The search for the Higgs particle has been dominated recently by the new kids on the block, the ATLAS and CMS experiments at the Large Hadron Collider [LHC], who benefit from the LHC’s record high energy per collision. But at its predecessor, the now-closed Tevatron, the CDF and DZero experiments still have a few tricks up their sleeves. Though the energy per collision in recent years at the Tevatron was 3.5 times smaller than was the LHC’s in 2011, CDF and DZero have twice as much data as do ATLAS and CMS right now. And there’s one more thing going for them. In contrast to the LHC, where protons collide with protons, at the Tevatron protons collided with antiprotons. That gives the Tevatron a little edge in one particular search mode for the Higgs. It won’t be enough to beat the LHC at the game for which it was designed, but it’s enough that the Tevatron experiments can at least play. And we’ll see results from the two experiments tomorrow (Wednesday) — with a preview already publicly available, as you’ll see below.
If the Higgs particle has a mass somewhere around 115-130 GeV/c2 ATLAS and CMS should eventually be able to measure several of its production rates and decay rates. But the Tevatron experiments CDF and DZero are essentially limited to the two production modes
- quark + anti-quark –> virtual W particle –> W + Higgs
- quark + anti-quark –> virtual Z particle –> Z + Higgs
which are relatively small. (Click here to learn what a virtual particle is, and isn’t.) Then they can only separate out these collisions when the Higgs decays in a particular way,
- Higgs –> bottom quark + bottom anti-quark
which is very common, and only when the W and Z decay in particular ways,
- W –> electron or muon + anti-neutrino
- Z –> neutrino + anti-neutrino or electron + anti-electron [``positron''] or muon + anti-muon
which happens roughly about 1/4 of the time.
But in these particular modes, the Tevatron experiments can do better (for now, anyway) than the experiments at the LHC. One of multiple reasons is that the LHC’s protons have relatively few anti-quarks with sufficient energy to combine with a quark to make a W or Z plus a Higgs in a proton-proton collision, while the Tevatron’s anti-protons have plenty of anti-quarks ready to do the job. To understand this better, you will need to understand more about the proton’s structure, which is described here. [For the anti-proton, just ``anti-'' everything: take the discussion of the proton and switch the quarks with the anti-quarks, leaving the gluons (which are their own anti-particles) as they were.]
When one of these collisions happens, what is observed in the detector is the following:
- two jets [sprays of hadrons], one from the bottom quark and one from the anti-quark, both of which are “b-tagged” [i.e. show signs of having contained a hadron that itself contained a b quark or a b anti-quark -- something I'll explain elsewhere.]
- zero, one or two `leptons’ (here a shorthand generically meaning electrons, muons, or their anti-particles), and, if the number of leptons is less than two, signs of undetected particles (an imbalance in the total momentum of the jets and [if present] the lepton)
Figure 1 shows what an event of this type with one `lepton’ often looks like.
Unfortunately, there are many other processes that occur at the Tevatron (and even more at the LHC) that look essentially the same, in the detector, as what I just described. [These are what we call ``backgrounds'' to the Higgs process, which we call the ``signal.'' Read about the meaning and use of these terms here.] For example, when a W particle and a Z particle are produced together, the W particle may decay to an electron and an anti-neutrino and the Z particle may decay to a bottom quark/anti-quark pair. The only way to tell the difference between this and a collision that makes W+Higgs is that the two jets from the bottom quark and anti-quark together have energies and momenta consistent with having come from a particle of mass of about 91 GeV/c2 (the mass of the Z particle) and not, say, 125 GeV/c2 (which might or might not be the mass of the Higgs particle.) [Technically, it is the invariant mass of the two jets that one computes to see whether it is somewhat close to 91 GeV/c2; see below.]And the energies and momenta of jets cannot be measured very precisely. Consequently, picking out the Higgs signal is not so easy.
