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Posts Tagged ‘muon’

This column by Fermilab Director Pier Oddone appeared in Fermilab Today on Jan. 17.

Last week we hosted the US-UK Workshop on Proton Accelerators for Science and Innovation. The workshop brought together scientists from the United States and the United Kingdom who are working on high-intensity proton accelerators across a variety of fronts. The meeting included not only the developers of high-intensity accelerators but also the experimental users and those involved in the applications of such accelerators beyond particle physics.

At the end of the conference, John Womersly, CEO of the UK’s Science and Technology Facilities Council, and I signed a letter of intent specifying the joint goals and activities of our collaboration for the next five years. We plan to have another workshop in about a year to review progress and explore additional areas of collaboration.

Our collaboration with scientists from the United Kingdom in the area of high-intensity proton accelerators is already well established. We have a common interest in muon accelerators, both in connection with neutrino factories and muon colliders. Both of these future projects require multi-megawatt beams of protons to produce the secondary muons that are accelerated. We collaborate on the International Muon Ionization Cooling Experiment at the Rutherford Appleton Laboratory. MICE is the first muon cooling experiment and an essential step in the road to neutrino factories and muon colliders. We also collaborate on the International Scoping Study for neutrino factories.

In our current neutrino program we are very appreciative of this collaboration and U.K. expertise in the difficult mechanical design of high-power targets, in particular for the MINOS, NOvA and LBNE experiments. The design of these targets is quite challenging as the rapid deposition of energy creates shock waves that can destroy them.The Project X experimental program also depends on having appropriate megawatt-class targets relatively close to experimental set-ups.

One of the primary interests in applications outside of particle physics is the development of intense proton accelerators that could be used for the transmutation of waste or even the generation of electrical power in subcritical nuclear reactors. The accelerators necessary for such subcritical reactors could not have been built just a decade ago, but the advent of reliable superconducting linacs changed that. Several programs abroad are developing such accelerators coupled to reactors. While the United States has no explicit program on accelerator-driven subcritical systems, the technologies that we are developing for other applications, such as Project X, place us in a good position should the United States decide to develop such systems.

Overall, the workshop was very productive and the areas of potential collaboration seemed to multiply through the meeting. Each one of the five working groups is preparing a brief summary of the potential areas of collaboration as well as a specific and focused plan for the next year.


This article first appeared in Fermilab Today on Oct. 7.

A muon collider is closer to reality after a successful high-pressure hydrogen gas-filled RF (HPRF) cavity beam test at Fermilab. The test, conducted in the MuCool Test Area (MTA) at Fermilab by the MuCool collaboration, shows the beginnings of a practical solution to a difficult obstacle.

From left: Ben Freemire, Katsuya Yonehara, Mukti Jana, Moses Chung and Giulia Collura standing behind the HPRF cavity (under the hood) and beam pipe section. Photo: Yagmur Torun, R&D

“This was years in the making,” said MTA coordinator Yagmur Torun. “This idea of using HPRF cavities for muon cooling was first proposed in the early 2000s.”

Muons, a heavier version of electrons, are elementary particles. They cannot break down into smaller components, like protons decaying into gluons and quarks. Muons have nearly 200 times the mass of electrons. Electrons would lose too much energy circling in an accelerator, while muons retain enough energy to reach collision speeds.

The problem is that the muons come into existence as a hot gas, which is much too large to fit through a conventional accelerator without beam cooling.

Muons also do not live long enough to complete the acceleration if standard beam cooling methods are used. With only 2.2 microseconds to accelerate and collide, every instance of muon action must be carefully controlled. Ionization cooling is the only practical method that is fast enough for muons and the MuCool R&D program at Fermilab is aimed at developing components for muon cooling.

For muon cooling, RF cavities are used to accelerate particles within a strong magnetic field. The magnets help contain and focus the beam of particles. However, there were significant problems with the RF cavities, as scientists found that the cavities did not work well inside the magnets.

“The cavity would break down, or start arcing. It was unusable,” said Torun, assistant professor at Illinois Institute of Technology with a joint appointment at Fermilab’s Accelerator Physics Center (APC). “There were various ways to attack the problem, but then Rolland Johnson suggested we fill the cavities with gas.”

