2012

Apr

CMS has discovered a new particle. No big deal, yo.

Posted by David on April 29, 2012 — Comments

OK, actually it is kind of a big deal. Discovering a new particle is not something that happens every day, and it's a concrete result of having a well-tuned detector. Besides, it's just cool. So congratulations to the CMS collaboration!

In case you haven't heard the story, late last week CMS announced that they had a statistically significant observation of the ${\Xi^*}_b^0$ baryon, a particle made up of an up quark, a strange quark, and a bottom quark. In this case, "statistically significant" means that they detected this particular decay signature 21 times, of which only $3\pm 1.4$ of them can be attributed to random coincidences in the detector. So they're about as sure as you can be in physics that they are seeing signs of a real particle. They've also managed to reconstruct various properties of this particle by examining the decay products, and everything matches up with the predicted properties of the ${\Xi^*}_b^0$ .

Now, why isn't this a bigger deal, and why didn't I write about it right away? Well, as I just mentioned, this particle was predicted to exist. Of course, the Higgs boson was also predicted to exist, and everyone gets very excited about that. The difference with this particle is that it's a baryon. All baryons are just different combinations of quarks; for example, the proton consists of two up quarks and a down quark, the neutron of two downs and an up, the neutral lambda baryon of an up quark, a down quark, and a strange quark, and so on. We've already discovered dozens of these baryons, all of which fit into a very well-understood pattern. That makes it easy (for a theoretical particle physicist) to predict the properties of any sort of baryon you can come up with. If you want to know what the mass and spin of a up-bottom-bottom baryon are, the theory can tell you that. We've actually used this pattern many times in the past to predict undiscovered baryons, and it's been pretty close every time. It's gotten to the point where nobody doubts the existence of all the particles predicted by this pattern, even though a bunch of them have never actually been detected. Up until recently, the ${\Xi^*}_b^0$ was one such particle.

2012

Apr

Dark matter on the mind

Posted by David on April 21, 2012 — Comments

There are a few interesting experimental results and analyses from the physics world this week, mostly having to do with dark matter. Probably the biggest of these is a fairly detailed paper on the local density of dark matter by the team of Moni Bidin, Carraro, Méndez, and Smith. As you may know, dark matter is astrophysicists' favorite method to explain how the tangential velocity of stars in large galaxies can be nearly constant all the way from the center out to the (visible) edge, despite the fact that a simple model would tell you that the velocity should be slower for stars further out. It explains a bunch of other observations too, including measurements of gravitational lensing by large galaxy clusters, so we're pretty confident that dark matter exists.

Dark matter density plot With that in mind, it's kind of surprising that the analysis done by Moni Bidin, Carraro, Méndez, and Smith finds no dark matter at all within a few kiloparsecs of the solar system! Basically, what they've done is apply Newtonian gravity (which applies fairly well on these scales), along with ten reasonable-sounding assumptions, to find a formula which relates the velocities of stars in some region of the galaxy to the local density of matter (regular and dark) within that region. They then took measurements of the velocities of 400 red giants in the vicinity of Earth, extrapolated to the entire stellar population using the known statistics of stellar motion, plugged the velocities into the formula, and came out with a density of $\Sigma(\SI{1.5}{kpc})= (55.6\pm 4.7)\mathrm{M}_\odot\,\si{pc^{-2}}$ , which exactly matches the density of visible stars — no dark matter needed. This is shown in the plot at the right: the dark matter density calculated from the formula is the solid black line, and the gray lines are various theoretical predictions. The line labeled "VIS" means "visible matter only."

Of course, there are a number of ways in which this model could be inaccurate; for example, maybe the velocities of the red giants don't reflect that of the overall stellar population as well as we think, or perhaps the measurements of the dimensions of the galactic disc are a little bit off, or perhaps one or more of the ten assumptions isn't quite right. That's why the entire second half of the paper is devoted to an analysis of how the result for $\Sigma(Z)$ would change if a measurement is incorrect or an assumption is wrong. And the conclusion from that part is that, within the constraints that we definitely know from other measurements, there's pretty much no combination of changed parameters or invalid assumptions that would make the result match any of the common models of dark matter. The only way people are seeing to make sense of the data is to assume that the dark matter is somehow clumped in particular regions of the galaxy, and we just happen to be in the middle of a pretty big dark-matter-free zone. That doesn't seem very likely, but it is possible. It's probably about as likely, though, that there's some new dark matter model nobody's thought up yet which will make more sense out of all this.

