Abstract: In the Standard Model for electroweak interactions, the Higgs sector is known to display a
custodial symmetry protecting the mass relation mW+- = mW3 from large corrections. When
considering extensions of the scalar sector, like the two-Higgs-doublet model, one could
introducethis global symmetryby hand in order to pass current electroweak precision tests
in a natural way.
Assuming the invariance of the potential under CP transformations, the existence of a second
scenario characterized by mH+- =~ mH0 instead of mH+- =~ mA0 can be proved .
The phenomenology associated with such a model is potentially interesting. For example, a
pseudoscalar (mA0 =~ 30 GeV) together with an heavy SM-like Higgs boson (mh0 =~ 300 GeV)
could perfectly survive all direct and indirect constraints. Such a scenario could lead to
unexpected signatures at hadron colliders, like an unusual top decay t>W+bbb via the charged
Higgs decay H+>W+A0, scalar decays of the SM-like Higgs
by the exotic ZZbbbb final state(gg>h0>H0H0>ZA0ZA0> ZZbbbb), ...
In this talk I will expose the definition of a twisted custodialsymmetry in a 2HDM and then
the phenomenology of this model. After summarizing alldirect and indirect constraints, I
the possible collidersignatures at Tevatron and LHCand some preliminary results 
using MadGraph v4 and the generic 2HDM implementation.
J. M. Grard, M. Herquet,Phys. Rev. Lett. 98 : 251802 (2007)
 S. de Visscher, J. M. Grard, M. Herquet, V. Lematre, and F. Maltoni (2007), in
Johan Alwall, Pavel Demin, Simon de Visscher, Rikkert Frederix, Michel Herquet, Fabio Maltoni, Tilman Plehn, David L. Rainwater, and Tim Stelzer,JHEP 09 : 028 (2007)
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