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Uncertain Principles

Physics, Politics, Pop Culture

Thursday, August 21, 2003

Nice Doggie

As noted on Kate's LiveJournal, we got a dog yesterday. Having been beaten to a couple of promising candidates, I decided to take the afternoon off, and swing by a local shelter and check out a couple of dogs that looked interesting on their web list.

Let me just note that I really don't like those places. It's so pathetic-- the dogs are all in concrete kennels in one big room, and whenever a shelter volunteer would come in, they'd all commence baying piteously, in hopes of being let out of their cages, producing a deafening racket. The worst ones are the senior dogs-- the eight, nine, ten-year old dogs, who just look sort of resigned to their fate. It's a terrible scene-- you want to take all of them home, which is, of course, impossible.

Anyway, I ended up really liking one of the dogs I'd gone there to see, so I brought her home. She's a German Shepherd mix (mixed with what, I don't know), mostly black and tan, with a white spot on her chest. Her right rear paw is deformed, but it hardly even slows her down, and she's got tan spots over her eyes that give her a perpetually quizzical expression. Unsurpisingly for a shelter dog, she's sort of pathetically needy right at the moment-- if I stop petting her for even a few minutes, she gets antsy, and comes over to beg for affection (though she's (finally) wearing down a little today, and may be going to sleep, which would let me get some work done). She's also a little antsy in general-- she was upset by the painters who are working on our house today, so I brought her in to the office, where hammerin sounds from the remodeling going on downstairs set off a barking fit a little while ago. Hopefully, she'll get past both of those issues as she gets more comfortable in her new home.

For now, though, she's yet another factor that will contribute to a general lack of uncertainly principled blog posts in the immediate future.

Also, name suggestions are welcome in comments-- the previous owners (who gave her up due to allergy issues) called her "Princess," which might work for a Maltese or some such thing, but doesn't really fit a raggedy-looking shepherd mix. We're leaning toward "Emmy," for no particular reason, but there's still time to come up with a better name.

Posted at 1:20 PM | link | follow-ups | 14 comments

Sunday, August 17, 2003

Needles in Haystacks Are Easy

(The second of two posts about particle data analysis. The first is here, or you can just scroll down...)

So what's the deal with the graph at the bottom of this page? The short answer is, it's a graph of the number of particles detected versus the energy of the collision, and the narrow peak highlighted in red indicates the new "pentaquark" particle. It's position horizontally tells you the mass of the particle (how much energy you needed to make it), while the height tells you how likely it is to be made (how many collisions produced that particle).

To unpack that a little, I need to sketch a bit of how the data analysis process actually works. The raw data from these experiments comes in gigantic chunks-- the CLAS detector generates something like a terabyte of data per day, giving the results of thousands or millions of collisions. This provides a gigantic metaphorical haystack which the experimenters sift for needles. (It's a slight simplification to think of the data as lists of particles and energies, but not a damaging one (it's a lie-to-children, as it were).)

If you have a particular reaction or particle you want to study, the first step is to identify the products-- what sort of particles will be detected after the reaction takes place or the particle decays. Then you write a computer program to sift through the massive piles of data to find collisions with those results.

To take a concrete example, if you wanted to study neutral pion production, you might ask the computer to pull out those collisions where two protons collided, and two protons were detected. That will whittle your big dataset down from, say, a million events to, say, ten thousand (numbers are fictitious). You can then comb through those ten thousand (again, with a computer program) to figure out how many of them are really what you're after-- look for cases where the energy loss is enough to account for a neutral pion, say, or cases where there were also two photons detected. That lets you eliminate collisions where the colliding protons just glanced off each other without producing anything else, and also cases where they produced other particles-- two pions instead of one, say, or something more exotic.

That narrows it down to, say, five thousand events, which then need to be checked to verify that they're really the right reactions-- making sure that the protons detected are really protons from the same reaction, and not stray particles from some other collision, and the photons were produced in the target region, and aren't just stray cosmic rays. By the time you do all that sorting out, you're left with a few thousand events, that you can plot up, and use to determine the mass of the pion and the cross-section for pion production ("cross-section" being physics-speak for "likelihood of a given reaction") as described above.

This process is relatively simple for reactions like pion production, and you end up with gobs of data. The more complicated the reaction, and the more exotic the particles, the less likely you are to find things, and the more data you have to sift to find what you're looking for. Particle physicists have to be very clever programmers, and sharp statisticians to tease meaningful results out of the vast masses of data they collect.

In the case of the pentaquark, the actual reaction is very complex, and is represented by the Feynman diagram in the other figure on the Ohio page. (Feynman diagrams probably deserve an entry of their own. Some other time.) Summarized in words, a high-energy photon strikes a neutron in a deuterium nucleus, creating a bunch of quarks out of thick vacuum, which arrange themselves into the pentaquark particle and a negative kaon. The pentaquark falls apart into a neutron and a positive kaon, while the negative kaon bangs into the proton on its way out of the nucleus, and all four particles move off to the detectors.

