A couple of weeks ago we met the Higgs boson and discussed its Feynman rules.

I had forgotten to put up the obligatory Particle Zoo plush Higgs picture in my last post, but US LHC readers will know that Burton has the best photos of the [plushy] Higgs. (It seems that the Higgs has changed color over that the Particle Zoo.)

We learned that the Higgs is a different kind of particle from the usual gauge boson “force” particles or the fermion “matter” particles: it’s a scalar particle which, for those who want to be sophisticated, means that it carries no intrinsic quantum mechanical spin. Practically for these posts, it means that we ended up drawing the Higgs as a dashed line. For the most part, however, the Feynman rules that we presented in the previous post were pretty boring…

Recall the big picture for how to draw Feynman diagrams:

1. Different particles are represented by lines. We now have three kinds: fermions (solid lines with arrows), gauge bosons (wiggly lines), and scalars (dashed lines).
2. When these particles interact, their lines intersect. The “rules” above tell us what kinds of intersections are allowed.
3. If we want to figure out whether a process is possible, we have to decide whether or not we can use the rules to convert the initial set of particles into the final set of particles.

If you’ve been following our posts on Feynman diagrams, then you might already be bored of this process. We could see how electrons could turn into muons, or even how the Higgs boson might be produced at the LHC; but now we’ve arrived at the Higgs boson—one of the main goals of the LHC—where is the pizzazz? What makes it special, and how do we see it in our Feynman rules?

The Higgs is special

It turns out that the Higgs has a trick up it’s sleeve that the other particles in the Standard Model do not. In the language of Feynman diagrams, a Higgs line can terminate:

The “x” means that the line just ends; there are no other particles coming out. Very peculiar! We know that ordinary particles don’t do this… we don’t see matter particles disappearing into nothing, nor do we see force particles disappearing without being absorbed by other particles. We can think about what happens when matter and anti-matter annihilate, but there we usually release energy in the form of force particles (usually photons). The above rule tells us that a single Higgs line—happily doing its own thing—can be suddenly be cut off. It shouldn’t be read as an initial state or final state particle. It’s just some intermediate line which happens to stop.

We’ll discuss the physical meaning of this in upcoming posts. Sometimes when people try to explain the physical meaning they can get caught up in their own analogies. Instead, let us use the Feynman diagrams as a crutch to see the effects of this weird Feynman rule. Recall that in the previous post we introduced a four-point Higgs self-interaction (“four-point” means four Higgs lines intersecting):

If we take one of the lines and terminate it, we end up with a three-point Higgs self interaction:

In fact, since the crossed out line isn’t doing anything, we might as well say that there is a new Feynman rule of the form

Now that’s somewhat interesting. We could have forgotten about the “crossed out Higgs line” rule and just postulated a three-point vertex. In fact, usually this is the way people write out Feynman rules (this is why our method has been “idiosyncratic“); however, for our particular purposes it’s important to emphasize that what people really mean is that there is implicitly a “crossed out Higgs line.” The significance is closely tied up to what makes the Higgs so special.

We could play this game again and cross one one of these three lines. This would lead us to a two-point Higgs interaction.

Once again, we could just as well chop off the two terminated lines and say that there is a ‘new’ two-point Higgs Feynman rule. But this is really just a line, and we already knew that we could draw lines as part of our Feynman rules. In fact, we know that that lines just mean that a particle moves from one place to another. So it seems like this interaction with two crossed out lines doesn’t give us anything news.

… except there’s more to it, and this is where we start to get a hint of the magic associated with the Higgs. Let me make the following statement without motivation:

Claim: the above Feynman rule is a contribution to the Higgs mass.

At this point, you should say something incredulous like, “Whaaaaaat?” Until now, we’ve said that particles have some particular mass. The number never really mattered that much, some particles are lighter than others, some particles have zero mass. Mass is just another property that each particle seems to have. Now, however, we’ve made a rather deep statement that puts us at the tip of a rather large iceberg: we’re now relating a particular Feynman rule to the mass of the particle, which we had previously assumed was just some number that we had to specify with our theory.

We’ll have to wait until my next post to really get into why such a relation should exist and really what we even mean by mass, but this should at least start to lend credence to the idea that the Higgs boson can give masses to particles. At this point this should still feel very mysterious and somewhat unsatisfying—that’s okay! We’ll get there. For now, I just want you to feel comfortable with the following string of ideas:

1. The Higgs boson has a special Feynman rule where a line can terminate.
2. This means we can take any interaction and effectively remove the Higgs line by terminating it immediately after the vertex.
3. In particular, this means that we generate a vertex with just two lines.
4. This vertex with two lines should—for reasons which are presently mysterious—be identified with mass.

Giving mass to the other particles

Now that we see how this game works, we should immediately go back to the first two Feynman rules we wrote down:

These are the interactions of the Higgs with fermions and gauge bosons. Here’s what you should be thinking:

Hm… I know that the Higgs boson line can terminate; I can just cross out the end points of a dashed line. And I just saw that when I do this to the Higgs self-interaction vertex enough times, I end up with a two-point interaction which Flip tells me is a mass for some weird reason. Now I these two vertexes representing the Higgs interaction with two matter particles or two force particles. Does terminating the Higgs line also give mass to these particles?

The answer is yes! We end up with vertices like this:

For aesthetic reasons (and really only for aesthetic reasons) we can shrink this diagram to:

We can even drop the “x” if you want to be even more of a purist… but for clarity we’ll leave it here to distinguish this from a normal line. These diagrams indeed represent a mass contribution to fermions and gauge bosons. Again, I’m just telling you this as a mysterious fact—we’ll explain why this interpretation is accurate later on. We’ll need to first understand what “mass” really is… and that will require some care.

Bumping up against the Higgs

In fact, instead of saying that particles “start out” with any masses, one can formulate our entire Feynman diagram program in terms of completely massless particles. In such a picture, particles like the top quark or Z boson undergo lots of the aforementioned two-point “mass” interactions and so are observed to have larger masses. Heuristically, heavy particles barrel along and have lots of these two-point interactions:

For comparison, a light particle like the electron would have fewer of these interactions. Their motion (again, heuristically) looks more like this:

We should remember that each of these crosses is really a terminated Higgs line. To use some fancy parlance which will come up in a later post, we say that the Higgs has a “vacuum expectation value” and that these particles are bumping up against it. The above pictures are just ‘cartoons’ of Feynman diagrams, but you can see how this seems to convey a sense of “inertia.” More massive particles (like the top quark) are harder to push around because they keep bumping up against the Higgs. Light particles, like the electron, don’t interact with the Higgs so much and so can be pushed more easily.

In this sense, we can think of all particles as being massless, but their interactions with the Higgs generates a two-point interaction which is effectively a mass. Particles which interact more strongly with the Higgs have more mass, while particles which interact weakly with the Higgs have less mass. In fact, once we assume this, we might as well drop all of the silly crosses on these lines—and then we’re left with the usual Feynman rules (with no terminating Higgs lines) that are usually presented.

(A small technical note: the Higgs isn’t actually responsible for all mass. For example, bound states get masses from their binding energy. Just look up the mass of the proton and compare it to the mass of its constituent quarks. The proton has a mass of about 1 GeV, while the up/down quarks are only one thousandth of this. Most of the proton mass comes from the binding energy of QCD.)

Some closing remarks

Before letting you ponder these things a bit more, let me make a few final remarks to whet your appetite for our next discussion.

