Isospin Mixing in the Nucleon andHe4and the Nucleon Strange Electric Form Factor

M. Viviani, R. Schiavilla, B. Kubis, R. Lewis, L. Girlanda, A. Kievsky, L. E. Marcucci, S. Rosati
2007 Physical Review Letters  
In order to isolate the contribution of the nucleon strange electric form factor to the parityviolating asymmetry measured in 4 He( e, e ′ ) 4 He experiments, it is crucial to have a reliable estimate of the magnitude of isospin-symmetry-breaking (ISB) corrections in both the nucleon and 4 He. We examine this issue in the present letter. Isospin admixtures in the nucleon are determined in chiral perturbation theory, while those in 4 He are derived from nuclear interactions, including explicit
more » ... ncluding explicit ISB terms. A careful analysis of the model dependence in the resulting predictions for the nucleon and nuclear ISB contributions to the asymmetry is carried out. We conclude that, at the low momentum transfers of interest in recent measurements reported by the HAPPEX collaboration at Jefferson Lab, these contributions are of comparable magnitude to those associated with strangeness components in the nucleon electric form factor. PACS numbers: 14.20.Dh,25.30.Bf,12.15.Ji One of the challenges of modern hadronic physics is to determine, at a quantitative level, the role that quarkantiquark pairs, and in particular ss pairs, play in the structure of the nucleon. Parity-violating (PV) electron scattering from nucleons and nuclei offers the opportunity to investigate this issue experimentally. The PV asymmetry (A P V ) arises from interference between the amplitudes due to exchange of photons and Z-bosons, which couple respectively to the electromagnetic (EM) and weak neutral (NC) currents. These currents involve different combinations of quark flavors, and therefore measurements of A P V , in combination with electromagnetic form factor data for the nucleon, allow one to isolate, in principle, the electric and magnetic form factors G s E and G s M , associated with the strange-quark content of the nucleon. Experimental determinations of these form factors have been reported recently by the Jefferson Lab HAPPEX [1] and G0 [2] Collaborations, Mainz A4 Collaboration [3], and MIT-Bates SAMPLE Collaboration [4]. These experiments have scattered polarized electrons from either unpolarized protons at forward angles [1, 2, 3] or unpolarized protons and deuterons at backward angles [4]. The resulting PV asymmetries are sensitive to different linear combinations of G s E and G s M as well as the nucleon axial-vector form factor G Z A . However, no robust evidence has emerged so far for the presence of strange-quark effects in the nucleon. Last year, the HAPPEX Collaboration [5, 6] at Jefferson Lab reported on measurements of the PV asymmetry in elastic electron scattering from 4 He at four-momentum transfers of 0.091 (GeV/c) 2 and 0.077 (GeV/c) 2 . Because of the J π =0 + spin-parity assignments of this nucleus, transitions induced by magnetic and axial-vector currents are forbidden, and therefore these measurements can lead to a direct determination of the strangeness electric form factor G s E [7, 8] , provided that isospin symmetry breaking (ISB) effects in both the nucleon and 4 He, and relativistic and meson-exchange (collectively denoted with MEC) contributions to the nuclear EM and weak vector charge operators, are negligible. A realistic calculation of these latter contributions [8] found that they are in fact tiny at low momentum transfers. The goal of the present letter is to provide a quantitative estimate of ISB corrections to the PV asymmetry. In the following analysis, we only need to consider the time components of the EM current and vector part of the weak NC current-the weak vector charge referred to above [8] . We account for isospin symmetry breaking in both the nucleon and α-particle. We first discuss it in the nucleon. Ignoring radiative corrections, the EM and weak vector charge operators can be decomposed as where j (0) and j (1) are respectively the isoscalar and isovector components of the EM charge operators, j (s) is the (isoscalar) component due to strange-quark contributions, and s 2 W = sin 2 θ W contains the Weinberg mixing angle. In a notation similar to that adopted by the authors of Ref. [9], we introduce form factors corresponding to the following matrix elements of j (0) and j (1) between proton (p) and neutron (n) states:
doi:10.1103/physrevlett.99.112002 pmid:17930429 fatcat:knrwcdhip5g3jjz5alztlx6ana