Effects Of Two-photon Process On Charmonia Production In E~+e~-Anihilation

Using the non-relactivistic quantum chromdynamics (NRQCD) factorization formalism,we calculate the exclusive (including e ⁺e ^-→ψ(nS)+ηc(mS), e ⁺e ^-→ψ(nS)+χ _cJ(mP), e ⁺e ^-→η c(nS)+ηc(mS), e ⁺e ^-→ηc(nS)+χ _cJ(mP), e ⁺e ^-→χ_cJ(nP)+χ _cJ(mP)) and inclusive (including e +e ^-→η c(nS)+ cc ) production for S-wave P-wave charmonia with C=+ via double cc through two photons in electron-positron annihilation at s = 10.6GeV.For the exclusive process,the only way of production for double charmonia with C=+ is by two-photon process,because the photon has the quantum number J PC= 1- -.Thus cross section of double charmonia with C=+ is suppessed.Charmoia with C=+ associated with a C=- charmoia can product by one virtual photon,but two-ponton process can give a considerable correction for single photon process.In the inclusive process,the contribution involving double virtual photons are suppessed by a factor ofα2 /αS2 compared to the process involving one virtual photon.But the crossing items between the amplitude of the double photons process and that of one photon process may be suppessed by a factor ofα/αs.So the double photons process is needed to calculate.Besides,we calculate the production for S-wave P-wave charmonia with C=+ associated lepton pair (μ +μ - andÏ„⁺Ï„ -) and light hadrons.The calculating result implicates that the theoretical correction of two-photon process enhance the cross section given by one^-photon process about 16.7% in e ⁺e ^-→ψ(nS)+η_c(mS) at s = 10.6GeV,.and about 10.1% in e ⁺e ^-→ψ(nS)+χc1 (mP),5.5% in e ⁺e ^-→ψ(nS)+χ_c2 (mP).Exclusive production rate of double charmonia with C=+ is tiny and negligible.Cross section for production of charmoia with C=+ associated lepton pair or light hadrons is also small,but it's still expected to be observed by experiment.