Rolland Johnson, a physicist who worked at Fermilab for 30 years and founded Muons, Inc., introduced the novel concept of filling the RF cavities with hydrogen. The hydrogen gas would suppress the electrons stripped from the cavity surface, which had previously caused the breakdown of the cavity.

The beam pipe leading into the solenoid magnet, with the HPRF cavity installed in the MTA experimental hall. Photo: Yagmur Torun, R&D

Physicists currently use RF cavities to bunch charged particles and move them forward through an accelerator. A standing wave, set at a particular frequency, pushes the beam particles forward to the next cavity.

“In 2005, we tested the hydrogen gas in the RF cavity,” Katsuya Yonehara, Peoples Fellow at the APC and spokesperson for the HPRF beam test, said. “The results were promising. We saw the cavity would work in a magnetic field, but we had a remaining question—could a very intense muon beam cause the field in the cavity to collapse?”

In 2007, a beam line from the Fermilab Linac accelerator was installed in the MTA. It took four years of adjustments and upgrades before the beam line was ready for the test in July of this year.

“It worked,” Torun said. “The cavity didn’t break down. This is a big step in our search for a potential path for muon colliders and accelerators at Fermilab.”

In the next few months, there will be a more detailed study.

“We’re adjusting the cavity, and making improvements for studying its application to muon acceleration,” Yonehara said. “We’re seeing progress.”

—Ashley WennersHerron


Don’t Stop Me Now…

Friday, July 29th, 2011

Today I’m going to describe the last, but definitely not least LHCb subdetector, the muon subsystem, which unsurprisingly from the name, is designed to detect muons. Just in case you’ve all forgotten what the LHCb detector looks like, I’ve included a schematic below. The muon subsystem is the rightmost one, with alternating layers of light and dark green.

So why is a completely separate subsystem required to detect muons on top of the previously described vertex location, tracking, particle identification and calorimeter subsystems?

It all comes down to how muons interact with matter. In my last post, I said that the goal of the LHCb calorimeter subsystem is to stop particles in the detector and measure how much energy is produced through interactions with the detector material. However, I left out the important fact that different particles interact differently with detector material. In particular, muons pass through the calorimeters almost without any energy loss. Flip has a very nice explanation about why in this post, where he compares electron interactions to muon interactions… which he hopefully won’t mind if I borrow…

Electrons are light, so let’s imagine that they’re ping pong balls. On the other hand, muons are heavy, so let’s imagine them as bowling balls. As you probably know, the LHC detectors are big and full of stuff… by that I mean atoms, which in turn are made up of a nucleus and a cloud of electrons. We can thus imagine a sea of ping pong balls (kind of like an IKEA ball pit). When electrons hit this ball pit, they end up distributing all of their energy into the other balls. Muons on the other hand, are so massive that they just barrel straight through the ball pit to reach the other side.

Why go to all this effort just to detect muons?

Apart from muons being the only particle you can make farm jokes about, the fact that muons are the only known particles which the calorimeters don’t stop is quite useful. It means that if any signals are seen in a detector that is located behind the calorimeters, they must originate from a muon. This makes searching for decays involving muons much simpler than searching for decays involving other particles, such as electrons. An example of such a decay is the rare \(B_s \rightarrow\mu\mu\) decay which may reveal new physics, as discussed previous by both Ken and Flip.

So how does LHCb detect muons?

The muon subsystem comprises five rectangular ‘stations’, gradually increasing in size and covering a combined area of 435 square metres. Each station contains chambers filled with a combination of three gases – carbon dioxide, argon, and tetrafluoromethane. The passing muons react with this mixture, and wire electrodes detect the results. In total, the muon subsystem contains around 1,400 chambers and some 2.5 million wires.

Here is a nice photo taken between two of the stations…

So now you know all about the LHCb detector, you should be able to understand the following event display of a \(B_s \rightarrow\mu\mu\) event. If not, don’t fear, because there’s a very good explanation here.

And that ends my series of posts describing the LHCb detector… I hope you all enjoyed reading them as much as I enjoyed writing them.


