Static QCD potential at r<{lambda}{sub QCD}{sup -1}: Perturbative expansion and operator-product expansion
- Department of Physics, Tohoku University, Sendai, 980-8578 (Japan)
We analyze the static QCD potential V{sub QCD}(r) in the distance region 0.1 fm < or approx. r < or approx. 1 fm using perturbative QCD and operator-product expansion (OPE) as basic theoretical tools. We assemble theoretical developments up to date and perform a solid and accurate analysis. The analysis consists of three major steps: (I) We study large-order behavior of the perturbative series of V{sub QCD}(r) analytically. Higher-order terms are estimated by large-{beta}{sub 0} approximation or by renormalization group, and the renormalization scale is varied around the minimal-sensitivity scale. A 'Coulomb'+linear potential can be identified with the scale-independent and renormalon-free part of the prediction and can be separated from the renormalon-dominating part. (II) In the frame of OPE, we define two types of renormalization schemes for the leading Wilson coefficient. One scheme belongs to the class of conventional factorization schemes. The other scheme belongs to a new class, which is independent of the factorization scale, derived from a generalization of the Coulomb+linear potential of (I). The Wilson coefficient is free from IR renormalons and IR divergences in both schemes. We study properties of the Wilson coefficient and of the corresponding nonperturbative contribution {delta}E{sub US}(r) in each scheme. (III) We compare numerically perturbative predictions of the Wilson coefficient and lattice computations of V{sub QCD}(r) when n{sub l}=0. We confirm either correctness or consistency (within uncertainties) of the theoretical predictions made in (II). Then we perform fits to simultaneously determine {delta}E{sub US}(r) and r{sub 0}{lambda}{sub MS}{sup 3-loop} (relation between lattice scale and {lambda}{sub MS}). As for the former quantity, we improve bounds as compared to the previous determination; as for the latter quantity, our analysis provides a new method for its determination. We find that (a) {delta}E{sub US}(r)=0 is disfavored, and (b) r{sub 0}{lambda}{sub MS}{sup 3-loop}=0.574{+-}0.042. We elucidate the mechanism for the sensitivities and examine sources of errors in detail.
- OSTI ID:
- 21023919
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 76, Issue 11; Other Information: DOI: 10.1103/PhysRevD.76.114009; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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