Another result that's getting a fair amount of attention is a possible actual detection of dark matter, discovered by Christoph Weniger in data collected by the Fermi Large Area Telescope. The FLAT has been pointed at the sky to collect gamma rays for almost four years now. There are many different sources for these gamma rays, but one possible source is the annihilation of dark matter particles with each other, which could happen if dark matter particles and their antiparticles both exist in large amounts in the same region (or if dark matter particles are their own antiparticles, as is predicted by several models). Now, if you assume that the dark matter particles are moving slowly relative to each other, then if two of them annihilate into a pair of photons, each of those photons will have the same energy as the mass of the original dark matter particle. And in fact, the standard model of cosmology, the Λ-CDM model, does specify that dark matter particles should be moving slowly. So if dark matter particles and antiparticles annihilate to produce photons, we should be able to detect a bunch of photons all at roughly the same energy, which will in turn tell us the mass of whatever particle constitutes the dark matter. This is kind of similar to what happens in particle accelerators: if the particles being collided have just enough energy to make, say, a heavy quark-antiquark pair, then that pair might decay into two photons, each of which has the same energy as the mass of one of the quarks.

Potential annihilation peak This is just the sort of phenomenon that Weniger has discovered (or at least that he's claimed to have discovered; from reading the paper, it's a little hard to see an effect as strong as what he reports). In gamma rays detected from a region near the center of the galaxy, there is a little bump in the photon spectrum around $\SI{130}{GeV}$ . This suggests that there may be dark matter particles with that mass annihilating in this region. It makes sense that the dark matter would cluster near the galactic center, since it responds to gravity more than to any other force. But the bump is still very small, and as Weniger himself points out, it can only be considered a tentative discovery at this time — not even a discovery, really, more like an observation. Still, this is exciting because, if the result turns out to be true, it would represent the first definitive, direct evidence that dark matter interacts in any way other than by gravity, and the first indication of what sort of particle might be making up this matter.

Yet another interesting result comes courtesy of Sean Carroll at Cosmic Variance, specifically in reference to this paper which reanalyzes data from CDMS. This paper is pretty technically dense, so I haven't been able to properly ~~read~~ skim it, but between Sean's blog post and what I can pick up from the paper, the claim is that the original analysis done by the CDMS collaboration is not sensitive enough to pick up the signal that would be generated by the dark matter at the density predicted by the common models. Specifically, the original analysis excludes a signal greater than $\SI{0.06}{events/keVnr kg day}$ (that's detected events per day, per kilogram of detector material, per unit energy bin width), but Collar and Fields say that the signal from WIMP dark matter should be $\SI{0.035}{events/keVnr kg day}$ . What's more, they run a different analysis and find that the CDMS data actually do show some events which can't be explained by the known (regular matter) interactions, but which do seem to match a signal found by their "competitor" CoGeNT. If this analysis is correct, it lends support to the idea that there is a substantial population of dark matter particles in the vicinity of the Earth, in contrast to what Moni Bidin et al. concluded. So one or the other of these results is probably going to be wrong, although it's likely going to be a very subtle correction. It's definitely going to be a very interesting time for dark matter detection research over the next few years.

For more information on these results, I'll point you to blog posts by Sean Carroll and Matt Strassler.

2012

Apr

Square wheels

Posted by David on April 14, 2012 — Comments

It hasn't escaped my notice that Mythbusters is back with a new season! Actually, it's not really that new, since we're now three (well, now four) weeks in, but I missed the first two episodes since I was out of the country. But it works out because this (actually last) week's myth is full of interesting physics to analyze!

This past Sunday, Adam and Jamie tested the myth that if you're driving fast enough, square wheels can actually provide a surprisingly smooth ride. At first, the idea of square wheels working at all, much less actually being smooth, can seem a little wacky, but with a bit of physical intuition, it's not hard to convince yourself that it's actually pretty plausible. As they explained in the show, the reason a square wheel is expected to bounce you up and down is that the distance from the axle to the bottom of the wheel changes as it turns. If you're going slowly, every time the wheel tips over another corner, it's going to fall down until its side is resting against the ground, taking you with it. But if you speed up enough, the wheel won't have time to fall very far before it rotates through a quarter turn, and the next corner gets under it to hold it up.

Simple model: a slowly turning wheel

You can actually calculate about how fast you would need to go to do this. Let's consider just a single square wheel, and at first, suppose it's going really slowly. That way, the wheel is going to constantly stay in contact with the ground. There are basically two "phases" in the cycle of a slowly turning square wheel:

Starting from a position where the wheel is "perched" on its corner with the corner pointing down, it's going to first just pivot forward around that corner, and fall down on its side.
After that, it'll pivot up around the next corner, until that next corner is now pointing down.

