Monthly Archives: October 2008

Centauros and CDF’s multi muon / lepton jets

An unexpected bump has the particle physics world busy tonight; (we’re too sedate to be “aflame”). The bump was discovered at Fermilab by the CDF collaboration: Study of multi-muon events produced in p-pbar collisions at sqrt(s)=1.96 TeV”, hep-ex/0810.5357. In short, they’ve discovered a particle that seems to produce jets of leptons.

CDF found that they have way too many events where there are a lot of muons going in the same direction. This sort of thing is called a jet. Normally jets are associated with the strong force, and consequently, they include hadrons as well as leptons. Getting jets without hadrons is very unusual behavior. This is quite exciting but some of the terminology may be a bit confusing in the original paper linked above. There are two types of particles, leptons which do not experience the strong force, and hadrons that do. Physics experiments can distinguish them because hadrons crash into matter and decay, while leptons do not. Leptons eventually end up as electrons and muons. Of these, the electrons are sufficiently light that they get stripped off leaving only the muons. Photons also get absorbed. What’s left is muons and these are detected in the outer parts of a detector. So “punch through” means hadrons that managed to survive all the matter in the inner part of the detector and survived to the part of the detector where muons are supposed to predominate.

Centauros
Cosmic ray data is pretty much ignored by particle theorists. When I go to conferences, I make sure to attend these lectures because cosmic rays have much greater energies than accelerators can produce, and consequently they are more likely to see new physics. Very few other theoreticians show up at these lectures. Partly for this reason, I haven’t stressed the cosmic ray data very much. But now that the same unusual behavior is being observed at an accelerator, it is time to revisit the cosmic ray data.

A similar set of events were discovered years ago in high energy cosmic ray experiments. They are called “anti-Centauros” (the Centauros are showers that have too many hadrons and not enough leptons, anti-centauros reverse the proportions). Typically, these experiments use photographic emulsion (film) to detect cosmic rays. The film is layered in between sheets of lead or air gaps. The lead breaks up the hadrons and the resulting showers are detected in the film. These events were called “Centauros”, see the article which discusses them: Are Centauros exotic signals of the QGP? by Ewa Gladysz-Dziadus (2001). A more recent update is Very High Energy Cosmic Rays and Their Interactions, Ralph Engel (2005).

The study of cosmic rays is largely ignored, other than the GZK measurement, but the emulsion cosmic ray researchers are still chasing after Centauros. CASTOR stands for “Centauro and Strange Object Research” and is the name for a calorimeter (to measure energy in particle tracks) at the Large Hadron Collider (LHC).

Cosmic ray experimentalists don’t get no respect. Consequently these observations are difficult to publish and when they are published, they are pretty much ignored. But unusual observations in cosmic rays have been piling up for years. Kopenkin and Fujimoto supposedly explained Centauros in 2006: Exotic models are no longer required to explain the Centauro events, but this hasn’t stopped the observations from lacking explanations.
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Help Save Bou’s Brain!

Things are flying in the physics world and there’s amazing things going on economically. And I owe some posts on these subjects.

But right now, more important for the brotherhood of blogs, is one of our own; Boudicca needs us. Her brain is at stake. a natural math talent could go to mush. We need to get her to quit marathoning (at age 43) and start doing mathematics again. We should start with the complex numbers. Right now she’s spending too much time quilting, and not enough time doing math.
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A New Parameterization for 3×3 Unitary Matrices

Given my final success in writing the CKM matrix as the sum of a real 1-circulant matrix and an imaginary 2-circulant matrix, the next step is to write down the parameterization that allows any 3×3 unitary matrix to be written in this elegant and natural form. Following the method used earlier to parameterize unitary 3×3 magic matrices, and correcting for a few typos (but the description of the method is correct).

We will use four real angles, \theta, \alpha, \beta, \gamma , as parameters. First, define 6 real numbers I, J, K, R, G, and B as follows:

The the following matrix is unitary:

This is the sum of a real 1-circulant matrix and an imaginary 2-circulant matrix. Note that the sum of the 3 elements of any row or column is equal to the complex phase \exp(\pm i\gamma) = I+J+K \pm i(R+G+B) .
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CKM in MNS form! Victory!

The MNS matrix (in tribimaximal form, which is compatible with all experimental measurements) can be written in elegant form as a unitary matrix which is the sum of a real 1-circulant matrix and an imaginary 2-circulant matrix. See Doubly Magic Matrices and the MNS. Now I’ve got the CKM matrix in the same form. And here it is:

The cool thing about the above is that it only involves 6 real numbers. Three reals define the 1-circulant matrix, +0.973313178, -0.008576543, and +0.000466480, while three more reals define the 2-circulant, +0.225761835, +0.040012680, and -0.004273188.

I’ve marked the larger contributions with red to help you see the symmetry. The real matrix has each of its rows shifted one to the right (i.e. 1-circulant), while the imaginary matrix has them shifted two to the right (i.e. 2-circulant). Note that the above matrix is unitary, which you will have to verify by taking dot products of its rows with the complex conjugatges of its rows, and the same for the columns. (You should get 1s and 0s.)

