Radiative transitions of χcJ→ ψγ and χbj→ Υγ

• Published in: The journal of high energy physics 2024-08, Vol.2024 (8), p.191-27, Article 191
• Main Authors: Pei, Su-Yan, Li, Wei, Wang, Tianhong, Wang, Guo-Li
• Format: Article
• Language: English
• Subjects: Approximation; Bethe-Salpeter equation; Classical and Quantum Gravitation; Elementary Particles; Particle decay; Physics; Physics and Astronomy; Properties of Hadrons; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quarkonium; Quarks; Regular Article - Theoretical Physics; Relativistic effects; Relativity Theory; String Theory; Wave functions
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2024)191

A bstract 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 → γ Υ ( 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 (2 P ) → γψ (1 S ) ( 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 (2 P ) → γ Υ(1 S ). The decay of χ cJ (2 P ) → γψ can be used to distinguish between χ c 0 (3860) and χ c 0 (3915), which particle is the charmonium χ c 0 (2 P ). Although our result of χ c 1 (3872)→ γψ (2 S ) is consistent with data, but the one of χ c 1 (3872)→ γψ (1 S ) is much larger than data, so whether χ c 1 (3872) is the conventional χ c 1 (2 P ) remains an open question. The undiscovered Υ(1 D ) and Υ(2 D ) have large production rates in decays of χ b 0 (2 P ) → γ Υ(1 D ) and χ bJ (3 P ) → γ Υ(2 D ) ( J = 0, 1), respectively. To search for χ bJ (3 P ) ( J = 0, 1, 2), the most competitive channels are the decays χ bJ (3 P ) → γ Υ(3 S ). And the best way to find χ b 2 (1 F ) is to search for the decay of χ b 2 (1 F ) → γ Υ(1 D ).