Diagram of rotating square wheel

Suppose the wheel has a side length of $2r$ and is rotating at angular speed $\omega$ , which I'm going to assume is constant for simplicity. Based on geometry, the height of the first corner relative to the wheel's center is

$y_1(t) = -\sqrt{2}r\cos(\omega t)$

and since the second corner trails by an angle of $\frac{pi}{2}$ (a quarter circle), its height relative to the center is going to be

$y_2(t) = -\sqrt{2}r\cos\biggl(\omega t - \frac{\pi}{2}\biggr)$

At any given time, the height of the lowest point on the wheel relative to its center will be the lesser of these two expressions: $y_1$ for the first eighth turn, and $y_2$ for the next eighth. But what we really want is the height of the center of the wheel above the ground, which will be the negative of that minimum:

$y_\text{slow}(t) = \begin{cases}\sqrt{2}r\cos(\omega t) & 0 \le t < \frac{\pi}{4\omega} \\ \sqrt{2}r\cos\biggl(\omega t - \dfrac{\pi}{2}\biggr) & \frac{\pi}{4\omega} \le t < \frac{\pi}{2\omega}\end{cases}$

This function tells us the height of the truck as a function of time as one quarter turn of the wheel elapses. It looks like this:

Height function for slow wheel

From this, we should be able to figure out how bumpy the ride on this slowly turning wheel would be. But that brings up another question: how exactly do you measure bumpiness?

Think back to the last time you were on a car driving on a road with a lot of potholes, or any other rough surface. What makes it unpleasant is that you get shaken up and down a lot. The larger the vibrations, the rougher the ride. So it makes sense to say that our measure of bumpiness should be related to the distance by which the car bounces up and down in a cycle — in other words, the maximum height minus the minimum height, which is often called peak-to-peak amplitude.

But if you think about it, the time scale over which these oscillations occur is also important. When you drive up and down a mountain, that's a huge bounce, but it doesn't feel like it because it's so slow. So the "bumpiness metric" should also be anti-correlated to the cycle time: quicker bumps at the same amplitude have more of an effect. Accordingly, I'm going to define a simple measure of bumpiness as the ratio of the peak-to-peak amplitude to the period for one up-and-down cycle of oscillation (which is actually a quarter cycle of the wheel). I'm sure there are more complicated (and more realistic) ways to define bumpiness, but this one should be good enough to make my point here.

For the model of a slowly rotating square wheel, we can find the peak-to-peak amplitude using the maximum value of $y(t)$ , which occurs at $t = 0$ (and again at $t = \pi/2\omega$ ), and the minimum value, which occurs at $t = \pi/4\omega$ .

$B = \frac{\sqrt{2}r\cos(0) - \sqrt{2}r\cos\bigl(\omega\times\frac{\pi}{4\omega}\bigr)}{\frac{\pi}{2\omega}} = \frac{2}{\pi}(\sqrt{2} - 1)r\omega$

Speeding it up

With the simple slow wheel model out of the way, let's see what happens when you speed the wheel's rotation up. The most important change comes from the fact that there is nothing actually holding the wheel's surface to the ground. In the first part of the cycle, the only thing pulling the wheel down is gravity, and gravity can't accelerate it any faster than $\SI{9.8}{m/s^2}$ . So if our slow-wheel model says that the wheel should be moving downward at faster than $g = \SI{9.8}{m/s^2}$ , that is if $y''(t) < -g$ , then we've got a problem.

Of course, it's not hard to figure out when this actually does happen, using basic Newtonian mechanics. There are two relevant forces acting on the wheel, gravity and the normal force from the ground. Their relationship is given by Newton's second law, $\sum F = ma$ , or in this case:

$-mg + F_N = my'' = -\sqrt{2}mr\omega^2\cos(\omega t)$

For a slowly rotating wheel, $\omega$ is small, and thus $F_N$ will need to be positive to make this equation true. Once $\omega$ gets large enough that $-mg > -\sqrt{2}mr\omega^2\cos(\omega t)$ , though, there will be no zero or positive value of $F_N$ that can make the equation true. That's when the wheel is going to leave the ground. This will happen at $t = 0$ as long as

$\omega^2 > \frac{g}{\sqrt{2}r}$

If the normal force is going to be zero, the wheel won't be touching the ground as it rotates. Instead, it's going to be in free fall for some amount of time. That's an easy situation to analyze; the height of an object in free fall is just $y = y_0 + v_0 (t - t_0) - g(t - t_0)^2/2$ , and since in this case the free-fall phase starts at time 0 with zero vertical velocity, that just reduces to

