Radiative transitions of χ cJ → ψγ and χ bj → Υγ

Abstract

Abstract In the framework of instantaneous Bethe-Salpeter equation, according to the J PC of quarkonia, we find that their wave functions all contain multiple partial waves, rather than pure waves. In the radiative electromagnetic transitions χ cJ →γψ and χ bJ →γΥ (J = 0, 1, 2), the main wave of quarkonium gives the non-relativistic contribution, while other waves provide the relativistic corrections. Our results indicate that the relativistic effect of charmonium, especially highly excited states, is significant. Such as the relativistic effects of χ cJ (2P) → γψ(1S) (J = 0, 1, 2) are {49.7%, 30.9%, 37.5%}, much larger than the corresponding {17.8%, 7.08%, 12.9%} of χ bJ (2P) → γΥ(1S). The decay of χ cJ (2P) → γψ can be used to distinguish between χ c0(3860) and χ c0(3915), which particle is the charmonium χ c0(2P). Although our result of χ c1(3872)→γψ(2S) is consistent with data, but the one of χ c1(3872)→γψ(1S) is much larger than data, so whether χ c1(3872) is the conventional χ c1(2P) remains an open question. The undiscovered Υ(1D) and Υ(2D) have large production rates in decays of χ b0(2P) → γΥ(1D) and χ bJ (3P) → γΥ(2D) (J = 0, 1), respectively. To search for χ bJ (3P) (J = 0, 1, 2), the most competitive channels are the decays χ bJ (3P) → γΥ(3S). And the best way to find χ b2(1F) is to search for the decay of χ b2(1F) → γΥ(1D).

Keywords

• Properties of Hadrons
• Quarkonium