Stopped pion beams have also been used for these

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Unformatted text preview: llected for analysis. Stopped pion beams have also been used for these electroweak tests at the Los Alamos National Laboratory in the Los Alamos Meson Physics Facility (LAMPF) (Allen et al., 1993) and Liquid Scintillator Neutrino Detector (LSND) (Auerbach et al., 2001) experiments. Table II provides a summary of the types of measurements made using pure neutrino-lepton scattering. D. Radiative corrections and GF Upon inspection of the cross section formalisms discussed above, it is clear that, with the exception of ratios, one is critically dependent on certain fundamental constants, such as the strength of the weak coupling constant GF . Ideally, one wants to separate the dependence on the weak mixing angle from the Fermi constant strength. Fortunately, measurements of the muon lifetime provides such a possibility, as it is inversely proportional to the coupling strength GF and the muon mass m ,   G2 m 5 3 m2   ½1 þ Áð ފ: (22) ð ÞÀ1 ¼ F 3 fðÞ 1 þ 2 5 MW 192 2 In the above expression, fðÞ is a phase factor, the m2 =MW  factor encapsulates the W -boson propagator, and Áð Þ encodes the QED radiative field corrections. For completeness, we list these correction factors: fðÞ ¼ 1 À 8 þ 83 À 4 À 122 ln ’ 0:999 813; (23) " sin2 MS ¼ 1 À W MW ðÞ2 : MZ ðÞ2 (25) Such radiative corrections, although small, often need to be accounted for in order to properly predict the sin2 W value. Theoretical compilation of such radiative effects can be found in a variety of papers [see, for example, Marciano and Parsa (2003)]. III. THRESHOLDLESS PROCESSES: E $ 0–1 MeV Having established the formalism of basic neutrino interactions, we turn our attention toward describing neutrino interactions across the various energy scales. The first step in our journey involves thresholdless interactions, which can be initiated when the neutrino has essentially zero momentum. Such processes include coherent scattering and neutrino capture.2  25 2 À À ð9 þ 42 þ 12 lnÞ 8 2  þ 162 3=2 þ Oð2 Þ þ Oð 2 Þ þ . . . ; Á¼ precision electroweak tests of the standard model. The best measurement of the muon lifetime to date has been made by the MuLan experiment (Webber et al., 2011), yielding a value for GF of 1:166 378 8ð7Þ Â 10À5 GeVÀ2 , a precision of 0.6 ppm. At tree level, knowing GF (and and MZ ) it is possible to exactly predict the value of sin2 W and test this prediction against the relevant cross section measurements. However, once one introduces one-loop radiative contributions, dependencies on the top and Higgs masses are also introduced. The size of these corrections depends partially on the choice of the normalization scheme. The two commonly used renormalization schemes include the Sirlin on-shell model (Sirlin, 1980) and the modified minimal subtraction scheme (Marciano and Sirlin, 1981). In the latter method, the Weinberg angle is defined by MW and MZ at some arbitrary renormalized mass sca...
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This document was uploaded on 09/28/2013.

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