Understanding the QCD Sum Rule: What is it and How Does it Work?

[Nixom]

i just wonder why we call it "sum rule"?

what do we sum, and what sum for?

 

[vanhees71]

This comes from the historical origin of sum rules in the early days of quantum theory. It's summed over energy levels. The first sum rules where the Thomas-Reiche-Kuhn and the Bethe sum rules. It's nicely described in Wikipedia,

http://en.wikipedia.org/wiki/Sum_rule_in_quantum_mechanics

 

[Meir Achuz]

Although 'sum rule' was originally a sum over discrete eigenstates, the term is also used to describe integrals over continuous spectra.

 

[tom.stoer]

In deep inelastic scattering one derives sum rules from structure Functions F(x,Q²) integrating over x where x is the fraction of the nucleon momentum carried by the scattering quark. So sum rules give us e.g. the fraction of energy, spin, etc. of the nucleon carried e.g. by a specific quark flavour.

 

[Nixom]

thanks, all guys