Current correlators to all orders in the quark masses

Abstract

The contributions to the coefficient functions of the quark and the mixed quarkgluon condensate to mesonic correlators are calculated for the first time to all orders in the quark masses, and to lowest order in the strong coupling constant. Existing results on the coefficient functions of the unit operator and the gluon condensate are reviewed. The proper factorization of short-and long-distance contributions in the operator product expansion is discussed in detail. It is found that to accomplish this task rigorously the operator product expansion has to be performed in terms of non-normal-ordered condensates. The resulting coefficient functions are improved with the help of the renormalization group. The scale invariant combination of dimension 5 operators, including mixing with the mass operator, which is needed for the renormalization group improvement, is calculated in the leading order.

Non-perturbative determination of improvement coefficients using coordinate space correlators in Nf=2+1 lattice QCD

“…The mixed condensate [25] is usually estimated to be |⟨ ⟩| ∼ 0.8 GeV 2 |⟨ ⟩| ∼ (430 MeV) 5 [26]. To leading order the Wilson coefficient accompanying this condensate reads /2 for and but vanishes for and [19]. We conclude that all mass dependent condensate contributions are bound by a respective power of a scale Λ ≈ 400 MeV.…”

“…III below we will correct for the leading order lattice artefacts as well as for the leading 2 and 4 correction terms to Eq. (19), to broaden the window of distances where the method described can be applied.…”

“…In Sec. II we describe the general approach and define the observables arXiv:1607.07090v2 [hep-lat] 19 May 2017 that will be studied. Next, in Sec.…”

Interesting features of scalar and pseudoscalar spectral function sum rules within aU(3) chiral framework

“…[13] the second integral in the above equation vanishes in the chiral limit for all the scalar and pseudoscalar spectral functions considered in our work. Then we only need to focus on the nonperturbative dynamics of different spectral functions represented by the first integral.…”

Broad sub-continuum resonances and the case for finite-energy sum-rules

“…The linear combination (46) represents the coefficient in the "minimally-subtracted basis," which is chosen so as to avoid mass-singularities [16]. For example, in the normal-ordered basis …”