$y_\text{free}(t) = \sqrt{2}r - \frac{gt^2}{2}$

The wheel will remain in free fall as long as this height $y_\text{free}$ is greater than the height difference between the center of the wheel and its lowest point. The latter quantity is something we've already calculated: it's $y_\text{slow}$ . So we need to identify the first nonzero time at which $y_\text{free}(t) = y_\text{slow}(t)$ , the solution to

$\sqrt{2}r - \frac{gt^2}{2} = \begin{cases}\sqrt{2}r\cos(\omega t) & 0 \le t < \frac{\pi}{4\omega} \\ \sqrt{2}r\cos\biggl(\omega t - \dfrac{\pi}{2}\biggr) & \frac{\pi}{4\omega} \le t < \frac{\pi}{2\omega}\end{cases}$

This is a little tricky for a couple of reasons: first, it's a transcendental equation, because it involves both a polynomial in $t$ and a trigonometric function of $t$ . That means you can't write the solution as a symbolic function. You can still solve it numerically, though, and that's what I'm going to do shortly. The other issue is that it has a piecewise function on the right. That's not that hard to deal with, at least not if you have numbers for everything; you can just solve the first case, and see if the solution you get satisfies the condition for that case ( $0 \le t < \frac{\pi}{4\omega}$ ); if not, then the solution comes from the second piece. It turns out that in our situation, because of the requirement $\omega^2 > g/\sqrt{2}r$ , the solution is almost always going to come from the second case; for most values of $\omega$ the first corner of the wheel never touches the ground again after the very beginning of the cycle, and the small region of $\omega$ where that's not the case is basically negligible. (Plus it would take a whole other post to do that analysis properly) So we can reduce this last equation to

$\sqrt{2}r - \frac{gt^2}{2} = \sqrt{2}r\cos\biggl(\omega t - \dfrac{\pi}{2}\biggr)$

The solution to this tells us when the second corner of the wheel is going to hit the ground. Call that solution $t_2$ . Then the height as a function of time for a square wheel which does not have to be moving slowly is

$y_(t) = \begin{cases}\sqrt{2}r\cos(\omega t) & 0 \le t < t_2 \\ \sqrt{2}r\cos\biggl(\omega t - \dfrac{\pi}{2}\biggr) & t_2 \le t < \frac{\pi}{2\omega}\end{cases}$

This function looks like this:

Height function for fast wheel

Notice the difference between this and the equivalent graph for a slow wheel (which is included in the background, for comparison). The peak-to-peak amplitude of this motion is considerably less. This will also be reflected in the formula for the bumpiness, which is

$B = \frac{\sqrt{2}r\cos(0) - \sqrt{2}r\cos\bigl(\omega t_2 - \frac{\pi}{2}\bigr)}{\frac{\pi}{2\omega}} = \frac{2}{\pi}\bigl(1 - \sin(\omega t_2)\bigr)r\omega$

Putting it all together

To recap, our measure of bumpiness over all possible rotational frequencies is given by the following piecewise function:

$B = \begin{cases}\frac{2}{\pi}(\sqrt{2} - 1)r\omega & \omega^2 \le \frac{g}{\sqrt{2}r} \\ \frac{2}{\pi}\bigl(1 - \sin(\omega t_2)\bigr)r\omega & \omega^2 > \frac{g}{\sqrt{2}r}\end{cases}$

For a square wheel with a $\SI{50}{cm}$ side length, a plot of this function looks like this:

Bumpiness plot

The horizontal axis shows speed in meters per second. There's a peak in the graph around $\SI{6.2}{m/s}$ , or $\SI{14}{mph}$ , and after that it starts going down — which means that for this size of wheel, once you pass 14 miles per hour, the ride actually should start getting smoother! And that's pretty close to what Jamie and Adam actually observed in the show.

2012

Mar

Day 5: Plenary sessions (again!)

Posted by David on March 30, 2012 — Comments

DIS 2012 wrapped up today, and the last day of the conference was filled with another round of plenary sessions (attended by everybody). This time, though, the talks were mostly devoted to summarizing the parallel sessions which took place over the previous three days.

The conference was divided up by topic into seven working groups: structure functions, the future of DIS, diffraction and vector mesons, electroweak and new physics searches, hadronic final states, heavy flavor, and spin physics. Each of these working groups was organized by two or three conveners, who were also responsible for putting together and presenting the summary slides. I have to recognize the impressive amount of work this must have taken: in one afternoon, the conveners went through every single presentation given in the conference, and organized and adapted the main conclusions from all of them into an experimental and a theoretical summary talk for each working group. Not to mention they had to stay awake and attentive for the entire three days of talks — much easier said than done!

