455 research outputs found
A Systematic Approach to the SILH Lagrangian
We consider the electroweak chiral Lagrangian, including a light scalar
boson, in the limit of small . Here is the electroweak scale
and is the corresponding scale of the new strong dynamics. We show how the
conventional SILH Lagrangian, defined as the effective theory of a
strongly-interacting light Higgs (SILH) to first order in , can be
obtained as a limiting case of the complete electroweak chiral Lagrangian. The
approach presented here ensures the completeness of the operator basis at the
considered order, it clarifies the systematics of the effective Lagrangian,
guarantees a consistent and unambiguous power counting, and it shows how the
generalization of the effective field theory to higher orders in has to
be performed. We point out that terms of order , which are usually not
included in the SILH Lagrangian, are parametrically larger than terms of order
that are retained, as long as . Conceptual
issues such as custodial symmetry and its breaking are also discussed. For
illustration, the minimal composite Higgs model based on the coset
is considered at next-to-leading order in the chiral expansion.
It is shown how the effective Lagrangian for this model is contained as a
special case in the electroweak chiral Lagrangian based on .Comment: 22 pages, 1 figure; improved presentation of the results in section
On the Power Counting in Effective Field Theories
We discuss the systematics of power counting in general effective field
theories, focussing on those that are nonrenormalizable at leading order. As an
illuminating example we consider chiral perturbation theory gauged under the
electromagnetic symmetry. This theory describes the low-energy
interactions of the octet of pseudo-Goldstone bosons in QCD with photons and
has been discussed extensively in the literature. Peculiarities of the standard
approach are pointed out and it is shown how these are resolved within our
scheme. The presentation follows closely our recent discussion of power
counting for the electroweak chiral Lagrangian. The systematics of the latter
is reviewed and shown to be consistent with the concept of chiral dimensions.
The results imply that naive dimensional analysis (NDA) is incomplete in
general effective field theories, while still reproducing the correct counting
in special cases.Comment: 14 pages, no figure
Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO
We consider the Standard Model, including a light scalar boson , as an
effective theory at the weak scale of some unknown dynamics
of electroweak symmetry breaking. This dynamics may be strong, with
emerging as a pseudo-Goldstone boson. The symmetry breaking scale is
taken to be at or above. We review the leading-order Lagrangian within
this framework, which is nonrenormalizable in general. A chiral Lagrangian can
then be constructed based on a loop expansion. A systematic power counting is
derived and used to identify the classes of counterterms that appear at one
loop order. With this result the complete Lagrangian is constructed at
next-to-leading order, . This Lagrangian is the most
general effective description of the Standard Model containing a light scalar
boson, in general with strong dynamics of electroweak symmetry breaking.
Scenarios such as the SILH ansatz or the dimension-6 Lagrangian of a linearly
realized Higgs sector can be recovered as special cases.Comment: 25 pages, no figures; v2: references added, matches published
version; v3: corrected matching of Higgs-portal example to chiral Lagrangian
in sec. 7.
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