Particle Scattering in Finite Volume

Jana, Priyajit (2025) Particle Scattering in Finite Volume. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Priyajit Jana (20MS101)) 20MS101_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (748kB)

Abstract

We investigate hadron-hadron scattering in finite volume, with a special focus on the DD� and DDs elastic scattering. We employ an effective theory-based formalism to extract DD� amplitudes, that accommodates cross channel nonanalyticities below threshold arising out of one pion exchange (OPE) process. We parametrize the short range interactions with a contact potential, whereas the long range interactions arising out of OPE are realized using a OPE potential determined using a heavy hadron chiral perturbation theory. In the infinite-volume this potential feature in the transcedental Lippmann- Schwinger Equation (LSE) for scattering amplitudes. The finite-volume data are fitted with this parameterized potentials appearing in the LSE to extract the associated low-energy constants that can reproduce the simulated finite-volume spectra. A similar approach is utilized also for DDs scattering, where the long-range interactions that are mediated by a K�-meson exchange ignored as the corresponding nonanalyticities are far from threshold. The extracted potentials are found to faithfully reproduce the finite-volume spectra. We observe the extracted amplitudes suggests an attractive interaction in the DD� scattering leading to subthreshold poles away from the threshold, and a repulsive interaction in DDs amplitudes with no resultant near-threshold poles. Lattice data with m� = 280 MeV, lattice spacing a � 0:9 fm and N = L/a = 24; 32 were utilized in this study.

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