High Energy Physics - Lattice
[Submitted on 21 May 2013 (v1), last revised 29 Aug 2013 (this version, v2)]
Title:Two-Nucleon Systems in a Finite Volume: (I) Quantization Conditions
View PDFAbstract:The quantization condition for interacting energy eigenvalues of the two-nucleon system in a finite cubic volume is derived in connection to the nucleon-nucleon scattering amplitudes. This condition is derived using an auxiliary (dimer) field formalism that is generalized to arbitrary partial waves in the context of non-relativistic effective field theory. The quantization condition presented gives access to the scattering parameters of the two-nucleon systems with arbitrary parity, spin, isospin, angular momentum and center of mass motion, from a lattice QCD calculation of the energy eigenvalues. In particular, as it includes all non-central interactions, such as the two-nucleon tensor force, it makes explicit the dependence of the mixing parameters of nucleon-nucleon systems calculated from lattice QCD when there is a physical mixing among different partial-waves, e. g. S-D mixing in the deuteron channel. We provide explicit relations among scattering parameters and their corresponding point group symmetry class eigenenergies with orbital angular momentum l smaller than or equal to 3, and for center of mass boost vectors of the form 2\pi (2n_1, 2n_2, 2n_3)/L, 2\pi (2n_1, 2n_2, 2n_3+1)/L and 2\pi (2n_1+1, 2n_2+1, 2n_3)/L. L denotes the special extent of the cubic volume and n_1,n_2,n_3 are integers. Our results are valid below inelastic thresholds up to exponential volume corrections that are governed by the pion mass.
Submission history
From: Zohreh Davoudi [view email][v1] Tue, 21 May 2013 18:15:26 UTC (504 KB)
[v2] Thu, 29 Aug 2013 07:51:49 UTC (506 KB)
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