RT Journal Article
T1 Relativistic many-body Hamiltonian approach to mesons
A1 Llanes Estrada, Felipe José
A1 Cotanch, Stephen R.
AB We represent QCD at the hadronic scale by means of an effective Hamiltonian, H, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicitly broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon applications for the u, d, s and c quark flavors and compute the mass spectrum for the pseudoscalar, scalar and vector mesons. We also perform a comparative study of alternative many-body techniques for approximately diagonalizing, H: BCS for the vacuum ground state; TDA and RPA for the excited hadron states. The Dirac structure of the field theoretical Hamiltonian naturally generates spin dependent interactions, including tensor, spin-orbit and hyperfine, and we clarify the degree of level splitting due to both spin and chiral symmetry effects. Significantly, we find that roughly two thirds of the pi-rho mass difference is due to chiral symmetry and that only the RPA preserves chiral symmetry. We also document how hadronic mass scales are generated by chiral symmetry breaking in the model vacuum. In addition to the vacuum condensates, we compute meson decay constants and detail the Nambu-Goldstone realization of chiral symmetry by numerically verifying the Gell-Mann-Oakes-Renner relation.
PB Elsevier Science Bv
SN 0375-9474
YR 2002
FD 2002-01-14
LK https://hdl.handle.net/20.500.14352/58833
UL https://hdl.handle.net/20.500.14352/58833
LA eng
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NO ©2002 Elsevier Science B.V. All rights reserved.The authors are grateful for comments and discussions with P. Bicudo, J.E. Ribeiro and A. Szczepaniak. This work is supported in part by grants DOE DE-FG02-97ER41048 and NSF INT-9807009. F.J. Llanes-Estrada was a SURA-Jefferson Laboratory graduate fellowship recipient. Supercomputer time from NERSC is also acknowledged.
DS Docta Complutense
RD 11 dic 2023