Renormalization group improvement of the NRQCD Lagrangian and heavy quarkonium spectrum

Details Renormalization group improvement of the NRQCD Lagrangian and heavy quarkonium spectrum Renormalization group improvement of the NRQCD Lagrangian and heavy quarkonium spectrum

2001-09-13

arxiv.org/abs/hep-ph/0109117v2

Phys.Rev. D65 (2002) 074007

Physics

High Energy Physics

High Energy Physics - Phenomenology

16 pages, LaTeX. Minor changes. Final version

Scientific paper

10.1103/PhysRevD.65.074007

We complete the leading-log renormalization group scaling of the NRQCD Lagrangian at $O(1/m^2)$. The next-to-next-to-leading-log renormalization group scaling of the potential NRQCD Lagrangian (as far as the singlet is concerned) is also obtained in the situation $m\alpha_s \gg \Lambda_{QCD}$. As a by-product, we obtain the heavy quarkonium spectrum with the same accuracy in the situation $m\alpha_s^2 \simg \Lambda_{QCD}$. When $\Lambda_{QCD} \ll m\alpha_s^2$, this is equivalent to obtain the whole set of $O(m\alpha_s^{(n+4)} \ln^n \alpha_s)$ terms in the heavy quarkonium spectrum. The implications of our results in the non-perturbative situation $m\alpha_s \sim \Lambda_{QCD}$ are also mentioned.

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