How can you identify interesting events?

In the context of neutrinos and 'invisible' particles (from the detector's point of view), let's talk about the momentum balance in the event.  Momentum could have units of kg times m/s (it's a mass multiplied by a speed), but just to confuse you, in particle physics jargon we typically use units of GeV/c....Like I've said many times, it's just a name.  Those are a standard unit when we talk about measuring momentum.

The total momentum in a given proton is divided up amongst its constituents – it's a 'share the load' sort of thing.  In Part III we learned how protons are made up of particles called quarks and gluons.  So if we have to split the proton's momentum up amongst its constituents, we could choose to give 20% of the momentum to the first quark, 34% to the second quark, and 17% to the third quark.  The rest we can give to the gluons that are in there.  I made those numbers up, but the momentum fraction concept is real.  Of course the various fractions should all add up to 100%. 

The only problem is that nature does the splitting up, and for a given proton, we have absolutely no way of knowing a priori how things are divided.  Weirder yet: the relative contributions from all of the various types of pieces depend on the energy of the proton as a whole (but in a way that can be measured at least in terms of averages).  Still, we don't have a way of knowing the actual breakdown of the momentum fractions in any particular collision at all.  Quantum mechanically it's neither possible nor meaningful to do so anyway.  Again, for this sort of stuff the best we can do is speak of averages:  reach into a proton with a blindfold on, metaphorically speaking, and there are a set of functions (dictated by nature but which we can measure!) which allow us to know the probability that you'll pull out an up quark, a down quark, a gluon, or whatever the case may be.  You get the idea.

What we do know is that regardless of how the momentum is split up amongst the constituents, the total momentum for each proton as a whole has to be a fixed value of 7 TeV/c (we've tuned the accelerator that way) and, perhaps more useful, that 100% of its momentum has to be in the forward direction. Remember after all: momentum has a direction, right?

And so even though those momentum fractions are a messy business is that the total momentum perpendicular to the beam line is zero!  This is of paramount importance in the collisions in ATLAS. 

Why? 

Well, it was zero to start off with, and there's a fundamental law of physics that tells us that momentum is conserved – like energy, it can neither be created nor destroyed but only passed from some objects to others, or from some form to another. 

Said another way, there was no net momentum in the transverse plane (i.e. the two-dimensional plane perpendicular to the beam line) before the collision, so there shouldn't be any afterwards.

Below I've drawn a cartoon depicting what I mean by the transverse plane:

As a direct consequence of what was just said, collision events in ATLAS which feature high-energy particles travelling in directions more perpendicular to the proton-proton beam direction are more likely to be of interest to us.  We say such particles are very central, which can be contrasted with what we call very forward -going particles closer to the proton beamline direction.  

The light-blue shaded portion in the cartoon below highlights the central region.

At ATLAS we have dedicated hardware tools and software algorithms to seek out exactly such events.  These are used to so-called trigger possible events of interest so we can save its data and have a more detailed look later.  Crucially we rely on the information that there's no initial significant momentum in any direction other than the beam directions.

Coming back to the first point about conserved momentum, you could be thinking: wait, what about neutrinos?  Won't those throw off the momentum balance we were taking for granted?

Yes!  Actually one of the key things we look at to look for signs of strange or new physics is with a quantity called the missing transverse energy.  Actually we call it that, but you might be confused thinking back to the fact that energy doesn't have a direction (whereas momentum does, remember?).  So really it's related to momentum (which has a direction) as opposed to energy (which doesn't).  So missing transverse energy (or, if you prefer, missing transverse momentum) boils down to an energy imbalance: a lot of energy measured on one side of the detector and comparatively less on the opposite side.  So a large amount of missing transverse energy suggests the presence of some non-interacting particle which carried the energy away that would have made things balance.  It's a very important quantity when looking for new exotic forms of matter!

Getting back to the neutrino, we sometimes attribute the missing transverse energy to the neutrino in the event.  After all, we just heard in Part VI how neutrinos essentially do not interact with our detector.  In many cases doing this works very well!  As long as the neutrino (which we assume is there) is the most significant non-interacting particle in the event, this is a safe thing to do.

