We study a simple extension of the standard model where scalar singlets that
mix with the Higgs doublet are added. This modification to the standard model
could have a significant impact on Higgs searches at the LHC. The Higgs doublet
is not a mass eigenstate and therefore the expected nice peak of the standard
model Higgs disappears. We analyze this scenario finding the required
properties of the singlets in order to make the Higgs "invisible" at the LHC.
In some part of the parameter space even one singlet could make the discovery
of the SM Higgs problematic. In other parts, the Higgs can be discovered even
in the presence of many singlets.Comment: 9 pages, 1 figure. V2- References added. V3- Several examples and one
fig. adde