Abstract
We propose a new finite-volume approach which implements two- and three-body dynamics in a transparent way based on an Effective Field Theory Lagrangian. The formalism utilizes a particle-dimer picture and formulates the quantization conditions based on the self-energy of the decaying particle. The formalism is studied for the case of the Roper resonance, using input from lattice QCD and phenomenology. Finally, finite-volume energy eigenvalues are predicted and compared to existing results of lattice QCD calculations. This crucially provides initial guidance on the necessary level of precision for the finite-volume spectrum.
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Acknowledgments
We thank A. Rusetsky and F. Müller for many useful discussions. This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), the NSFC through the funds provided to the Sino-German Collaborative Research Center CRC 110 “Symmetries and the Emergence of Structure in QCD” (DFG Project-ID 196253076 - TRR 110, NSFC Grant No. 12070131001). The work of UGM was further supported by VolkswagenStiftung (grant No. 93562) and by the Chinese Academy of Sciences (PIFI grant 2018DM0034). MM was further supported by the National Science Foundation under Grant No. PHY-2012289.
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Severt, D., Mai, M. & Meißner, UG. Particle-dimer approach for the Roper resonance in a finite volume. J. High Energ. Phys. 2023, 100 (2023). https://doi.org/10.1007/JHEP04(2023)100
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DOI: https://doi.org/10.1007/JHEP04(2023)100