Aidan Randle-Conde | Université Libre de Bruxelles | Belgium

What next for the Higgs?

There’s a good chance that there will be a Higgs discovery “just around the corner”, so it’s time to look to the future to see where to go next with Higgs analyses. At the very least, we need to know the mass of the Higgs boson so that we can manufacture the next big experiment, a TeV scale linear collider (TLC). Without knowing the mass of the Higgs boson we can’t determine the center of mass energy of such an collider and that would severely delay development. Given that, we need to have a discovery before the LHC shuts down for 2013, so we need to get moving!

The Higgs is running out of space as the LHC experiments squeeze the allowed region (CMS)

We usually require a $$5\sigma$$ observation to declare a discovery, and there are two ways to do this. We can wait until we have $$5\sigma$$ observations on both ATLAS and CMS, but this would take a long time and a lot of luminosity, or we can combine the results of ATLAS and CMS in order to get a global $$5\sigma$$ observation.

This second option is a controversial one, because once we combine results to get the final observation we can no longer use each experiment as a crosscheck for the other. (Well we can, but it gets quite subtle and we have to ask ourselves to what extent we trust the agreement between the two experiments if we’re going to combine results in this way.) To an extent the question is a moot one. Someone will combine the results from ATLAS and CMS (and CDF and D0 as well) whether we want them to or not. Even so, it’s long been a strategy and a benchmark of excellence to have two experiments for each major field of study. CDF and D0 crosscheck each other, BaBar and Belle crosscheck each other, and UA1 and UA2 crosschecked each other with the discovery of the $$W$$ and $$Z$$ bosons. If we compromise that standard then we could set a dangerous precedent for future discoveries. When
we look to other experiments when conducting our own research we run the risk of experimenter bias.

Looking beyond the discovery we also need to consider how we are going to study the properties of the Higgs boson. Assuming a mass of 125GeV we can look forward to a lot of different decay channels, including the high statistics but messy $$b\bar{b}$$ final state, the smeared out $$\tau\tau$$ and $$WW^*$$ final states, the clean but somewhat boring $$\gamma\gamma$$ final state, and the and intriguing $$ZZ^*$$ and $$Z\gamma$$ states. This huge range of final states means that there would be a very rich range of analyses.

Branching fractions of the Higgs boson at 125GeV

Perhaps the most exciting part of the available Higgs decays is that it could give us access to the quark masses. The masses of the quarks are not visible to most processes, because the quarks get tangled up in the QCD that surrounds them. The Higgs boson couples directly to the quarks, coupling to their masses. We can measure the ratio of branching fractions to quarks and muons, then with the knowledge of the muon mass and the effective color of the quarks we can get the mass of the $$b$$, $$c$$, and $$s$$ quarks. It would be an ambitious project, but a worthwhile one that would finally answer many questions about QCD.

A major part of the Higgs studies is the width of the Higgs. We measured the width of the $$Z$$ boson at LEP and this confirmed that there were only three generations of neutrinos. This goes a long way to showing that there is no fourth generation particles (and the LHC has since ruled out a fourth generation of quarks.) We can apply the same trick to the Higgs boson to see if there are any particles less than 62GeV that we have not discovered yet. For example if there is a SUSY particle at 50GeV that only couples to the Higgs boson then we would see extra invisible decays of the Higgs boson. (The largest invisible decay of the Higgs boson in the Standard Model is the process $$H\to ZZ^*\to\nu\nu\nu\nu$$ and accounts for approximately 0.08% of all Higgs decays.)

In order to perform these studies we need a different kind of collider. Producing the Higgs at the LHC is relatively straightforward: we just pump protons through the machine and smash them together. Eventually we have enough Higgs bosons to see a signal, and it’s just a matter of waiting. Unfortunately the performance of the machine is just not good enough for precision measurements. We can only see the visible decays at the LHC (so we cannot measure the width directly), we do not know the center of mass energy of the collisions so complicated states such as associated production are less accessible, and the energy scales of many objects dominate uncertainties. To see a lot of the decays of the Higgs boson we need an electron-positron collider. These give very clean working environments and a known center of mass energy. In this scenario we look for Higgstrahlung, where a $$Z$$ boson is produced which emits a Higgs boson. We can reconstruct the $$Z$$ boson and then the Higgs boson is what recoils against it to balance the momentum.

Simulation of a field inside a resonator at ILC, a contender for the next collider for Higgs physics (ILC/DESY)

If the Higgs boson is discovered at 125GeV this year then we have our work cut out of for us for the next few decades. ATLAS and CMS will continue to produce results and paper after paper. After the Phase I and Phase II upgrades the focus will change from Higgs discovery to high statistics measurements and searches for new phenomena. We’ll look towards the TLC for precision measurements and stringent constraints on the Standard Model. If all goes well with a Higgs discovery, then the next couple of decades are going to be a golden age for particles physics.

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