Quarkonium spectroscopy and perturbative QCD: a new perspective

Abstract

We study the energy spectrum of bottomonium in perturbative QCD, taking α s (M Z ) = 0.1181 ± 0.0020 as input and fixing m MS b (m MS b ) on the Υ(1S) mass. Contrary to wide beliefs, perturbative QCD reproduces reasonably well the gross structure of the spectrum as long as the coupling constant remains smaller than one. We perform a detailed analysis and discuss the size of non-perturbative effects. A new qualitative picture on the structure of the bottomonium spectrum is provided. The lowest-lying cc and bc states are also examined. * The full formula up to O(α 4 s m) for the S state spectrum was derived in [7] and later confirmed in [9]; additional corrections necessary for the spectrum of l ≥ 1 states can be found in [16]; the formula for the unequal mass case was derived in [21].

Improved perturbative QCD approach to the bottomonium spectrum

“…6. We see that with respect PSfrag replacements PSfrag replacements to the treatment in [2], the support functions are shifted slightly towards higher momentum. This is reasonable, since the wave functions calculated here are peaked closer to the origin in coordinate space than the Coulomb wave functions (see e.g.…”

“…2,3. The c-quark MS mass is taken as m c = 1.243 GeV [2]. We will explain how we fix m b in our analysis below.…”

“…In [2,3] the scale µ = µ ψ for each quarkonium state | ψ was fixed by minimizing the µ-dependence of each energy level calculated in a fixed-order perturbative expansion (minimalsensitivity prescription). The scale fixed in this way turns out to represent the physical size of the corresponding quarkonium state fairly well.…”

“…This is the fixed-order formula used in [2,3]. In this formula, the Coulomb wave function | ψ C is used to compute the expectation value.…”

Neural network parametrization of the lepton energy spectrum in semileptonic B meson decays

“…The b quark mass has been determined using different techniques, like the sum rule approach, using either non-relativistic [34,35,37,38] or relativistic [39,40] sum rules, global fits of moments of differential distributions in B decays, [28,33,41], the renormalon analysis of Ref. [42], and several other methods related to heavy-quarkonium physics [43,44] (see [45] for a review). To compare our results with some of the above references, it is useful to relate the m 1S b mass to the MS-barm b (m b ) mass [35,46], and once the conversion is performed 6 the valuē…”