## Thursday, May 29, 2014

### LEP's, LHC's $$98$$, $$126\GeV$$ Higgses may match (N)MSSM

Peter Higgs is 85 today: Congratulations!
I want to mention a rather interesting paper
Invisible decays of low mass Higgs bosons in supersymmetric models
by Pandita and Patra. The LHC has discovered the $$125-126\GeV$$ Higgs boson and there seem to be no other particles around so far – a situation that may dramatically change in less than a year. Recall that supersymmetry is the most well-motivated theory that (aside from more important things) ultimately requires an extension of the Higgs sector. The simplest supersymmetric model(s) called the MSSM (Minimal Supersymmetric Standard Model) have five Higgs bosons. The NMSSM (Next-to-MSSM) has an extra Higgs-like chiral superfield $$S$$, a fieldized $$\mu$$-parameter of the MSSM.

I think it's fair to say that most people expect that if there are new bosons related to the Higgs mechanism, they are heavier than the Higgs boson that has already been discovered.

However, there is this interesting loophole – one may be thinking outside the box. The other Higgs bosons of the supersymmetric extensions of the Standard Model may actually be lighter than the Higgs boson that has already discovered. The immediate question is "Why hasn't such a lighter particle already been discovered?" But once you acknowledge that the decays may naturally be hard to see, it's tempting to say that the scenario in which the so-far-unknown Higgs bosons are lighter than the known one is as likely as the conventional scenario where the particles discovered in the future are heavier.

In fact, these two authors analyze various questions that lead them to conclude that the possibility that there are Higgs bosons lighter than the known one is actually more likely than the conventional wisdom.

By this comment, I mean that they show that the new "reverted hierarchy" scenario is not only compatible with the existing experimental bounds but it will survive for a longer time in the case that the LHC continues to be compatible with the Standard Model! In other words, more LHC collisions are needed to constrain the "reverted model's" parameters, especially the neutralino mass, than the data needed to constrain the parameters of the "conventional hierarchy".

This reverted model may also be made naturally compatible with the astrophysical bounds – especially with the right concentration of dark matter which is composed of neutralinos. And a particularly interesting detail is that they suggest that the lighter Higgs boson could have mass of $$98\GeV$$ which could agree with the hints of a Higgs particle in the LHC's predecessor in the tunnel, LEP. As this 2003 paper reported, there was an excess of events below $$100\GeV$$, near this very value – see e.g. Figure 7 on page 19.

Most of the Pandita-Patra paper is dedicated to the survey of various parameter spaces describing the invisible decays of the Higgs bosons (decays to invisible missing energy, particularly neutrinos). It's only possible when some inequalities are obeyed by the masses etc.

But I do think that one must avoid the tempting but naive opinion that "everything up to the mass scale $$M$$" e.g. for $$M=126\GeV$$ has been discovered. Various particles of a given mass may be harder to discover because they interact less strongly or because they decay less visibly, or some combination of these two and other properties. If we turn our heads backwards, we may sometimes make some new discoveries.

1. It looks like the LEP had a 2.3 sigma bump at 98 GEV. That was dismissed in one line as too few events to be a higgs. When LHC announced a 2.3 bump in early data at 126 GEV in 2011 that was widely reported as likely the Higgs.
Seems like there should be some looking at that with LHC

2. Dear Rehbock,
you're mistaken.

The reason why the LEP excess couldn't have been "the Higgs" (of the Standard Model) is that the Standard Model Higgs around 100 GeV would predict a much stronger effect, a much stronger deviation from the "Standard Model minus Higgs" (incomplete) theory. So the LEP data actually falsified the Standard Model with the 100 GeV boson despite the 2+ sigma excess.

The excess is compatible with a lighter MSSM or NMSSM Higgs but it is not compatible with being due to the only Standard Model Higgs!

So it's not about the significance only. You must be careful what are the statements that the significance actually speaks about. The LEP falsified the 100 GeV Standard Model Higgs boson and the small excess couldn't have changed it because the 100 GeV Standard Model Higgs predicts a much stronger signal (see the dashed lines on Figure 7, for example, they would imply a much much larger significance if the HIggs were there).

Cheers
LM

3. “The simplest supersymmetric model(s) called the MSSM
(Minimal Supersymmetric Standard Model) have five Higgs bosons.”
What does the MSSM imply for changes to Turner’s 1993
review?
http://www.pnas.org/content/90/11/4827.full.pdf "Dark
matter: Theoretical perspectives" by Michael S. Turner, 1993