It’s time to return to our ongoing exploration of the structure of the Standard Model. Our primary tools are Feynman diagrams, which we introduced in previous posts (part 1, part 2). By now we’ve already familiarized ourselves with quantum electrodynamics (QED): the theory of electrons, positrons, and photons. Now we’re going to start adding on pieces to build up the Standard Model. We’ll start with the muon, portrayed below by Los Angeles artist Julie Peasley. (These handmade plushes can be found at her website, The Particle Zoo.)


We’re all familiar with the electron. Allow me to introduce its heavier cousin, the muon (μ). Where did this muon come from? Or, as Nobel Prize winner I. I. Rabi once asked, “Who ordered that?” (This is still an unanswered question!) Besides its mass, the muon has the same fundamental properties as the electron: it has the same charge, feels the same forces, and—like the electron—has an anti-particle partner.

Feynman rules for QED+μ

This makes it really easy to extend our Feynman rules. We’ll call our theory “QED+μ,” quantum electrodynamics with an additional particle. We just have to write the rules for two copies of QED:


Let’s recall how to interpret this. The three lines tell us that we have three kinds or particles in the theory: electrons (e), muons (μ), and photons (γ). Recall that the matter particles, the ones whose lines have an arrow, also have antiparticles. We indicate antiparticles by arrows pointing in the wrong direction when we read the diagrams from left-to-right. The vertex rules tell us that we have two kinds of interactions: a photon can either interact with two electrons or two muons.

It’s important to note that we cannot have photon couplings that mix electrons and muons. In terms of conservation laws, we say that electron and muon number are each conserved. For example, in the theory we’ve developed so far, you cannot have a muon decay into an electron and a photon. (We’ll introduce these sorts of interactions next time when we discuss electroweak theory.)

Exercise: Is the following diagram allowed in QED + μ?


Answer: Yes! But doesn’t this violate conservation of electron and muon number? You start out with two e‘s on the left and end up with two μ’s. Hint: what are the arrows telling you?

Once you’ve convinced yourself that the above diagram doesn’t violate electron or muon conservation, let me remark that this is an easy way to produce muons at low energy electron colliders. You just smash an electron against a positron and sometimes you’ll end up with a muon-antimuon pair which you can detect experimentally.

Exercise: when we previously did electron-positron to electron-positron scattering, we had to include two diagrams. Why is there only one diagram for eμ to eμ? Hint: draw the two diagrams for ee to ee and check if the Feynman rules still allow both diagrams if we convert the final states to muons.

Detecting muons, some collider physics

If you think about this a little, you might wonder: if electrons and muons are so similar, how can experimentalists distinguish between them at a collider? Seth and Mike might scold me for skipping over some information about the interaction of charged particles through matter, but one simple way to distinguish muons from electrons is to measure their energy and momenta. We know that (away from a potential) a particle’s energy is the sum of its kinetic energy plus it’s mass energy added in quadrature E2=m2c4+p2c2 (this is the “real” version of E=mc2). Since muons are heavier than electrons, we can just check the mass of the particle by plugging in the measured energy and momentum.

Actually, this is an oversimplified picture. In order not to annoy the other US/LHC bloggers, I’d better provide a slightly less oversimplified “cartoon.” Electrons are light, so let’s imagine that they’re ping pong balls. On the other hand, muons are heavy, so let’s imagine them as bowling balls. As you probably know, the LHC detectors are big and full of stuff… by that I mean atoms, which in turn are made up of a nucleus and a cloud of electrons. We can thus imagine a sea of ping-pong balls (think of a Chuck-E-Cheese ball pit). When electrons hit this ball pit, they end up distributing all of their energy into the other balls. This happens in the electromagnetic calorimeter, or ECAL. “Calor” is Latin for heat, so you can guess that the ECAL is really just a big fancy thermometer that measures the energy that the electron dissipates. Muons on the other hand, are bowling balls that are so massive that they just barrel straight through the ball pit to get to the other side. Here’s a very scientific illustration:


I hope we don’t get any comments saying, “oh man, muons are jerks.” In fact, they’re quite the opposite: muons are the only Standard Model particles that make it all the way to the outside of the detector, making it easy for us to identify them. In fact, the big distinctive toroidal magnets on the ATLAS detector below are there to bend the path of muons to help the outermost detector determine the muon momentum by measuring the curvature of their trail.

