from the fact that I have frequently seen a gap between the tester and BA/Product Owner's understanding of the requirements. I accept that the BA comes from the business perspective and the tester from the system/specification perspective. How can the two reach the same understanding of what the end system will deliver?