## Open days at CERN: a few answers April 5, 2008

Posted by dorigo in physics.

Today is a CERN open day, and the ATLAS and CMS detectors will receive scores of visitors who will tour the LHC caverns, grabbing their last chance to be treated by a really amazing display of technology and engineering. These detectors are indeed unprecedented for their size and complexity, although the overall concept behind their construction is not much different from that of the experiments that have preceded them in thirty-five years of Collider Physics. But anybody who visits these apparata will no doubt re-emerge from the pits with several unanswered questions. For instance, why are they so BIG? What drives their shape, their design, the tens of thousands of engineering choices that have been made in the last 15 years to get to the result on display today ?

The detectors are designed to satisfy several important requirements, connected to the need to measure trajectory and energy of all particles crossing them. Let me discuss the most important ones in turn, in the hope of answering at least in part the sample questions above.

Hermeticity

When you study a head-on collision between beams of particles of high energy, one concept is clear to you: you wish to detect all the bodies produced in the interaction, and measure their properties. By doing so, you have a chance at figuring out the dynamics of the collision. Understanding the dynamics -the extrinsecation of the forces acting on the particles- allows you to discover a new interaction, or observe new processes mediated by known interactions, or measure previously undetermined details of a known process. These are the breakthroughs particle physicists are really after.

The requirement of a complete detection is what we refer to as “hermeticity”: one needs to surround the interaction point with a hermetic detector system, which measures every energetic particle, without allowing any to leave unseen: missing some of the produced particles may corrupt one’s capability to exactly determine the nature of the collision.

Of course, holes have to be provided in the direction of incoming and outgoing beams, so a part of the solid angle around the interaction point cannot be covered by detection devices. Additional defects in hermeticity are also imposed by constraints coming from the need of cables for the readout of the detectors, pipes to cool them down, and electric lines to provide them with the necessary power. These functions imply that the detector system contains non-sensitive components along with the sensitive parts, worsening its measuring capabilities. They of course also add complexity to the design, to the mechanical construction, and to the whole project.

Redundancy

Detectors for colliding beams also need to be redundant in the measurement of the particles that cross them. Redundancy allows some forgiveness to the measuring devices, and increases the overall precision with which particles are tracked. Imagine, for instance, that you detect the direction of an incoming pion with several layers of silicon microstrip detectors, as is done in the core of CMS. As the pion traverses each 300 micron-thick silicon layer it creates about 20,000 electron-hole pairs, which then drift guided by an electric field to a detection electrode (the “strip”), causing a digitized pulse which signals the passage of the particle at the coordinate of the electrode. By reading the strip signals, you thus get a set of position measurements along the trajectory, which allow a precise tracking of the pion.

With one pion three layers would be more than enough – even the occasional failure of one of them would not impair your ability to guess where the track passed. But now imagine what happens if there are a hundred particles crossing the same devices not far from the pion path: you now need several layers, not just three, in order to sort out the sets of hits that line up along probable particle trajectories. Thus, redundancy protects from ambiguities or occasional failure of a detector component.

Versatility

If you happened to hear the statement that the mission of LHC is to discover the Higgs boson, you may well have frowned: is it sufficient to justify such a challenging endeavour ? Indeed, the LHC project does much more for us than promise a discovery if the Higgs boson exists: it furthers the high-energy frontier – the limit of our knowledge – by almost one order of magnitude. If, as many theorists speculate, some form of Supersymmetry is the right description of the subnuclear world, then it is virtually guaranteed that the LHC experiments will find not one, but several new particles, allowing us to understand much more of reality than we currently do.

In order to provide the capability of discovering supersymmetry, CMS and ATLAS need to be versatile. If they had been built just for the Higgs discovery, in fact, a block of magnetized iron surrounded by muon detectors would have been the design of choice: All particles would be absorbed in the iron, while the four muons produced in the $H \to ZZ \to \mu^+ \mu^- \mu^+ \mu^-$ would have been easily detected outside of it; their energy would have been deduced by the difference between their detected direction and the radial one (since the higher their energy, the smaller the amount of bending they undergo in a magnetic field), and a Higgs mass would have been reconstructed easily on top of residual backgrounds.

