Top–antitop production from \(W^+_L W^-_L\) and \(Z_L Z_L\) scattering under a strongly interacting symmetry-breaking sector
Eur. Phys. J. C
Top-antitop production from W + W − and ZL ZL scattering under L L a strongly interacting symmetry-breaking sector
Andrés Castillo 1 2
Rafael L. Delgado 0 1
Antonio Dobado 0 1
Felipe J. Llanes-Estrada 0 1
0 Departamento de Física Teórica I, Universidad Complutense de Madrid , 28040 Madrid , Spain
1 Rafael L. Delgado: on leave at SLAC , 2575 Sand Hill Rd, Menlo Park, CA 94025 , USA
2 Departamento de Física, Facultad de Ciencias, Universidad Nacional de Colombia , Sede Bogotá, Ciudad Universitaria, Bogotá 111321 , Colombia
By considering a non-linear electroweak chiral Lagrangian, including the Higgs, coupled to heavy quarks, and the equivalence theorem, we compute the one-loop scattering amplitudes W +W − → t t¯, Z Z → t t¯ and hh → t t¯ (in the regime Mt2/v2 √s Mt /v2 s/v2 and to NLO in the effective theory). We calculate the scalar partial-wave helicity amplitudes which allow us to check unitarity at the perturbative level in both Mt /v and s/v. As with growing energy perturbative unitarity deteriorates, we also introduce a new unitarization method with the right analytical behavior on the complex s-plane and that can support poles on the second Riemann sheet to describe resonances in terms of the Lagrangian couplings. Thus we have achieved a consistent phenomenological description of any resonant t t¯ production that may be enhanced by a possible strongly interacting electroweak symmetry breaking sector.
1 Introduction
The Higgs-like particle with a mass of 125 GeV found at
the Large Hadron Collider (LHC) [1,2] completes a
possible framework of the fundamental interactions, as this new
boson has quantum numbers and couplings compatible with
those expected for the Higgs of the Standard Model (SM) in
its minimal version. In addition, new scalar-resonances
associated to new-physics effects have been constrained roughly
up to 600–700 GeV [3,4]. For new vector bosons, the lowest
energy for a possible resonance to lie at is even higher [5–
7]. The discrepancy among the Higgs mass scale and that of
any new-physics appearance is suggestive of a
Goldstoneboson (GB) interpretation of the Higgs boson that (together
with the Goldstone bosons associated with the WL± and Z L
components of vector bosons) may be related to some global
spontaneous symmetry breaking that in turn prompts a
breaking of the electroweak gauge symmetry SU (
2
)L ×U (
1
)Y →
U (
1
)Q .
To describe such pseudo-Goldstone behavior of the
Higgs boson, some effective description of the Electroweak
Symmetry-Breaking Sector (EWSBS) of the SM must be
taken into account [8–16]. These effective field theory (EFT)
descriptions are useful even when the Higgs boson is not
a GB. In consequence, EFTs are a convenient way of
parametrizing the EWSBS.
The energy gap may also favor a non-linear Lagrangian
description of the symmetry breaking, which is a very
general approach to the EWSBS in the EFT. The old electroweak
chiral Lagrangian (ECL) technique [17–22], built up on
standard chiral perturbation theory for hadron physics [23–25],
can be extended to include the scalar Higgs-like particle h
transforming as a singlet of custodial SU (
2
)C to give the
socalled Higgs Effective Field Theory (HEFT). Meanwhile, the
longitudinal gauge bosons transform as a triplet. This pattern
is analogous to low-energy hadron physics, where pions fall
in a triplet and the η meson is embedded in a singlet
representation of the strong SU (
2
)V isospin group. The global
symmetry-breaking scheme, SU (
2
)L ×SU (
2
)R → SU (
2
)C ,
is common to both effective field theories of the strong and
electroweak interactions.
As the HEFT theories are derivative expansions, for most
of parameter space (saliently excluding that of the Standard
Model and perhaps other very carefully tuned sets), the
interactions will generically become strong at sufficiently high
energy, and we have argued that a second, very broad scalar
pole is expected [26,27]. This motivates theoretical studies
of new resonances with energies 700 GeV < E < 4π v ∼
3 TeV, which require methods extending perturbation
theory in the HEFT Lagrangian – which we exploit to next to
leading order, (NLO). One strategy is extending the
lowenergy amplitudes through dispersion relations (DR)
compatible with analyticity and unitarity. Resonances can then
be found as poles in the second Riemann sheet due to the
proper analytical behavior of the amplitudes.
Such unitarization methods introduce some level of
arbitrariness, as unitarity, analyticity, and the low-energy
behavior are not sufficient to determine a scattering amplitude with
arbitrary accuracy. Nevertheless, in [28] we showed that the
analytical and unitary description of higher energy
dynamics provided by DRs extending the one-loop results is
essentially unique qualitatively; at least so up to the first resonance
in each spin–isospin channel. Other groups have recently
pursued related unitarization methods in the context of the
EWSBS (...truncated)