Phys.org has picked up on the results from the LHC pilot pA run showing the formation of The Ridge in high-multiplicity collisions. I wrote about this last month, when it was first presented at the High-pT LHC Physics Workshop in Wuhan, and at that time, the sentiment at the conference seemed to be that it wasn’t clear what could be causing the ridge.

Now, people are starting to lean toward the color glass condensate (CGC) as an explanation. The CGC has been called a new state of matter, which probably isn’t the worst description, but I think that makes it sound like more than it is. It’s a model that predicts the behavior of gluons within a proton or nucleus, under conditions in which the gluons are so numerous that they regularly “bump into” each other and fuse, or “recombine” to use the technical term. (That’s an extreme oversimplification, of course; perhaps someday I’ll do a post explaining this in more detail.) This model predicts some correlations among gluons which might be able to explain the ridge. But it’s not at all clear yet that that is the case. The LHC didn’t …

Back in February I did a post on scale invariant functions of one variable. These are functions that satisfy the condition

Depending on which source you look at, you might find a more specific definition, but I think this is the most general condition that you can sensibly use to call a function scale invariant. Under this definition, I showed that all scale invariant functions of interest to physicists are power laws, of the form

Homogeneous functions

There is a related concept called a homogeneous function (thanks to that site’s creator, Ondřej Čertík, for pointing it out), defined as those functions \(h(x)\) which satisfy

for some \(k\), called the degree of homogeneity. While the definition is similar to the one I’m using for scale invariant functions, it’s less restrictive. A homogeneous function has to satisfy the condition for only one particular choice of \(C(\lambda)\), not any arbitrary choice, so you can have homogeneous functions which are not scale invariant.

Multivariate scale invariant functions

The definitions of homogeneous functions apply to multivariate functions too, so let’s see …

As we go out shopping for gifts this holiday season, given the state of the economy, a lot of people will be thinking about how to get the best value from their gift budget. A lot more people than usual, in fact, because as you’ll hear on TV or read online from time to time, the income gap in this country is exceptionally large.

It’s probably common knowledge that a large income gap means roughly a large difference between the richest and poorest income levels. But that’s not a very precise statement by itself. Suppose you have two tiny countries of six people each, and their incomes are distributed like this:

The difference between richest and poorest is the same in both countries, but the other values are significantly higher in Lolistan. We need to calculate something that takes into account everyone’s income, not just the extremes.

OK, how about the standard deviation? That’s the usual way to characterize how widely a bunch of numbers are distributed.

Sudakov parameters are a common mathematical tool in the realm of high-energy physics — so I was surprised not to find a web page describing them at the top of a list of Google search results.

Since these are both null vectors, \(k_1^2 = k_2^2 = 0\), and they also satisfy \(k_1\cdot k_2 = 1\). They form two components of a complete basis. Any arbitrary four-vector can thus be parametrized as

where \(A_\perp^\mu\) is a four-vector that contains only two nonzero components, the ones orthogonal to \(k_1^\mu\) and \(k_2^\mu\). This is the Sudakov parametrization of the vector.

The Sudakov parametrization is useful because for an object moving at or near the speed of light, if the directions of the coordinate axes are appropriately chosen, only one of \(\alpha\) or \(\beta\) will be large, and the other will be nearly zero, as will both components of \(A_\perp^\mu\).

Source: appendix B of Transverse spin physics by Vincenzo Barone and Philip …

The “official” start of the Christmas season is here, and you know what that means: rampant commercialism! 5 AM sales, crowded mall parking lots, and frilly and sparkly red and green things that have already been filling store shelves since October August. ‘Tis the season, I guess.

Anyway, odds are that you’ll be buying gifts for somebody soon — if not for Christmas, then for a birthday or graduation or wedding or some other special occasion, unless you’ve achieved a level of social awkwardness that most of us can only dream of. Shopping for gifts is usually tricky, because you have to guess what to get people. Or at least that seems to be the popular opinion. Personally, though, I have no objection to gifting money, because it’s actually mathematically better.

Let’s say you’re going to buy me a book (because I did you a huge favor last summer, and what happens in Vegas stays in Vegas, and shut up it’s a hypothetical scenario). Suppose you spend $25 on this book. I’m certainly going to appreciate the thought, but there might be only an 80% chance than I’m going to like the gift …

As if last week’s announcements of new Higgs results, B-dimuon decay, the rediscovered Y(4140), and all sorts of other goodies at HCP 2012 weren’t enough, there’s more big news from the world of experimental particle physics this week. A paper published just a few days ago in Physical Review Letters (here’s the PDF, and the arXiv page) describes the first observation ever of actual time reversal asymmetry: a difference between the behavior of a particular physical process and the time-reversed version of the same process.

