Cross sections divided by neutrino energy and plotted

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Unformatted text preview: scattering cross section, early experiments relied heavily on the formalism first written down in Llewellyn-Smith (1972). In the case of QE scattering off free nucleons, the QE differential cross section can be expressed as   d G2 M 2 sÀu ðs À uÞ2 ¼ F 2 AÆ Bþ C; (57) dQ2 M2 8E M4 where ðÀÞþ refers to (anti)neutrino scattering, GF is the Fermi coupling constant, Q2 is the squared four-momentum transfer (Q2 ¼ Àq2 > 0), M is the nucleon mass, m is the lepton mass, E is the incident neutrino energy, and s À u ¼ 4ME À Q2 À m2 . The factors A, B, and C are functions of the familiar vector (F1 and F2 ), axial-vector (FA ), and pseudoscalar (FP ) form factors of the nucleon  m2 þ Q2 2 2 2 A¼ ð1 þ ÞFA À ð1 À ÞF1 þ ð1 À ÞF2 M2  m2 þ 4F1 F2 À ðF1 þ F2 Þ2 þ ðFA þ 2FP Þ2 4M 2 2   Q 2 (58) À þ 4 FP ; M2 B¼ Q2 FA ðF1 þ F2 Þ; M2 12 2 2 C ¼ ðFA þ F1 þ F2 Þ; 4 (59) (60) where  ¼ Q2 =4M2 . Much of these equations should be familiar from Sec. IV. Historically, this formalism was used to analyze neutrino QE scattering data on deuterium, subject to minor modifications for nuclear effects. In this way, experiments studying neutrino QE scattering could in principle measure the vector, axial-vector, and pseudoscalar form factors given that the weak hadronic current contains all three of these components. In practice, the pseudoscalar contribution was typically neglected in the analysis of  QE scattering as it enters the cross section multiplied by m2 =M2 . Using CVC, the vector form factors could be obtained from electron scattering, thus leaving the neutrino experiments to measure the axial-vector form factor of the nucleon. For the axialvector form factor, it was (and still is) customary to assume a dipole form gA ; (61) FA ðQ2 Þ ¼ 2 ð1 þ Q2 =MA Þ2 which depends on two empirical parameters: the value of the axial-vector form factor at Q2 ¼ 0, gA ¼ FA ð0Þ ¼ 1:2694 Æ 0:0028 (Nakamura, K. et al., 2010), and an ‘‘axial mass’’ MA . With the vector form factors under control from electron scattering and gA determined with high precision from nuclear beta decay, measurement of the axial-vector form factor (and hence MA ) became the focus of the earliest A value of MA ¼ 1:014 Æ 0:014 GeV was obtained from a recent global fit to the deuterium data in Bodek et al. (2007), while a consistent value of MA ¼ 0:999 Æ 0:011 GeV was obtained in Kuzmin et al. (2008) from a fit that additionally includes some of the early heavy target data. 9 Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 1325 2.5 ANL, PRD 16, 3103 (1977), D GGM, NC A38, 260 (1977), C H8CF3 Br 3 2 BEBC, NP B343, 285 (1990), D 2 MiniBooNE, PRD 81, 092005 (2010), C BNL, PRD 23, 2499 (1981), D NOMAD, EPJ C63, 355 (2009) 2 2 FNAL, PRD 28, 436 (1983), D NUANCE (M =1.0 GeV) A 2 Serpukhov, ZP A320, 625 (1985), Al SKAT, ZP C45, 551 (1990), CF Br 3 1.5 1 µ n 0.5 ( measurements of neutrino QE scattering. Values of MA ra...
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