Exercise: [for those who want to do some actual calculations, requires a high school physics background] Convince yourself that this heuristic picture is correct by calculating the final momenta of a ball colliding elastically with (a) a ball of the same mass and (b) a ball of much lighter mass.


ATLAS toroidal magnets. Image from the Interactions.org Image Bank

Neat things that muons can do

Let me make a few more semi-historical remarks: our QED+μ model is just a theoretical toy. Historically, scientists knew immediately that something was weird about the muon: unlike electrons, it decayed into other particles and seemed to interact with mesons in unusual ways. In fact, for a while people thought that muons were a kind of meson. These differences ended up being a harbinger of something more interesting: the weak force.

Exercise: convince yourself that our Feynman rules for QED+μ do not allow muon decay, i.e. μ turning into non-μ stuff.

Muons are generated in the sky when cosmic rays hit atoms of the upper atmosphere. These rain down onto the Earth and force us to put our dark matter experiments deep underground to avoid their ‘noise.’ What’s really neat, however, is that the fact that muons make it to the surface of the Earth is a rousing experimental check of relativity. We know that muons at rest decay in microseconds. In this time, it seems like there’s no way for them to traverse the kilometers (about 4 km) between the Earth and its upper atmosphere; even if they were traveling at the speed of light! (c ~ 3.  108 m/s). What’s happening is the phenomenon of time dilation!

Introducing the tau (via the Socratic method)

Exercise: the Standard Model actually has another cousin of the electron, the tau (τ), leading to three charged leptons in total. Write down the Feynman rules for the theory QED+μ+τ, i.e. the theory of electrons, muons, and taus interacting via photons. Make sure that electron, muon, and tau number are all conserved. Draw the diagram for tau production in an electron-positron collider.

Exercise: Above we argued that muons are special because they barrel right through our detectors like bowling balls through an array of ping pong balls. Taus are even heavier, shouldn’t they also make it to the outside of the detector?

Answer: This was a bit of a trick question. The logic is correct that sufficiently energetic taus should make it all the way to the outside of the detector in our QED+μ+τ theory. However, this is not the full story for electrons, muons, and taus (collectively known as leptons) in the Standard Model. Like muons, taus are unstable and will decay. In fact, they decay much more quickly than muons because they have more mass and can decay into stuff (they have more “phase space”). While muons are like bowling balls barreling through the detector, taus are more like grenades that burst into hadronic “shrapnel” inside the calorimeters. They are usually very difficult to reconstruct from the data.

A preview of things to come:

Now we’re very familiar with putting together multiple copies of QED. For now, there are only three copies we have to worry about. It is an open question why this is the case. The existence of at least three copies, however, turns out to be significant for the imbalance of matter and anti-matter in the universe. In the next post we’ll introduce the weak force and really see what we can do with these leptons.

I’m currently in the middle of my “Advancement to Candidacy” exam, so my posts might be a little more delayed than usual this month. By the end of it, however, I hope to be blogging as an official PhD candidate. 🙂

Erratum: virtual particles

I wanted to correct a misleading statement I made in my previous QED post: I discussed the visualization of virtual particles as balls that two kids toss back and forth while standing on frictionless ice. Conservation of momentum causes the two kids to slide apart as they throw and catch the ball, generating what we observe macroscopically as a repulsive force. We mentioned that it’s more difficult to see how this could give rise to an attractive force. I suggested that this is a phenomenon coming from the accumulated effect of many quantum exchanges. While this is true, there is a simpler way to understand this: pretend the ball has negative momentum! Since the particle is virtual, it is inherently quantum mechanical and needn’t have ‘on-shell’ (physical) momentum. Thus one could imagine tossing the ball with negative momentum, causing one to be deflected in the same direction as the ball was tossed. Similarly, catching the ball with negative momentum would push one in the direction that the ball came from.

Does it make sense classically? No! But that’s okay because they’re virtual particles.

That’s all for now, folks!
Flip, on behalf of the US/LHC blog.