On Monday, during the concluding session of the SEARCH Workshop on Large Hadron Collider [LHC] physics (see also here for a second post), and at the start of the panel discussion involving a group of six theorists, Michael Peskin, professor of theoretical particle physics at the Stanford Linear Accelerator Center *[and my Ph.D. advisor]* opened the panel with a few powerpoint slides. He entitled them: “My Advice in Four Slogans” — the advice in question being aimed at experimentalists at ATLAS and CMS (the two general-purpose experiments at the LHC) as to how they ought best to search for new phenomena at the LHC in 2012, and beyond. Since I agree strongly with his points (as I believe most LHC theory experts do), I thought I’d tell you those four slogans and explain what they mean, at least to me. *[I'm told the panel discussion will be posted online soon.]*

**1. No Boson Left Behind**

There is a tendency in the LHC experimental community to assume that the new particles that we are looking for are heavy — heavier than any we’ve ever produced before. However, it is equally possible that there are unknown particles that are rather lightweight, but have evaded detection because they interact very weakly with the particles that we already know about, and in particular very weakly with the quarks and antiquarks and gluons that make up the proton.

Peskin’s advice is thus a warning: **don’t just rush ahead to look for the heavy particles; remember the lightweight but hard-to-find particles you may have missed.**

The word “boson” here is a minor point, I think. All particles are either fermions or bosons; I’d personally say that Peskin’s slogan applies to certain fermions too.

**2. Exclude Triangles Not Points**

The meaning of this slogan is a less obscure than the slogan itself. Its general message is this: if one is looking for signs of a new hypothetical particle which

- is produced mostly or always in particle-antiparticle pairs, and
- can decay in multiple ways,

*one has to remember to search for collisions where the particle decays one way and the antiparticle decays a different way*; the probability for this to occur can be high. Most LHC searches have so far been aimed at those cases where both particle and anti-particle decay in the same way. This approach can in some cases be quite inefficient. In fact, **to search efficiently, one must combine all the different search strategies.**

Now what does this have to do with triangles and points? If you’d like to know, jump to the very end of this post, where I explain the example that motivated this wording of the slogan. For those not interested in those technical details, let’s go to the next slogan.

**3. Higgs Implies Higgs in BSM**

*[The Standard Model is the set of equations used to predict the behavior of all the known particles and forces, along with the simplest possible type of Higgs particle (the Standard Model Higgs.) Any other phenomenon is ***by definition** Beyond the Standard Model: **BSM**.]

* [And yes, one may think of the LHC as a machine for converting theorists' B(SM) speculations into (BS)M speculations.]*

One of the main goals of the LHC is to find evidence of one or more types of Higgs particles that may be found in nature. There are two main phases to this search, Phase 1 being the search for the “Standard Model Higgs”, and Phase 2 depending on the result of Phase 1. You can read more about this here.

Peskin’s point is that **the Higgs particle may ****itself**** be a beacon, signalling new phenomena not predicted by the Standard Model**. It is common in many BSM theories that there are new ways of producing the Higgs particle, typically in decays of as-yet-unknown heavy particles. Some of the resulting phenomena may be quite easy to discover, if one simply remembers to look!

Think what a coup it would be to discover not only the Higgs particle but also an unexpected way of making it! Two Nobel prize-winning discoveries for the price of one!!

Another equally important way to read this slogan *(and I’m not sure why Peskin didn’t mention it — maybe it was too obvious, and indeed every panel member said something about this during the following discussion)* is that everything about the Higgs particle needs to be studied in very great detail. Most BSM theories predict that the Higgs particle **will** behave differently from what is predicted in the Standard Model, possibly in subtle ways, possibly in dramatic ways. Either its production mechanisms or its decay rates, or both, may easily be altered. So we should not assume that a Higgs particle that *looks* at first like a Standard Model Higgs actually *is* a Standard Model Higgs. *(I’ve written about this here, here and here.)* * Even a particle that looks very much like a Standard Model Higgs may offer, through precise measurements, the first opportunity to dethrone the Standard Model.*

**4. BSM Hides Beneath Top**

At the Tevatron, the LHC’s predecessor, top quark/anti-quark pairs were first discovered, but were rather rare. But the LHC has so much energy per collision that it has no trouble producing these particles. ATLAS and CMS have each witnessed about 800,000 top quark/anti-quark pairs so far.

Of course, this is great news, because the huge amount of LHC data on top quarks from 2011 allowed measurements of the top quark’s properties that are far more precise than we had previously. *(I wrote about this here.)* But there’s a drawback. Certain types of new phenomena that might be present in nature may be very hard to recognize, because the rare collisions that contain them look too similar to the common collisions that contain a top quark/anti-quark pair.