To see this — and to see a preview of what we will face when CDF and DZero present their results — look at Figure 2 below, which was shown at the La Thuile conference by Homer Wolfe, representing the CDF experiment. What the plot shows is the number of events observed for a given invariant mass of the two b-tagged jets, for collisions that look similar to what is shown in Figure 1. You can see predictions [a combination of theoretical calculations and inferences from other data samples] for various background processes, shown in colors.
- The largest (dark green) involves production of a W particle along with random production, via the strong nuclear force, of a bottom quark and bottom anti-quark.
- The blue represents a W combined with a Z, the case I mentioned above; notice it peaks actually a bit above 91 GeV, and is quite wide. [This tells you how hard it is to measure the mass of a particle that decays to a bottom-quark jet and a bottom-antiquark jet; the result is not very precise.]
- And the third large process, in yellow, is from production of a top quark and a top antiquark, which collectively decay to two W particles and a bottom quark and anti-quark; if one of the W’s decays to a lepton and a neutrino, while the other decays to jets (as often happens) then the result is background to the Higgs signal.
And finally, the red line shows what the signal of the simplest possible Higgs particle [the ``Standard Model Higgs''] of mass 115 GeV/c2 would look like — if it were multiplied by five! In other words, the white region between the red curve and the green region will be five times smaller in the Standard Model than is shown on the graph. This tells you that CDF and DZero are looking for a very small effect on a very substantial background. If the Standard Model Higgs is present in nature, this measurement is not going to provide a smoking gun. It will provide at best another hint.
One can’t help noticing, though, that in the region where the red curve is largest, many of the black dots — the data — lie well above the sum of the predicted backgrounds (green curve). Hmmm…
Should we get excited?
But I’d advise against it. If you’ve been keeping track, you know we’ve seen a significant number of excesses at the Tevatron and the LHC in the past year. Most were small. There was the summer’s excess in the Higgs search. Remember those “hints of a Higgs particle” from July? Like most small excesses, they went away when more data was collected and certain potential errors in the analysis were corrected. There was the excess in multi-leptons (here are articles 1 and 2); that hasn’t disappeared, but gathering more data didn’t make it more convincing, which is a bad sign. The excess in the rate at which certain B mesons decay to a muon and an anti-muon went away [and in fact a new limit on this process was just announced by the LHCb experiment.] There were four events at CDF with two leptons and two anti-leptons, which were consistent with a particle of mass of about 325 GeV/c2. But these went unconfirmed by CDF itself (looking for other signs of the same particle) and also by the other experiments. Then there was the excess at CDF and DZero in the asymmetry for top quarks that I wrote about, which too is in danger of turning out to be a false alarm.
So. I’m not particularly excited. Excesses, either due to random chance or due to a mistake in understanding the backgrounds to a signal, happen all the time.
By the way, two excesses that are still alive and kicking are those showing up in the search for the Standard Model Higgs particle at ATLAS and CMS (which are still too small to merit confidence, in my view, but are certainly more compelling than were/are most of the others I’ve mentioned) and the observation of CP violation in D meson decays, first at LHCb and then at CDF (though it is no longer so clear what the theoretical prediction is in this case.)
And let’s not forget that ATLAS found, rather convincingly, evidence for a new state of the “atom” made from a bottom quark and a bottom anti-quark. I mention this just to reassure you that not every excess goes away. Sometimes nature really does have something for us to identify, study, put into our textbooks and pass on to future generations.
What Might Lead to Such an Excess?
Ok, back to the plot in Figure 2, and the excess that it shows. I expect we’ll see six similar plots (at least), three from CDF (for W + Higgs, Z + Higgs where the Z decays to neutrinos, and Z + Higgs where the Z decays to a lepton/anti-lepton pair) and a similar three from DZero. We’ll be watching to see if all six show a similar feature. What might be causing this excess?
One possibility is that the excess on this plot is due to random chance — a few extra events just due to statistics. Only CDF can tell us what that probability is, but it doesn’t look that high to me.
Another possibility, much more likely to my eye and based on my experience, is that it is due to mis-estimating one of the backgrounds. That happens all the time. CDF, of course, will tell us that’s not possible, but experts outside of CDF will all be suitably skeptical, as we always are in this type of measurement.