• The photon, as we know, is massless. We thus expect that the Higgs does not interact with the photon, or else we could have ‘terminated’ the Higgs lines in the interaction vertex and generated a photon mass.
• On the other hand, the Higgs gives the W and Z bosons mass. This means that it costs energy to produce these guys and so the weak is only really effective over a short distance. Compare this to photons, which are massless, and so can produce a long range force. (Gluons are also massless, but they have a short range force due to their confinement.) Thus the Higgs is responsible for the “weakness” of the weak force.
• … on that note, it’s worth noting that the “weak” force isn’t really so weak—it only appears weak at long distances due to the mass of the W and Z. If you look at shorter distances—say on distances shorter than the distance between two Higgs crosses in the cartoon picture above—then you’d find that the weak force is actually quite potent compared to electromagnetism. Thus a more accurate statement is that the Higgs is responsible for the short-ranged-ness of the weak force.

There are also a few open questions that are worth pointing out at this point. We’ll try to wrap these up in the upcoming posts on this subject.

• The big elephant in the room is the question of why the two-point interaction from terminating a Higgs line should be interpreted as a mass. We got a hint in the picture above of how “bumping off the Higgs” can at least heuristically appear to have something to do with inertia. We’d like to better understand what we really mean by mass.
• We also very glibly talked about treating everything as massless and only generating ‘effective’ masses through such Higgs interactions. Special relativity tells us that there is a very big difference between a particle with exactly no mass and those with some mass… this has to do with whether or not it is possible in principle to catch up to a particle. How does this mesh with our picture above that masses can come from ‘bumping off the Higgs?”
• What does it mean physically that the Higgs line can terminate? What do we mean by the “vacuum expectation value?” This will turn out to be related to the idea that all of our particles are manifested as quantum fields. What does this mean?
• This whole business is related to something called electroweak symmetry breaking, and that is the phenomenon associated with the Higgs which is really, really magical.

Hi everyone! Readers of this blog might enjoy some of the following recent multimedia by some well-known  particle physicists.

• First, a podcast from Jim Gates of the University of Maryland about his path in  Go Tell It on the Mountain (link to iTunes, link to mp3) from The Moth. The talk is from the 2008 World Science Festival, which will be held again this year in New York City in a month.
• Next, a very nice animated discussion with Daniel Whiteson and Jonathan Feng from UC Irvine on PhD Comics. They discuss dark matter, particle physics, and the Large Hadron Collider.
• Along the lines of dark matter and particle physics, here’s a mission briefing from NASA on AMS-2, the “particle detector in space,” featuring principal investigator (and Nobel laureate for the discovery of the J/ψ particle) Sam Ting. Matt mentioned AMS-2 in his inaugural post. A lot of particle physicists are excited about AMS due to recent anomalies in the spectrum cosmic positrons and anti-protons that may be a result of dark matter interactions.
• Finally, some time ago I had a general-public-level post about Nima Arkani-Hamed‘s (and collaborators) work in scattering amplitudes. For those with a technical background who interested in learning more, his informal lectures to the Cornell particle theory group are now posted online: part 1, part 2, part 3, part 4, part 5. For those who can’t get enough, there’s also an ongoing program at the KITP with lots of recorded talks. These links are at the level of theoretical physicists doing work in the field; for a general public version, see Nima’s messenger lectures.

We’ve mentioned jets a few times here on the US LHC blog, so I’d like to go into bit more detail about these funny unavoidable objects in hadron colliders. Fortunately, Cornell recently had a visit from David Krohn, a Simons Fellow at Harvard University who is an expert at jet substructure. With his blessing, I’d like to recap parts of his talk to highlight a few jet basics an mention some of the cutting edge work being done in the field.

Hadronic Junk

Let’s review what we know about quantum chromodynamics (QCD). Protons and neutrons are composite objects built out of quarks which are bound together by gluons. Like electrons and photons in quantum electrodynamics (QED), quarks and gluons are assumed to be “fundamental” particles. Unlike electrons and photons, however, we do not observe individual quarks or gluons in isolation. You can pull an electron off of a Hydrogen atom without much ado, but you cannot pull a quark out of a proton without shattering the proton into a bunch of other very different looking things (things like pions).

The reason is that QCD is very nonperturbative at low energies. QCD hates to have color-charged particles floating around, it wants them to immediately bind into color-neutral composite objects, even if that means producing new particles out of the quantum vacuum to make everything neutral. These color-neutral composite objects are called hadrons. Unfortunately, usually the process of hadronizing a quark involves radiating off other quarks of gluons which themselves hadronize. This process continues until you end up with a messy spray of particles in place of the original colored object. This spray is called a jet. (Every time I write about jets I feel like I have to reference West Side Story.)

Simulated event from ATLAS Experiment © 2011 CERN

As one can see in the image above, the problem is that the nice Feynman diagrams that we know how to calculate do not directly correspond to the actual mess of particles that form the jets which the LHC experiments measure. And it really is mess. One cannot effectively measure every single particle within each jet and even if one could, it is impractically difficult to calculate Feynman diagrams for very large numbers of particles.

Thus we’re stuck having to work with the jets themselves. High energy jets usually correspond to the production of a single high-energy colored particle, so it makes sense to talk about jets as “single objects” even though they’re really a spray of hadrons.

Identifying Jets

So we’ve accepted the following fact of life for QCD at a particle collider:

Even though our high energy collisions produce ‘fundamental’ particles like quarks and gluons, the only thing we get to observe are jets: messy sprays of hadrons.

Thus one very important task is trying to make the correspondence between the ‘fundamental’ particles in our Feynman diagrams and the hadronic slop that we actually measure. In fact, it’s already very hard to provide a technical definition of a jet. Our detectors can identify most of the “hadronic slop,” but how do we go from this to a measurement of some number of jets?

This process is called clustering and involves developing algorithms to divide hadrons into groups which are each likely to have come from a single high energy colored particle (quarks or gluons). For example, for the simple picture above, one could develop a set of rules that cluster hadrons together by drawing narrow cones around the most energetic directions and defining everything within the cone to be part of the jet:

Simulated event from ATLAS Experiment © 2011 CERN

One can then measure the energy contained within the cone and say that this must equal the energy of the initial particle which produced the jets, and hence we learn something about fundamental object. I’ll note that this kind of “cone algorithms” for jet clustering can be a little crude and there are more sophisticated techniques on the market (“sequential recombination”).

Boosted Jets

Even though the above cartoon was very nice, you can imagine how things can become complicated. For example, what if the two cones started to approach each other? How would you know if there was one big jet or two narrow jets right next to each other? In fact, this is precisely what happens when you have a highly boosted object decaying into jets.

By “boosted” I mean that the decaying particle has a lot of kinetic energy. This means that even though the particle decays into two colored objects—i.e. two jets—the jets don’t have much time to separate from one another before hitting the detector. Thus instead of two well-separated jets as we saw in the example above, we end up with two jets that overlap:

Collimation of two jets into a single jet as the decaying particle is boosted. Image from D. Krohn.

Now things become very tricky. Here’s a concrete example. At the LHC we expect to produce a lot of top/anti-top pairs (t–t-bar). Each of these tops immediately decays into a b-quark and a W. Thus we have

t, t-bar → b, b-bar, W W

(As an exercise, you can draw a Feynman diagram for top pair production and the subsequent decay.) These Ws are also fairly massive particles and can each decay into either a charged lepton and a neutrino, or a pair of quarks. Leptons are not colored objects and so they do not form jets; thus the charged lepton (typically a muon) is a very nice signal. One promising channel to look for top pair production, then, is the case where one of the Ws decays into a lepton and neutrino and the other decays into two quarks:

t, t-bar → b, b-bar, W W → b, b-bar, q, q-bar, lepton, ν

The neutrino is not detected, and all of the quarks (including the bottoms) turn into jets. We thus can search for top pair production by counting the number of four jet events with a high energy lepton. For this discussion we won’t worry about background events, but suffice it to say that one of the reasons why we require a lepton is to help discriminate against background.

