Two-Loop QCD Corrections to the Heavy Quark Pair Production Cross Section ine+e−Annihilation near Threshold

Abstract

We present the O(α 2 s ) corrections to the cross section for the reaction e + e − → γ * → QQ in the energy region close to the threshold. We assume that the energy of the reaction is such that both the perturbative expansion in the strong coupling constant α s and expansion in the velocity β of the heavy quarks can be used. We explicitly obtain terms O(α 2 s /β 2 , α 2 s /β, α 2 s ) in the relative correction to the threshold cross section. Using the ideas of asymptotic expansions, we demonstrate how an expansion of Feynman diagrams in the threshold region is constructed. From this analysis we obtain a matching relation between the vector current in full QCD and the quark-antiquark current in NRQCD at leading order in 1/m and the second order in the strong coupling constant.Theoretical predictions for the cross section of the reaction e + e − → QQ in the energy region close to the QQ threshold are of considerable interest for various phenomena. They are important for determinations of the b and c quark masses, as well as the value of the QCD coupling constant α s (µ), with µ ∼ 1 − 2 GeV, if one uses the sum rule approach for Υ and J/ψ hadrons proposed in [1]; achievement of the O(α 2 s ) accuracy is considered very important for these quantities. One should also mention the ongoing efforts to determine the decay rates of the heavy quarkonia to leptons with the O(α 2 s ) accuracy [2]. Also, for the future e + e − or µ + µ − colliders one is considering precision measurements of the top quark properties by studying its threshold production region. It is well known that for these and other applications, where the threshold region is of interest, the fixed order perturbative calculations break down and a resummation of the terms singular at threshold is mandatory. In the leading order, such resummation yields the well known Sommerfeld-Sakharov factor for the threshold production cross section. Aiming at the O(α 2 s ) accuracy for the threshold cross section, the first thing to be calculated is the perturbative expression for the cross 1

Electroweak production of top-quark pairs ine+e−annihilation at NNLO in QCD: The vector current contributions

“…(49) are denoted by "C F ", "C A ", "N l ", and "N h " respectively in the following figures and discussions. Analytical results for R (2) are presented for production near threshold [8,9] or in the high-energy expansions [16,17] with which we compare our numerical results. Note that for the O(α 2 s ) results on inclusive cross sections or R (2) in below we include the real corrections with four top-quark final states, which are also present in above calculations of high-energy expansions.…”

“…Fig. 3 shows detailed comparison of our numerical results with the threshold [8,9] and high-energy expansion results [16,17] in a wide range of energy. The cut-off parameter is chosen as δ E = 2 × 10 −4 .…”

Reconstruction of heavy quark current correlators at

“…The O(α 2 s ) matching coefficients are derived in Ref. [46,47] for the vector current (see also Refs. [48,49]), and in Ref.…”

Heavy quark pair production near threshold with potential non-relativistic QCD

“…It is essential to manipulate the potential consistently in D dimensions, since it allows us to use the same hard matching coefficients defined in the MS-scheme obtained in Refs. [36,37]. We then bring the potential in a form that is more suitable to be combined with the RGI coefficients as presented in Ref.…”