Lüscher equation with long-range forces
Rishabh Bubna (Helmholtz-Institut für Strahlen- und Kernphysik (Theorie), and Bethe Center for Theoretical Physics, Universität Bonn, Bonn, 53115, Germany); Hans-Werner Hammer (ExtreMe Matter Institute EMMI and Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, 64291, Germany, Department of Physics, Technische Universität Darmstadt, Darmstadt, 64289, Germany); Fabian Müller (Helmholtz-Institut für Strahlen- und Kernphysik (Theorie), and Bethe Center for Theoretical Physics, Universität Bonn, Bonn, 53115, Germany); Jin-Yi Pang (College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China); Akaki Rusetsky (Tbilisi State University, Tbilisi, 0186, Georgia, Helmholtz-Institut für Strahlen- und Kernphysik (Theorie), and Bethe Center for Theoretical Physics, Universität Bonn, Bonn, 53115, Germany); et al - Show all 6 authors
We derive the modified Lüscher equation in the presence of the long-range force caused by the exchange of a light particle. It is shown that the use of this equation enables one to circumvent the problems related to the strong partial-wave mixing and the t-channel sub-threshold singularities. It is also demonstrated that the present method is intrinsically linked to the so-called modified effective-range expansion (MERE) in the infinite volume. A detailed comparison with the two recently proposed alternative approaches is provided.
