I haven’t said much since this year’s start-up of the LHC, but there have been some interesting developments, so I’ll add one last update. If you haven’t been following the LHC status, it has been exponentially increasing in collision rate while maintaining a fixed collision energy (about 3 pb-1 of 7 TeV collisions have been collected by the LHC experiments, which is a few thousand times less than the Tevatron’s 9 fb-1 of 1.96 TeV collisions, collected since 2001). My “particle body counts” are now completely obsolete: nearly all known particles have been re-discovered in the LHC experiments. And today, the first unexpected effect has been presented by an LHC experiment: “Long-range, near-side angular correlations,” which is presented in detail on the CMS public page. Below the cut here, I’ll explain what this means.
Archive for the ‘Basic Grad Student’ Category
… if all goes well. The LHC has been circulating two 3.5 TeV beams off and on for the past week, and tonight they plan to turn off the separators keeping them apart. We should then see the first 7 TeV collisions ever produced in a laboratory. If there are any undiscovered particles with a mass in the new energy range that is being opened up, it would now become possible for them to be spontaneously produced in a detector where we can see them (as opposed to cosmic ray air showers). Our view of particle physics is about to become three and a half times larger than it has ever been.
The plan at first is just to let the beams collide without focusing them, so the luminosity will be low, and the rate at which new particles could be produced would be correspondingly low. As time goes on, the beams will be focused and the intensity will be raised, which increases the rate of collisions and therefore the probability of seeing new stuff. This is the beginning of an 18–24 month period of continuous data-taking and open-ended exploration.
Tonight I’ll be following this from the Fermilab control room (the LHC is in Switzerland— this is a remote control room). I’ll post any interesting updates as comments to this article (they won’t come up in RSS feeds). Here are other sources of information, all more direct than this blog (I mostly try to avoid repeating them):
- CERN twitter (from the LHC control room)
- ATLAS control room blog
- CMS e-commentary
- LHC page 1: live update of machine status. When I last looked, the energy was 3.5 TeV and the beam intensities were 1.5e10 (higher than the past few weeks). The red and blue lines are intensities of the clockwise and counter-clockwise beams versus time.
- CMS data aquisition: live update of CMS data collection. The main plot is data accumulated versus time; it’s a constant slope for cosmic rays (no LHC beam), but could jump up if we get a lot of events from the beams.
- CMS event display: pictures of the events as we see them (in three projections: face-on, side view, and 3D). Yellow lines are particle trajectories, red and blue bars are calorimeter energy deposits. If a yellow line goes beyond the calorimeters, it’s a muon! Right now, I think it’s re-playing events from the low-energy collisions of 2009; that will change sometime tonight.
In my timezone, the sun is setting. Happy Passover!
As a result of today’s talks, here’s the updated body-count (all four experiments with a lot of overlap):
|Particle||Original discovery||Method of observation in the LHC experiments|
|Electron/positron||1896 (e–), 1932 (e+)||Peak at 1.0 in calorimeter energy to track momentum ratio, also observed in pairs from photon conversions in matter (X γ → X e+e– where X is a nucleus)|
|Photon||1900 (Planck’s quanta)||Photon conversions and π0→ γγ|
|Proton||1911||Energy loss charged particle’s trajectory (dE/dx)|
|Deuteron||1931||Also seen in dE/dx|
|Muon||1936||Specialized muon detectors|
|Pion||1950 (π0)||Neutral pion in π0→ γγ, charged pions in dE/dx|
|Eta meson||1961||η → γγ|
|Kaon||1947 (KS)||Neutral kaon in KS → π+π–, charged kaons (K+ and K–) in dE/dx and ring-imaging Cerenkov detectors
|Phi meson||1962||φ → K+ K–
|Lambda||1947 (Λ0)||Λ0→ π+p– / Λ0→ π–p+|
|Xi baryon||1964||Ξ → π Λ0|
|Dark matter WIMPs||not yet||two candidates in the unblinded signal region of the Cryogenic Dark Matter Search (CDMS) (not an LHC experiment)|
The last entry is for yesterday’s CDMS paper, which shows two candidate events surviving all analysis cuts, set prior to looking at the result (unblinding). The probability for background fluctuating up to account for these two events is 20-23%, so no one is calling it a signal. Both are close to the edges of the analysis cuts, so even if the observed events had significantly exceeded the background estimates, there would be room for doubt. This may be the tip of the iceberg for direct dark matter detection, but then again, it may not.
