Abstract
In this paper, we present a detailed next-to-leading-order (NLO) study of J/ψ angular distributions in e+e−→ J/ψ + ηc, χcJ (J = 0, 1, 2) within the nonrelativistic QCD factorization (NRQCD). The numerical NLO expressions for total and differential cross sections, i.e., frac{dsigma}{dcos theta } = A + B cos2θ, are both derived. With the inclusion of the newly-calculated QCD corrections to A and B, the αθ (= B/A) parameters in J/ψ + χc0 and J/ψ + χc1 are moderately enhanced, while the magnitude of αθJ/ψ+χc2 is significantly reduced; regarding the production of J/ψ + ηc, the αθ value remains unchanged. By comparing with experiment, we find the predicted αθJ/ψ+ηc is in good agreement with the Belle measurement; however, αθJ/ψ+χc0 is still totally incompatible with the experimental result, and this discrepancy seems to hardly be cured by proper choices of the charm-quark mass, the renormalization scale, and the NRQCD matrix elements.
Highlights
Calculation formalismFollowing the NRQCD factorization, the differential cross sections of e+(p1) + e−(p2) → J/ψ(p3) + ηc, χcJ (p4) can be generally written as dσ = dσe+e−→cc[n1]+cc[n2] OJ/ψ(n1) Oηc(χcJ )(n2) ,
In this paper, we present a detailed next-to-leading-order (NLO) study of J/ψ angular distributions in e+e− → J/ψ + ηc, χcJ (J = 0, 1, 2) within the nonrelativistic
In the context of NRQCD factorization, due to the inadequate knowledge about the heavy-quarkonium production mechanism, the calculated σe+e−→J/ψ+ηc,χcJ suffer severely from the indeterminacy inherent to the nonperturbative NRQCD long distance matrix elements (LDMEs), which would significantly weaken the predictive power of NRQCD
Summary
Following the NRQCD factorization, the differential cross sections of e+(p1) + e−(p2) → J/ψ(p3) + ηc, χcJ (p4) can be generally written as dσ = dσe+e−→cc[n1]+cc[n2] OJ/ψ(n1) Oηc(χcJ )(n2) ,. Where dσe+e−→cc[n1]+cc[n2] is the perturbative calculable short distance coefficients, denoting the production of a configuration of cc[n1] intermediate state associated with cc[n2]. By neglecting the color-octet contributions, which are discovered to be trivial for the production of e+ + e− → J/ψ + ηc(χcJ ) [4], n1 =3 S11 and n2 =1 S01(3PJ1). The universal nonperturbative LDMEs OJ/ψ(n1) and Oηc(χcJ )(n2) stand for the probabilities of cc[n1] and cc[n2] into J/ψ and ηc(χcJ ), respectively. Dσe+e−→cc[n1]+cc[n2] can be further expressed as dσe+e−→cc[n1]+cc[n2] = |M|2dΠ2 = Lμν H μν dΠ2,. Where Lμν and Hμν are the leptonic and hadronic tensors, respectively, and dΠ2 is the standard two-bodies phase space
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