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Richard Ruiz | Univ. of Pittsburgh | U.S.A.

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How Difficult is it to Find the Higgs?

Really difficult, and I mean really, really difficult. It is such an arduous job that even after 30 years worth of searching, by literally tens of thousands of physicists, it has yet to be found. However, that may all change Tuesday when spokespeople for the ATLAS and CMS experiments, the Large Hadron Collider‘s two general-purpose detector experiments, unveil the long-awaited results of their independent searches for the higgs boson.

Now, what makes Tuesday’s announcement so different is that it will be the first time any higgs analysis will be publicly shown using 5.5 inverse femtobarns (fb-1), or a data set worth over 380 trillion proton collisions. To explain why 5.5 fb-1 is so special requires us to go back in time to late August, when this graph started making the rounds at conferences and summer schools:

Essentially, this graph tabulates how much data is needed for ATLAS and CMS to be sensitive to discovering the higgs boson. According to these numbers, with 5 fb-1 worth of data, ATLAS & CMS can either jointly rule out the existence of higgs boson as predicted by the Standard Model of Physics, or with equal excitement, claim evidence of its existence. Now I need to mention two important caveats: (1) this table assumes (1) benchmark parameters which are entirely worthless if there is any type of new physics (which is pretty likely, IMO); and (2) the numbers also assume that ATLAS and CMS combine their data sets. This last point is important because this is not the case tomorrow.

What will be seen live, from this link, are two 30-minute presentations by a spokesperson from each collaboration unveiling and announcing whatever conclusions that can justifiably be made considering the amount of data presently available. After that, there will be a 1 hour Q & A session with two spokespeople. My colleagues here at QD will definitely be live-blogging the event! I, on the other hand, will be teaching my undergraduates the importance of thermodynamics……

In summary, I am expecting three possible outcomes on Tuesday (Disclaimer! I am not a part of any experiment and currently am in Wisconsin, not CERN):

  1. The higgs boson is discovered and we all dance around in merriment while enjoying waterfalls of champagne. Twitter is credited with breaking the news. Wagers between physicists are also paid off.
  2. The higgs boson, as predicted by the Standard Model, is definitively ruled out. This, of course, would be a terrible disappointment. However, the higgs boson is a very wonderfully rich piece of physics; if one of the slickest things in all of physics does not exist… I cannot even fathom what does. (See this post!)
  3. The higgs boson is not “discovered” but it is definitely not ruled out; there remains a mass window in which the higgs boson may still lie; and an elephant-shaped couch appears in the room near 120 GeV. This is still pretty satisfying because it gives us an idea what to expect from a fully combined analysis.  Personally, I think this is the most likely outcome.

 

In light of results from last month using half the data (below), Tuesday will be very interesting.

The Proverbial Needle in the Proverbial Haystack

Now that I built up the anticipation, here are some numbers I calculated to give an idea why discovering the higgs boson is such an incredible scientific feat. (Technical details as to how I generated these numbers can be found at the very bottom of this post.)

Okay, so suppose the higgs boson, as predicted by the Standard Model, were to exist. If we were to produce one at the LHC, then we would expect it to decay into something more familiar like photons or b-quarks. We physicists call the probability of this happening a “cross section,” and it is measured in barns.

As a concrete example, let us take a look at the first process where two protons (pp) collide and produce a higgs boson (h), which in turn decays into a b-quark and an anti-b-quark. The cross section (probability) is 16,320 femtobarns, or 0.00000000001632 barns. All you need to know is that 0.00000000001632 barns is a very small number and hence pp->h->bb is a very rare thing to happen. In 70 trillion proton-proton collisions (or 1 inverse femtobarn), our theory predicts we will have produced 16,320 higgs bosons. In 5.5 inverse femtobarns (or 380 trillion proton-proton collisions), our theory predicts we will have generated

16,320 fb x 5.5 fb-1 = 89,760 pp-> higgs -> bb Events.

89,000 higgs boson events may seem like a lot, but just wait until the next table. Here are some common ways a higgs is expected to decay and how many higgs events we expect to have produced this year. That is 102, 756 higgses in all!

Here is where things become absolutely unbearable. Let’s pretend now that the higgs boson does not exist. So ignoring the contribution from higgs bosons, we may calculate how many of these higgs-like events we expect to see. For example, let’s consider pp -> γγ (2 photons) and pp -> gg (2 gluons), then out of 380 trillion proton-proton collisions (5.5 fb-1) the Standard Model predicts almost 3 trillion gluon pairs and over 800,000 photon pairs. Trying to find the higgs with b-quarks requires us to sift through 2.6 trillion bb pairs in order to find almost 90,000 higgs -> bb events.

In other words, experimentalists are trying to find an excess of 0.0000034% more bb quarks than the Standard Model predicts, or 0.3% more ZZ events than the Standard Model predicts. Fortunately, it only means looking for an extra 0.014% photon pairs in 380 trillion protons-proton collisions.

So yeah, the higgs boson… it’s hard to find. Personally, I think finding a needle in a haystack would be easier.

 

At any rate, congratulations to all those who helped with the effort. I am just giddy with anticipation regarding tomorrow’s seminar, though that might also be my body telling me to go to sleep.

 

Happy Colliding!

– richard (@bravelittlemuon)

 

* Technical note: I calculated the higgs boson cross sections with MadGraph5 using the Higgs Effective Field Theory v4 model. To calculate the Standard Model background cross sections, I used MadGraph5 Standard Model v4. mh = 120 GeV. Additionally, I resorted to using the default parameter card for MadGraph4. Each calculation used 25, 000 proton-proton events at 7 TeV center of mass. Only basic (read: default) kinematic and fiducial cuts have been applied. Uncertainty was ignored for clarity. This ignores all acceptance cuts.

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