In fact one can argue a very similar mis-estimate must have afflicted CDF in a similar (but importantly different) measurement, one that got a huge amount of press in April 2011, with articles irresponsibly hailing the excess seen there as a “potential discovery of a new particle”. Skepticism in the particle physics community was quite a bit higher than in the press, though it should have been higher still. I must emphasize, though, that CDF’s April 2011 result has not convincingly been refuted even now, though there’s no sign of any confirmation. DZero does not see the same effect, but since they do something slightly different from CDF, it’s hard to be sure whether the CDF result is clearly refuted, especially since CDF and DZero have been unable to agree as to which of the two experiments is making the mistake. And CDF has done more analysis and claims the excess is still there. CMS and ATLAS don’t see anything like this, but again one can argue that this process is hard to study at the LHC. This is all to say that measurements of this type are particularly difficult, and prone to controversy and error.
Similar issues were also probably partly responsible for the hints of a Higgs particle last summer. I wrote a lot about why those hints rested on uncertain ground, and if you read that old article you’ll see, when I discuss broad excesses in the context of a Higgs decaying to two W particles, that the excess back then that caused all the ruckus bore some mild similarity to the excess in Figure 2, which is likely to cause this week’s ruckus.
A third possibility is that the excess is due to the Higgs signal being much larger than expected. That, of course, would be very exciting. However… while logically possible, it is unlikely, for very profound reasons. To understand why requires us to explore the very heart of the Higgs mechanism.
Why is it unlikely that the signal is much larger in nature than predicted in the Standard Model?
Logically speaking, there are three ways that CDF’s signal could be larger than expected.
First, perhaps the production rate for W + Higgs or Z + Higgs was miscalculated by theorists, and it is larger than people thought? This seems very unlikely. Very similar calculations are needed to predict the production rates for processes in which two W particles are produced in a collision, or in which a W and a Z particle are produced together. And the calculations agree well with the measurements of these rates. (In fact, you can see some evidence that the calculations are pretty accurate in Figure 2. Imagine how the graph would look different if the blue peak were made twice as big as expected; this would in turn push up the green peak, putting it well above the data [the black dots] at the highest point.) Estimates of the uncertainties in the probabilities for W + Higgs and Z + Higgs production are in the 10% range, not 100%.
Second, perhaps the Higgs particle is not at all a Standard-Model-like Higgs, and the production rate for W + Higgs or Z + Higgs is intrinsically much larger than in the Standard Model? As I emphasized in my articles on how the Standard Model Higgs particle is produced, decays, and is searched for, one of the really important things about W + Higgs and Z + Higgs production is that its size in the Standard Model is determined by the Higgs mechanism itself — the fact that the W and Z particles get their masses from the Higgs field is directly tied to the probability of making W or Z + Higgs at the Tevatron and at the LHC. Moreover, if the Higgs particle is different from what it is in the Standard Model — if there are several Higgs particles, for instance — the W + Higgs and Z + Higgs production rates can only decrease! You can take my word for that, or, if you’re willing to stomach a little bit of technical argument, I’ll explain why in the next section.
Finally, perhaps the probability for the Higgs to decay to a bottom quark/anti-quark pair is much larger than in the Standard Model? But that probability is already very large (see Figure 1 of this article), 80% for a Higgs of mass 115 GeV/c2, and 60% for one of 125 GeV/c2. Since you can’t make the probability bigger than 100%, there’s almost nowhere to go. Such a change can’t produce an increase in the observed rate of more than about a factor of about 1.2 for a Higgs at 115 and about 1.6 for a Higgs at 125. Moreover, if you do this, it can become difficult (but not impossible) to make everything seen in 2011 by ATLAS, CMS and (given Figure 2) CDF consistent at the same time. On the other hand, maybe part or all of the hints at ATLAS and CMS are themselves just small excesses destined to disappear. So for the moment we have to keep an open mind.