Lest you get too excited, though: this has nothing to do with actual reversing of time, so it doesn’t mean time travel is possible or anything like that. And in fact, nobody in physics is the least bit surprised that it worked out the way it did. There is a theorem in physics called the CPT theorem (or sometimes PCT, or TCP, but not that TCP) which basically guaranteed that time reversal asymmetry had to show up somewhere. The theorem is suddenly getting a lot of attention in the news coverage of the discovery, but it’s technical enough that most people aren’t bothering to explain it. I …

I was all set to write a lovely blog post about something sciency and then I saw this. It’s truly disturbing just how misguided some of the representatives who seek to control science funding and regulation in this country are.

Slashdot pulled out this quote from Rep. Rohrabacher:

My analysis is that in the global warming debate, we won. There were a lot of scientists who were just going along with the flow on the idea that mankind was causing a change in the world’s climate. I think that after 10 years of debate, we can show that that there are hundreds if not thousands of scientists who have come over to being skeptics, and I don’t know anyone [who was a skeptic] who became a believer in global warming.

wtf I don’t even

Yes, I did intentionally run off the end of a sentence there.

OK, here’s my problem with this: not only does Rep. Rohrabacher not understand the science he’s talking about, but he’s making up false facts to support his opinion. If he can present valid sources to back up his story, then sure, I’ll listen, but I’m …

Earlier this month I promised to show you a simple example of regularization. Well, here it is. This is a particular combination of integrals I’ve been working with a lot lately:

A quick look at the formulas shows you that both integrands have singularities at \(\mathbf{x} = 0\) and \(\mathbf{y} = 0\).

OK, well, that’s why we have two integrands. We can change variables from \(\xi\mathbf{y}\to\mathbf{x}\), subtract them, and the singularities will cancel out, right? You can do this integral by hand in polar coordinates, or just pop it into Mathematica:

Just one problem: that’s not the right answer! You can tell because the value of this integral had better depend on \(\xi\), but this expression doesn’t. This isn’t anything so mundane …

If you do a lot of computational work, you’re probably familiar with PBS, the Portable Batch System. PBS is a specification for software that allows you to submit jobs to a computer cluster and have them executed. While it’s usually used on large, highly parallel cluster computers (with hundreds or thousands of processors), sometimes you might want a copy on a home computer for testing or just to queue up your own personal tasks.

Some time ago I installed TORQUE, an open-source PBS implementation, on my main desktop which runs Gentoo. Here are some tips on the basic procedure I followed.

Enable the server USE flag and emerge the package:

echo "sys-cluster/torque server" >> /etc/portage/package.use
emerge sys-cluster/torque
emerge --config sys-cluster/torque

Check the contents of /var/spool/torque/server_name to make sure it matches your hostname (output of hostname), and /var/spool/torque/server_priv/nodes to make sure that your computer is listed.

your_hostname np=1

where np is the number of processors on your system.

Then start it up!

/etc/init.d/pbs_server start
/etc/init.d/pbs_mom start
/etc/init.d/pbs_sched start

At this point you’re good to go. You …

Note: I’m posting this from the road, so it will be somewhat lacking in pictures and details. Stay tuned for an update that fills all that in!

I’ve spent a lot of time poring over the results coming out of the Hadron Collider Physics conference this week, and I’ve noticed a trend. Higgs candidate cross sections are consistent with the standard model. B meson branching ratios are consistent with the standard model. Multijet event counts are consistent with the standard model. Maybe you can see where this is going. Vector boson production rates are consistent with the standard model. CMS rediscovered an unknown particle. Meson masses are consistent with—

Wait, what?

Yeah, that happened. CMS announced the second observation ever [PDF] of a mysterious new particle which defies classification.

This mystery object, called the Y(4140) or sometimes X(4140), was first seen in 2009 by CDF, one of the experiments at the Tevatron. It wasn’t just a slight fluctuation, either; the CDF data excluded the background-only hypothesis at more than a \(5\sigma\) level, which is the threshold physics uses to define a proper discovery. Certainly much ado has been made about less strong statistical …