Calculation of the quarkonium spectrum andmb,mcto order

A. Morelos Pineda

¹

,

Félix Ynduráin

²

Abstract

We include two loop, relativistic one loop and second order relativistic tree level corrections, plus leading nonperturbative contributions, to obtain a calculation of the lower states in the heavy quarkonium spectrum correct up to, and including, O(α

Heavy flavours at colliders

“…the error is already much less than Λ QCD , and to within 10% for the case of charm [24] (extracted from the charmonium spectrum).…”

Bottom quark mass from $ \varUpsilon $ sum rules to $ \mathcal{O}\left( {\alpha_s^3} \right) $

“…The first two coefficients of the series for the binding energy are well known [30] and listed in the appendix A. The third-order term can be decomposed according to the powers of the logarithm where ζ(z) is the Riemann zeta-function, ζ(3) = 1.20206 .…”

“…The first and the second-order coefficients of the series (2.15) for general n read [18,19,30,32] e (1) n = β 0 (L n + S 1 (n)) + 31 18 C A − 10 9 n l T F , (A.1) e (2) n = 3 4 β 2 0 L 2 n + β 1 4 + 3 2 S 1 (n) − 1 2 β 2 0 + 31 12 C A − 5 3 n l T F β 0 L n + S 1 (n) 4 β 1 + π 2 24 + ζ(3) 2 n − 1 2 + 1 2n S 1 (n) + 3 4 S 2 1 (n) + S 2 (n) − n 2 S 3 (n) β 2 0 + 31 12 S 1 (n) − 31 36 C A + 5 9 − 5 3 S 1 (n) n l T F β 0 + 221 54 + π 2 2 − π 4 32 + 11 12 ζ(3) C 2 A − 403 108 + 7 3 ζ(3) n l T F C A + π 2 n C F C A + 25 27 n 2 l T 2 F + 2ζ(3) − 55 24 n l T F C F + 2 3 − 11 16n…”

Improved perturbative QCD approach to the bottomonium spectrum

“…(See e.g. [11,12,13,14].) Considering an application to the bottomonium states, we assume the quark (antiquark) to be the b-quark (b-quark).…”