Here’s what such an event might look like:

Simulated event from ATLAS Experiment © 2011 CERN

Here “pT” refers to the energy (momentum perpendicular to the beam) of the top quarks. In the above event the tops have a modest kinetic energy. On the other hand, it might be the case that the tops are highly boosted—for example, they might have come from the decay of a very heavy particle which thus gives them a lot of kinetic energy. In the following simulated event display, the tops have a pT that is ten times larger than the previous event:

Simulated event from ATLAS Experiment © 2011 CERN

Now things are tricky! Instead of four clean jets, it looks like two slightly fat jets. Even though this simulated event actually had the “b, b-bar, q, q-bar, lepton, ν” signal we were looking for, we probably wouldn’t have counted this event because the jets are collimated.

There are other ways that jets tend to be miscounted. For example, if a jet (or anything really) is pointed in the direction of the beam, then it is not detected. This is why it’s something of an art to identify the kinds of signals that one should look for at a hadron collider. One will often find searches where the event selection criteria requires “at least” some number of jets (rather than a fixed number) with some restriction on the minimum jet energy.

Jet substructure

One thing you might say is that even though the boosted top pair seemed to only produce two jets, shouldn’t there be some relic that they’re actually two small jets rather than one big jet? There has been a lot of recent progress in this field.

Distinguishing jets from a boosted heavy particle (two collimated jets) from a "normal" QCD jet with no substructure. The plot is a cylindrical cross section of the detector---imagine wrapping it around a toilet paper roll aligned with the beam. Image from D. Krohn.

The main point is that one can hope to use the “internal radiation distribution” to determine whether a “spray of hadrons” contains a single jet or more than one jets. As you can see from the plots above, this is an art that is similar to reading tea leaves. (… and I only say that with the slightest hint of sarcasm!)

[For experts: the reason why the QCD jets look so different are the Alterelli-Parisi splitting functions: quarks and gluons really want to emit soft, collinear stuff.]

There’s now a bit of an industry for developing ways to quantify the likelihood that a jet is really a jet (rather than two jets). This process is called jet substructure. Typically one defines an algorithm that takes detector data and spits out a number called a jet shape variable that tells you something about the internal distribution of hadrons within the jet. The hope is that some of these variables will be reliable and efficient enough to help us squeeze as much useful information as we can out of each of our events. There also seems to be a rule in physics that the longer you let theorists play with an idea, the more likely it is that they’ll give it a silly name. One recent example is the “N-subjettiness” variable.

Jet superstructure

In addition to substructure, there has also been recent progress in the field of jet superstructure, where one looks at correlations between two or more jets. The basic idea boils down to something very intuitive. We know that the Hydrogen atom is composed of a proton and an electron. As a whole, the Hydrogen atom is electrically neutral so it doesn’t emit an electric field. (Of course, this isn’t quite true; there is a dipole field which comes from the fact that the atom is actually composed of smaller things which are charged.) The point, however, is that far away from the atom, it looks like a neutral object so we wouldn’t expect it to emit an electric field.

We can say the same thing about color-charged particles. We already know that quarks and gluons want to recombine into color-neutral objects. Before this happens, however, we have high energy collisions with quarks flying all over the place trying to figure out how to become color neutral. Focusing on this time scale, we can imagine that certain intermediate configurations of quarks might already be color neutral and hence would be less likely to emit gluons (since gluons are the color-field). On the other hand, other intermediate configurations might be color-charged, and so would be more likely to emit gluons. This ends up changing the distribution of jet slop.

Here’s a nice example from one of the first papers in this line of work. Consider the production of a Higgs boson through “quark fusion,” i.e. a quark and an antiquark combining into a Higgs boson. We already started to discuss the Higgs in a recent post, where we made two important points: (1) once we produce a Higgs, it is important to figure out how it decays, and (2) once we identify a decay channel, we also have to account for the background (non-Higgs events that contribute to that signal).

One nice decay channel for the Higgs is b b-bar. The reason is that bottom quark jets have a distinct signature—you can often see that the b quark traveled a small distance in the detector before it started showering into more quarks and gluons. Thus the signal we’re looking for is two b-jets. There’s a background for this: instead of qq-bar → Higgs → b-jets, you could also have qq-bar → gluon → b-jets.

The gluon-mediated background is typically very large, so we would like to find a clever way to remove these background events from our data. It turns out that jet superstructure may be able to help out. The difference between the Higgs → b-jets decay versus the gluon → b-jets decay is that the gluon is color-charged. Thus when the gluon decays, the two b-quarks are also color-charged. On the other hand, the Higgs is color-neutral, so that the two b-quarks are also color neutral.

One can draw this heuristically as “color lines” which represent which quarks have the same color charge. In the image below, the first diagram represents the case where an intermediate Higgs is produced, while the second diagram represents an intermediate gluon.

Color lines for qq-bar → Higgs → b-jets and qq-bar → gluon → b-jets. Image from 1001.5027

For the intermediate Higgs, the two b-jets must have the same color (one is red, the other is anti-red) so that the combined object is color neutral. For the intermediate gluon, the color lines of the two b-jets are tied up to the remnants of the protons (the thick lines at the top and bottom). The result is that the hadronic spray that makes up the jets tend to be pulled together for the Higgs decays, while pushed apart for the gluon decays. This is shown heuristically below, where again we should understand the plot as being a cylindrical cross section of the detector:

Higgs decays into two b-jets (signal) versus gluon decays (background). Image from 1001.5027

One can thus define a jet superstructure variable (called ‘pull‘) to quantify how much two jets are pulled together or pushed apart. The hope is that this variable can be used to discriminate between signal and background and give us better statistics for our searches for new particles.

Anyway, that’s just a sample of the types of neat things that people have been working on to improve the amount of information we can get out of each event at hadron colliders like the LHC. I’d like to thank David Krohn, once again, for a great talk and very fun discussions. For experts, let me make one more plug for his workshop next month: Boost 2011.

Update: for those who read this in time, there will be a seminar on this result broadcast online through the Fermilab webpage. (The talk will be at the level of physicists working in the field.) This result was also mentioned in the NY Times today.

Even though its running days are numbered, the Tevatron reminds us that it can still muster up an interesting hint of new physics. This is a quick post on a brand new result from the CDF collaboration, “Invariant Mass Distribution of Jet Pairs Produced in Association with a W boson in p-pbar Collisions at Sqrt(s) = 1.96 TeV” [arXiv:1104.0699]. Just to whet your appetite, here’s one of the plots that we’d like to understand (hot off the press!):

Unpacking the title

Before diving in, let’s first understand what the title means. It’s somewhat cumbersome, but that’s because it encodes a lot of good physics. It turns out that it’s easier to start at the end of the title and work our way backwards.

