Rigorous QCD evaluation of spectrum and ground state properties of heavyqq¯systems, with a precision determination ofmb,M(ηb)

1993/10/06 by S. Titard, Félix Ynduráin, F. F. Yndurain · 2 citations
Mathematics · Physics and Astronomy · #Algorithm #Atomic physics #Ground state #Hadron #High-Energy Particle Collisions Research #Mathematics #Order (exchange) #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quarkonium #State (computer science) #hep-ph

paper · pdf · doi:10.1103/physrevd.49.6007

published as Phys.Rev. D49 (1994) 6007-6025 · 35 pages, preprint UM-TH 93-25

arxiv created 1993/10/06 · openalex publication_date 1994/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We present an evaluation of heavy quarkonium states bb, cc from first principles. We use tree-level QCD (including relativistic corrections) and the full one-loop potential; nonperturbative effects are taken into account at the leading order through the contribution of the gluon condensate 〈\ensuremathα_sG²〉. We use the values \ensuremathΛ(2loops,4flavors)=200_\ensuremath-60⁺⁸⁰ MeV, 〈\ensuremathα_sG²〉=0.042\ifmmode±\else\textpm\fi0.020GeV⁴, but we trade the value of the quark mass with the masses of \fracJ\ensuremathψ, \ensuremathΥ as input. We get good agreement in what is essentially a zero parameter evaluation for the masses of the 1S, 2S, 2P states of bb, the 1S state for cc, and the decay \ensuremathΥ\ensuremath→e⁺e^\ensuremath-. As outstanding results we obtain the precise determination of m_b as well as an estimate of the hyperfine splitting M(\ensuremathΥ)\ensuremath-M(\ensuremathη_b):m_b(m_b²)=4397_\ensuremath-2⁺⁷(\ensuremathΛ)₊₄^\ensuremath-3(〈\ensuremathα_sG²〉)_\ensuremath-32⁺¹⁶(syst) MeV, M(\ensuremathΥ)\ensuremath-M(\ensuremathη_b)=36_\ensuremath-7⁺¹³(\ensuremathΛ)_\ensuremath-6⁺³(〈\ensuremathα_sG²〉)_\ensuremath-5⁺¹¹(syst) MeV, the first error due to that in \ensuremathΛ, the second to that in 〈\ensuremathα_sG²〉 (varied independently). For the c quark, we find m_c(m_c²)=1306_\ensuremath-34⁺²¹(\ensuremathΛ)₊₆^\ensuremath-6(〈\ensuremathα_sG²〉) MeV (up to systematic errors). The \stackrel-MS b, c masses correspond to pole mass values of m_b(pole)=4906_\ensuremath-51⁺⁶⁹(\ensuremathΛ)₊₄^\ensuremath-4(〈\ensuremathα_sG²〉)_\ensuremath-40⁺¹¹(syst) MeV and m_c(pole)=1570_\ensuremath-19⁺¹⁹(\ensuremathΛ)₊₇^\ensuremath-7(〈\ensuremathα_sG²〉) MeV.

Citations

• Quark masses

Cited by

• MS renormalization of S-wave quarkonium wavefunctions at the origin
• QCD result for the hyperfine splittingMΥ(1S)−Mηband the value ofαs