Interactions fortunately the cvc hypothesis allows us

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Unformatted text preview: st that: p n F1 ðq2 Þ ¼ F1 ðq2 Þ À F1 ðq2 Þ; p n F2 ðq2 Þ ¼ F2 ðq2 Þ À F2 ðq2 Þ: n;p n;p Here F1 and F2 are known in the literature as the electromagnetic Dirac and Pauli form factors of the proton and neutron, respectively. In the limit of zero-momentum transfer, the Dirac form factors reduce to the charge of the nucleon, while the Pauli form factors reduce to the nucleon’s magnetic moments  1 if proton; N F1 ð0Þ ¼ qN ¼ 0 if neutron; 8 < p À 1 if proton; N F2 ð0Þ ¼ N  : n if neutron: N Here qN is the nucleon charge, N is the nuclear magneton, and p;n are the proton and neutron magnetic form factors. To ascertain the q2 dependence of these form factors, it is common to use the Sachs electric and magnetic form factors N N and relate them back to F1 and F2 , 1317 fV ð0Þ  F1 ð0Þ ¼ 1; p À n À 1 ’ 3:706; fP ð0Þ  F2 ð0Þ ¼ N fA ð0Þ  FA ð0Þ ¼ ÀgA ; with   fA ð0Þ=fV ð0Þ  À1:2694 Æ 0:0028, as before (Nakamura, K. et al., 2010). The above represents an approach that works quite well when the final states are simple, for example, when one is dealing with a few-nucleon system with no strong bound states or when the momentum exchange is very high (see the next section on quasielastic interactions). Seminal articles on neutrino (and electron) scattering can be found in earlier review articles by Donnelly et al. (1974), Donnelly and Walecka (1975), Donnelly and Peccei (1979), and Peccei and Donnelly (1979). Peccei and Donnelly equate the relevant form factors to those measured in ðe; e0 Þ scattering (Drell and Walecka, 1964; de Forest Jr. and Walecka, 1966), removing some of the model dependence and q2 restrictions prevalent in certain techniques. This approach is not entirely model independent, as certain axial form factors are not completely accessible via electron scattering. This technique has been expanded in describing neutrino scattering at much higher energy scales (Amaro et al., 2005, 2007) with the recent realization that added nuclear effects come into play (Amaro et al., 2011b). N N GN ðq2 Þ ¼ F1 ðq2 Þ À F2 q2 Þ; E E. Estimating fermi and Gamow-Teller strengths N N GN ðq2 Þ ¼ F1 ðq2 Þ þ F2 ðq2 Þ; M with   Àq2 =4MN and Gp ðq2 Þ ¼ GD ðq2 Þ; Gn ðq2 Þ ¼ 0; E E p  GD ðq2 Þ; Gn ðq2 Þ ¼ n GD ðq2 Þ: Gp ðq2 Þ ¼ M M N N Here GD ðq2 Þ is a dipole function determined by the charge radius of the nucleon. Empirically, the dipole term can be written as   q2 À1 ; (42) G D ð q2 Þ ¼ 1 À 2 mV where mV ’ 0:84 MeV. We now turn our attention to the axial portion of the current, where the terms FA ðq2 Þ and FP ðq2 Þ play a role. For FA ðq2 Þ, one also often assumes a dipolelike behavior, but with a different coupling and axial mass term (mA ) FA ðq2 Þ ¼ ÀgA GA ðq2 Þ; GA ðq2 Þ ¼ 1 : ð1 À q2 =m2 Þ2 A The Goldberger-Treiman relation allows one to also relate the pseudoscalar contribution in terms of the axial term as well; typically F...
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