• “…in p-pbar Collisions at Sqrt(s) = 1.96 TeV“
  This is telling us about the general Tevatron experiment: they collide a proton (p) with an anti-proton (p-bar) at an energy of about 2 TeV. A TeV is roughly the kinetic energy of a flying mosquito. In Feynman diagram calculations it’s often useful to use the parameter s, which is the square of the energy, rather than the energy itself, hence the weird “Sqrt(s) = 1.96 TeV.” For comparison, recall that the LHC is now operating at 7 TeV and will eventually go up to 14 TeV.
• “…in association with a W boson …”
  This should sound a lot like the “associated production” diagram that we drew for the Higgs boson in a previous post:Reading from left to right, we have a quark and an antiquark producing a gauge boson (in this case the W boson) along with a Higgs. I’ll tell you right now: the CDF result does not appear to be the Higgs, but if there is a new particle responsible for it, it is produced from the same diagram (with the dashed line representing the new particle). [Correction, 6 Apr: a few people have correctly pointed out that the new state could also come from a "t-channel" diagram with an intermediate fermion. (I'll leave the actual diagram as an exercise for those who have been reading my Feynman diagram posts).] By the way, the W decays before it reaches the detector. Two signals are W?e? or W???, which appear in the detector as a charged lepton and “missing energy” (the neutrino).
• “… Jet Pairs Produced …“
  We also know that the Higgs decays into other stuff before it reaches our detectors. Thus we have to tell our detectors to keep an eye out not for the exotic particle, but for the ordinary stuff that it decays into. If it decays into quarks or gluons, then we know that we end up with jets. Thus this paper is looking for a W boson (which itself becomes a lepton + neutrino/missing energy) and a pair of jets. This is the criterion for picking out ‘interesting’ events relevant for this analysis.
• “Invariant mass distribution of…“
  Now that we’ve picked out interesting events, we want to plot them in a way that can tell us if there’s a new particle hidden in the data. The easiest way to do this is to go “bump hunting,” which is what we discussed for the detection of the Z boson. The key idea is this: if we sum the energy and momentum of the two jets, we should get the mass of the intermediate particle that produced them (if they were produced by the same particle). This sum is called the invariant mass, and by plotting the number of interesting events based on the invariant mass, we can look for bumps that are characteristic of new particles.

Phew—that was quite a lot packed into a title. But now we’ve established most of the physics to understand the plot and see what people are [cautiously] excited about!

Results

Here’s the plot, once again:

On the horizontal axis is the invariant mass of the two jets, which is roughly the sum of the jet energies. The vertical axis is the number of events in the data set with the given invariant mass. If there were a particle which produced the two jets, then there should be a bump in the number of events with an invariant mass around the mass of the new particle.

So… what’s all of that colorful mess in the plot? It’s the thing that makes experiments hard: background. We have identified a particular experimental signal (2 jets, a lepton, and missing energy) which could come from a new particle. What we still have to account for are “boring” processes which could lead to the same signal. By “boring” I mean Standard Model processes that we already understand. Here’s the inventory from the plot above:

• The red contribution to the histogram are events where a pair of Ws or a WZ pair are produced. The second W (or the Z) then decays into a pair of jets.
• The big green contribution comes from various processes where a single W is produced and the two jets are separately produced independently of the W.
• The white (with a pink border) sliver are events where a top-anti-top pair are produced. These tops each immediately decay into b (or anti-b) and a W boson. One of these W bosons decays to lepton + neutrino and is tagged by the experiment, while the other one might decay into jets. Now we have four jets (2 from the b quarks, two from the decay of a W), but it is possible for two of those jets to get ‘lost’ because they don’t fulfill the detector criteria for identifying jets. (This is a notoriously subtle thing.) There is also a contribution from the production of a single top.
• The blue sliver is the production of a single Z boson with two jets. The Z decays into two leptons One of the leptons can be ‘hidden’ because the particular search only looks at particles which are fairly perpendicular to the beam direction, or misidentified as a jet.
• Finally, the shaded sliver is QCD background: these are gluon mediated processes that can give two jets and a lepton.

Once we take all of these background effects into account—and this is a very nontrivial thing to do—we can subtract these from the actual number of observed events per invariant mass bin. This “background subtracted data” is plotted below:

Now things look rather interesting. First note that not all of the background is subtracted: they leave in the WW and WZ background because these will also produce a characteristic bump (red line) because the 2 jets come from a single particle (indeed the bump is around the W and Z mass). The other backgrounds have broad, smooth profiles and can be reliably subtracted—bumps are harder to subtract so we keep them in. (Update: I’m told that this may also be partly included for comparison reasons: the W/Z bump is really well understood, so it helps to be able to use it as a measuring stick.)

What’s particularly neat, however, is that there seems to be a second bump with a peak right around 150 GeV. This is what is shown in the blue line. The significance of this bump is around 3.2 standard deviations, which roughly means that we can be 99.7% sure that this is not a statistical fluctuation.

It’s not the (standard) Higgs

If this bump really does come from a particle with mass around 150 GeV, then the first thing one might think is that this is the first hint of the Higgs boson. Indeed, we even showed above that the production of the Higgs includes diagrams that would give this particular signal when the Higgs decays into two quarks. However, one very, very interesting part of the analysis is that it does not seem like this bump could come from the standard Higgs boson!

The reason is simple: we understand the standard Higgs well enough to know that if it had a mass of 150 GeV, then we would expect an effect (a bump) that would be about three hundred times smaller. In the parlance of the field, the observed bump corresponds to a particle with a 4 picobarn dijet cross section, while a 150 GeV Higgs is expected to have a 12 femtobarn dijet cross section.

Further, CDF has already done a closely related analysis: WH ?l? b b-bar. This is basically the same analysis as the present paper, except that they are able to identify jets that come from b-quarks (this is called b-tagging). The analysis with b-tagged jets showed that there was no significant excess in the range 100 — 150 GeV.

What this means is that if this bump is indeed coming from a new particle, then it must not be a particle which decays into b-quarks, at least not very often. We know, however, that the standard Higgs does decay into b-quarks, so this hypothetical new particle could not be the usual Higgs.

This is actually much more interesting, since this could either suggest a non-standard Higgs sector or it could be a sign of completely different new physics.

I should note that there is one sentence whose significance is a little unclear to me:

We compare the fraction of events with at least one b-jet in the excess region (120-160 GeV) to that in the sideband regions (100-120 and 160-180 GeV) and find them to be compatible with each other.

Basically, they look at how many b-quark jets were in the bump versus those that weren’t in the bump, and they find that the number is roughly the same. This seems to imply that whatever is causing the bump is not decaying into b quarks, but I’m not an expert on this and might be misreading it.

Where to go from here

Don’t get too excited, though. Nobody is breaking out champagne bottles yet. Three standard deviation effects have been known to come and go—i.e. it is possible that it is just an unlucky statistical/systematic fluctuation. For example, it might be a mis-modeling of the background that had to be subtracted. (The three standard deviation significance assumes that one “knows how to estimate what one doesn’t know,” as one person explained it to me.) All the same, I expect that there will be plenty of model-building papers by eager theorists in the next few weeks. [By the way, CDF has known about this effect for some time; the current excitement comes from breaking the 3 standard deviation significance and their subsequent publication of the result.]

There are a few things to look out for:

1. More data! We measure data in “inverse femtobarns” (1/fb). The current paper is based on the analysis of 4.3/fb. My [outsider's] understanding is that CDF should have around 10/fb by the end of the year, so the collaboration should be able to say something with more significance if this is a real effect.
2. What about D0? Fermilab’s other collaboration should be able to corroborate (or refute) this effect.
3. I do not believe that the LHC has enough data to say much about this at the moment, though I understand that we could be looking at 1/fb of data by summer time, and maybe a few inverse femtobarns through 2012. If the signal is real, there might be some hope to see the effect before the long shutdown at the end of 2012.

There are a lot of people who are cautiously optimistic about this. It’s almost certain that many theorists will jump on this to see if their favorite models can be tweaked to give a 150 GeV particle decaying to jets (but visible in the b-jet analysis), and that’s part of the fun. I look forward to seeing how things develop (and perhaps jumping in if the opportunity presents itself)!

Acknowledgements: I would like to thank my experimental colleagues, SP and DP for many helpful conversations. Any errors in this post are purely due to my own misunderstanding. I challenged some hep-ex grad students to foosball to try to squeeze info out of them before the paper was published… but I lost and they didn’t spill any beans. [They're also strictly prohibited from such gossip... especially to theorists.]

