Strange nucleon form factors : Solitonic approach to G sM , G s E , G̃ p A and G̃ nA and comparison with world data .
چکیده
We summarize the results of the chiral quark-soliton model (χQSM) concerning basically all form factors necessary to interpret the present data of the parity violating electron scattering experiments SAMPLE, HAPPEX, A4 and G0. The results particularly focus on the recently measured asymmetries and the detailed data for various combinations of GsM , G s E , G̃ p A and G̃ n A at Q 2 = 0.1 GeV. The calculations yield positive strange magnetic and electric form factors and a negative axial vector one, all being rather small. The results are very close to the combined experimental world data from parity violating electron scattering and elastic νpand ν̄pscattering. PACS. 1 2.40.-y, 14.20.Dh 1. The strange quark contribution to the distributions of charge and magnetization in the nucleon has been a very important issue well over decades, since it provides a vital clue in understanding the structure of the nucleon and in particular in probing the qq̄-sea. There are some indications of about 4% contribution to the momentum sum rule of deep inelastic lepton scattering, of roughly 15% to the spin of the nucleon extracted from polarized deep inelastic scattering, or of up to 30% contribution to the mass of the nucleon, where all these numbers show rather large uncertainties. Recently, the strangeness content of the nucleon has been studied particularly intensively since parity-violating electron scattering (PVES) has demonstrated to provide an essential tool for probing the sea of ss̄ pairs in the vector channel [1]. In fact, various PVES experiments have been already conducted from which the strange vector form factors can be extracted [2,3,4,5,6,7,8,9,10,11, 12]. The results from the SAMPLE, HAPPEX, PVA4, and G0 collaborations have shown evidence for a non-vanishing strange quark contribution to the structure of the nucleon. In particular, evidence was found that the strange magnetic moment of the proton is positive [11], suggesting that the strange quarks reduce the proton’s magnetic moment. This is an unexpected and surprising finding, since a majority of theoretical studies favors a negative value. One of the models, which yield a positive strange magnetic moment of the proton, is the chiral quark soliton model (χQSM). It will be used in the present paper to investigate the form factors GsM , G s E , G̃ p A and G̃ n A and to compare them with world data. Using the χQSM the present authors have recently investigated the set of six electromagnetic form factors (G E,M ) and three axial-vector ones (G A ) [19,28,29,30]. The results show a good agreement with the data of the SAMPLE, HAPPEX, A4 and G0 experiments. This includes parity violating asymmetries (PVA) which have been measured by the G0 experiment over a range of momentum transfers in the forward direction [12]. We even predicted the PVAs of the future G0 experiment at backward angles [31]. In the present contribution we perform more detailed comparison including the most recent data of the HAPPEX experiment on He-4 and the results of the PVAs combined with elastic νpand ν̄p-scattering. 2. TheχQSM has been used several times to calculate strange properties of the nucleon and of hyperons. It is an effective relativistic quark theory based on the instanton-degrees of freedom of the QCD vacuum and has been derived from QCD in the large-Nc limit. In the end it turns out to be the simplest possible quark theory which allows for spontaneously broken chiral symmetry. It results in an effective chiral action for valence and sea quarks both moving in a static self-consistent Goldstone background field [13,14,15]. For this model it is absolutely natural to have strange quark contributions to the nucleon. The χQSM has very successfully been applied to mass splittings of hyperons, to electromagnetic and axial-vector form factors [13] of the baryon octet and decuplet and to forward and generalized parton distributions of the nucleon. With one set of four parameters, unchanged for years, it reproduces all appropriate observables of light baryons with an accuracy of (10–30)%. This parameter set consists of an effective current mass for upand down quarks, a cut-off parameter in the relativistic proper-time regularization scheme, and a quark-pion coupling constant corresponding to a constituent mass. These parameters are fitted 2 K. Goeke et al.: Strange nucleon form factors to the pion decay constant, the pion mass, and baryonic properties as proton charge radius and delta-nucleon mass splitting. In addition we assume an effective current strange quark mass of 180 MeV. A numerical iteration procedure yields then the self-consistent mean field whose lowest states get occupied until baryon number B = 1 is reached. The resulting solitonic state is semiclassically rotated in space and iso-space in order to project on proper spin and hypercharge quantum numbers. As far as strange form factors are concerned the formalism used in the present investigation can be found in the paper of Silva et al. [31] and references therein. We just mention for clarity some relations between form factors, which are often differently denoted in the literature. We refer to the papers of Musolf et al. [32], of Alberico et al. [33] and of Maas et al. [7]. Altogether we have: G̃ p A = −(1 +R 1 A)G (3) A (Q ) +R A +G s A (1) G̃nA = −3(1 +R 1 A)G (3) A (Q ) +R A +G s A (2) G̃ p A = G e A = − 1