UV contributions to energy of a static quark-antiquark pair in large ${\beta }_0$ approximation

Abstract

The total energy of a static quark-antiquark pair $E_{\mathrm{tot}}(r)=2m_{\mathrm{pole}}+V_{\mathrm{QCD}}(r)$ is known to be predictable up to $\mathcal{O}({\Lambda }_{\mathrm{QCD}}^3{r}^2)$ and $\mathcal{O}(\frac{{\Lambda }_{\mathrm{QCD}}^3}{{\overline{m}}^2})$ renormalon uncertainties in the large-${\beta }_0$ approximation, after canceling $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ renormalons. We compute the predictable part (genuine UV part) in terms of the $\overline{\mathrm{MS}}$ mass $\overline{m}$, extending a recently-proposed method which conforms with OPE. In particular the $r$-independent part is determined. The result would help understanding the nature of $E_{\mathrm{tot}}(r)$ in the context of OPE with renormalon subtraction.

arXiv commentVersion to appear in Physics Letters B, modification of the expression of delta_{G,0} is added; other modifications are minor, 10 pages, 4 figures

References in corpus (17)

• Effective field theories for heavy quarkonium
• A quark mass definition adequate for threshold problems
• Naive nonabelianization and resummation of fermion bubble chains
• Resummation of $({\beta }_0{\alpha }_s{)}^n$ Corrections in QCD: Techniques and Applications to the $\tau$ Hadronic Width and the Heavy Quark Pole Mass
• Determination of the bottom quark mass from the ${\rm Y}(1S)$ system
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• Quarkonia and the Pole Mass
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
• QCD potential as a "Coulomb-plus-linear" potential
• Static QCD Potential at r < 1/Lambda_QCD: Perturbative expansion and operator-product expansion
• Exploring the Invisible Renormalon: Renormalization of the Heavy-Quark Kinetic Energy
• Determination of ${\alpha }_s$ from static QCD potential with renormalon subtraction
• "Coulomb+linear" form of the static QCD potential in operator-product-expansion
• Subtracting IR Renormalons from Wilson Coefficients: Uniqueness and power dependences on ${\Lambda }_{\mathrm{QCD}}$
• UV contribution and power dependence on ${\Lambda }_{\mathrm{QCD}}$ of Adler function
• Off-shell Suppression of Renormalons in Non-relativistic QCD Boundstates
• Determination of ${\alpha }_s$ from static QCD potential: OPE with renormalon subtraction and lattice QCD

Cited by in corpus (3)

• Hyperasymptotic approximation to the top, bottom and charm pole mass
• Renormalons beyond the Borel plane
• Renormalon subtraction using Fourier transform: Analyses of simplified models