Modified Lüscher zeta-function and the modified effective range expansion in the presence of a long-range force

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Abstract
A bstract: An efficient numerical algoritm is proposed for the calculation of the modified Lüscher zeta-function in the presence of a long-range force. Using the formalism developed in ref. JHEP05(2024)168 for the analysis of synthetic data on the finite-volume energy levels in a toy model, it is demonstrated that, in contrast to the standard Lüscher approach, the truncation of the higher partial waves has very little effect on the final result. Furthermore, the regularization and renormalization of the modified Lüscher zeta-function is discussed in detail, as well as the problems arising within the cutoff regularization. It is shown that, using the renormalization scheme proposed in the present paper, one obtains modified effective range expansion parameters of natural size in all partial waves.
Funding Information
  • National Natural Science Foundation of China (12135011)
  • National Natural Science Foundation of China (12175239)
  • National Natural Science Foundation of China (12221005)
  • Deutsche Forschungsgemeinschaft (196253076 - TRR 110)
  • Deutsche Forschungsgemeinschaft (279384907 - SFB 1245)
  • Chinese Academy of Sciences (CAS) President's International Fellowship Initiative (2024VMB0001)
  • Chinese Academy of Sciences (YSBR-101)
  • German Federal Ministry of Education and Research (05P24RDB)
  • National Key R\&D Program of China (2020YFA0406400)
  • German Research Foundation (458854507 - FOR 5327)

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