Relativistic corrections toϒexclusive decay into doubleS-wave charmonia

Abstract

Within the framework of nonrelativisitic QCD factorization formalism, we present the next-toleading-order relativistic corrections to Υ exclusive decay into η c plus J/ψ. The double charmonia can be produced through several immediate channels, i.e., Υ → g * g * g * → η c + J/ψ, Υ → g * g * γ * → η c + J/ψ, and Υ → γ * → η c + J/ψ. The amplitudes of these three channels are obtained accurate, and O(αα 2 s v 2 ), respectively, where v indicates the typical heavy quark velocity in bottomonium and/or charmonium rest frame. The decay rates are also presented. We find that the next-to-leading-order relativistic corrections to the short-distance coefficients as well as the decay rates are both significant and negative, especially for the corrections from bottomonium. More seriously, the decay rates are even brought into negative by including the relativistic corrections, which indicates the poor convergence for the velocity expansion in this kind of process. Detailed analysis is given in the paper.

Average speed and its powers $v^n$ of a heavy quark in quarkonia

“…We find that in charmonium system, see Table 1 and Table 2, the results indicate the poor convergence if we make the velocity expansion (Ref. [45] got a similar conclusion), especially for highly excited states, where the convergence is vary bad. For example, we get v J/ψ = 0.46, v 2 J/ψ = 0.26, v 3 J/ψ = 0.18 and v 4 J/ψ = 0.14, the convergence rate on the power of v is very slow, Table 3: Average values of q n and v n of bottom quark inside 0 −+ and 1 −− bottomonia, where the masses of ground 1S states are input.…”

Higher-order QCD corrections to $Υ$ decay into double charmonia

“…To date, the processes of double charmonia production from a bottomonium have been intensively studied, exemplified by η b → J/ψ + J/ψ [2][3][4][5], χ bJ → J/ψ + J/ψ [6][7][8][9][10], Υ → J/ψ + η c [11,12] and Υ → J/ψ + χ cJ [13] based on the NRQCD or light-cone factorization. On the experimental side, the Belle collaboration has collected enormous Υ(1S) and Υ(2S) samples, and for the first time, observed the process Υ(1S) → J/ψ + χ c1 with the branching fraction 3.90 ± 1.21(stat.)…”

Exclusive decay of the upsilon intohc, theX(3940)andX(Zhu1 2015Phys. Rev. D130110View full textAdd to dashboardCite

“…Double-charmonium production has attracted a large amount of attention among theorists and experimentalists in the last ten years, especially the large discrepancy between theory [7][8][9][10] and data [11,12] in the B factory, that is later solved through QCD corrections [13][14][15][16][17]. In recent years, some exclusive decay channels of bottomonium into double charmonia have been investigated intensively, e.g., Υ → J/ψ + η c [18][19][20], [29]. The branching fractions of these channels are predicted to be order from 10 −6 to 10 −8 in the above literatures.…”