Ok, that’s probably all that can be said before we actually see the data from CDF and DZero. Obviously there will be a lot more to say once we actually see the interpretation of Figure 2, the other two similar plots from CDF, and the three corresponding plots from DZero… and when we see how the statistical analysis of those plots works itself out. Til tomorrow! (Or read on to learn why it is very tough to make the W+Higgs and Z+Higgs production rates larger than for a Standard Model Higgs particle.)
Quasi-Technical Section: Why the Rate for W + Higgs and Z + Higgs Production can only be Smaller than in the Standard Model
The following section, partly quoted from my Standard Model Higgs articles, is a tiny bit technical. However, even if you have no technical background but still feel you can follow algebra, you may find yourself comfortable with this argument. Give it a try! It’s not so hard.
Schematically, here’s how the Higgs mechanism works: before the Higgs field has a non-zero value, the world allows interactions of the form
- H H W W
- H H Z Z
where “H” here is the Higgs field when its average value is zero, and “W” and “Z” are the W and Z fields with corresponding massless W and Z particles. There is no interaction involving just one Higgs particle at a time. But once the Higgs field develops its non-zero average constant value throughout all of space and time (its value is usually called “v”, historically) then we are motivated to write H = v + H, where H represents any difference of H from its average value v. When we do this we find
H H Z Z –> v2 Z Z + 2 v H Z Z + H H Z Z
The first term, in red, (a constant times Z Z) shifts the energy of a Z particle that is at rest — in other words, it provides what we call mass-energy! That’s the Higgs mechanism! This is how the Higgs field gives the Z particle a mass.
The second term, in blue, allows a virtual Z particle to turn into a Z particle and a Higgs particle (as described here) and makes the process quark + anti-quark –> Z + Higgs possible.
You notice that v appears in both the first term and the second term — and thus the Z particle’s mass and the rate for Z + Higgs production are related to each other. It turns out the production rate, and the square of the Z mass, are both proportional to v2.
Now suppose the Higgs field is not that of the Standard Model. For instance, suppose there were two Higgs fields H and H’, and a Higgs particle for each one. What would happen then? Well, we start with interactions like
- H H W W
- H H Z Z
- H’ H’ W W
- H’ H’ Z Z
Now imagine both H and H’ become non-zero, and take values v and v’. Then when we shift them both, we get
H H Z Z –> v2 Z Z + 2 v H Z Z + H H Z Z
H’ H’ Z Z –> v’2 Z Z + 2 v’ H’ Z Z + H’ H’ Z Z
Now the Z particle’s mass comes from both of the red terms, and is proportional to v2 + v’2, but the production of Z + the first Higgs is proportional to v2 while that of Z + the second Higgs is is proportional to v’2. But since any real number squared is positive, v2 < v2 + v’2, and also v’2 < v2 + v’2. Consequently, relative to the Z particle mass (which we know from experiment) the production rate for either of the two Higgs particles is smaller than it is in the Standard Model.
If the two Higgs particles had exactly the same mass, the sum of the rates would be equal to the rate for Z + Higgs in the Standard Model. But if one is light and the other heavy, then the rate for Z + the light one is reduced, and the one for Z + the heavy one is very reduced — just because it is heavy. No matter what you do, there is no way to make the rate for such a process larger than in the Standard Model.
Everything I’ve said for the Z is true for the W, too.
Well, you might ask, maybe there’s some other type of process that we can add in that makes the rate for W + Higgs larger than expected. The problem is that this in turn is likely to make the rate for W + Higgs even larger still at the LHC, because any other type of interaction that you add will necessarily grow with energy, and since the LHC has larger energy than the Tevatron, the relative increase in the rate at the LHC would be bigger than at the Tevatron. CMS and ATLAS don’t yet have enough data to see the Standard Model W + Higgs process with clarity, but if you make that process much larger, it is likely they would already have noticed. In Figure 3 is a plot from CMS, showing they cannot exclude a rate of 3-5 times the Standard Model but showing also that their observed rate is only slightly larger than their expected rate, which makes it unlikely that the true rate is several times larger than for a Standard Model Higgs particle.