The experimental values I’m using for the CKM matrix come from hep-ph/0706.3588) and are:

If you square the elements of a row or column of the above, and add them up, you get 1, but it is not unitary. To put it into unitary form, we supplement each of the above real numbers by multiplying by a complex phase. The matrix is unitary when the resulting rows and columns are orthonormal.

The experimental measurement has 9 real numbers. Multiplying them by complex phases so as to make the matrix unitary is going to give you 18 real numbers. And yet I’ve been able to do this, put the experimental numbers into unitary form, and ended up with only 6 real numbers, and those are used in an elegant and symmetrical manner. This is by far the most elegant version of the CKM matrix around. It is the number crunched result of an observation by Marni Sheppeard that the CKM matrix is approximately the sum of a 1-circulant and a 2-circulant matrix. Well, now we have it exactly that way. Victory! But more to come.

To get an experimental measurement from the new magic form, compute the magnitude of the complex number. For instance, to get the top right value of 0.0042982, compute

|+0.000466480 – 0.004273188 i| = sqrt(0.000466480^2 + 0.004273188^2)
Uh, I get 0.0042986, which is within rounding errors on the experimental measurement number.

More generally, the nine elements of the experimental CKM matrix can be found by taking one element from the set {+0.973313178, -0.008576543, +0.000466480} along with one element from the set {+0.225761835, +0.040012680, -0.004273188} and computing the RMS value.
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CKM as a magic unitary matrix II

It seems much longer but it was only two months ago that I wrote a post giving the CKM matrix in magic unitary form. With half the Nobel prize in physics going to Kobayashi and Maskawa, the K and M of the CKM matrix, I should include a quick update.

The CKM matrix is usually written in absolute magnitude form. Recent experimental measurements, after correcting to ensure compatibility with unitarity (from hep-ph/0706.3588), is:

If you square the elements of a row or column of the above, and add them up, you get 1, but it is not unitary. To put it into unitary form, we supplement each of the above real numbers by multiplying by a complex phase. The matrix is unitary when the resulting rows and columns are orthonormal.

There are a lot of ways we could choose the complex phases. However, there is only one way (except for the sign of the imaginary unit i) of writing the matrix as a unitary matrix whose rows and columns sum to unity. This is called the “magic” property. The MNS matrix is quite simple when written this way. So I wrote a computer program and found the magic unitary form for the CKM matrix, to see if it would also have a simple form. Here it is:

Note that each row and column sums to 1, the rows and columns are orthonormal, and the absolute value of each element is as given for the experimental measurements at the top of the page.

The above is a slight improvement from the data I gave before. This is due to an error in one of the digits of the input data, that is, in the experimental measurements. Of course it is not accurate to all its digits, but I’ve included them because it’s a complicated nonlinear relationship between the absolute values of a unitary matrix and its magic unitary form; I don’t know how to properly scale the errors. (I could get them by varying the input data to the computer program that finds the magic solution. If someone wants this data, ask for it in the comments.) Below the fold, I’ll include the data in LaTeX format so you can copy it more easily:
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The X(3872) Files: Scanning for new mesons

New mesons! Let’s begin with a picture (from encarta) showing how new particles (states) were discovered back in the good old days:

Work on the big meson paper is continuing. I’m almost done with the isoscalar mesons. So in addition to describing just what these things are, I’m including a few lines on the new J/psi states, the X(3872), X(3940), X(3945), X(4260), and X(4360).

How to Find a New Hadron

Hadrons (mesons and baryons) are found by analyzing large numbers of particle interactions. When you plot the data, the graphs have little, uh, well the technical term is “bump” . Yes, hadrons, like children, begin as bumps. A hadron bump looks like this:

The above is from hep-ph/0510365. This bump happens to be one of the states, the X(3940), with which this post is concerned.
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The Barbarous Relic Rises Again

There’s gold in them thar’ shops: the rush is on

Tucked away beside the ornate entrance of the Savoy hotel in London are the discreet premises of ATS Bullion. Over the last few days staff there have witnessed an unprecedented phenomenon: queues.

The US Mint, responsible for ensuring an adequate supply of American coinage since 1792, has been forced to halt sales of its American Buffalo solid 24 carat gold coin because it was running out of supplies. It is also limiting the availability of its 22 carat American Eagle alternative. [I don’t believe this is a fact. The US makes money on sale of these coins and will mint however many the public wants. Any lack of them is just temporary. But I do believe that demand for gold bullion has gone way up.]

Demand for gold coin is undoubtedly higher outside the US than inside. The reason is that in panics, foreign investors tend to buy US dollars. This raises the value of the dollar, which drops the price of gold, as priced in US dollars. The effect is that the US consumer does not see a big drop in the value of the dollar. Hence they have no reason to hedge with gold. (This will change if the Fed gives up and begins using inflation to save the banking system.) Foreigners, on the other hand, see the price of gold going up, and worry about the financial headlines about the US. So they move into gold.
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