A different presentation of the Higgs

There have been several very clever attempts to explain the Higgs to a general audience using analogies; one of my favorites is a CERN comic based on an explanation by David Miller. Science-by-analogy, however, is a notoriously delicate tightrope to traverse. Instead, we’ll take a different approach and jump straight into the physics. We can do this because we’ve already laid down the ground work to use Feynman diagrams to describe particle interactions.

In the next few posts we’ll proceed as we did with the other particles of the Standard Model and learn how to draw diagrams involving the Higgs. We’ll see what makes the Higgs special from the diagrammatic point of view, and then gradually unpack the deeper ideas associated with it. The approach will be idiosyncratic, but I think it is closer to the way particle physicists really think about some of the big ideas in our field.

This first post we’ll start very innocently. We’ll present simplified Feynman rules for the Higgs and then use them to discuss how we expect to produce the Higgs at the LHC. In follow-up posts we’ll refine our Feynman rules to learn more about the nature of mass and the phenomenon called electroweak symmetry breaking.

Feynman Rules (simplified)

First off, a dashed line represents the propagation of a Higgs boson:

You can already guess that there’s something different going on since we haven’t seen this kind of line before. Previously, we drew matter particles (fermions) as solid lines with arrows and force particles (gauge bosons) as wiggly lines. The Higgs is indeed a boson, but it’s different from the gauge bosons that we’ve already met: the photon, W, Z, and gluon. To understand this difference, let’s go into a little more depth on this:

• Gauge bosons, things which mediate “fundamental” forces, carry angular momentum, or spin. Gauge bosons carry one unit of spin; roughly this means if you rotate a photon by 360 degrees, it returns to the same quantum mechanical state.
• Fermions, matter particles, also carry angular momentum. However, unlike gauge bosons, they carry only half a unit of spin: you have to rotate an electron by 720 degrees to get the same quantum state. (Weird!)
• The Higgs boson is a scalar boson, which means it has no spin. You can rotate it by any amount and it will be the same state. All scalar particles are bosons, but they don’t mediate “fundamental” forces in the way that gauge bosons do.

This notion of spin is completely quantum mechanical, and it is a theorem that any particle with whole number spin is a boson (“force particle”) and any particle with fractional spin is a fermion (“matter particle”). It’s not worth dwelling too much about what kind of ‘force’ the Higgs mediates—it turns out that there are much more interesting things afoot.

Now let’s ask how the Higgs interacts with other particles. There are two Feynman rules that we can write down right away:

Here we see that the Higgs can interact with either a pair of fermions or a pair of gauge bosons. This means, for example, that a Higgs can decay into an electron/positron pair (or, more likely, a quark/anti-quark pair). For reasons that will become clear later, let’s say that the Higgs can interact with any Standard Model particle with mass. Thus it does not interact with the photon or gluon, and for argument’s sake we can ignore the interaction with the neutrino.

The interaction with fermions is something that we’re used to: it looks just like every other fermion vertex we’ve written down: one fermion coming in, one fermion coming out, and some kind of boson. This reflects the conservation of fermion number. We’ll see later that because the Higgs is a scalar, there’s actually something sneaky happening here.

Finally, the Higgs also interacts with itself via a four-point interaction: (This is similar to the four-gluon vertex of QCD.)

There are actually lots of subtleties that we’ve not mentioned and a few more Feynman rules to throw in, but we’ll get to these in the next post when we will see what happens with the Higgs gets a “vacuum expectation value”. Please, no comments yet about how I’m totally missing the point… we’ll get to it all gradually, I promise.

Higgs Production

Thus far all we’ve been doing is laying the groundwork in preparation for a discussion of the neat things that make the Higgs special. Even before we get into that stuff, though, we can use what we’ve already learned to talk about how we hope to produce the Higgs at the LHC. This is an exercise in drawing Feynman diagrams. (Review the old Feynman diagram posts if necessary!)

The general problem is this: at the LHC, we’re smashing protons into one another. The protons are each made up of a goop of quarks, antiquarks, and gluons. This is important: the protons are more than just three quarks! As we mentioned before, protons are terribly non-perturbative objects. Virtual (anti-)quarks and gluons are being produced and reabsorbed all over the place. It turns out that the main processes that produce Higgs bosons from proton collisions comes from the interaction of these virtual particles!

One of the main “production channels” at the LHC is the following gluon fusion diagram:

This is kind of a funny diagram because there’s a closed loop in the middle. (This makes it a very quantum effect… and somewhat more tricky to actually calculate.) What’s happening is that a gluon from one proton and a gluon from the other proton interact to form a Higgs. However, because the gluons don’t directly interact with a Higgs, they have to do so through quarks. It turns out that the top quark—which is heaviest—has the strongest interaction with the Higgs, so the virtual quarks here are tops.

Another way to get a Higgs is associated production with a top pair. The diagram looks like this:

Here gluons again produce a Higgs through top quarks. This time, however, a top quark and an anti-top quark are also produced along with the Higgs. We can draw a similar diagram without the gluons:

This is called vector fusion, because virtual W or Z bosons produce a Higgs. Note that we have two quarks being produced as well.

Finally, there is associated production with a W or Z. As homework you can fill in the particle labels assuming the final gauge boson is either W or Z:

There are other ways of producing a Higgs out of a proton-proton collision, but these are the dominant processes. While we know a lot about the properties of a Standard Model Higgs, we still don’t know its mass. It turns out that the relative rates of these processes depends on the Higgs mass, as can be seen in the plot below (from the “Tevatron-for-LHC” report):

The horizontal axis is the hypothetical HIggs mass, while the vertical axis measure the cross section for Higgs production by the various labeled processes. For our purposes, the cross section is basically the rate at which these processes occur. (Experimentally, we know that a Standard Model Higgs should have a mass between about 115 GeV and 200 Gev.) We can see that the gg → h is the dominant production mechanism throughout the range of possible Higgs masses—but this is only half of the story.

We don’t actually directly measure the Higgs in our detectors because it decays into lighter Standard Model particles. The particular rate at which it decays to different final states (“branching ratios”) are plotted above, image from CDF. This means we have to tell our detectors to look for the decay products of the Higgs in addition to the extra stuff that comes out of producing the Higgs in the first place. For example, in associated production with a top pair, we have gg → tth. Each of the tops decay into a b quark, a lepton, and a neutrino (can you draw the diagram showing this?), while the Higgs also decays—say, into a pair of b quarks. (For now I’m not distinguishing quarks and anti-quarks.) This means that one channel we have to look for is the rather cumbersome decay,

gg → tth →blν blν bb

Not only is this a lot of junk to look for in the final state (each of the b quarks hadronizes into a jet), but there are all sorts of other Standard Model processes which give the same final state! Thus if we simply counted the number of “four jets, two leptons, and missing energy (neutrinos)” events, we wouldn’t only be counting Higgs production events, but also a bunch of other background events which have nothing to do with the Higgs. One has to predict the rate of these background events and subtract them from the experimental count. (Not to mention the task of dealing with experimental uncertainties and possible mis-measurements!)

The punchline is that it can be very tricky to search for the Higgs and that this search is very dependent on the Higgs mass. This is why we may have to wait a few years before the LHC has enough data to say something definitive about the Higgs boson. (I’ve been somewhat terse here, but my main point is to give a flavor of the Higgs search at the LHC rather than explain it in any detail.)

Next time

In our next post we’ll introduce a completely new type of Feynman rule representing the Higgs “vacuum expectation value.” In doing so we’ll sort out what we really mean when we say that a particle has mass and continue our march towards the fascinating topic of electroweak symmetry breaking (“the Higgs mechanism”).

