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Register a new userRenormalons in static QCD potential: review and some updates
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Authors
Hiromasa Takaura
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We give a brief review of the current understanding of renormalons of the static QCD potential in coordinate and momentum spaces. We also reconsider estimate of the normalization constant of the $u=3/2$ renormalon and propose a new way to improve the estimate.
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We investigate the $u=1/2$ [$mathcal{O}(Lambda_{rm QCD})$] and $u=3/2$ [$mathcal{O}(Lambda_{rm QCD}^3)$] renormalons in the static QCD potential in position space and momentum space using the OPE of the potential-NRQCD effective field theory. This is an old problem and we provide a formal formulation to analyze it. In particular we present detailed examinations of the $u=3/2$ renormalons. We clarify how the $u=3/2$ renormalon is suppressed in the momentum-space potential in relation with the Wilson coefficient $V_A(r)$. We also point out that it is not straightforward to subtract the IR renormalon and IR divergences simultaneously in the multipole expansion. Numerical analyses are given, which clarify the current status of our knowledge on the perturbative series. The analysis gives a positive reasoning to the method for subtracting renormalons used in recent $alpha_s(M_Z)$ determination from the QCD potential.
We derive a static potential for a heavy quark-antiquark pair propagating in Minkowski time at finite temperature, by defining a suitable gauge-invariant Greens function and computing it to first non-trivial order in Hard Thermal Loop resummed perturbation theory. The resulting Debye-screened potential could be used in models that attempt to describe the ``melting of heavy quarkonium at high temperatures. We show, in particular, that the potential develops an imaginary part, implying that thermal effects generate a finite width for the quarkonium peak in the dilepton production rate. For quarkonium with a very heavy constituent mass M, the width can be ignored for T lsim g^2 M/12pi, where g^2 is the strong gauge coupling; for a physical case like bottomonium, it could become important at temperatures as low as 250 MeV. Finally, we point out that the physics related to the finite width originates from the Landau-damping of low-frequency gauge fields, and could be studied non-perturbatively by making use of the classical approximation.
Following the procedure and motivations developed by Richardson, Buchmuller and Tye, we derive the potential of static quarks consistent with both the three-loop running of QCD coupling constant under the two-loop perturbative matching of V and MS-bar schemes and the confinement regime at long distances. Implications for the heavy quark masses as well as the quarkonium spectra and leptonic widths are discussed.
We report results on the static quark potential in two-flavor full QCD. The calculation is performed for three values of lattice spacing $a^{-1}approx 0.9, 1.3$ and 2.5 GeV on $12^3{times}24, 16^3{times}32$ and $24^3{times}48$ lattices respectively, at sea quark masses corresponding to $m_pi/m_rho approx 0.8-0.6$. An RG-improved gauge action and a tadpole-improved SW clover quark action are employed. We discuss scaling of $m_{rho}/sqrt{sigma}$ and effects of dynamical quarks on the potential.
We determine the strong coupling constant $alpha_s$ from the static QCD potential by matching a theoretical calculation with a lattice QCD computation. We employ a new theoretical formulation based on the operator product expansion, in which renormalons are subtracted from the leading Wilson coefficient. We remove not only the leading renormalon uncertainty of $mathcal{O}(Lambda_{rm QCD})$ but also the first $r$-dependent uncertainty of $mathcal{O}(Lambda_{rm QCD}^3 r^2)$. The theoretical prediction for the potential turns out to be valid at the static color charge distance $Lambda_{rm overline{MS}} r lesssim 0.8$ ($r lesssim 0.4$ fm), which is significantly larger than ordinary perturbation theory. With lattice data down to $Lambda_{rm overline{MS}} r sim 0.09$ ($r sim 0.05$ fm), we perform the matching in a wide region of $r$, which has been difficult in previous determinations of $alpha_s$ from the potential. Our final result is $alpha_s(M_Z^2) = 0.1179^{+0.0015}_{-0.0014}$ with 1.3 % accuracy. The dominant uncertainty comes from higher order corrections to the perturbative prediction and can be straightforwardly reduced by simulating finer lattices.
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