Bled Workshops in Physics Vol. 10, No. 1 p. 28

Axial charges of nucleon resonances*
Ki-Seok Choi, W. Plessas, and R.F. Wagenbrunn
Theoretical Physics, Institute of Physics, University of Graz, Universitatsplatz 5, A-8010 Graz, Austria
Recently, first results have become available from lattice quantum chromodynam-ics (QCD) for two of the nucleon excitations, namely, the negative-parity N * (1535) and N*(1650) resonances [1]. The axial charge of the nucleon ground state had been studied before by different lattice-QCD groups in quenched calculations and with dynamical quarks [2-7]. In some of these works one has used chiral extrapolations (for a recent discussion of the associated problems see Ref. [8]), and the bulk of results obtained for gA of the nucleon varies between about 1.10 - 1.40.
Lately, the issue of axial constants of N* resonances has become debated a lot due to the suggestion of chiral-symmetry restoration in the higher hadron spectra [9,10]. According to this scenario there should appear chiral doublets of positive- and negative-parity states and as a further consequence their axial charges should became small or almost vanishing. The first parity partners above the nucleon ground state are supposed to be the N*(1440)-N*(1535), the next ones the N*(1710)-N*(1650). The axial charges of the negative-parity partners in these pairs have been calculated in lattice QCD to be -0.00 and -0.55, respectively [1]; for the positive-parity states no results are yet available.
We have performed a study of the axial charges of N* resonances in the framework of the relativistic constituent quark model (RCQM). Specifically we have extended a previous investigation of the nucleon axial form factors [11,12] to the first Jp = ^ nucleon excitations. Our approach relies on solving the eigenvalue problem of the Poincare-invariant mass operator in the framework of rela-tivistic quantum mechanics. The axial current operator is chosen according to the spectator model (SM) [13]. For the RCQM we employed in the first instance the extended Goldstone-boson exchange (EGBE) RCQM [14], as it produces the most elaborate nucleon and N* wave functions.
In Table 1 we present a selection of results for the axial charges gA of the nucleon and the N*(1440), N*(1710), N*(1535), as well as N*(1650) resonances in case of the EGBE RCQM. It is immediately evident that the EGBE RCQM produces reasonable values for the axial charges in all instances without any further fittings. In the cases where a comparison is possible it produces the same pattern as lattice QCD. The gA of the nucleon and of N*(1440) are practically of the same size, with the theoretical result for the nucleon being quite close to the experi-
* Talk delivered by Ki-Seok Choi
mental value of gA=1.2695±0.0029 [15]. The nonrelativistic calculations cannot produce this value, neither in the simplistic SU(6) x O(3) quark model nor in the nonrelativistic limit of the RCQM. For the negative-parity N * (1535) resonance the gA is predicted to be compatible with 0, while for the negative-parity N*(1650) resonance it is 0.51; both cases agree with the lattice-QCD results of Ref. [1]. Accidentally, the gA value of the nonrelativistic SU(6) x O(3) quark model is similar in the N*(1650) case but the nonrelativistic limit of the EGBE RCQM shows deviations for both of the \ resonances. At this time nothing is known from lattice QCD for the j+ resonances. For the latter, it would also be most interesting to check our results against lattice QCD, and we look forward to corresponding calculations.
Table 1. Predictions for axial charges gA of the EGBE in comparison to available lattice QCD results [1-7], the values calculated by Glozman and Nefediev [9] within the SU(6) x O(3) nonrelativistic quark model, and the nonrelativistic limit from the EGBE RCQM.
State JP EGBE Lattice QCD SU(6) x O(3) QM EGBE nonrel
N(939) 1 +
1.15 1.10-1.40
1.66
1.65
N(1440) 1 + N(1535)
1.16 0.02
0.00
1.66 -0.11
1.61 -0.20
N(1710) 1 + N(1650)
0.35 0.51
0.55
0.33 0.55
0.42 0.64
It is particularly satisfying to find the RCQM predictions for the axial charges of the N*(1535) and N*(1650) resonances in agreement with the lattice-QCD results. We may thus be confident that at least for zero momentum-transfer processes the mass eigenstates of these nucleon excitations as produced especially with EGBE RCQM are quite reasonable. The latter is supposed to model the SBxS property of low-energy QCD. This type of hyperfine interaction, which also introduces an explicit flavor dependence, has been remarkably successful in describing a number of phenomena in low-energy baryon physics. Most prominently, it produces the correct level orderings of the positive- and negative-parity N* resonances and simultaneously the ones in the other hyperon spectra, notably the A spectrum. The RCQM with GBE dynamics does not have any mechanism for chiral-symmetry restoration built in. As such it cannot be expected to produce parity doublets due to this reason. Nevertheless the EGBE RCQM describes the N* resonance masses with good accuracy (mostly within the experimental error bars or at most exceeding them by 4%).
Acknowledgments K-S. C. is grateful to the organizers of the Mini-Workshop for the invitation and for creating such a lively working atmosphere. This work was supported by the Austrian Science Fund (through the Doctoral Program on Hadrons in Vacuum, Nuclei, and Stars; FWF DK W1203-N08).
References
1.	T. T. Takahashi and T. Kunihiro, Phys. Rev. D 78, 011503 (2008).
2.	D. Dolgov et al. [LHPC collaboration and TXL Collaboration], Phys. Rev. D 66, 034506 (2002).
3.	R. G. Edwards et al. [LHPC Collaboration], Phys. Rev. Lett. 96, 052001 (2006).
4.	A. A. Khan et al, Phys. Rev. D 74, 094508 (2006).
5.	T. Yamazaki et al. [RBC+UKQCD Collaboration], Phys. Rev. Lett. 100,171602 (2008).
6.	H. W. Lin, T. Blum, S. Ohta, S. Sasaki and T. Yamazaki, Phys. Rev. D 78, 014505 (2008).
7.	C. Alexandrou etal, PoS(LATTICE 2008), 139 (2008); arXiv:0811.0724 [hep-lat].
8.	V. Bernard, Prog. Part. Nucl. Phys. 60, 82 (2008).
9.	L. Y. Glozman, Phys. Rept. 444, 1 (2007).
10.	L. Y. Glozman and A. V. Nefediev, Nucl. Phys. A 807, 38 (2008).
11.	L. Y. Glozman, M. Radici, R. F. Wagenbrunn, S. Boffi, W. Klink and W. Plessas, Phys. Lett. B 516,183 (2001).
12.	S. Boffi, L. Y. Glozman, W. Klink, W. Plessas, M. Radici and R. F. Wagenbrunn, Eur. Phys. J. A 14,17(2002).
13.	T. Melde, L. Canton, W. Plessas and R. F. Wagenbrunn, Eur. Phys. J. A 25, 97 (2005).
14.	K. Glantschnig, R. Kainhofer, W. Plessas, B. Sengl and R. F. Wagenbrunn, Eur. Phys. J. A 23, 507 (2005).
15.	C. Amsler et al. [Particle Data Group], Phys. Lett. B 667,1 (2008).