Exclusive decay of P-wave Bottomonium into double J/ψ

We calculate the order-v^2 relativistic correction of J/ψ, including electromagnetic correction, to χ_{bJ}-> J/ψJ/ψ, in the framework of NRQCD factorization formula. The relativistic order-v^2 effect is found to increase the lower-order prediction for the decay width by about 10%, while the electromagnetism contribution is very small about 0.2% for χ_{b0} and χ_{b2}. The total branching ratios are predicted to be of order 10^{-5} for χ_{b0,b2}-> J/ψJ/ψ, but 10^{-11} for χ_{b1}-> J/ψJ/ψ, since there is only electromagnetism contribution in this channel. We predict it is possible to observe these reactions in LHC. Finally, we estimate the decay width and branch ratio of χ_{cJ}-> ωω,ϕϕ) in the constituent quark model by our formula at the leading-order of relativistic correction and electromagnetic correction. The obtained branch ratio of χ_{c0,2}-> ϕϕis in agreement with the experimental measurement in the order of magnitude.

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