Higgs decay to 2 top quarks

[Malamala]

Hello! I haven't really seen a feynman diagram with a higgs boson decaying to a top-anti top quark pair. The mass of a top pair is much higher than the Higgs mass on shell, but is there any reason why we can't have a Higgs boson (very) off-shell decay to 2 top quarks. The probability of that happening must be quite low, but is there any reason to not happen at all? Thank you!

 

[Vanadium 50]

How do you make this very off-shell Higgs boson? You seem to be confusing the Higgs being off-shell with the top being off-shell.

 

[Reggid]

When you calculate the amplitude for a process like $q\bar{q}\to t\bar{t}$, where the q's should stand for any light quarks in the proton, then you also have a tree-level diagram with only one Higgs-propagator, that contributes to the full amplitude (though it will be strongly suppressed).

But you would usually not call this a "Higgs decay".

 

[mfb]

We only call processes "decays" if the parent particle is real, i.e. on-shell (within its decay width of course).

Technically the process via a virtual Higgs goes into the top pair production cross section, in practice it's completely negligible as you can produce them directly from two gluons.
People do look for s-channel virtual Higgs bosons elsewhere, for example in the two photon or four lepton final states, as this cross section is related to the Higgs width. Here is a CMS measurement for example.

 

[Malamala]

How do you make this very off-shell Higgs boson? You seem to be confusing the Higgs being off-shell with the top being off-shell.

I am not sure I understand what you mean. If you produce an off shell higgs boson with a $q^2 = 2 m_t$, the higgs can in principle decay to 2 on shell top quarks. Isn't that right? I am not sure what you mean by off-shell top in this case.

 

[Malamala]

When you calculate the amplitude for a process like $q\bar{q}\to t\bar{t}$, where the q's should stand for any light quarks in the proton, then you also have a tree-level diagram with only one Higgs-propagator, that contributes to the full amplitude (though it will be strongly suppressed).

But you would usually not call this a "Higgs decay".

Thanks a lot! Right, it is not really a decay, I was just wondering if it can happen at all (even if strongly suppressed). This answered my question.

 

[malawi_glenn]

I was just wondering if it can happen at all (even if strongly suppressed).

Everything that is possible can happen, but it will be supressed due to two top-propagators and phase space of at least 4 particles. Also, the background would be huge, considering the amount of top and anti-tops being produced from gluon-gluon fusion etc without an intermediate Higgs... Your signal would be completely blurred