How Do QCD Sum Rules Calculate Hadron Properties?

[BuckeyePhysicist]

What is QCD sum rule(s)?

 

[Meir Achuz]

A QCD sum rule is an integral, usually from x=0 to x=1(Bjorken), of something (e.g. spin projection), Usually some PQCD conjecture implies a particular value for the integral. One difficulty is getting to x=0 experimentally. Another is what corrections to the conjecture do to the sum rule.

 

[sir-pinski]

QCD sum rules, or Quantum Chromodynamics sum rules, are a theoretical framework in particle physics that allows for the calculation of properties of hadrons (particles made up of quarks and gluons) using the fundamental theory of the strong interaction, Quantum Chromodynamics (QCD).

The basic idea behind QCD sum rules is to relate the properties of hadrons, such as their masses and decay rates, to the behavior of QCD at short distances, where perturbation theory can be applied. This is achieved by using a mathematical technique known as operator product expansion (OPE), which decomposes the QCD correlation functions into a series of terms with increasing powers of the strong coupling constant, alpha_s.

By equating the OPE with a phenomenological representation of the correlation function, known as the hadronic representation, one can extract information about the hadron properties from the QCD parameters. This is known as the QCD sum rule, and it allows for the calculation of hadron properties in terms of QCD parameters, such as the quark masses and the strong coupling constant.

There are various types of QCD sum rules, including the Borel sum rules, the finite energy sum rules, and the Laplace sum rules. Each of these methods has its own advantages and limitations, and they are used to study different aspects of hadron properties.

In summary, QCD sum rules are a powerful tool in theoretical particle physics that allow for the calculation of hadron properties from the fundamental theory of the strong interaction, QCD. They have been successfully used to study a wide range of phenomena, from the properties of individual hadrons to the behavior of the strong interaction at high energies.