Instead than a block of magnetized iron, the detectors are a concentrate of technology. They allow the measurement of jets, electrons, photons, neutrinos with performances similar to or exceeding those of other experiments, despite the complexity of the collisions and their extremely fast rate. The menu of detector components –silicon tracker, electromagnetic and hadronic calorimeters, muon chambers– is not new, but their integration and synergy is perfected by almost forty years of trial and error.

Of course, with such complex devices there are trade-offs. As an example, CMS boasts an excellent electromagnetic calorimeter -a “photon detector” – made of lead tungstate crystals, which enables a very good energy resolution on the $H \to \gamma \gamma$ decay, helping spot a peak in the diphoton mass, as the red bump in the yellow background shown in the graph on the left. The CMS electromagnetic calorimeter cost a lot of money and it weighed on the budget of the experiment: other parts of the detector needed to be designed to be more cost-effective.

Momentum resolution

None of the above requirements demand a huge size for the LHC detectors. However, one important parameter does. The dimensions of a tracker are directly connected with the resolution with which they measure the momentum of charged particles. A high momentum resolution can be critical if we need to reconstruct the decay of a particle such as the Higgs boson in its decay to lepton tracks, as in the simulated graph on the right.

Because of the Lorentz force, charged particles travel in helical paths (with axis along the beam direction) in the axial magnetic field produced by the cylindrical solenoids surrounding the tracker. These helices have a radius of curvature approximately given by R in the formula $P_t = 0.3 B R$, where $P_t$ is the momentum component transverse to the beam -and thus orthogonal to the field lines- measured in GeV/c; B is the magnetic field in Tesla units, and R is measured in meters.

If the above formula gives the momentum for a given radius of curvature, we can compute how the measurement of momentum for a track from its displacement x of a circular path from a straight line is affected by the detector size L (see figure).

We can write $x=R-\sqrt{R^2-L^2}$, where L is the distance over which you measure the track, and x the displacement from a straight line. Extracting R from that formula we obtain $R=(x^2+L^2)/(2x)$, which can be inserted in the formula for transverse momentum:

$P_t = 0.3 B L^2/(2x)$

(where we neglect the tiny x with respect to L in the numerator), from which

$x=0.15 B (L^2/P_t)$.

We are done with math, promise! The formula above is our result. It tells you that if x is the thing you measure, to keep it constant as you multiply by four times the momentum you need to increase L by a factor two. As momentum increases, x becomes smaller: if your ability to measure small values of x with some accuracy is limited, so is your measurement of large momenta. Since LHC runs at a center-of-mass energy seven times larger than that of the Tevatron, the highest momentum particles its detectors need to measure may be seven times larger than those measured by the Tevatron experiments too. So we may naively expect detector size to scale by the square root of 7, or about 2.6 times. About right!

Of course, if you have a chance of increasing the B field you can leave L the same; but our technology currently does not allow us to build very big superconducting magnets with fields much larger than a few Tesla.

Particle identification

Regardless of the specific details of the construction of a particle detector, what you can directly detect with it are of course only those particles that live long enough to travel away from the interaction point. This narrows down the list of candidates you need to be sensitive to. Ordinary matter and radiation – protons, neutrons, electrons, photons – are joined by only a few additional bodies: the other leptons (muons, tauons, neutrinos), and just a few light hadrons (basically pions and kaons). That is about it. Since those listed above are also the final states of the decay of all the shorter-lived particles and resonances, however, by measuring the former one can detect and measure the latter.

We have little chance to identify with certainty each of these different particles. If they traveled at non-relativistic speed, we could infer their identity by measuring their speed $v$ from the time they take to cross our apparatus, and simultaneously their energy $E$ – because we would then be able to guess their mass $m$ from the formula $E = 1/2 m v^2$. However, they all travel to speeds too close to that of light, so the method cannot be applied save in very special cases.