Lecture on Fukushima radiation

Forgive me for digressing a bit from the LHC focus of this blog, but I wanted to take time to share a timely and accessible public lecture by UCSB particle physicist Benjamin Monreal about the science of the Fukushima reactor meltdowns in Japan. I strongly recommend it for those who want to be able to make sense of the news regarding radiation in Japan and elsewhere.

One of our jobs as scientists is to be there to inform the public when something like this happens, and Benjamin rises to the occasion with exceptional clarity. As he mentions towards the end of his talk, it is often the case that misinformation is one of the biggest dangers after an event like this, and he goes a long way to explain what’s actually going on. I learned quite a lot from the presentation and it has helped me provide a proper scientific context for the news about the region.

It’s always very difficult to cope with the aftermath of a natural disaster on the scale of the Tohoku earthquake two weeks ago. The particle physics community is especially international and the news of the disaster hit quite close to home for many of us with friends and colleagues in Japan. Our hearts go out to everyone affected.

Coleman’s QFT Lectures

Sidney Coleman. Image from L. Motl.

Now to change gears quite a bit, I’d like to share another link that has been making a splash in particle physics circles: a typed up version of Sidney Coleman’s 1985-1986 Physics 253a quantum field theory course at Harvard, thanks to the heroic typesetting efforts of Bryan Gin-ge Chen and Ting Yuan Sen. (See also the videos of the lectures from 1975-76.) The link is perhaps most useful for young physicists who are learning field theory (or older physicists who are teaching field theory), but as a concession for the non-physicists reading this blog, here’s a link to Coleman’s well known seminar, “Quantum Mechanics in your face.”

Let me provide some background. Sidney Coleman is one of the towering figures of theoretical physics in our time and one of the true masters of quantum field theory. While he doesn’t have the same popular image as Richard Feynman, his unique charm and wit as well as his dexterity as a teacher are nothing short of legendary in the physics community.

Coleman’s life and work were commemorated at Harvard in 2005 at “Sidneyfest.” The list of famous presenters and speakers speak volumes about Coleman’s influence. Sadly, Coleman passed away in 2007. He left behind an indelible mark on the history of quantum field theory as well as several lectures (most notably his Erice lectures, published in Aspects of Symmetry) which continue to educate generation after generation of particle physicists.

Hi everyone! Today I wanted to share something that is less about physics, but more about what it’s like to be a physicist. For those who have been asking for more “Physics through Feynman Diagrams” posts, don’t worry: I’ve been spending a lot of time thinking about how to explain the Higgs mechanism, and this is something I’m looking forward to typing up.

One of my first blog posts on US LHC was titled “My Workbench,” following the style of the regular column in Seed magazine. This semester our group finally moved to a new building, so I wanted give a snapshot of my research environment. So, without further ado, here’s my annotated office.

Before going into details… yes, it’s an office. I don’t have a lab, I don’t wear a lab coat, I don’t even wear closed-toed shoes. (When indoors I’m usually shuffling around in comfy Birkenstocks.) This is partly because I’m a theorist and my experimental colleagues wouldn’t let my clumsy hands anywhere near lab equipment—but actually most experimentalists have very similar offices where they do much their analysis work (Christine’s rappelling onto the ALICE detector notwithstanding!).

1. One important feature is a nice window that gets natural lighting (it looks into an atrium with a skylight, which is why the immediate view is the building next door). It may sound a bit superficial, but we often work long hours and getting some sunlight makes a big difference. My officemates and I also have several plants, which brightens the atmosphere a bit. (You can tell that my plant has grown since my original workbench post!)

2. Penguins. This is a bit of an inside joke, but two of my first projects as a graduate student had to do with the calculation of a particular process called a ‘penguin diagram.’ I seem to have collected various penguin-themed posters and stuffed animals from friends who were amused by my odd paper and talk titles (most recently, “Warped Penguins”).

3. Headphones. It’s nice to have some ambient background noise when concentrating. Some of the other students in my group swear by pink noise, but I’m usually listening to something silly like this spoof from PhD comics. These headphones are also very helpful when having Skype discussions with collaborators who are far away.

4. Here you can see my basketball shoes. I haven’t played basketball in a while (these days I spend more time swimming), but as a student it is really important to maintain some balance in one’s life otherwise it’s easy to go off the deep end. Other common recreational activities in our group include foosball and ping pong. I’ve found that many of my most interesting physics discussions have happened while during non-physics recreation with other physicists.

5. This is my trusty messenger bag, which I carry with me everywhere I go like Linus and his blanket. I usually carry a notepad with the current research idea I’m obsessing over, my laptop, and several journal articles which I’m supposed to read. Most of the latter get skimmed over on the bus in the mornings. During the winter (which seem to last forever here in upstate New York) I usually have an extra pair of gloves and a pull-over packed in case of inclement weather.

6. This is my messy desk. Usually various bits of scratch paper, print outs, and reference books find their way strewn about. I’m a relatively tidy person and clean up every other night or so, but my style of working is to sprawl everything out as I use them. (I’m sure my officemates get annoyed by this, but thus far they’ve been very accommodating.)

7. In my upper storage units I have several reference books. You can also see my ping pong paddle peeking through. When I’m confused with my work I’ll start pulling down books to try to sort things out… and when that doesn’t work, I’ll try to work through the problem with a colleague over ping pong.

8. This is my officemate’s desk. There’s a total of three of us in the office, which I think is a good balance of having company while not becoming too distracting. It’s nice to be able to have other people around when you have “stupid questions” about physics… especially since more often than not these “stupid questions” can have surprisingly profound answers. You can see that my neighbor is much neater than I am.

Here’s a close-up of my desk:

9. This is an old t-shirt from the SLAC National Accelerator Laboratory. I fell in love with particle physics as a undergraduate at Stanford and got my first taste of research at SLAC as a summer student. I highly recommend the experience to all undergraduates interested in particle physics.

10. Unlike some of the other students, I don’t usually have lots of work on the tack board directly in front of me. Instead, I’ve put up several photos of other physicists, mostly graduate students whom I have gotten to know over the past few years. (If you’ve spent any appreciable time doing particle physics with me, I probably have your photo up here.) This is more than just nostalgia; a large part of doing physics is collaboration. The best way to generate and test new ideas is to bounce them off of colleagues and work with people with complimentary skill sets. As such, there is a strong sense of camaraderie in the particle physics community. The people whom you get to know in grad school tend to be the same people you keep bumping into and working with the rest of your career.

11. This is my laptop. I spend a lot of time on it. These days we access all of the latest research papers directly from the Internet, we communicate with collaborators using video conferencing, we correspond via e-mail, we run simulations over computing farms…. all through our computers. That being said, I’ve also been working on knowing when to turn off my computer (and its associated distractions) when I need to bunker down and do an old-fashioned pen-and-paper calculation.

12. Here are some of my most commonly used books. Apparently you can tell a lot about a physicist by what kinds of books are on his or her bookshelf… so for those of you who care, here’s a short summary of what I keep at arm’s reach:

• The QFT books by Peskin, Ryder, Weinberg, Zee, and Srednicki
• Aspects of Symmetry by Coleman
• Current Algebra and Anomalies (an old volume of reprints)
• The particle physics books by Cheng & Li and Mohapatra
• The SUSY texts by Terning, Bailin & Love, Wess & Bagger, and Binetruy
• Some mathematically-oriented reading: Anomalies in QFT by Bertlmann, the text by Nakahara, and the monograph by Gockeler and Schuker
• Perfectly Reasonable Deviations from the Beaten Path, a collection of Richard Feynman’s letters. This isn’t a physics book, but I find it inspiring to skim through it when I’m having a rough research day.
• Just for fun: on my desk I also have two volumes of PhD comics, the “Scientific Progress goes Boink” Calvin and Hobbes collection, and Our Dumb World by the Onion

I have a bunch of other books… but they’re hidden behind the plush versions of the Standard Model, via the Particle Zoo:

13. This is a plush dog that I picked up during a Guy Fawkes carnival at Cambridge University. It’s followed me through my postgraduate studies. (There’s a lot of silliness in my office; would you believe me if I said that it is balanced by a very serious focus on my research? Well, that’s what I tell my adviser, anyway…)

14. When I finish up a project I have several sheets of hand-written notes and calculations. I’ve collected these into large binders, initially as “trophies” of past work, but I’ve since found that there are times when one has to refer back to a subtle detail long after the project is done.