More than one high-energy neutrino and we run into trouble. 

Why? 

Well consider the situation that you had two neutrinos produced and which travel outwards in perfectly opposite directions (e.g. one goes straight up, one goes straight down).  In such a case we wouldn't really think anything was wrong, would we?  There wouldn't really be an imbalance of momentum in the event at all.   What's worse is that our detector triggering system likely wouldn't even catch the event since it wouldn't look interesting enough.  We'd miss it entirely!

Either way though, one thing's clear: if we do see huge amounts of missing transverse energy in cases where we didn't expect a high-energy neutrino, then that's a good sign something really interesting happened.

Seeing huge amounts of missing energy is the sort of stuff that physicists dream about – that missing energy could be some exotic new type of matter we were hoping to create.  Why don't we measure it?  Well, according to many theoretical models, exotic matter (just like neutrinos) also shouldn't interact with the detector material.  If it did, it likely wouldn't be so tough to spot, and we could have maybe observed it in our everyday lives already, right?

The same thing about two neutrinos mentioned above is regrettably also likely true for these new exotic forms of matter: if they're produced in pairs and the two exotic particles travel in opposite directions, we might miss them entirely with this approach.  We could be producing copious amounts of them and our detector would be throwing out the data.  Right under our noses, so to speak.

Luckily all is not lost.  Although we wouldn't be able to see them from such a direct measurement, their presence could be detected indirectly via other measurements.  New, exotic forms of matter can manifest themselves in other ways, and in some cases missing transverse energy wouldn't help us.  More on this to come in a later section.

But the key point to remember: large amounts of missing transverse energy could be the hint that we've witnessed something new and exciting! 


Knowing where to look

Often it’s useful to have a sense of where (i.e. in what regions of the detector) you’re expecting to see whatever it is you’re looking for.  Sometimes this is obvious and you can expect to know beforehand.  Sometimes it isn’t.

Let’s take the case of Z bosons decaying to pairs of muons (so each one in this case decays to a muon and an anti-muon).  If the Z bosons were to have no extra energy, by which I mean there's just enough energy for the production to happen and it’s all perfectly balanced, then what would one expect to see?

First let’s draw a standard three-dimensional coordinate system (that x-y plane you’d remember from graphing functions in high school math, together with a 3rd dimension sticking out of the page – don’t worry, you don’t have to draw any functions!).  

Now let’s stick our Z boson right dead at the centre of the coordinate system – or at the origin as we call it – and watch what happens.

Unsurprisingly, there’s nothing special about any direction, right?  The whole setup is spherically symmetric.  So if the Z boson is going to decay (and make no mistake, it'll decay faster than you could ever time with the world’s best clock), its decay products will blast out in any direction.  Almost.  Since there are two decay products, they have to balance one another in momentum.  For two identical decay products (like the two muons) that’s easy: they'll have the same energy, the same momentum, and they'll shoot off in perfectly opposite directions – back-to-back, as we say.

[An interesting side note: this back-to-back concept is at the root of a technology you might have heard of called Positron Emission Tomography (or PET for short).  The decay products in that case are photons, not muons.  But do a google image search and see if anything looks familiar to you now that you're armed with the knowledge of the past few sections.]

If the decay products of the initial particle were different (they’re not in this case), you'd have to go back to that small car / giant truck analogy we used when talking about momentum.  It’s not the speeds that have to balance but rather the ‘speed-times-mass’ or momentum.

So here’s what we would get for the spherically symmetric scenario we just described:

Easy enough, right?

But hold on, as we said from the get-go, this would only be the situation if the Z bosons were produced at rest and sitting right at the origin (where x = y = z = 0).

In the LEP accelerator (predecessor of the LHC) where electrons and positrons were collided, they could actually tune the accelerator’s energy and beams just right such that they would really have the above scenario more or less!  They’d turn it on and bam!, they’d start seeing evidence of Z bosons being produced more or less at rest right near the centre of the detector.

