1 p n 1 1 p n 1 fs q2 2 2 f2

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Unformatted text preview: form factors, assuming a dipole form. The strange axial-vector form factor is commonly denoted as s FA ðQ2 Þ ¼ Ás ; 2 ð1 þ Q2 =MA Þ2 (67) C. Resonant single pion production Now that we discussed quasielastic and elastic scattering mechanisms, we consider another interaction possibility: this time an inelastic interaction. Given enough energy, neutrinos can excite the struck nucleon to an excited state. In this case, the neutrino interaction produces a baryon resonance (N Ã ). The baryon resonance quickly decays, most often to a nucleon and single pion final state  N ! À N Ã ; where Ás is the strange quark contribution to the nucleon spin and MA is the same axial mass appearing in the expression for CC QE scattering [Eq. (61)]. Over the years, experiments typically measured NC elastic cross section ratios with respect to QE scattering to help minimize systematics. Table VIII lists a collection of historical measurements of the NC elastic and QE cross section ratio  p !  p= n ! À p. These ratios have been integrated over the kinematic range of the experiment. More recently, the MiniBooNE experiment measured the NC elastic and QE ratio on carbon in bins of Q2 (Aguilar-Arevalo et al., 2010b). Experiments such as BNL E734 and MiniBooNE have additionally reported measurements of flux-averaged absolute differential cross sections d=dQ2 for NC elastic scattering on carbon. From these distributions, measurements of parameters appearing in the cross section for this process, MA and Ás, can be directly obtained. Table IX summarizes those findings. As with QE scattering, a new appreciation for the presence of nuclear effects in such neutral-current interactions has also recently arisen with many new calculations of this cross section on nuclear targets (Amaro et al., 2006; Benhar and Veneziano, 2011; Butkevich and Perevalov, 2011; Meucci, Giusti, and Pacati, 2011). Just as in the charged current case, nuclear corrections can be on the order of 20% or more. N Ã ! N 0 ; Experiment Target Ratio Q2 ðGeV2 Þ BNL E734 BNL CIB Aachen BNL E613 Gargamelle CH2 Al Al CH2 CF3 Br 0:153 Æ 0:018 0:11 Æ 0:03 0:10 Æ 0:03 0:11 Æ 0:02 0:12 Æ 0:06 0.5–1.0 0.3–0.9 0.2–1.0 0.4–0.9 0.3–1.0 Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 (69) where N , N 0 ¼ n, p. Other higher multiplicity decay modes are also possible and will be discussed later. The most common means of single pion production in intermediate energy neutrino scattering arises through this mechanism. In scattering off of free nucleons, there are seven possible resonant single pion reaction channels (seven each for neutrino and antineutrino scattering), three charged current:  p ! À pþ ;  p ! þ pÀ ; " (70)  n ! À p0 ;  p ! þ n0 ; " (71)  n ! À nþ ;  n ! þ nÀ " (72) and four neutral current:  p !  p0 ;  p !  p0 ; " " (73)  p !  nþ ;  p !  p0 ; " " (74)  n !  n0 ;  n !  p...
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