I came here from the link provided on your latest post, but my reading another link there to Wikipedia discussing top quark physics seems to belie the following statement.

"...theory indeed prevents us from having any composite particle containing a top quark or a top antiquark."

The Wikipedia page states:

"...the Higgs boson is composed of a pair of top and antitop quarks."

So, I wonder how this is resolved in your research into top quark physics, in which your first assertion seems supported by the lack of Higgs bosons generated by the data you have considered. I also recall the Higgs being confirmed a few years ago, and, without researching that announcement further, wonder if that resulted from exactly the top-antitop pairing being observed at CERN? Isn't the Higgs toponium? If not what is the difference between toponium and the Higgs?

The coming order of magnitude upgrade of CERN's capabilities seems potential of shedding light (ahem!) on the extension of the standard model into topcolor and colorons. You must be like a kid on Christmas Eve, eager to open the presents higher energies might leave under the tree of your research - but having to wait 4 years for them to erupt from the quantum foam into existence.

Thanks!