To find these events, they look for all four particles being produced in a single reaction: a proton, a neutron, and a pair of kaons. Plotting those events gives you the graph mentioned above. The narrow feature indicates the real reaction of interest-- cases where the photon energy was just right to produce the required quarks, and they happened to pair off in the right way. The broader peak is just background noise-- a collection of events where the proton, neutron, and kaons were produced by some other process.

To find this peak, they sifted through the entire Jefferson Lab dataset-- running to a few billion collisions. Out of all that data, they found thirty collisions where a pentaquark was produced. That gives you some idea just how rare this particle is, and explains why it took thirty-odd years to find it.

Posted at 10:40 AM | link | follow-ups | 2 comments

Elementary (Particle) Deduction

In the last installment of the particle-physics story I've been telling, I talked about the different detectors used to puzzle out what the various particles produced in a collision are. This is basically a matter of tracing their tracks through various detectors, to work out their energy, momentum, and charge. Once you've got that information-- what particles were produced, and how much energy they had-- you can begin the process of piecing together what actually happened.

This might seem like a trivial step. After all, if you know what went in, and what came out, you must know what happened, right?

Yes and no. This is true for simple reactions. To choose one out of a handy textbook, consider the case where two protons collide, and a proton, a neutron, and a positively charged pion come out. You can write this reaction symbolically as:

p + p -> p + n + π+

This is a relatively straightforward reaction, and easy to sort out if you look at the quark content of these particles (where "u" represents an "up" quark, and "d" a "down"):

uud + uud -> uud + udd + ud-

That last "d-" indicates an anti-down quark (my HTML-fu isn't strong enough to get bars over the letters), and makes it clear what happened. The two protons collided, with enough energy to produce a quark-anti-quark pair (a down and an anti-down in this case. The new quarks popped into existence, with the "down" joining a couple of the original quarks to form a neutron, while the "anti-down" ran off with an "up" to form a pion.

As I said above, this is a simple reaction, as such things go. You know what you sent in, and you can directly detect everything that comes out, which means that the reconstruction is a snap. It's one new pair of particles, a quick re-shuffling, then everybody moves off to the detectors.

The problem is, it's not always this simple, and not usually interesting when it is. For a lot of reactions , you can't directly detect all the products, and have to work out what happened from other clues. For example, the same reaction above, with a seemingly trivial re-arrangement of quarks, produces a case where you can't detect everything. Instead of splitting up the down-anti-down (which, as an aside, sounds like a phrase from exceptionally dorky doo-wop) to make a neutron and a charged pion, we could keep everything as protons:

p + p -> p + p + π0

0 represents a neutral pion). Or, in quark terms:

uud + uud -> uud + uud + dd-

This seems even simpler than the first one, right? The catch, though, should be obvious to any reader of SF: that "dd-" represents a particle coupled to its own antiparticle-- give them a bit of time, and they'll annihilate each other. In fact, give them 8.5 10-17s, and they'll annihilate each other, producing two photons. That's such a short time that the neutral pion never makes it out of the target region and into a place where it might be detected, so we never see it.

That doesn't mean we can't figure out what happened, though, just that it has to be done indirectly. One way of doing it is to invoke conservation of energy-- one of the absolute bedrock principles of physics that you first encounter in mechanics. You know the energy of the particles you sent in, and you know that the energy of all the particles that come out has to add up to the same total. If you measure the energies of the protons leaving the target region, you'll find that they're moving a little too slowly to account for all the initial energy, and if you work out how much energy is missing, you'll find that it's just enough to account for a neutral pion.

The other way to determine that a neutral pion was produced is to detect what was produced when it falls apart-- in this case, two photons. When you look at the list of collisions and collision products, and see that two protons were sent in, and two protons plus two photons came out, you know that there was an intermediate state where a neutral meson was produced. By either measuring the photon energies, or repeating the conservation of energy calculation above, you can determine that it was a pion.

I use protons and pions as examples, but the same basic process can be extended to all kinds of reactions. In the case of the Jefferson Lab experiments I know the most about, they're actually bombarding their target with high-energy photons, but the process is essentially the same: you know what came in, you detect what came out, and you deduce what happened in the collision. We had two students working on campus this summer doing data analysis-- one used the conservation of energy method to look at neutral meson production, the other used the photon detection method.

This can also be extended to multi-step processes (particles that decay into particles, that decay into something you can detect), and more complicated reactions (particles that decay into particles that interact with each other before getting detected). But it always comes back to the same thing: you look at the tracks of the particles emerging from a collision, then work your way back down to what happened in the collision. And from what happened in the collision, you can learn a few things about how the Universe is put together.

Posted at 10:32 AM | link | follow-ups | 12 comments

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