  In QCD sum-rule methods, the fundamental field-theoretical quantities are
correlation functions of composite operators that serve as hadronic
interpolating fields. One of the challenges of loop corrections to QCD
correlation functions in conventional approaches is the renormalization-induced
mixing of composite operators. This involves a multi-step process of first
renormalizing the operators, and then calculating the correlation functions in
this mixed basis. This process becomes increasingly complicated as the number
of operators mixed under renormalization increases, a situation that is
exacerbated as the operator mass dimension increases in important physical
systems such as tetraquarks, pentaquarks, and hybrids. Diagrammatic
renormalization provides an alternative to the conventional operator
renormalization approach. Diagrammatic renormalization methods are outlined and
applied to a variety of QCD sum-rule examples of increasing complexity. The
results are benchmarked, and the diagrammatic method is contrasted with the
conventional operator mixing approach. Advantages and conceptual
interpretations of the diagrammatic renormalization approach are outlined and
technical subtleties are explored.
