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Unformatted text preview: hird is to do experiments at such high
energy E that the effects of these operators, of order
ðE=ÃÞ2 , become large. If E > Ã, then one must abandon
this formalism, because operators of arbitrarily high dimensionality become signiﬁcant; however, the new physics
should then be directly observable. If no effects beyond the
SM are observed, then one can place bounds on the coefﬁcients of the dimensionsix operators c=Ã2 , where c is a
dimensionless number. These bounds apply only to the product c=Ã2 , not to c and Ã2 separately; in fact, there could even
be two different scales of new physics involved (Ã1 Ã2 in
place of Ã2 ).
This approach to physics beyond the SM, dubbed an
effectiveﬁeldtheory approach (Weinberg, 1979), has the
advantage of being model independent. Whatever new physics lies at the scale Ã, it will induce dimensionsix operators,
whose only dependence on the new physics lies in their
coefﬁcients, c=Ã2 . Another advantage of this approach is
that it is universal; it can be applied to both treelevel and
looplevel processes, and any ultraviolet divergences that
appear in loop processes can be absorbed into the coefﬁcients
of the operators. Thus, one need not make any ad hoc
assumptions about how the ultraviolet divergences are cut
off. This effectiveﬁeldtheory approach thus provides an
excellent framework to parametrize physics beyond the SM
(De Rujula et al., 1992; Hagiwara et al., 1993).
Hadron colliders contribute to the study of the electroweak
interactions in three distinct ways. First, because they operate
at the energy frontier, hadron colliders are uniquely suited to
searching for the effects of dimensionsix operators that are Hobbs, Neubauer, and Willenbrock: Tests of the standard electroweak model at . . . suppressed by a factor of ðE=ÃÞ2 . Second, they are able to
contribute to the precision measurement of a variety of
electroweak processes, most notably to the measurement of
the W boson mass and the topquark mass. Third, they are
able to search for new particles associated with the electroweak interactions, in particular, the Higgs boson. These three
virtues of hadron colliders will manifest themselves throughout this review.
A. Electroweak interactions The electroweak theory is a spontaneously broken gauge
theory based on the gauge group SUð2ÞL Uð1ÞY . There are
three parameters that describe the theory: the gauge couplings
g and g0 , and the order parameter of spontaneous symmetry
breaking v. In the SM, this order parameter is the vacuumexpectation value of a fundamental Higgs ﬁeld. These
parameters are not measured directly, but rather inferred
from precision electroweak measurements. The three measurements that are used to ﬁx these parameters are the Fermi
constant GF determined from the muon lifetime formula; the
ﬁnestructure constant , determined from a variety of lowenergy experiments; and the Z boson mass MZ . With these
three inputs, the predictions of all other ele...
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This document was uploaded on 09/28/2013.
 Fall '13
 Energy

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