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### Higgs update (CIPANP 2012)

Now that we’re in the conference season we’re treated to the latest results from the LHC and Tevatron. For now we focus on squeezing as much as we can from the 2011 data, so it’s a great time to look at the status of the Higgs searches. We’ll see some of the 2012 results at ICHEP in July (as summer abruptly turns into winter, with ICHEP being held in Australia.) Until then we must be content with what we can see with the data up to the end of 2011.

Both CMS and ATLAS are still searching for the Higgs boson, and that means that if it exists, it must exist in the difficult low mass region. This is something that Standard Model advocates have “known” all along, since the global fit to electroweak data all point to a Higgs mass around 95GeV. The further away the mass of the Higgs is from 95GeV the more we need to explain why it has the mass that it does. The diagram below shows the electroweak fit and the right hand axis shows how many sigmas away the point is from what we expect. (I explained about sigmas in a previous post. About one third of all results are more than $$1\sigma$$ away from expectation. For 2, 3, 4 and 5$$sigma$$ these numbers are about 5% , 0.25%, 1 in 15,000, and 1 in 1.7 million respectively.) As we can see, moving up to about 160GeV the probability for discovering the Higgs is already as low as a few percent.

The electroweak fit ( arXiv:1107.0975v1 hep-ph)

It gets very tricky to reconcile a very high mass Higgs boson with existing constraints, so a high mass Higgs suggests physics beyond the Standard Model. The high mass region is cleaner, it’s easier to study, and it’s more exciting if there is a discovery. By contrast the lower mass region is takes much longer to see any evidence, the final states are more complicated and take more time to analyze. If we discover the Higgs bosons and only the Higgs boson then all that happens is we confirm that the Standard Model is an accurate description of reality. It looks like nature is teasing us with a low mass scenario.

Taking a look into the low mass regime (less than about 150GeV) we can see why there is such a challenge. The dominant decays of the Higgs boson are $$b\bar{b}$$ quarks, $$\tau^+\tau^-$$ pairs, and other quark and gluon processes. There are rarer decays too, and the most important is the $$\gamma\gamma$$ final state. The branching fractions are shown in the plot below. A branching fraction is the fraction of Higgs bosons which will decay into each final state:

The Standard Model Higgs boson branching fractions (arXiv:1101.0593v3 hep-ph)

The analyses from ATLAS and CMS are closing in on the Standard Model Higgs boson now. The limits are a few times the Standard Model, and once the yellow and green bands (“Brazil band plots”, as one speaker called them) pass below the line $$1\times$$Standard Model we can exclude the Higgs boson. If the Higgs boson exists then one point will stay far above the $$1\times$$Standard Model line, and that’s the location of the Higgs boson. If you want a primer on how to read these plots see my previous post on the topic.

There are three main ways to produce a Higgs boson:

• • from gluon gluon fusion, which is the dominant process. In this case we get a Higgs boson, some jets from QCD and not much else. It’s a higher statistics sample, but there is nothing remarkable about the events.
• • with associated production, which is about a factor of ten smaller. Higgs bosons love to couple of massive vector bosons, so whenever we have a massive vector boson there’s a small but significant chance we’ll also see a Higgs boson. We can use the massive vector boson to “tag” these extraordinary events, making the search with lower statistics, but cleaner.
• • from vector boson fusion, a weird process that has a similar rate to associated production. In this mode the quarks from the protons exchange some massive bosons, which create a Higgs, and then the protons scatter off each other, leaving two jets at shallow angles. These events can be hard to reconstruct, but they are cool to look at.

The size of the background for $$b\bar{b}$$ quarks is about 50 million times larger than the Higgs processes, so any analysis using a $$b\bar{b}$$ final state must be very crafty. Generally we require that the Higgs is produced in association with a massive vector boson. When this happens the two bosons usually move back to back in the lab frame, so we can look for a high momentum Higgs boson. This makes things easier for the $$b\bar{b}$$ final state because the two b-jets should be on the same side of the detector, and look like a “fat” jet. Even so, there are still large backgrounds from QCD processes. Since December 2011 physicists have been busy working to get as much discrimination between the Higgs and the background processes as possible, so its no surprise that we see more use of multivariate analyses in these searches. With a more dedicated study we can split up our searches based on the final states and tailor each final state accordingly. This “divide and conquer” method has lead to improved limits. The current exclusion for $$H\to b\bar{b}$$ is already a few times the Standard Model:

ATLAS limits for Higgs decaying to b quarks (B LaForge, CIPANP2012)

CMS limits for Higgs decaying to b quarks (C Palmer, CIPANP2012)

For the next dominant mode, the $$\tau^+\tau^-$$ final state, we have a different set of challenges. $$tau$$ leptons produce neutrinos, which carry away some of the momentum, making it harder for us to reconstruct the event. To make things worse, the $$\tau$$ can decay to leptons or to hadrons, so we need to split up our analyses and treat each case separately. And if that wasn’t enough, we also have a large background from decays of the Z boson, which have exactly the same final state. Given all this it’s a wonder we can use this channel at all. Unfazed by the challenges, both ATLAS and CMS have shown great improvements in this channel:

ATLAS limits for Higgs decaying to tau leptons (B LaForge, CIPANP2012)

CMS limits for Higgs decaying to tau leptons (C Palmer, CIPANP2012)

The next dominant processes are $$c\bar{c}$$ and $$gg$$, which are of no use to us at all. Backgrounds from QCD processes are just too high for these modes to be useful. So that leaves the $$\gamma\gamma$$ final state, and this is the cleanest mode for the lower mass scenarios. To decay $$\gamma\gamma$$ the Higgs boson must go through some intermediate particles in a loop. The challenges presented by the $$\gamma\gamma$$ final states are mostly associated with the detectors. How do we know when we see a photon in the detector, and not a jet? What control samples can we use to calibrate our energy scale? These are tough questions to answer, and since the backgrounds for this channel are so high we need to have confidence in our abilities to recognize and reconstruct photons. (I’m actually a bit skeptical that we have seen hints of a Higgs based on these kinds of questions. Our most sensitive channel is the one with some of the biggest questions.) Even so, the limits are looking encouraging:

ATLAS limits for Higgs decaying to photons (B LaForge, CIPANP2012)

CMS limits for Higgs decaying to photons (C Palmer, CIPANP2012)

I’ve skipped the massive vector boson final states ($$ZZ^*$$ and $$WW^*$$), although these are sensitive to some of the range too. As we look to lower and lower mass ranges the contributions from these final states diminish rapidly, and the kinematic constraints get worse and worse. (At high mass the Higgs boson would produce real $$WW$$ and $$ZZ$$ pairs, giving us fantastically clean mass peaks. At lower masses one of the bosons must be virtual, and we lose one of our most useful constraints.)

Combining the results gives better exclusions. As we can see there is not much space left for the Higgs boson!

ATLAS limits for combined Higgs channels (B LaForge, CIPANP2012)

CMS limits for combined Higgs channels (C Palmer, CIPANP2012)

Most people’s money is on the region 124-126GeV. All we need to do now is collect the 2012 data and see if it shows the same bump. The waiting is the hardest part.

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