Applications of Diagrammatic Renormalization Methods in QCD Sum-Rules

TL;DR

This paper explores diagrammatic renormalization techniques in QCD sum-rules, offering an alternative to traditional operator mixing methods, with applications to complex hadronic systems and benchmarking against conventional approaches.

Contribution

It introduces and applies diagrammatic renormalization methods to QCD sum-rules, demonstrating advantages over conventional operator mixing, especially for complex operators.

Findings

Diagrammatic renormalization simplifies operator mixing calculations.

The method is benchmarked and shown to be effective for complex systems.

Advantages include conceptual clarity and technical efficiency.

Abstract

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.