Can Nonrelativistic QCD Explain theγγ*→ηcTransition Form Factor Data?

Abstract

Unlike the bewildering situation in the γγ * → π form factor, a widespread view is that perturbative QCD can decently account for the recent BaBar measurement of γγ * → ηc transition form factor. The next-to-next-to-leading order (NNLO) perturbative correction to the γγ * → η c,b form factor, is investigated in the NRQCD factorization framework for the first time. As a byproduct, we obtain by far the most precise order-α 2 s NRQCD matching coefficient for the η c,b → γγ process. After including the substantial negative order-α 2 s correction, the good agreement between NRQCD prediction and the measured γγ * → ηc form factor is completely ruined over a wide range of momentum transfer squared. This eminent discrepancy casts some doubts on the applicability of NRQCD approach to hard exclusive reactions involving charmonium.

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.…”

“…It was found in refs. [13,19] that the choice of factorization scale µ Λ = 1 GeV results in a better convergence in perturbative expansion rather than the conventional choice of µ Λ = m c for charmonium. We find this conclusion still holds for γ+η c exclusive production, and hence µ Λ = 1 GeV is adopted in our numerical evaluation.…”

“…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.…”

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

“…Although each of the four cut topologies contains IR divergences as severe as ǫ −4 , miraculously, only a single IR pole survives in their sum. Intriguingly, the coefficient of the single pole, to an exquisitely high numerical precision, can be identified with what was encountered in the NNLO correction to Γ(η c → γγ) [15,16].…”

“…To date, perturbative calculations beyond NLO have been conducted only for a few exclusive processes involving quarkonium, exemplified by O(α 2 s ) corrections to Υ(J/ψ) → e + e − [11,12] (Notice the O(α 3 s ) coefficients were also available recently [13,14]), η b,c → γγ [15,16], χ c0,2 → γγ [17], and B c → ℓν [18,19], as well as the O(α 2 s ) correction to the γγ * → η c,b transition form factor [16]. Only two-loop virtual corrections are required in calculating these hard matching coefficients, since they correspond to exclusive quarkonium decays or productions.…”