Factorization and NLO QCD correction in e^+ e^- \to J/ψ(ψ(2S))+ χ_{c0} at B Factories}

Abstract

In nonrelativistic QCD (NRQCD), we study $e^+ e^- \to J/ψ(ψ(2S)) +χ_{c0}$ at $B$ factories, where the P-wave state $χ_{c0}$ is associated with an S-wave state $J/ψ$ or $ψ(2S)$. In contrast to the failure of factorization in most cases involving P-wave states, e.g. in B decays, we find that factorization holds in this process at next to leading order (NLO) in $α_s$ and leading order (LO) in $v$, where the associated S-wave state plays a crucial rule in canceling the infrared (IR) divergences. We also give some general analyses for factorization in various double charmonium production. The NLO corrections in $e^+ e^- \to J/ψ(ψ(2S)) +χ_{c0}$ at $\sqrt{s}=10.6$ GeV are found to substantially enhance the cross sections by a factor of about 2.8; hence crucially reduce the large discrepancy between theory and experiment. With $m_c=1.5{\rm GeV}$ and $μ=2m_c$, the NLO cross sections are estimated to be $17.9(11.3)$ fb for $e^+ e^- \to J/ψ(ψ(2S))+ χ_{c0}$, which reach the lower bounds of experiment.

Figures (4)

• Figure 1: Two of four Born diagrams for $e^- e^+ \to J/\psi \chi_{c0}$.
• Figure 2: Twelve of the twenty-four box and pentagon diagrams for $e^-(k_1) e^+ (k_2)\to J/\psi(2p_1) \chi_{c0}(2p_2)$. Two upper charm legs are for $J/\psi$ while two lower ones for $\chi_{c0}$.
• Figure 3: Half of the diagrams for one-loop virtual IR corrections with two charm quark pairs $c(p_1) \bar{c} (p_1')$ and $c(p_2+q) \bar{c} (p_2-q)$. The other two diagrams can be obtained by replacing $c(p_1)$ with $\bar{c} (p_1')$.
• Figure 4: Cross sections of $e^+ e^-\to J/\psi +\chi_{c0}$ as functions of the renormalization scale $\mu$.