Earlier today, the LHC finished its 2009 run. They did everything they said they were going to do: provide physics-quality 900 GeV collisions and break the world record by colliding protons with a combined energy of 2.36 TeV (that happened Monday), as well as many other studies to make sure that everything will work for 7 TeV collisions next year. We’ve been busily finding the familiar particles of the Standard Model— I wrote two weeks ago about the re-discovery of the π0; since then new particles been dropping in almost daily. I’ll explain some of the already-public results below the cut, but first I want to point out that there will be another LHC Report this Friday at 12:15 (European Central Time = 6:15 AM Eastern U.S. = 3:15 AM Pacific) on CERN’s webcast site. This is where all of the LHC experiments will present their results and probably make a few more public.
Also, in case you haven’t heard, there have been a lot of rumors that the Cryogenic Dark Matter Search (CDMS) has discovered something interesting. They’ll be presenting whatever it is tomorrow with a paper on the arXiv, a Fermilab presentation at 4:00 PM Central U.S. (webcast here), and a SLAC presentation at the same time, 2:00 PM Pacific (webcast here). It might be the direct detection of dark matter particles, which would be incredibly exciting.
A little over a year after the highly publicized start-up and break-down of the LHC, the damage has been repaired, new protection systems are in place, and all sectors are cold and ready for beam. Yesterday, the first injection test of 2009 was completed— beams of protons and heavy ions were successfully threaded into the LHC beampipe from its predecessor, the Super Proton Synchrotron (SPS). The beams were allowed to flow as far as the first experiments in both directions, ALICE on the clockwise side, LHCb on the other.
New York City, 1956
Leaning on a Chinese restaurant at a busy street corner in Greenwich Village, I crossed my legs, tipped my hat low, and quietly panicked. This case is turning into a nightmare: dozens of suspects, growing daily, and they all seem to swap places when you’re not looking. A pion couldda done it; pions seem to be some kind of front for the nuclear force that Madame Curie was playing with before she died. But leave a pion to itself and it disintegrates into a muon and a neutrino, neither of which claims to have ever heard of nuclear forces. Radiation in the form of muons and neutrinos has been raining down on us since the beginning of time, and it’s never even hurt. If pions are just glowing with nuclearness, where does the nuclearness go when they die?
For that matter, what is a particle, anyway? I have to admit, I wasn’t suspicious when I first heard the word— I thought they were talking about little rocks or marbles or something. But rocks don’t just change into different kinds of minerals on their own, except for Curie’s rocks, that is. What are these particles? The physicists themselves don’t seem to know: everyone I ask gives a different answer. They seem to be some shadowy energy-clouds, sometimes insubstantial and sometimes infinitely hard. What kind of world are we living in, anyway?
I felt a crumpled slip of paper in my pocket. Pulling it out, I read the well-worn handwriting under my breath, “Seek the Dragon Lady.” I scanned the crowd. I’d bet none of them knew the half of what’s going on, right under their noses! Well, not just their noses, but everywhere in fact. “Any of you folks know a Dragon Lady?”
“Are you looking for Madame Wu?” The young man startled me. From the high-necked sweater and the pipe in the corner of his mouth, I’d reckon he was a student.
Ithaca, NY, 1948
After a wrong turn in Albuquerque, I caught up with Bugs Bunny, alias Richard Feynman, somewhere near the ends of the earth. Up to my elbows in snow-drifts, I spied on the little window to his office, in which he seemed to be doing normal professor-things, plus wild gesticulations. I decided on a particularly frozen morning that I would have to risk visibility if I was to get answers, so I enrolled at Cornell, posing as a G.I. bill student. In Professor Feynman’s introductory physics lectures, I could see that there was something remarkable happening here. People researching physics is about as natural as fish studying water: it’s the very stuff we’re made of. He had a knack of getting down to the ground floor, asking the basic questions, just as much in a block sliding down a plane as in neutrinos.
His teaching assistant, a quirky bow-tied Brit by the name of Freeman Dyson, knew the man personally, so I inquired. “Oh, he’s working on something, yes. The trouble is he just won’t publish, no matter how much I cajole him. He says he’s depressed, but Dick depressed is just a little more cheerful than any other person exuberant. It’s the Bomb, I think, and of course Arlene, his poor wife who died in New Mexico. I probably shouldn’t be telling you this, but Dick and Arlene got married knowing she hadn’t long to live, she having T.B. Bit like Dick to give it a go anyway.”
“What do you suppose he’s up to?”
“Well, he’s got his own private quantum theory for starters. Quantum theory, that’s the theory of the atom and electrons. Until recently, no one’s been able to make it work with Einstein’s relativity; it’s riddled with infinities, you know. Schwinger’s done some remarkable work reconciling the two— all operator theory and renormalization, I’m still trying to understand it. Somehow, there’s a way to replace the infinities with experimental measurements, then the beast is well behaved and gives very nice results. Dick manages calculate the same thing with these funny little pictures, and he puts plus signs between them like they were real mathematical formulae. Quite a ball at conferences: squiggle plus squiggle equals whatever. I mean to pick his brain about it before he flies off to Brazil.”
