Two-Loop Static QCD Potential for General Colour State

In this letter, we extend the known results for the QCD potential between a static quark and its antiquark by computing the two-loop corrections to the colour-octet state. PACS numbers: 12.38.Bx, 12.38.-t The QCD potential between a static quark and its antiquark has for a long time been used as a probe of the fundamental properties of the strong interactions such as asymptotic freedom and confinement [1]. Historically, the potential for a quark-antiquark pair in the colour-singlet state attracted the most attention because it is a basic ingredient in the theory of heavy quarkonium and, therefore, of primary phenomenological interest. Nowadays, however, there is growing interest in its colour-octet counterpart. The latter naturally appears in effective-theory calculations of high-order corrections to the heavyquarkonium spectrum and decay rates through the so-called ultrasoft contribution [2]. Moreover, it determines the properties of glueballinos and is necessary for the analysis of gluino-antigluino threshold production [3,4]. It is also used in lattice QCD for studying the behavior of strong interactions at long distances and the interplay between perturbative and non-perturbative physics [3]. This requires knowledge of the corresponding perturbative corrections which, in contrast to the colour-singlet case, are not available beyond one loop. In the present letter, we fill this gap and compute the O(α s) correction to the colour-octet static potential. The perturbative expansion of the colour-singlet potential reads V (|q|) = − 4πCFαs(|q|) q [ 1 + αs(|q|) 4π a1 + (