Instanton contribution to scalar charmonium and glueball decays

Abstract

We study instanton contributions to hadronic decays of the scalar glueball, the pseudoscalar charmonium state ${\eta }_c$, and the scalar charmonium state ${\chi }_c$. Hadronic decays of the ${\eta }_c$ are of particular interest. The three main decay channels are $K\bar{K}\pi$, $\eta \pi \pi$ and ${\eta }^{\prime }\pi \pi$, each with an unusually large branching ratio $\sim 5$. On the quark level, all three decays correspond to an instanton type vertex $(\bar{c}c)(\bar{s}s)(\bar{d}d)(\bar{u}u)$. We show that the total decay rate into three pseudoscalar mesons can be reproduced using an instanton size distribution consistent with phenomenology and lattice results. Instantons correctly reproduce the ratio $B(\pi \pi \eta )/B(\pi \pi {\eta }^{\prime })$ but over-predict the ratio $B(K\bar{K}\pi )/B(\pi \pi \eta ({\eta }^{\prime }))$. We consider the role of scalar resonances and suggest that the decay mechanism can be studied by measuring the angular distribution of decay products.

arXiv comment29 pages, added references

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Cited by in corpus (8)

• X(1835) as the Lowest Mass Pseudoscalar Glueball and Proton Spin Problem
• ${\eta }_c$ - glueball Mixing and Resonance X(1835)
• Prompt hadroproduction of ${\eta }_c(1S,2S)$ in the $k_T$-factorization approach
• Lectures on nonperturbative QCD ( Nonperturbative Topological Phenomena in QCD and Related Theories)
• Ultra-light Glueballs in Quark-Gluon Plasma
• FKS subtraction for quarkonium production at NLO
• How to observe the QCD instanton/sphaleron processes at hadron colliders?
• Instanton induced spin-spin correlations