“Yes, he’s taking a visiting professorship. Says he hates the cold.”
On my way home that evening, I saw a shadow linger on my doorstep, then dart away. I broke into a run to pursue it, but not a trace was left, not even footprints in the snow. With one exception, that is: crinkled under the door and sodden with melt-water was a little envelope. Inside was a note, which read,
“The killer is left-handed.
Los Alamos, 1946
I should have sought Dr. Fermi right away, back when it was easy. When Mademoiselle Curie gave me the lead, Enrico was a quiet university professor in Rome. Since then, he’s got a lot harder to find, and it seems that the professor has government ties— secrets as big as the men who hide them. I chanced upon a tip leading me to a project in Manhattan, and though I found Fermi on the books as a Columbia professor, I had just missed the man himself. Asking an associate about where in the New World this Italian Navigator might be, he turned bright red and insisted that there was absolutely nothing in the basement. Nothing at all.
Sometimes you just get lucky. I asked one of his students to give me a tour of the basement, and was shown a room-sized apparatus for creating artificial radiation. “Artificial radiation?”
“Radiation is just ordinary particles, accelerated to high speeds. Naturally radioactive elements like radium spontaneously break off parts of themselves and shoot them at us, but we can accelerate them on our own with rapidly oscillating electric fields.”
“So this,” I asked, “is a sort of ‘particle-accelerator?'”
“I guess you could call it that.”
I was on the right track! “What do you use it for?”
“Well, Dr. Fermi did a lot of experiments with neutron capture, but by far the most exciting was the splitting of uranium atoms by a neutron beam. He disappeared soon after that.”
So Enrico wasn’t content to let atoms do all of the dirty work— this cat shoots back!
I was called to investigate the recent death of a famous physicist: Marie Curie, born Manya Skłodowska. When I arrived on the scene, she was in her death-bed, her face long and grey, a ghostly shadow in the warm light of the mountain sanatorium. Her daughter Eve was there. “It’s so quiet,” she said, “so fearfully motionless—”
We made our introductions, but she was obviously distracted. “So motionless, those hands. No longer nervously shaking, constantly moving, always working…”
I took a look at the hands, still and limp on the bed. They were hardened, calloused, deeply burned and thick-skinned. “What is this?” I asked myself, but I must have said it out loud because Eve heard me.
“Radium,” she said.
“Those were her last words— ‘Was it done with radium or with mesothorium?’ As she was stirring her tea with a spoon— no, no, not a spoon, but a glass rod or some delicate laboratory instrument… She had drawn away from human beings; she had joined those beloved ‘things’ to which she had devoted her life, and joined them forever.”
A cup of tea and now dead? That didn’t sound good. “Poisoned?” I asked. I never mind stating the obvious.
“Yes, poisoned. By radium. In the laboratory, she always used to say, ‘That polonium has a grudge against me.'”
“Radium— or polonium?”
In my previous post on card shuffling, I established a basic framework in which we will work. We are given a probability distribution on and we wish to determine when first begins to decay exponentially, where is the -fold convolution of One key feature of card shuffling theory, as well as much of finite Markov chains in general, is that the tools available are often very particular to a small class of problems. There just aren’t very many big hammers around. Even though the theorem described in the previous post was quite general, it was non-quantitative, and so not especially useful in practice.
The standard shuffling technique is called the “riffle shuffle.” In this shuffle, the deck is cut in half, and the two halves are zippered together. We need to come up with a mathematical way of describing the riffle shuffle, and I’ll list three different methods (I’m assuming the deck has cards here, but any will do):
First Way. The first thing to think about is how we cut the deck. Mathematically speaking, we will assume the number of cards in the top half of the deck after we cut is binomially distributed. All this means is that to determine the number of cards we cut from the top, flip 52 coins and count the number of heads to figure out how many cards go in the top half. It may seem strange that there is a positive probability of having all 52 cards in the deck sitting in the “top half” but the probability is extremely small and so doesn’t matter so much. For most shufflers, the size of the two “halves” are often quite different. Anyway, suppose that our result is cards in the top half. From here, we think of having 52 boxes lined up and put the cards in them. We pick of the boxes (assuming each box is equally likely) and put the top half of the deck in those boxes, keeping them in the same order. Put the remaining cards in the remaining boxes, keeping them in the same order relative to each other. Stack the cards back up. Note that there are ways to put cards in 52 boxes, so that the probability of any box choice is .