Search for C= plus charmonium and bottomonium states in e+e-→γ plus X at B factories

We study the production of C=+ charmonium states X in e(+)e(-)->gamma+X at B factories with X=eta(c)(nS) (n=1, 2, 3), chi(cJ)(mP) (m=1, 2), and D-1(2)(1D). In the S- and P-wave case, contributions of QED with one-loop QCD corrections are calculated within the framework of nonrelativistic QCD (NRQCD), and in the D-wave case only the QED contribution is considered. We find that in most cases the one-loop QCD corrections are negative and moderate, in contrast to the case of double charmonium production e(+)e(-)-> J/Sigma+X, where one-loop QCD corrections are positive and large in most cases. We also find that the production cross sections of some of these states in e(+)e(-)->gamma+X are larger than that in e(+)e(-)-> J/Sigma+X by an order of magnitude even after the negative one-loop QCD corrections are included. We then argue that search for the X(3872), X(3940), Y(3940), and X(4160) in e(+)e(-)->gamma+X at B factories may be helpful to clarify the nature of these states. For completeness, the production of bottomonium states in e(+)e(-) annihilation is also discussed.