Our best bet is to detect their different behavior as they interact with matter: their different interaction properties. Electrons and photons produce electromagnetic showers as they interact with matter, because of the two processes of bremsstrahlung and pair production, both of which require a heavy nucleus to exchange four-momentum with them; electromagnetic calorimeters (in red above) take care of measuring their energy. Muons traverse large amounts of matter with minimal losses of energy, and they are best detected downstream of anything else (the green part in the diagram above); hadrons (protons, neutrons, pions and kaons) instead interact by strong force with the nuclei of the traversed material, producing a hadronic shower – much longer and more complex than electromagnetic ones. Fortunately, we need not identify each hadron separately, since they show a collective behavior – they come in narrow sprays called jets, which are originated by the fragmentation of a hard quark or gluon. We measure collectively their energy by absorbing them in thick slabs of matter – the light blue sector in the picture above. Since calorimeters destroy the particles they measure, we have better measure their momentum beforehand if we can: that is why charged particles get sorted out in the blue sector on the left before reaching the calorimeters.

In summary…

The requirements discussed above are just a few among those a good detector design must satisfy, of course. A more complete treatment would exceed the scope of this post… And your patience. In another post, if I find the energy to write it, I will discuss the challenges connected to the architecture of the system responsible for acquiring, processing, and storing the data that CMS and ATLAS will produce once particles finally will collide in their cores: the trigger system.

1. DB - April 5, 2008

“If, as many theorists speculate, some form of Supersymmetry is the right description of the subnuclear world, then it is virtually guaranteed that the LHC experiments will find not one, but several new particles, allowing us to understand much more of reality than we currently do.”

I understand you are betting on a null result, T., but the string theorists have already created their fallback position if the LHC fails to detect supersymmetry: namely: Split Supersymmetry, i.e., the supersymmetric particles are so far above the TeV scale you’ve no realistic hope of ever detecting them. It no longer solves the hierarchy problem, which was the main reason for proposing supersymmetry in the first place, but to hell with all that – it’s more important to save string theory – which collapses if supersymmetry isn’t found.

2. Fred - April 5, 2008

Thanks T.,

Fine reading for a Saturday morning.

“We are done with math, promise!”

Funny, a life saver for me towards understanding certain passages which lead to another hour or so of reading about the Lorentz force. Now, off to the golf course where the little white ball always seems to defy the known laws of physics, where palm trees literally survive on a steady diet of \$4 golf balls and supersymmetry is only found in the thread patterns of certain golf clothes. Keep the math coming, please.

3. dorigo - April 5, 2008

Good point DB. I tend to rate that as a really weird speculation. I understand split susy can have some merits, but hiding it out from us for the sole purpose of staying alive is the kind of thing that makes me wonder if that is really science after all.

Fred, thank you. Sorry for the formulas – I thought a few would not kill anybody once in a while. I envy your golfing time. It is a game I am sure I would enjoy, but have never managed to try.

Cheers,
T.

4. Fred - April 6, 2008

Tee,

Golf gives me tremendous pleasure even when I’m only practicing on the driving range. The instant feedback after each shot is rewarding in a way that rehearsing a song on an instrument is for a musician, especially on the ones that go awry because the cursing that follows is spontaneous and often very imaginative. How many times have you banged and sworn at the piano keys because your fingers or mind aren’t responding gracefully? The only reason I have time for sports, music and such is that I am neither married nor have children. But these extra-curricular activities pale in comparison to the love one receives from their family and friends. Actually, I wish you would include more formulas. For some reason they make me happy but at the same time they seem like a lonely lot. Your accompanying diagrams make them less so.

5. Calorimeters for High Energy Physics experiments - part 1 « A Quantum Diaries Survivor - April 6, 2008

[…] experiments – part 1 April 6, 2008 Posted by dorigo in physics. trackback Yesterday I discussed some of the most important features that characterize the detectors with which the Large Hadron […]

6. Paolo - April 8, 2008

By the way, after my recent regular visit, I decided to return to CERN for the Open Day and it was a GREAT time! Just as an example, in Building 27 I learned a lot about those crystals used in CMS which Tommaso discusses in another recent post. Ah, if people are interested I can post more about my LHC 2008 day…

7. dorigo - April 8, 2008

Hi Paolo,

sure, be my guest and post here your impressions. If you write a detailed piece on your open day there we can even put it up as a guest post. The rules are: two to five pages, at least a pic or two, a short bio of yourself, and attending to the comments thread for the forthcoming week or so.

Cheers,
T.

8. dorigo - April 8, 2008

Fred, I did not answer promptly to your last comment above, but I did post another piece with some formulas, after your instigation.

Cheers,
T.

Sorry comments are closed for this entry