Unformatted text preview: trengths for the known fermion
ﬁelds is shown in Table I. A more in-depth discussion of these
topics can be found in a variety of introductory textbooks. We
highlight the work of Giunti and Kim (2007) as an excellent
in-depth resource for the interested reader.
As such, neutrino-electron scattering is a powerful probe of
the nature of the weak interaction, both in terms of the total
cross section as well as its energy dependence (Marciano and
Parsa, 2003). We will brieﬂy examine the experimental tests
of these reactions in the next section.
Before leaving neutrino-lepton interactions completely, we
turn our attention to the last possible reaction archetype,
where the charged current and neutral-current amplitudes
interfere with one another. Such a combined exchange is
realized in e þ e ! e þ e scattering (see Fig. 3). The
interference term comes into play by shifting gf ! gf þ 1
and gf ! gf þ 1 .
One remarkable feature of neutrino-electron scattering is
that it is highly directional in nature. The outgoing electron is
emitted at very small angles with respect to the incoming
neutrino direction. A simple kinematic argument shows that
e 2m e : 1311 and the standard model as a whole. Consider as an example
the ﬁrst observation of the reaction þ eÀ ! þ eÀ
made with the CERN bubble chamber neutrino experiment,
Gargamelle (Hasert et al., 1973); see Fig. 4. This observation,
in conjunction with the observation of neutral-current deep
inelastic scattering (Hasert et al., 1973; Benvenuti et al.,
1974), conﬁrmed the existence of weak neutral currents and
helped solidify the SUL ð2Þ Â Uð1ÞY structure of the standard
model (Weinberg, 1967; ’t Hooft, 1971). The very observation of the phenomena made a profound impact on the ﬁeld of
Subsequent experiments further utilized the information
from the observed rates of neutral-current reactions as a
gauge for measuring sin2 W directly. Neutrino-lepton scattering is a particularly sensitive probe in this regard because
to ﬁrst order (and even to further orders of , see Sec. II.D),
the cross sections depend only on one parameter, sin2 W .
Various experimental methods have been employed to
measure neutrino-lepton scattering. Among the ﬁrst included
the observation of e þ eÀ ! eÀ þ e scattering by Reines,
Gurr, and Sobel (1976) at the Savannah River Plant reactor
complex. Making use of the intense e ﬂux produced in
reactors, a Æ20% measurement of the weak mixing angle
was extracted. A more recent result from the Taiwan
EXperiment On Neu-trinO (TEXANO) experiment (Deniz
and Wong, 2008; Deniz et al., 2010) also utilizes reactor
antineutrinos as their source. There exists an inherent difﬁculty in extracting these events, as they are often masked by
large low-energy backgrounds, particularly those derived
from uranium and thorium decays.
The majority of the recent precision tests have been carried...
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