15. I should note that this sheep is not part of the Standard Model. I think I picked it up during a wine tasting trip with one of our seminar speakers. Below are random fridge magnets which I’ve stuck to a large filing cabinet containing several more papers: mainly saved documents, important references, notes for old talks, and material related to teaching.

Before I sign out, there is one very conspicuous omission: my office doesn’t yet have any chalkboards! (These are in the process of being installed.) Chalkboards are really useful since so much of our daily work involves explaining ideas to one another; though there’s a bit of a divide in the particle physics community between theorists who love chalkboards and experimentalists who (for reasons I don’t really understand) tend to prefer whiteboards.

Well, that’s my office! I don’t expect MTV to visit for an episode of Cribs any time soon, but at least now you know where I am when I’m typing up blog posts every couple of weeks.

Last time I posted, we looked at the “Eightfold way” classification of mesons. We argued that this is based only on symmetry and allowed physicists in the 60s to make meaningful predictions about mesons even though mesons are ultimately complicated “non-perturbative” objects where quarks and anti-quarks perform an intricate subatomic ‘dance’ (more on this below!).

Historical models of mesons

In fact, physicists even developed theories of mesons as fundamental particles—rather than bound states of quarks—which accurately described the observed light meson masses and interactions. These theories were known as “phenomenological” models, chiral perturbation theory, or nonlinear sigma models. These are all fancy names for the same idea.

From a formal point of view these models suffered a theoretical sickness: while they agreed well with experiment at low energies, they didn’t seem to make much sense if you used them to calculate predictions for high energies. It’s not that the predictions didn’t match with experiments, it’s that theory seemed to make no predictions! (Alternately, its predictions were nonsense.) The technical name for this illness is non-renormalizability, and it was American Nobel Laureate Ken Wilson who really clarified the correct way to understand these theories.

Ken Wilson (b. 1936) may not have the public fame as Richard Feynman or Robert Oppenheimer, but he is without a doubt one of the great American theoretical physicists of the century. His research focused on the theoretical framework of quantum field theory and its applications to both particle physics and condensed matter physics. He was one of the great thinkers of our field who really understood the “big idea,” and I think he is nothing short of a hero of modern physics.

Rather than going into the precise sense in which a non-renormalizable theory is a ‘sick’ theory, let’s emphasize Wilson’s key insight: these sick theories are fine as long as we are careful to ask the right questions. Wilson made this statement in a much more mathematically rigorous and elegant way—but in this post we’ll focus on getting the intuition correct.

Effective theories

The point is that these “non-renormalizable” theories are just approximations for the behavior of a more fundamental theory, which we call an effective theory (here’s a very old post on the big idea). These approximations get the “rough behavior” correct, but doesn’t sweat the details. If you then try to ask the approximate theory something about the details that it neglects, then it gives you a gibberish response. Wilson taught us how to understand the gibberish as the theory saying, “I’m not sophisticated enough to answer that!”

Here’s a concrete example. One of my previous posts presented a pixelated image of the Mona Lisa to demonstrate “lattice QCD.” (This is actually exactly the effective theory that Ken Wilson was working on.)

The pixelated Mona Lisa is an “effective” image with details blurred out compared to the “fundamental” image. Even with these details removed, from far away the images look the same. In fact, the effective image is sufficient to answer questions like

• What is the overall color of the image or of different patches of the image? (Beige/brown)
• How many figures are in the image? (One… but keep this in mind for later)

On the other hand, effective Mona Lisa is completely unequipped to answer more subtle questions like

• Where is the Mona Lisa looking?
• Is the Mona Lisa happy or sad?

Okay, arguably even art historians can’t come up with answers to those questions. But the point is that the pixelated image can’t even begin to try to answer them—the questions ask about details that were left out of the “effective” image. Such questions are outside of the domain of validity of the effective image.

Now here’s a very important lesson in particle physics:

Models of particle physics also have a domain of validity, beyond which they are ill equipped to make sensible predictions.

For some models, like the effective theories of mesons, asking questions outside of the model’s domain of validity leads to nonsense answers. On the other hand, within the domain of validity the models are perfectly predictive. In fact, different “effective models” have to agree when their domains of validity overlap. Here’s an example from an old post where classical electromagnetism is an effective theory for quantum electrodynamics, as manifested by the formula for the electric field.

Dancing with the quarks

Now let’s get back to mesons, albeit though an analogy. We know that a pion is really a quark–anti-quark caught up in a subatomic dance. They spin about one another, exchange gluons, and can even interact with other particles as a joint entity. Here’s a rough picture:

But here’s the thing: that’s the picture that we see only if we can really look very closely and observe the quarks directly. This requires having front row seats at “Dancing with the Quarks” (or at least an HDTV). For someone who can only watch the broadcast at low resolution, the dance looks very different: everything is blurred out:

In fact, this is now just like the case of the pixelated Mona Lisa. Note that because the quarks are so meticulously coordinated, the blurry picture looks like there’s only one object dancing! We call that object a pion and we can make careful measurements of how it spins and interacts… all without knowing that if we only had better resolution we would actually see two quarks dancing in unison rather than one pion.

Things brings us back to the state of particle physics in the 1960s. We can create an entire effective theory to describe the pion, but we have to accept that we’ve put on our fuzzy glasses and can’t make out any details. We can’t ask our effective theory something like “how many hands are in the picture above?” Well, it looks like two… but it’s hard to be sure. I could ask an even more difficult question: what is the gender of the dancers in the picture above? Now the effective theory completely falls apart. Any answer that it can give must be manifestly wrong because it doesn’t even know that there are two dancers, much less the particular gender of either. In the same way, the effective theories of mesons seemed to fall apart when you asked questions about energies higher than their regime of validity.

Modern Effective Theories

Let me end by remarking that even though the underlying goal of high energy physics is to probe nature at a fundamental level, effective theories are still incredibly useful tools.

1. Matching theories to low-energy experiments. It is often the case that theories of exotic new particles at high energies are constrained by experiments that are conducted at much lower energies. For example, many models of new physics are limited by how they would affect the physics of ordinary W and Z bosons.  By writing an effective theory of W and Z bosons that parameterizes the effect of new physics, we can provide robust bounds on the properties of whatever new particles appear at high energies. (For experts: these are the electroweak precision constraints, see hep-ph/0405040, hep-ph/0412166, hep-ph/0604111) The analogy to the dancing quarks is to use the blurry picture to tell us that, “I don’t know how many hands there are, but if there are more than two, then they have to be pretty close to one another.” (For experts: this approach has recently been applied to direct detection of dark matter.)
2. “Phenomenological models.” In the previous case we simplify a calculation of a fundamental theory by working with an effective theory; this is a top-down approach. We can also consider the bottom-up approach where we write down a model that describes known low-energy physics and figure out at what energy it breaks down. We can then predict that there should be some new physics not encapsulated in our model appearing at those energies. This is where we are with particle physics: we have observed a bunch of neat particles and measured their properties—but the entire framework breaks down somewhere around the TeV scale unless we have something like the Higgs boson appearing.
3. Strong coupling and duality. This brings us back to mesons. Recall that our effective meson theory was a way for 1960s physicists to describe the particles coming out of early colliders without ever having to worry about the horrible non-perturbative QCD substructure that we now know is actually there. In some cases, there is a much stronger relation between the fundamental and effective theories and the two theories are said to be dual to one another. The 1990s were revolutionary for the development of formal dualities between seemingly unrelated theories: Witten’s web of dualities in M-theory, Seiberg duality in supersymmetric gauge theories, and gauge/gravity dualities like the AdS/CFT correspondence proposed by Maldacena. (For theoretical physics fans: those are some really big names in the field; each one of them is a MacArthur”Genuis” fellow!)

