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Unformatted text preview: interaction
Lagrangian with anomalous coupling parameters gV , V , and
1
V is given by (Hagiwara et al., 1987; Hagiwara, Woodside,
and Zeppenfeld, 1990)
þ
À
Leff ¼ igWWV gV ðW W À À W þ W ÞV
WWV
1
À
þÀ
þ
þ V W W V þ V W W V :
2
MW
Note that Leff reduces to LSM for the values ¼ Z ¼ 0
and g ¼ gZ ¼ ¼ Z ¼ 1. Deviations from the SM val1
1
ues of the coupling parameters are denoted by ÁgV , ÁV , and
1
ÁV . We have assumed that C and P are conserved in the
interaction Lagrangian. There is no reason to believe that this
assumption is valid unless the physics that leads to anomalous
couplings respects these symmetries. It is straightforward to
include additional terms that violate C and P, but we refrain
from doing so in order to keep the discussion simple.
Electromagnetic gauge invariance requires Ág ¼ 0. The
1
W boson magnetic moment W and the electric quadrupole
moment QW are related to the coupling parameters by
W ¼ e
ð1 þ þ Þ
2m W and
QW ¼ À e
ð À Þ:
m2
W The anomalous couplings (aside from g ) are usually
1
assumed to have some dependence on an energy scale
(form factors) which suppresses them at large scales to avoid
violation of treelevel unitarity in the diboson production
amplitude (Baur and Zeppenfeld, 1988; Zeppenfeld and
Willenbrock, 1988). The parametrization generally used for
the energy dependence of a given coupling parameter is
^ ðsÞ ¼ 0
;
^
ð1 þ s=Ã2 Þ2 pﬃﬃﬃ
^
where s is the partonic centerofmass collision energy, 0
^
is the value of the coupling parameter in the limit s ! 0, and
Ã is the ﬃﬃﬃ
cutoff scale.
p
^
The s distribution used in the measurements described in
this section is obtained through Monte Carlo simulation of the
collision physics. With the substantially increased diboson
statistics that will be available at the LHC,ﬃ anomalous TGC
pﬃﬃ
^
searches can be reported as a function of s in diboson decayﬃ
pﬃﬃ
^
channels resuting in fewer than two neutrinos, where the s
can be estimated on an eventbyevent basis. This approach
would lead to improved sensitivity and less dependence on
ad hoc form factors as compared to the standard approach.
When reporting coupling limits from hadron collider data,
the value of Ã is taken to be close to the hadron collision
energy; even large variations (e.g., 50%) of Ã around this
scale have minimal impact on the results. Physically, the scale
Ã can be considered the scale at which the new physics
responsible for the anomalous coupling is directly accessible
(e.g., through pair production of new particles). This
Rev. Mod. Phys., Vol. 84, No. 4, October–December 2012 1487 approach is different from the effectiveﬁeldtheory approach
discussed in Sec. II, where the coefﬁcients of higherdimension operators are constants. While in the same spirit
as effective ﬁeld theory, the effective Lagrangian approach to
anomalous couplings is different in practice. In particular, the
form facto...
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This document was uploaded on 09/28/2013.
 Fall '13
 Energy

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