RevModPhys.84.1307

Is typically set to the electroweak scale mz a

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Unformatted text preview: le , which is typically set to the electroweak scale MZ A. Coherent scattering (24) where  ¼ ðme =m Þ2 and is the fine structure constant. Radiative QED corrections have been calculated to second order and higher in electroweak theory paving the way to Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 Coherent scattering involves the neutral-current exchange where a neutrino interacts coherently with the nucleus, 2 Technically, neutrino elastic scattering off of free electrons also falls within this definition, as discussed earlier in this paper. Joseph A. Formaggio and G. P. Zeller: From eV to EeV: Neutrino cross sections . . .  þ AZ !  þ AÃZ : N N (26) Shortly after the discovery of neutral-current neutrino reactions, Freedman, Schramm, and Tubbs pointed out that neutrino-nucleus interactions should also exist (Freedman, Schramm, and Tubbs, 1977). Furthermore, one could take advantage of the fact that at low energies the cross section should be coherent across all of the nucleons present in the nucleus. As a result, the cross section grows as the square of the atomic number A2 . Such an enhancement is possible if the momentum transfer of the reaction is much smaller than the inverse of the target size. Letting Q represent the momentum transfer and R the nuclear radius, the coherence condition is satisfied when QR ( 1. Under these conditions, the relevant phases have little effect, allowing the scaling to grow as A2 . Given a recoil kinetic energy T and an incoming neutrino energy E , the differential cross section can be written compactly as the following:   d G2 2 MT ¼ F Q W MA 1 À A 2 F ðQ 2 Þ2 ; dT 4 2E  (27) where MA is the target mass (MA ¼ AMnucleon ), FðQ2 Þ is the nucleon form factor, and QW is the weak current term QW ¼ N À Zð1 À 4sin2 W Þ: (28) The cross section essentially scales quadratically with neutron (N ) and proton (Z) number; the latter highly suppressed due to the 1 À 4sin2 W ’ 0 term. The form factor FðQ2 Þ encodes the coherence across the nucleus and drops quickly to zero as QR becomes large. Despite the strong coherent enhancement enjoyed by this process, this particular interaction has yet to be detected experimentally. Part of the obstacle stems from the extremely small energies of the emitted recoil. The maximum recoil energy from such an interaction is limited by the kinematics of the elastic collision, Tmax ¼ E ; 1 þ M A =2E  (29) similar to that of any elastic scatter where the mass of the incoming particle is negligible. Several experiments have been proposed to detect this interaction, often taking advantage of advances in recoil detection typically utilized by dark matter experiments (Scholberg, 2006; Formaggio, FigueroaFeliciano, and Anderson, 2012). The interaction has also been proposed as a possible mechanism for cosmic relic neutrinos, due to its nonzero cross section at zero momentum. However, the G2 suppression makes detection beyond the reach of any F realizable experim...
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