Low-lying spectrum of the Y-string three-quark potential using hyper-spherical coordinates
Апстракт
We calculate the energies of three-quark states with definite permutation symmetry (i.e. of SU(6) multiplets) in the N=0, 1, 2 shells, confined by the Y-string three-quark potential. The exact Y-string potential consists of one term, the so-called three-string term, and three angle-dependent two-string terms. Due to this technical complication we treat the problem at three increasingly accurate levels of approximation: (1) the (approximate) three-string potential expanded to first order in trigonometric functions of hyper-spherical angles; (2) the (approximate) three-string potential to all orders in the power expansion in hyper-spherical harmonics, but without taking into account the transition(s) to two-string potentials; (3) the exact minimal-length string potential to all orders in a power expansion in the hyper-spherical harmonics, and taking into account the transition(s) to two-string potentials. We show the general trend of improvement of these approximations: the exact non-per...turbative corrections to the total energy are of the order of one per cent, as compared with approximation (2), yet the exact energy differences between the [20,1(+)],[70,2(+)],[56,2(+)],[70,0(+)]-plets are shifted to 2:2:0.9, from the Bowler and Tynemouth separation rule 2:2:1, which is obeyed by approximation (2) at the one per cent level. The precise value of the energy separation of the first radial excitation (Roper) [56(),0(+)]-plet from the [70,1(-)]-plet depends on the approximation, but does not become negative, i.e. the Roper remains heavier than the odd-parity [70,1(-)]-plet in all of our approximations.
Извор:
European Physical Journal C. Particles and Fields, 2009, 62, 2, 383-397
DOI: 10.1140/epjc/s10052-009-1050-y
ISSN: 1434-6044; 1434-6052
WoS: 000267687700009
Scopus: 2-s2.0-67650046769
Колекције
Институција/група
VinčaTY - JOUR AU - Dmitrasinovic, V. AU - Sato, Toru AU - Šuvakov, Milovan PY - 2009 UR - https://vinar.vin.bg.ac.rs/handle/123456789/3737 AB - We calculate the energies of three-quark states with definite permutation symmetry (i.e. of SU(6) multiplets) in the N=0, 1, 2 shells, confined by the Y-string three-quark potential. The exact Y-string potential consists of one term, the so-called three-string term, and three angle-dependent two-string terms. Due to this technical complication we treat the problem at three increasingly accurate levels of approximation: (1) the (approximate) three-string potential expanded to first order in trigonometric functions of hyper-spherical angles; (2) the (approximate) three-string potential to all orders in the power expansion in hyper-spherical harmonics, but without taking into account the transition(s) to two-string potentials; (3) the exact minimal-length string potential to all orders in a power expansion in the hyper-spherical harmonics, and taking into account the transition(s) to two-string potentials. We show the general trend of improvement of these approximations: the exact non-perturbative corrections to the total energy are of the order of one per cent, as compared with approximation (2), yet the exact energy differences between the [20,1(+)],[70,2(+)],[56,2(+)],[70,0(+)]-plets are shifted to 2:2:0.9, from the Bowler and Tynemouth separation rule 2:2:1, which is obeyed by approximation (2) at the one per cent level. The precise value of the energy separation of the first radial excitation (Roper) [56(),0(+)]-plet from the [70,1(-)]-plet depends on the approximation, but does not become negative, i.e. the Roper remains heavier than the odd-parity [70,1(-)]-plet in all of our approximations. T2 - European Physical Journal C. Particles and Fields T1 - Low-lying spectrum of the Y-string three-quark potential using hyper-spherical coordinates VL - 62 IS - 2 SP - 383 EP - 397 DO - 10.1140/epjc/s10052-009-1050-y ER -
@article{ author = "Dmitrasinovic, V. and Sato, Toru and Šuvakov, Milovan", year = "2009", abstract = "We calculate the energies of three-quark states with definite permutation symmetry (i.e. of SU(6) multiplets) in the N=0, 1, 2 shells, confined by the Y-string three-quark potential. The exact Y-string potential consists of one term, the so-called three-string term, and three angle-dependent two-string terms. Due to this technical complication we treat the problem at three increasingly accurate levels of approximation: (1) the (approximate) three-string potential expanded to first order in trigonometric functions of hyper-spherical angles; (2) the (approximate) three-string potential to all orders in the power expansion in hyper-spherical harmonics, but without taking into account the transition(s) to two-string potentials; (3) the exact minimal-length string potential to all orders in a power expansion in the hyper-spherical harmonics, and taking into account the transition(s) to two-string potentials. We show the general trend of improvement of these approximations: the exact non-perturbative corrections to the total energy are of the order of one per cent, as compared with approximation (2), yet the exact energy differences between the [20,1(+)],[70,2(+)],[56,2(+)],[70,0(+)]-plets are shifted to 2:2:0.9, from the Bowler and Tynemouth separation rule 2:2:1, which is obeyed by approximation (2) at the one per cent level. The precise value of the energy separation of the first radial excitation (Roper) [56(),0(+)]-plet from the [70,1(-)]-plet depends on the approximation, but does not become negative, i.e. the Roper remains heavier than the odd-parity [70,1(-)]-plet in all of our approximations.", journal = "European Physical Journal C. Particles and Fields", title = "Low-lying spectrum of the Y-string three-quark potential using hyper-spherical coordinates", volume = "62", number = "2", pages = "383-397", doi = "10.1140/epjc/s10052-009-1050-y" }
Dmitrasinovic, V., Sato, T.,& Šuvakov, M.. (2009). Low-lying spectrum of the Y-string three-quark potential using hyper-spherical coordinates. in European Physical Journal C. Particles and Fields, 62(2), 383-397. https://doi.org/10.1140/epjc/s10052-009-1050-y
Dmitrasinovic V, Sato T, Šuvakov M. Low-lying spectrum of the Y-string three-quark potential using hyper-spherical coordinates. in European Physical Journal C. Particles and Fields. 2009;62(2):383-397. doi:10.1140/epjc/s10052-009-1050-y .
Dmitrasinovic, V., Sato, Toru, Šuvakov, Milovan, "Low-lying spectrum of the Y-string three-quark potential using hyper-spherical coordinates" in European Physical Journal C. Particles and Fields, 62, no. 2 (2009):383-397, https://doi.org/10.1140/epjc/s10052-009-1050-y . .