With the proton-proton collisions at the LHC, remember that the actual interactions are from the pieces inside the protons (quarks and gluons), so it’s a lot messier and it’s relatively rare that you’d get a nice balanced scenario.  Often the piece from the first proton has a ton of energy and the piece from the second proton with which it interacts is tiny by comparison.  In other words: things are unbalanced. Moreover the centre-of-mass energy involved in the collisions at the LHC is much higher than the Z boson mass, (by more than a factor of 100) so that extra energy has to go somewhere.  In the case that only a single Z boson is created, it’s then often not created at rest, but with a bit of extra energy – a boost, we call it.

Then for one last complication, we have a bit of a broken symmetry because of the directions of the LHC beams!

Suddenly the z-axis is very different from the x- and y-axes.

So, big surprise, we end up building a detector that’s not spherically symmetric.  But since the x- and y-axes are on equal footing, our detector does more or less have cylindrical symmetry!

All to say that the directions of those muon decay products of the Z bosons produced in ATLAS will fly off in directions that won’t be as straightforward.

That’s as much as we’ll go into it.  But the key point: sometimes our models and simulated data can give us a sense of where to look (and we can subsequently compare with data to fine-tune our simulations).  And that really helps refine our search methods.

Boosted Particles

Let's come back to the idea of a boost, since the boost of a particle can also have a huge effect on what its decay products do.  The boost of a a particle with non-zero mass is really a measure of how much overall energy (the energy of the matter itself plus the energy of motion) the particle has compared to its mass.  The smallest that number can be is 1, but there’s no upper limit.  The higher the value of the boost is, the more the decay products will tend to go in the same direction the parent particle was initially travelling.  If the parent particle has a boost of exactly one, it means that the only energy it has is in the form of mass (no energy of motion), so it's stationary.

Instead of a Z boson, let’s switch it up and use a Higgs boson as our initial particle.  We'll also consider the case in which the Higgs boson decays to two photons rather than a muon-antimuon pair as we had previously in the case of the Z boson decay.  The choice of the type of parent particle (i.e. whether it's a Higgs versus a Z boson in our case), its initial energy of motion, and the masses of the particles it decays to all govern the ultimate decay kinematics – the energies and directions of the decay products after they were produced.  And those energies and directions also depend on who's reference frame we're in!

Cartoons illustrating the concept of high-energy boosts in particle physics. 

Putting the Pieces Back Together...

ATLAS has teams of physicists looking for all kinds of signals.  It's a divide-and-conquer sort of strategy.  Some try to identify Higgs bosons, or even measure their properties if they can identify enough of them, some (such as myself during my time as a grad student) aim to reconstruct top quarks produced in the collisions.  Yet others look for exotic matter we've never seen before, and so on.  I can't imagine we could ever really run out of interesting studies to do.  Of course those are just the actual physics analyses.  It also takes a ton of people to actually run the experiment, and to develop the common software tools needed by physicists in actually analyzing the vast amounts of data (so they can find what they're looking for!).

At the end of the day a particle physicist's job (or one of the best parts of their jobs) is to put pieces of particles – pieces here being energy and momentum, and so indirectly mass as well – back together to build up candidates of the heavier particles they're truly interested in studying or searching for.

The different types of detector measurements provide them with a broad palette of reconstructed particles which allows them to study various processes.  They could be looking for Z bosons which decayed to a muon/anti-muon pair – in this case they reconstruct the muons, put them together, and use that as a probe to the Z bosons they're really interested in.  Or perhaps they're looking for the elusive Higgs boson which should sometimes decay to a pair of photons (particles of light), or sometimes four leptons (such as an electron, anti-electron, muon and anti-muon ... phew: mouthful!).    A few of these examples are illustrated below.

At the end of the day the basic idea is the same: put the pieces back together and reconstruct the heavier particle.

In terms of what properties they actually measure and how that's done, wait for the coming sections.

A cartoon depicting the reconstruction of heavier particles via the signals left by their decay products in the ATLAS detector.

