Higgs Was At LEP

Everybody knows that the LEP experiment set a stringent limit on the Higgs boson mass - it has be larger than 114.4 GeV. The common expectation is that Higgs is just around the corner, and will be hunted down and roasted alive at the LHC or at the Tevatron. But this is not the only conceivable scenario that future may unfold: the world can be Higgsless, or the Higgs may be too wide or too invisible or too whatever to be detected at a hadron collider. There is yet another possibility that is definitely a bit crazy but is nevertheless not completely excluded. Namely, it is possible that the Higgs is lighter than 115 GeV and therefore kinematically available at LEP but ... we missed it.

How could Higgs have been missed? The point is that the 114.4 GeV limit strictly applies to a particle that walks, talks and couples just like the Standard Model Higgs boson. If we meddle with the Higgs couplings then, with a bit of skill, we can make Higgs effectively invisible to LEP. One obvious way to achieve that is to suppress the production rate. At LEP, Higgs would be dominantly produced by the process petnamed Higgsstrahlung where the e+e- collision first produces a Z boson which then radiates a Higgs boson. The LEP limits can be relaxed by suppressing the Higgs-Z-Z vertex by a factor of 3-4, see the black line on the plot below. However, this is not a theoretically plausible direction, as the electroweak precision observables suggest the existence of a light Higgs particle whose coupling to W and Z bosons is not suppressed. Besides, on the more philosophical side, a particle with a reduced coupling to Z should not be called Higgs (but rather, a scalar particle that slightly mixes with the Higgs). So let's leave the Higgs-Z-Z vertex alone. In that case we can still try to hide the Higgs from LEP by meddling with the Higgs decays.

The LEP collaboration was not that stupid and they also searched for the Higgs decaying in a non-standard way. You could think that Higgs could be hidden by making it invisible, that is to say, it could decay to some light, almost non-interacting particles that leave the detector undetected. This does not work: the signature involving a Z boson plus missing energy (carried out by the invisible stuff) is not easy to miss in a lepton collider, and in consequence the limit on the invisible is 114 GeV, almost as strong as that on the standard Higgs. Thus, paradoxically, to make Higgs invisible one must make it decay into something visible. LEP has concluded the following:

• Higgs decaying to a pair of jets of any flavor (rather than dominantly into b-jets as the standard Higgs) has to be heavier than 113 GeV
• Fermiophobic Higgs decaying dominantly to off-shell WW and ZZ has to be heavier than 110 GeV
• Higgs decaying dominantly into two photons has to be heavier than 117 GeV

All in all, Higgs lighter than 110 GeV decaying into a two-body final state is excluded. But the situation is far less clear if the final state contains more particles. For example, the Higgs can undergo a cascade decay: it first decays into a pair of light scalars or pseudoscalars which subsequently decay into a pair of quarks or leptons each. In that case we deal with a four-body final state, for example with four b-quarks or four tau-leptons (typically, the pseudoscalars decays into the heaviest quark or lepton that is kinematically available). This is of course impossible in the Standard Model, while in the MSSM it occurs only in an obscure corner of the parameter space. But in several popular extensions of the Standard Model, for example in the NMSSM (MSSM adorned by a singlet superfield) or in little Higgs theories such cascade decays appear often and willingly.

The possibility of avoiding the LEP bounds via the cascade decays was first pointed out by Radovan Dermisek and Jack Gunion in the context of NMMSM. In that model, there are new pseudoscalar states in the Higgs sector which can naturally be light and to which the true Higgs (the one that couples to Z with the largest strength) can decay. These pseudoscalars then decay into a pair of b quarks each, or into tau quarks if the pseudoscalar is lighter than twice the b-quark mass. The former possibility was excluded by a subsequent LEP analysis - the limit on the Higgs decaying into four b-jets is now 110 GeV - but the four-tau or the four-light-jet final states allow for a much lighter Higgs particle. See the exclusion limits for the case of four-tau cascade decay - the allowed region on this plot is almost non-existing but there is no limit above the Higgs mass of 85 GeV. The reason why that analysis stopped at 85 GeV is not physical but psychological: in the MSSM there is no parameter space that would allow to consider Higgs heavier than 85 GeV. This is a clinical case of the damage that happens when experimenters take theorists and their theories too seriously (following this logic, if the MSSM did not allow for a light Higgs one could completely skip the LEP experiment).

Hiding the Higgs is a nice prank in itself, but there are also some theoretical and phenomenological motivations for playing this game. Firstly, the electroweak precision observables are best fitted by a fairly light Higgs mass with the central value of order 80 GeV,
and the light Higgs of 90-100 GeV would alleviate the tension. Secondly, LEP saw a 2.3 sigma excess of Higgs-like bbar events around the mass of 100 GeV. That cannot be interpreted as the standard Higgs (the number of events would have been five times much higher), but can be perfectly explained by the Higgs decaying most of the times into four light quarks or leptons and one fifth of the times into the b quarks. Recall that in the final year of LEP a smaller excess created much larger theoretical activity.

Of course, a light elusive Higgs is a nightmare for the LHC. Fortunately, theories that motivate such a scenario typically predict a lot of new phenomena at the TeV scale to provide enough fun for the LHC experiment. Just that some people will have to wait a bit longer for their Nobel prize.

Here is the review of the non-standard Higgs decays.