Strongly Interacting Light Higgs

Three weeks ago, Gian Giudice & friends came up with a paper that deserves attention. For two reasons. One, that it was conceived in the murky corridors of CERN TH. Two, that it deals with an interesting though somewhat neglected subject: the impact of strong dynamics at higher energies on higgs physics at the LHC.

The title is Strongly Interacting Light Higgs. This longish name refers to a scenario where strongly coupled dynamics at a few TeV gives rise to a composite higgs state with mass of order 100 GeV. The paper does not present us with yet another bright model of electroweak breaking. Rather, the purpose is to put several existing approaches into a wider perspective. The models falling into this class include composite pseudo-goldstone higgs, little higgs and 5D holographic higgs. The paper proposes a model independent parametrization and rough estimates of the expected experimental signals.

The Strongly Interacting Light Higgs class has the following features

• At the weak scale v = 246 GeV, the available particles are those of the Standard Model with one higgs doublet. Electroweak symmetry is broken by the higgs who acquires a vacuum expectation value. The associated higgs boson is not much heavier than 100 GeV.
• Higgs is a pseudo-goldstone boson, similarly as pions in QCD. Much as the pions, it comes with a new scale f , which controls non-linearities of the higgs self-interactions.
• There is yet another scale mR. It is set by the masses of the resonaances associated with the strong dynamics that gave birth to the pseudo-goldstone higgs. mR may be smaller than 4\pi f - the naive cut-off of the low energy theory.

The question is how such a scenario would show up at the LHC. Obviously, the clean signal would be a discovery of new particles at the scale mR. That's what the majority of phenomenological studies concentrates on. But there are good reasons not to bet all your money on that. First of all, the current constraints from the precision electroweak tests often push the masses of the new particles beyond the LHC reach. Even if the new particles are light enough, they might be too broad (too short-lived) to be identified as resonaances. We should be prepared to wake up into the nightmare: just the higgs boson at the LHC. In that case, we can still learn something by studying the properties of the higgs.

Gian&others discuss several imprints of strong dynamics at higher scales on the low-energy higgs physics:

1. Modified higgs couplings to fermions and gauge bosons. Due to its goldstone nature, the higgs couplings are modified by a factor of order v^2/f^2. Both, the total higgs decay rate and various branching ratios are affected. In the parametrization proposed by the authors, the leading deviations from the Standard Model can be described by just two parameters in the low-energy effective lagrangian.
2. Strong WW and WZ scattering. Scattering amplitudes of longitudinally polarized electroweak gauge bosons grow with energy as E^2/v^2. In the Standard Model this dangerous behaviour is tamed by the higgs boson exchange. However, for a pseudo-goldstone higgs, the relevant higgs couplings are modified. In consequence, the amplitude grows quadratically with energy, even above the higgs mass, until it is tamed by the resonaances at the scale mR.
3. Strong higgs production. In this scenario, higgs couplings are directly related to those of the longitudinally polarized gauge bosons. Therefore, the amplitude for the higgs pair production, e.g. ZZ->hh, also grows quadratically with energy.

Each of these points deserves a separate post, and i may scribble something in future...

One sad conclusion of the paper is that sensitivity of the LHC to the discussed effects is not astounding. The deviations of higgs physics from the Standard Model could be measured for v^2/f^2 of order 0.5. The ILC would have much better sensitivity, up to v^2/f^2 of order 0.01. The problem is that finding just the higgs at the LHC would likely postpone the high energy physics program for many years (similar depressive view was recently expressed by Burton Richter). If you prefer to think positive, you may get another message from the paper: stop plotting the mSugra parameter space, think how to measure WW scattering at the LHC.