First Look at a Simulated ATLAS Event

A nice way to wrap up this section is to have a look at a real event display from ATLAS.  Here the term 'real' is used since it's an actual ATLAS event, but watch out: this is a simulated event corresponding to a proposed theoretical model (or one variation of it) called Supersymmetry; it's not from measured data.  Supersymmetry is a model that aims to address several of the 'holes' in the current Standard Model.  Among others one of its predictions is the existence of supersymmetric 'partners' to the regular Standard Model particles (the ones you were introduced much earlier on).  That would make our table of fundamental particles in Part I about twice as large!

What's important to note here is that:

(1) We haven't actually observed (directly or indirectly) any of these exotic particles, but that could be for a variety of reasons – the model has a lot of flexibility and there are no concrete predictions for the actual masses of the particles (they could be larger than anything we can even produce given our current energy limitations!).  That said, the theory itself of course does make concrete predictions!

(2) Supersymmetric particles are expected to not really interact with the detector material at all.

The second point might remind you of another type of particle we've been talking about: a neutrino!  And it's true, the signature that supersymmetric particles would leave (or rather not leave) in the detector would be similar to that of a neutrino.  Crucially then, we can look for evidence of Supersymmetry by searching for events with large amounts of missing transverse energy in the detector (just like with neutrinos) together with observing what other particles are produced in the same event.  Seeing large excesses – seeing far more of a given type of interaction than the Standard Model predicts – would be a clear giveaway that we could be seeing something new.  This could of course be supersymmetric particles, but possibly something else.

As a side note, you might be wondering why Supersymmetry is so popular then, given that we haven't seen anything to suggest that it actually describes nature at all.  Maybe it's nothing more than a beautiful theory – fancy math and a neat idea and all that, but ultimately not a theory that describes how our universe behaves.  That could be true.  But actually, the fact that it's a beautiful theory is not a statement to be taken lightly.  It's an important point: it is a beautiful theory!  In the past some physicists have held so firmly to the idea that nature, at its deepest level, must be simple and beautiful. Supersymmetry is a theory to which some people have spent their careers dedicated.  And there are ways that its predictions modify the predictions made by the Standard Model which move us more in the direction of a 'unified theory', where at a high enough energy the fundamental forces become unified!

So you're going to be looking at a simulated supersymmetric event in ATLAS.  And voilà, here it is:

Credit: ATLAS Experiment © 2014 CERN

Credit: ATLAS Experiment © 2014 CERN

What you're looking at is a side view of ATLAS.  Actually it's not just a regular side view:  It's the view you'd get if you were to squeeze and flatten the whole ATLAS detector along what used to be its largest dimension.  So the lines you see (they're actually reconstructed tracks!) could be coming partly at you, moving partly away from you, or they could actually be going exactly in the directions as shown.  You're looking at it in a kind of flat space.

The centre of the circle corresponds to the centre of the ATLAS detector where the collision would have taken place.  You see different types of tracks in the very central part compared to the next or more busy-looking layer (where again, there are still tracks reproduced, but the technology is somewhat different).  At the extremes of the image you see big block-like towers.  Those represent calorimeter energy deposits.  If they're really big it means the energy deposited there is really small.  I'm kidding, it's the other way around.  You notice two tracks that make it past the calorimeters: any guesses as to what type of particles could have led to those? (I won't give it away – they're one of the main categories of particles we talked about earlier).

Remember that when you look at an event like this things should originally have been more or less balanced.  Even by eye, you can see that that doesn't seem to be the case: something invisible must have headed off in the direction represented by about 10 o'clock (if we treat the whole picture like the face of a clock).  Of course we don't know exactly because we haven't done the actual balance – depends not just on the angles, but on what the actual energies and momenta are that are involved!  And crucially there could be more than one 'invisible' particle in there.  But that, in effect, is an indication that something – in this case supersymmetry – is throwing off the balance.  It's of course possible to get some normal run-of-the-mill Standard Model process which could produce such an event, but the number of such cases should be quite limited (and, crucially, predictable).  We can count events and see if we see an 'excess'.  

More on this (and more!) in the next section.

And that's it!

In the next sections we look at how we could actually make a particular measurement with all of the data –  it could be the potential discovery of something new or unexpected, it could be the setting of an upper or lower bound on some value, or it could be a precision measurement of something we already know exists.