Low-energy effective theory, unitarity, and non-decoupling behavior in a model with heavy Higgs-triplet fields

We discuss the properties of a model incorporating both a scalar electroweak Higgs doublet and an electroweak Higgs triplet. We construct the low-energy effective theory for the light Higgs-doublet in the limit of small (but nonzero) deviations in the rho parameter from one, a limit in which the triplet states become heavy. For small deviations in the rho parameter from one, perturbative unitarity of WW scattering breaks down at a scale inversely proportional to the renormalized vacuum expectation value of the triplet field (or, equivalently, inversely proportional to the square-root of the deviation of the rho parameter from one). This result imposes an upper limit on the mass-scale of the heavy triplet bosons in a perturbative theory/ we show that this upper bound is consistent with dimensional analysis in the low-energy effective theory. Recent articles have shown that the triplet bosons do not decouple, in the sense that deviations in the rho parameter from one do not necessarily vanish at one-loop in the limit of large triplet mass. We clarify that, despite the non-decoupling behavior of the Higgs-triplet, this model does not violate the decoupling theorem since it incorporates a large dimensionful coupling. Nonetheless, we show that if the triplet-Higgs boson masses are of order the GUT scale, perturbative consistency of the theory requires the (properly renormalized) Higgs-triplet vacuum expectation value to be so small as to be irrelevant for electroweak phenomenology.

electroweak interaction: rho parameter
Higgs particle: doublet
Higgs particle: triplet
mass: upper limit
effective Lagrangian
W W: elastic scattering
W W: scattering amplitude
W: longitudinal
scalar particle: exchange
unitarity: violation

References(33)

Figures(0)

The Interplay Between the Top Quark Mass and the Structure of the Higgs System

Giampiero Passarino
(
- Turin U. and
- INFN, Turin
)

- Phys.Lett.B 231 (1989) 458-462
•
DOI:
- 10.1016/0370-2693(89)90694-1

Radiative corrections to the Rho parameter versus the top quark mass

Gaimpiero Passarino
(
- Turin U. and
- INFN, Turin
)

- Phys.Lett.B 247 (1990) 587-592
•
DOI:
- 10.1016/0370-2693(90)91906-R

Radiative corrections in unconstrained SU(2) x U(1) and the top mass problem

Bryan W. Lynn
(
- CERN and
- Stanford U., Phys. Dept.
)
,
E. Nardi
(
- CERN and
- SISSA, Trieste and
- INFN, Trieste
)

- Nucl.Phys.B 381 (1992) 467-500
•
DOI:
- 10.1016/0550-3213(92)90486-U

Precision observables in SU(2) x U(1) models with an additional Higgs triplet

T. Blank
(
- Karlsruhe U.
)
,
W. Hollik
(
- Karlsruhe U.
)

- Nucl.Phys.B 514 (1998) 113-134
•
e-Print:
- hep-ph/9703392
•
DOI:
- 10.1016/S0550-3213(97)00785-2

Violation of the Appelquist-Carazzone decoupling in non-SUSY GUT

Piotr H. Chankowski
(
- Warsaw U.
)
,
Jakub Wagner
(
- Warsaw U.
)

- Phys.Rev.D 77 (2008) 025033
•
e-Print:
- 0707.2323
•
DOI:
- 10.1103/PhysRevD.77.025033

Constraining new models with precision electroweak data

- Int.J.Mod.Phys.A 21 (2006) 4045-4070
•
e-Print:
- hep-ph/0504286
•
DOI:
- 10.1142/S0217751X0603388X

Higgs triplets and limits from precision measurements

- Phys.Rev.D 74 (2006) 035001
•
e-Print:
- hep-ph/0604102
•
DOI:
- 10.1103/PhysRevD.74.035001

(Non)decoupling of the Higgs triplet effects

- Eur.Phys.J.C 50 (2007) 919-933
•
e-Print:
- hep-ph/0605302
•
DOI:
- 10.1140/epjc/s10052-007-0259-x

Infrared Singularities and Massive Fields

Thomas Appelquist
(
- Harvard U.
)
,
J. Carazzone
(
- Harvard U.
)

- Phys.Rev.D 11 (1975) 2856,
- In *Lichtenberg, D. B. ( Ed.), Rosen, S. P. ( Ed.): Developments In The Quark Theory Of Hadrons, Vol. 1*, 267-272. ( Phys. Rev. D11 ( 1975) 2856-2861)
•
DOI:
- 10.1103/PhysRevD.11.2856

Unity of All Elementary Particle Forces

H. Georgi
(
- Harvard U.
)
,
S.L. Glashow
(
- Harvard U.
)

- Phys.Rev.Lett. 32 (1974) 438-441,
- Also in *Lichtenberg, D.B. (ed.), Rosen, S.P. (ed.): Developments In The Quark Theory Of Hadrons, Vol. 1*, 492-495, and in *Froggatt, C.D., Nielsen, H.B.: Origin of symmetries* 330-333
•
DOI:
- 10.1103/PhysRevLett.32.438