Peskin’s message is that the *LHC* *experimenters need to do very precise measurements of all the data from collisions that appear to contain the debris from top quarks, just in case it’s a little bit different from what the Standard Model predicts.*

*A classic example of this problem involves the search for a supersymmetric partner of a top quark, the “top squark”. Unlike the t’ quark that I described a couple of slogans back, which would be produced with a fairly high rate and would be relatively easy to notice, top squarks would be produced with a rate that is several times smaller. [Technically, this has to do with the fact that the t' would have spin-1/2 and the top squark would have spin 0.] Unfortunately, if the mass of the top squark is not very different from the mass of the top quark, then collisions that produce top squarks may look very similar indeed to ones that produce top quarks, and it may be a big struggle to separate them in the data. The only way to do it is to work hard — to make very precise measurements and perhaps better calculations that can allow one to tell the subtle differences between a pile of data that contains both top quark/anti-quark pairs and top squark/anti-squark pairs, and a pile of data that contains no squarks at all.*

**Following up on slogan #2: An example with a triangle.**

Ok, now let’s see why the second slogan has something to do with triangles.

One type of particle that has been widely hypothesized over the years is a heavy version of the top quark, often given the unimaginative name of “top-prime.” For short, top is written **t**, so top-prime is written **t’**. The t’ may decay in various possible ways. I won’t list all of them, but three important ones that show up in many speculative theories are

- t’ → W particle + bottom quark (t’ → Wb)
- t’ → Z particle + top quark (t’ → Zt)
- t’ → Higgs particle + top quark (t’ → ht)

But we don’t know **how often** t’ quarks decay to Wb, or to Zt, or to ht; that’s something we’ll have to measure. *[Let's call the probability that a t' decays to Wb ``P*_{1}'', and similarly define P2 and P3 for Zt and ht].

Of course we have to look for the darn thing first; maybe there is no t’. Unfortunately, **how we should look for it depends on ***P*_{1}*,*_{ }*P2*, *and P3*, which we don’t know. For instance, if P_{1} is much larger than P2 and P3, then we should look for collisions that show signs of producing a t’ quark and a t‘ antiquark decaying as t’ → W^{+} b and t‘ → W^{-} b. Or if P_{2} is much larger than P_{1} and P_{3}, we should look for t’ → Zt and t‘ → Z t.

Peskin's triangle for a t' quark; at each vertex the probabilty for the decay labeling the vertex is 100%, while at dead center all three decays are equally probable. One must search in a way that is sensitive to all the possibilities.

Peskin has drawn this problem of three unknown probabilities, whose sum is 1, as a triangle. The three vertices of the triangle, labeled by Wb, Zt and ht, represent three extreme cases: P_{1}=1 and P_{2}=P_{3}=0; P_{2}=1 and P_{1}=P_{3}=0; and P_{3}=1, P_{1}=P_{2}=0. Each point inside this triangle represents different possible non-zero values for P_{1}, P_{2} and P_{3} (with P_{1}+P_{2}+P_{3} assumed to be 1.) The center of the triangle is P_{1}=P_{2}=P_{3}=1/3.

Peskin’s point is that if the experiments only look for collisions where both quark and antiquark decay in the same way

- t’ → W
^{+} b and t‘ → W^{-} b;
- t’ → Zt and t‘ → Z t;
- t’ → ht and t‘ → h t;

which is what they’ve done so far, then they’ll only be sensitive to the cases for which P_{1} is by far the largest, P_{2} is by far the largest, or P_{3} is by far the largest — the regions near the vertices of the triangle. But we know a number of very reasonable theories with P_{1}=1/2 and P_{2}=P_{3}=1/4 — a point deep inside the triangle. So the experimenters are not yet looking efficiently for this case. Peskin is saying that to cover the whole triangle, one has add three more searches, for

- t’ → W
^{+} b and t‘ → Z t, or t’ → W^{-} b and t’ → Zt;
- t’ → W
^{+} b and t‘ → h t, or t‘ → W^{-} b and t’ → ht;
- t’ → Zt and t‘ → h t, or t’ → ht or t‘ → Z t;

so as to cover that case (and more generally, the whole triangle) efficiently. Moreover, no one search is very effective; one has to combine them all six searches together.

His logic is quite general. If you have a particle that decays in four different ways, the same logic applies but for a tetrahedron, and you need ten searches; if two different ways, it’s a line segment, and you need three searches.