Bethe Logarithms and Leptonic Widths in Quarkonium Decays
Explore the calculation procedure and numerical results related to Bethe logarithms and leptonic widths in quarkonium decays. The study incorporates the Lamb shift and is in collaboration with Prof. Yu Jia.
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Presentation Transcript
A tale of Bethe logarithms: leptonic widths of ???and Lamb shift arxiv: 2411.18560 In corporation with Prof. Yu Jia
Outline Introduction and motivation Calculation procedure Numerical result Summary 2
Introduction and motivation S S- -wave wave quarkonium quarkonium leptonic leptonic decay decay P P- -wave wave quarkonium quarkonium leptonic leptonic decay decay 3
Introduction and motivation ?+? ??11? ??/? ??+? ?+? ?ISR?/? ?ISR?+? ?+? ??+? ????= 210 52(4.1?) ????= 63 24(2.8?) +0.13keV ??= 0.12 0.08 Ablikim M, et al. Phys. Rev. Lett., 2022, 129(12): 122001 4
Introduction and motivation M P a m K uhn b ??0 Kuhn J H, et al, Nucl. Phys. B, 1979, 157: 125-144
Introduction and motivation ? ?3?? ? ?3?1? | ??? = | + | ? ultrasoft ? ? hard soft potential 1. 2. Deshan Yang, Shuai Zhao, Eur. Phys. J. C 72, 1996 (2012) Kivel N, Vanderhaeghen M. JHEP, 2016, 02: 032
Introduction and motivation ??? ?+? ??? ?? VS ? ?3?? ? ?3?1? ? ?3?? ? ?3?1? | ??? = | + | | ??? = | + | 1. 2. soft NRQCD static soft quark 1. 2. ultrasoft 1. Kivel N, Vanderhaeghen M. JHEP, 2016, 02: 032 1. 2. Bodwin G T, Braaten E, Lepage G P. Phys. Rev. D, 1995, 51: 1125-1171. Huang H W, Chao K T. Phys. Rev. D, 1997, 55: 244-248. 7
Introduction and motivation ultrasoft Lamb shift ~1000MHz ~ MHz Bethe Bethe Log Log 1. 2. A.Pineda, J.Soto PLB 420 1998 391 396 H. A. Bethe, Phys. Rev. 72, 339-341 (1947)
Introduction and motivation 1. 2. A.Pineda, J.Soto PLB 420 1998 391 396 H. A. Bethe, Phys. Rev. 72, 339-341 (1947) 9
Goal ??? ?+? leading Fock state High Fock State 10
Calculation procedure 1. 2. ??2 ?+? ??2 ?? ??1 ?+? ??1 ?? - 3. hard ? ?? ? ?? , , ??
Calculation procedure 1. ? ? meson loop Chao, et al, Phys. Rev. D 79, 094004 (2009) ? ? ?? 1/?? ? ? meson loop Duan, Phys. Rev. D 110, no.3, 034027 (2024) 2. S-wave
Calculation procedure ? ? ??? 3?1 ?+ Sum up Sum up
Numerical result In shark contrast In shark contrast with the Lamb shift with the Lamb shift in hydrogen atom! in hydrogen atom! 15
Numerical result Zhi Zhi- -Guo He, et al, PRD 88, 011501(R) (2013): Guo He, et al, PRD 88, 011501(R) (2013): N. Brambilla, et al, arXiv:2411.14306, N. Brambilla, et al, arXiv:2411.14306, H. Li, C. Shi, Y. Chen, et al H. Li, C. Shi, Y. Chen, et al, arXiv:2402.14541: < ??% , arXiv:2402.14541: 16
Summary P-wave High Fock State Bethe log Lamb shift Bethe log 2 ??1(2?) quarkonium X(3872) 17
