New LEP Paper

Twelve years ago, LEP -- the Large Electron-Positron collider -- finished taking data.  That's so long ago I was still an undergraduate, YouTube and Facebook didn't exist and even Google was relatively unknown.  So I was quite surprised to see a new paper on the arXiv from the LEP collaborations.

Now, it's worth remembering that experimental collaborations continue to publish results well after the actual experiment finished.  It takes time to properly analyse the data, after all.  But this is quite impressive.  Not only has the experiment finished, but they had enough time to remove the detectors and build something entirely new.

There are a few reasons for this.  The recent Higgs discovery has, unsurprisingly, attracted a lot of attention.  Some of this has been very speculative.  (The CMS and ATLAS experiments differ in their mass measurements by 2%?  Obviously there are two particles!)  One idea that's been floated is based on the idea that there are two Higgs doublets.  This is an old idea, and shows up in Supersymmetry as a specific example.

Now, when you have one Higgs doublet, you have one new particle.  When you have two Higgs doublets, you have five new particles.  The reason is that each Higgs doublet has four new degrees of freedom, but three are needed to to be longitudinal polarisations of the W and Z gauge bosons.  So four minus 3 is one, but eight minus three is five.  Three of the new particles are electrically neutral, and the last two are charged and form a particle-antiparticle pair.

There are a lot of theoretical possibilities with two Higgs doublets.  The "standard" one is that the lightest neutral particle is very much like the Standard Model Higgs, and the other other states are much heavier.  This is known as the decoupling regime, and is easiest to fit to indirect constraints.  The particle we have discovered would be that lightest one if this is true.

However, a few people have speculated that this might not be the case: that there are lighter Higgs we haven't found yet.  In particular, there was a small excess in the LEP searches for the Standard Model Higgs at, I think, around 100 GeV.  While LEP was able to rule out the Standard Model Higgs in this mass range, production and decay rates in two Higgs doublet models are generically suppressed, especially when the spectrum is compressed (the particles are close in mass).  So the claim was that it might be possible to have the lightest Higgs at around 100 GeV (and very non-Standard Model); the heaviest at 125 GeV (and very Standard Model-like); and one neutral and one charged state between those limits.

Theoretically there are two motivations for this idea.  First is that we haven't ruled it out yet.  The second is that it might make indirect constraints on Supersymmetry weaker.  I'll get into this more in a later post, but ironically, the Higgs is actually too heavy to easily fit SUSY models, which predict it to be lighter than the Z boson up to quantum corrections.  Having a lighter state would ease those constraints and reduce the tuning needed to make SUSY models fit the data.

The problem with such light Higgses is that they are hard to see at the LHC.  They tend to decay to jets, and there are lots of jets at produced in a proton-proton collision.  The high energy of the LHC means that jets with 100 GeV energies can be produced by soft QCD (i.e. processes at low momentum transfer where the QCD coupling is large).  So the backgrounds can not be theoretically predicted with any real accuracy and totally swamp the signal.

In contrast, LEP collided electrons and positrons, so high-energy jets where only produced through processes with high momentum transfer.  This lower background means that setting limits from LEP is low hanging fruit, and we would be foolish not to take advantage of this.  And it turns out that the charged Higgs search had not been done with the full data set.

Unfortunately, the actual limits that are drawn can not say anything about the specific model I discussed above.  But they do make clear exactly how much wiggle room we have till the LHC collaborations can overcome those obstacles I mentioned.  The LEP teams set limits in two classes of model: one where the charged Higgs decays exclusively to fermions, and one where it can also decay to the W and one of the neutral scalars.  The exclusions are pretty similar, between 70 and 90 GeV.

For the former case (fermionic decays), the four LEP experiments give the following exclusions:

The yellow regions are forbidden, while the vertical axis shows the branching ratio for the charged Higgs to decay to the tau.  It is assumed that the only other decay of relevance is to jets (specifically strange + charm quarks), which is generally a good approximation in these models as the Higgses couple proportional to charge.

In the second class of models, the exclusion limits are given in terms of a mixing parameter.  They also depend on the mass of the daughter scalar, and are in general slightly less restrictive:

Again, the yellow regions are forbidden.  The drop at intermediate values of tan beta (the mixing parameter) is caused by a cross over in the dominant decay mode.

In all, it was worth checking these limits (and a little surprising it had not been done).  While I'm not convinced by this idea of an undiscovered light Higgs, it does at least offer something to play with for a couple of years.