Feature is its angular dependence the vector portion

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Unformatted text preview: r portion has a clear 1 þ e cos dependence, while the axial portion has a 1 À ð e =3Þ cos behavior, at least to first order in the nucleon mass. The overall angular effect is weakly backward scattered for antineutrino-proton interactions, showing that the vector and axial-vector terms both contribute at equivalent amplitudes. This is less so for cases where the interaction is almost purely Gamow-Teller in nature, such as d reactions. In such reactions, the backwards direction is more prominent. Such angular distributions have been posited as an experimental tag for supernova detection (Beacom, Farr, and Vogel, 2002). The final aspect of the cross section that is worthy to note is that it has a near one-to-one correspondence with the beta decay of the neutron. We explore this property in greater detail in the next section. B. Beta decay and its role in cross section calibration In the above equation, fV , fA , and fP are nuclear vector, axial vector, and Pauli (weak magnetism) form factors evaluated at zero-momentum transfer (for greater detail on the form factor behavior, see Sec. IV.D). To first order, the differential cross section can therefore be written as 4 T -odd triple product Theoretical phase space factor Neutron lifetime The weak interaction governs both the processes of decay and scattering amplitudes. It goes to show that, especially for simple systems, the two are intimately intertwined, often allowing one process to provide robust predictions for the other. The most obvious nuclear target where this takes place is in the beta decay of the neutron. In much the same way as muon decay provided a calibration of the Fermi coupling constant for purely leptonic interactions (Sec. II.D), neutron beta decay allows one to make a prediction of the inverse beta decay cross section from experimental considerations alone. For the case of neutron beta decay, the double differential decay width at tree level is given by (Nico and Snow, 2005) d3 À ~ ¼ G2 jVud j2 ð1 þ 32 Þjpe jðTe þ me Þ F dEe de d  ~~ m p Áp  ðE0 À Te Þ2 1 þ a e  þ b e Te E Te   ~ ~ ~ ~ pe p pe  p : þ n Á A þ B ~ þD Te E Te E Joseph A. Formaggio and G. P. Zeller: From eV to EeV: Neutrino cross sections . . . ~ ~ Here pe and p are the electron and neutrino momenta, Te is the electron’s kinetic energy, E is the outgoing antineutrino energy, E0 is the end-point energy for beta decay, and n is the neutron spin. The definitions of the other various constants are listed in Table III. Integrating over the allowed phase space provides a direct measure of the energy-independent portion of the inverse beta decay cross section, including internal radiative corrections. That is, Eq. (35) can also be written as  dðe p ! eþ nÞ " 22 ¼5 Ee pe ð1 þ e cosÞ d cos 2me fð1 þ R Þn   (36) þ 32 1 À e cos : 3 The term fð1 þ R Þ is a phase space factor that includes several inner radiative corrections. Additional radiative...
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This document was uploaded on 09/28/2013.

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