Anyway, there’s a surprising amount of “deep” physics that one can glean from thinking about mesons… even if they are somewhat “boring” particles that aren’t even fundamental. The notion of effective field theory is one of the central pillars of particle physics (as well as statistical physics), and in fact perhaps provides the most solid intuition about the entire field of high energy physics.

Happy Valentine’s Day everyone… well, unless you were expecting hints for supersymmetry (SUSY) at the LHC. Last night the ATLAS collaboration posted the results for one of its supersymmetry searches to the arXiv. They corroborate last month’s results from CMS on a similar type of search. (The CDF site has an excellent public summary that should be at the right level for physics enthusiasts with no formal background.)

What is supersymmetry?

Supersymmetry is an extension of the Standard Model in which every particle and anti-particle has a superpartner particle with a silly name, such as “gluinos” as the partners of gluons and “squarks” as the partners of quarks. The neat thing about supersymmetry is that the partner of a matter particle is a force particle (with a prefix s-), while the partner of a force particle is a matter particle (with a suffix -ino). SUSY does a lot of great stuff for us theoretically, but it must be broken so that the Standard Model particles and the SUSY particles are split up and have different masses. Because this is Valentine’s day, let’s leave the details of this splitting up to another post.

What is the LHC telling us?

Here’s one of the key plots from the ATLAS paper (which includes the CMS result):

I’ll not get into the details here and will keep the discussion as accessible as possible. The axes of the plot are parameters in a particular supersymmetric model. The horizontal axis is the “universal scalar mass” m0 (related to the mass of the squarks) while the vertical axis is the “universal gaugino masses” (related to the mass of the gluinos and its cousins). The area inside the curves (lighter masses) are ruled out. The red line is the ATLAS result, the black line is the recent CMS result, and the other lines are various exclusions from older experiments.

These parameters aren’t quite the same as the masses of the superparnters, but they are related by some formulae which experts in the field have memorized. A good estimate for the stringency of the bounds on the actual superpartner masses come from the conclusion of the paper:

For a chosen set of parameters within MSUGRA/CMSSM, and for equal squark and gluino masses, gluino masses below 700 GeV are excluded at 95% CL.

Some translations:

• MSUGRA/CMSSM: These stand for “minimal supergravity” and “constrained minimal supersymmetric Standard Model.” The most general supersymmetric version of the Standard Model has over 115 free parameters… this would be a nightmare to plot. For simplicity, experimentalists typically plot their results against simplified reference models with much smaller parameter spaces.
• Squark and gluino masses: squarks are the partners of quarks and gluinos are the partners of gluons. The experiment is setting a lower bound on these masses. (Recall: heavier things are harder to produce.) The 700 GeV lower bound on the squark/gluino mass (in the case where they’re equal) is much heavier than any particle in the Standard Model—recall that the top quark is ‘only’ 172 GeV.
• 95% CL. This is a confidence level that explains the statistical strength of this bound. Roughly it answers the question, “based on the data, how sure are you of the statement you’re making?” Here’s a great explanation.

What’s actually happening at the LHC?

The general idea is that a common feature of most SUSY models is that when supersymmetric partner is produced at a collider, it will eventually decay into familiar stuff and a particle which escapes undetected. This escaping particle is called the lightest supersymmetric particle (LSP) and is a natural dark matter candidate, but its presence is only experimentally determined because the measured momenta of all the familiar stuff doesn’t balance. Thus a good way to search for the presence of supersymmetric partners is to look for:

1. A high energy “normal” particles (typically QCD “jets”)
2. Large “missing energy,” i.e. momentum that doesn’t add up

The high energies are important to tell us that something heavy (like a new particle) may have been involved, and the missing energy is important to tell us that something escaped undetected. By looking for decays of this type, ATLAS and CMS are able to constrain the existence of supersymmetric partners up to a certain mass. In fact, the reason why the LHC has been able to greatly improve the bounds on SUSY—even at such an early stage of running—is that the previous constraints from the Tevatron were limited not by how much data they could take, but by the energy scale of the collision.

Here’s an example, another plot from the ATLAS paper:

This plot shows the number of events in a particular range of “effective mass,” a kind of kinematic variable which characterizes the energy of an event. Here’s what’s happening:

1. ATLAS records a bunch of data over the past year or so. For each recorded particle collision (“event“), ATLAS records information about what its detectors see (“signal“).
2. Physicists go through this data when they want to search for new particles. The set of physicists who worked on this search focused only on the events whose signals included a lepton (e or μ), QCD jets (quarks and gluons), and missing energy.
3. They then plot the number of events whose “effective mass” is in a certain energy range. This gives the data points on the plot above.
4. In order to compare to the Standard Model, they run a “Monte Carlo” simulation of the kind of signal that known physics would produce in this particular channel. These are all of the different colored pieces of the histogram—they represent events that we expect to be counted even if there is no new physics in these events.
5. If the data points line up with the sum of expected events, then we conclude (up to a certain statistical significance) that there was no new physics observed.

For reference, the dotted line is the expected contribution from one particular choice of SUSY parameters. That line would have to be added to the Standard Model sum (shown as a thin red line); clearly the data points do not show this excess.

What does this mean for supersymmetry?

This isn’t great news for supersymmetry. One of the appealing features of supersymmetry is that it can solve the hierarchy problem of the Higgs mass. This problem is only really solved, however, if the SUSY particles are not that much heavier than their Standard Model partners. Thus the more we push up the lower bound on the super partner masses, the more trouble we have explaining the Higgs paradigm within the Standard Model.

I think I am not yet enough of an expert to comment on how severe the recent ATLAS/CMS results are in terms of current favorite models of supersymmetry. However, I will note that the particular model that was used to make these bounds represents a very narrow subset of possible supersymmetric extensions of the Standard Model. As explained above, this is by necessity: a plot over a 115-dimensional parameter space is simply not possible. Most of these parameters are related in plausible ways and the bounds from ATLAS and CMS are probably farily robust over huge swaths of parameter space, but in principle there is a lot of freedom to tweak a parameter here or there to try to evade particular experimental bounds. [For experts: last I heard there was some nit picking about the tan-β dependence of these results?]

This is actually a fairly important point. For the past two decades theorists have worked hard to come up with clever supersymmetric models which can either give novel experimental signatures or which are otherwise “generic” in a way that is not captured by the usual models used to experimentally constrain SUSY. With the advent of the LHC era, however, more thought has gone into better interfacing with our experimental colleagues to connect the results of the LHC to a more robust set of SUSY parameters. (This is part of a larger shift in the particle physics community over the past decade to have better communication between our theoretical and experimental practitioners.)

Anyway, there’s one thing that’s for sure: the Standard Model particles will be without super partners once again on Valentine’s day.

PS — [from Cosmic Variance] apparently the White House is also due to release its FY2012 budget request this Valentine’s day. Given the push towards spending cuts, it’s not looking like fundamental science will get much love… but I’m crossing my fingers anyway. (I don’t want to get political, but fundamental research is an investment in the American science and engineering infrastructure and the future of the American economy.)