Next-to-Next-to-Leading-Order QCD Corrections to the Hadronic Width of Pseudoscalar Quarkonium

Abstract

We compute the next-to-next-to-leading order (NNLO) QCD corrections to the hadronic decay rates of the pseudoscalar quarkonia, at the lowest order in velocity expansion. The validity of NRQCD factorization for inclusive quarkonium decay process, for the first time, is verified to relative order α 2 s . As a byproduct, the renormalization group equation (RGE) of the leading NRQCD 4-fermion operator O1( 1 S0) is also deduced to this perturbative order. By incorporating this new piece of correction together with available relativistic corrections, we find that there exists severe tension between the state-of-the-art NRQCD predictions and the measured ηc hadronic width, and in particular the branching fraction of ηc → γγ. NRQCD appears to be capable of accounting for η b hadronic decay to a satisfactory degree, and our most refined prediction is Br(η b → γγ) = (4.8 ± 0.7) × 10 −5 . Heavy quarkonium decay has historically played a preeminent role in establishing asymptotic freedom of QCD [1,2]. Due to the nonrelativistic nature of heavy quark inside a quarkonium, the decay rates are traditionally expressed as the squared bound-state wave function at the origin multiplying the short-distance quarkantiquark annihilation decay rates. With the advent of the modern effective-field-theory approach, the nonrelativistic QCD (NRQCD), this factorization picture has been put on a firmer ground, and one is allowed to systematically include the QCD radiative and relativistic corrections when tackling various quarkonium decay and production processes [3].

NNLO QCD corrections to γ + η c (η b ) exclusive production in electron-positron collision

“…In recent years, at the NNLO level many calculations are performed for quarkonium production and decays [16][17][18]. It is interesting to note that in recently, the NNLO corrections to γγ * → η c (η b ) transition form factor and η c (η b ) → light hardrons were calculated numerically [19,20]. Numerical calculation is an unique and promising way for higher order radiative corrections, nevertheless right now it experiences the shortage of proper numerical packages, especially for the kinematics in physical region.…”

“…The bottom quark mass first takes the value in MS scheme, i.e. m b (m b ) = 4.18 GeV in PDG [39], and then converts to the 2-loop pole mass m b = 4.78 GeV [19,20]. In order to evaluate the bottom-quark-mass dependence of the final result, in our numerical calculation the bottom quark mass varies from 4.7 to 4.8 GeV.…”

Inclusive decays of ηc and ηb at NNLO with large nfBrambilla1, Chung2, Komijani3 2018Phys. Rev. D100140View full textAdd to dashboardCite

“…[9,10], and the corrections at next-to-next-to-leading order (NNLO) in α s have been calculated recently in Ref. [11]. The SDC 2 Im[g 1 ( 1 S 0 )/m 4 ] at LO in α s has been computed in Ref.…”

“…We can combine our results for R Resum with fixed-order calculations of R, so that the corrections at NLO and NNLO in α s are valid beyond the large n f limit. By using the expressions for Γ η Q and Γ η Q →γγ valid to NNLO in α s , we obtain [11,15,16]…”

“…The large n f limit of R (2) is given in Ref. [11] as lim n f →∞R (2) /n 2 f = 0.37581 (3). The full n f dependence ofR (2) can be obtained from Refs.…”