Processes have been studied extensively in neutrino

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Unformatted text preview: een studied extensively in neutrino experiments. 3 In principle, any elastic interaction on a free target has a finite cross section at zero momentum, but such interactions would be impossible to discern due to the extremely small transfer of momentum. Joseph A. Formaggio and G. P. Zeller: From eV to EeV: Neutrino cross sections . . . 1314 TABLE III. (2010). Neutron decay parameters contributing to Eq. (36). Values extracted from Nico and Snow (2005) and Nakamura, K. et al. Constant Expression Numerical value Comment  gA j gV jei À1:2694 Æ 0:0028 Axial and vector coupling ratio a 1Àjj2 1þ3jj2 À0:103 Æ 0:004 Electron-antineutrino asymmetry b A 0 2  À2 jj 1þj3jj cos þ j 2 0 À0:1173 Æ 0:0013 Fietz interference Spin-electron asymmetry B  þ2 jj 1Àj3jj cos þ j 2 0:9807 Æ 0:0030 Spin-antineutrino asymmetry 2 D f ð1 þ  R Þ n j sin 2 1j 3j þ j2 À4 ðÀ4 Æ 6Þ Â 10 1:71480 Æ 0:000002 ð885:7 Æ 0:8Þ s 5 ½2me3 fR G2 jVud j2 ð1 þ 32 ފÀ1 F  A. Inverse beta decay The simplest nuclear interaction that we can study is antineutrino-proton scattering, otherwise known as inverse beta decay e þ p ! eþ þ n: " (33) Inverse beta decay represents one of the earliest reactions to be studied, both theoretically (Bethe and Peierls, 1934) and experimentally (Reines, Gurr, and Sobel, 1976). This reaction is typically measured using neutrinos produced from fission in nuclear reactors. The typical neutrino energies used to probe this process range from threshold4 (E ! 1:806 MeV) to about 10 MeV. As this reaction plays an important role in understanding supernova explosion mechanisms, its relevance at slightly higher energies (10–20 MeV) is also of importance. In this paper, we follow the formalism of Beacom and Vogel (1999), who expand the cross section on the proton to first order in nucleon mass in order to study the cross section’s angular dependence. In this approximation, all relevant form factors approach their zeromomentum values. The relevant matrix element is given by  GF Vud " M ¼ pffiffiffi hnj  fV ð0Þ À  5 fA ð0Þ 2   if ð0Þ " À P  q jpihe j  ð1 À 5 Þjei : 2M n (34)  dðe p ! eþ nÞ G2 jVud j2 Ee pe 2 " ¼F fV ð0Þð1 þ e cosÞ d cos 2   2 (35) þ 3fA ð0Þ 1 À e cos ; 3 where Ee , pe , e , and cos refer to the electron’s energy, momentum, velocity, and scattering angle, respectively. The neutrino energy threshold Ethresh in the laboratory frame is  defined by ½ðmn þ me Þ2 À m2 Š=2mp . p Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 A few properties in Eq. (35) immediately attract our attention. First and foremost is that the cross section neatly divides into two distinct ‘‘components’’; a vectorlike component, called the Fermi transition, and an axial-vectorlike component, referred to as Gamow-Teller. We talk more about Fermi and Gamow-Teller transitions later. A second striking feature is its angular dependence. The vecto...
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This document was uploaded on 09/28/2013.

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