Anyway, the full summary presentations can be found on Indico, so if you're interested, go ahead and check those out. I'll post a more detailed summary, or perhaps multiple summaries, once I have some time to go through the presentations again (perhaps in a few days when I recover high-speed internet access), but for now, I just wanted to highlight a few key developments:

LHC data is starting to dominate the input for various sorts of theoretical calculations, including constraints on the mass of the weak boson, the coupling constants of the standard model, and parton distribution functions (which describe the structure of the proton), among other things. Several of the groups which calculate these parton distribution functions will shortly be releasing updated numbers which take the 2011 LHC data into account.
The first collisions in the LHC at $\SI{8}{TeV}$ actually took place today!
Although the Tevatron is shut down, analysis of its data is still yielding interesting results, especially with respect to the nature of parity violation in the weak force. Since the Tevatron collided two beams of different particles, it's well-placed to look for these parity violations (as opposed to the LHC, where the two beams are the same and thus most parity violations are hidden).
The COMPASS experiment continues to produce data which is very useful for analyzing the spins of constituents of the proton.
We've known for a while now, but the Higgs boson is excluded at $2\sigma$ (95% chance that it doesn't exist) outside of two narrow ranges, a $\SI{1}{GeV}$ -ish range around $\SI{118}{GeV}$ and a $\SI{5}{GeV}$ range around $\SI{125}{GeV}$ . (I might be a tiny bit off on the numbers, I forgot to write them down as they came up)
Pretty much everything still agrees with the standard model (so, no big experimental surprises).
Future plans for the LHC include two upgrades to the luminosity over the next 10 years or so, and also — if the plans are approved — the addition of an electron accelerator to form the LHeC, Large Hadron-electron Collider. This new machine will enable a whole host of new physics experiments that are impractical or impossible using the current LHC.
In addition, there is a long-term plan to build the EIC (Electron-Ion Collider) to complement the LHeC.

Finally, although it didn't actually happen at this conference, we did find out today that the OPERA experiment has tentatively adjusted their analysis to account for the equipment errors they discovered earlier, and the new time-of-flight discrepancy is $\delta t = -1.7\pm 3.7\ \si{ns}$ , which is perfectly consistent with relativity. I'll be writing more about this tomorrow, but for now Matt Strassler has a post on it which will surely be updated with additional details.

2012

Mar

Midweek report: parallel sessions

Posted by David on March 28, 2012 — Comments

We are now in the middle of DIS 2012, the part known as the parallel sessions because, well, they are in parallel. Specifically, at any given time during the conference there will be 5-7 presentations going on in different rooms. With four sessions per day and three or four 20-minute talks per session, that means there have probably been almost 200 physics presentations given in this one building in just the past two days!

With that breadth of material, I can't hope to cover them all — in fact, I haven't even been able to properly "digest" just the ones I've been to! Unfortunately there are no particularly attention-grabbing talks like major experimental results, so nothing necessarily stands out of the pack; instead, here's a somewhat arbitrary selection of some of the interesting presentation titles. If you are interested in this sort of thing, feel free to follow the links and read them; if not, make it into a drinking game or something.

I'm sure I'll be posting thoughts on some of the interesting presentations over the coming days.

2012

Mar

Day 1: Plenary sessions

Posted by David on March 26, 2012 — Comments

DIS 2012 kicked off today with a full day of plenary sessions, general talks that everyone in the conference attends. (Well, not everyone attends, but there's nothing else going on at any rate.) The slides of all the talks presented today are available on the conference website, but here are some of the interesting results.

Results from the Tevatron and LHC

Under the principle of "save the best for last," I am getting this out of the way first: none of the major experiments have any new results of widespread importance to present. In particular, the Higgs search stands exactly where it was two weeks ago when the Moriond results were presented. This is no surprise because, for one thing, the Higgs boson is an electroweak phenomenon whereas DIS is more about the strong force; also, any major results would be presented at a bigger conference. DIS is a fairly specialized field of study so it doesn't attract all that many people, in the grand scheme of things.

Of course, that's not to say there is nothing to report at all. The Tevatron experiments are finishing up analysis of their data and they have found some interesting tidbits, like $\mathrm{W}$ boson production in conjunction with charm quarks. And the ATLAS and CMS talks contain a pretty detailed overview of the results of the Higgs search that have been made public over the past several weeks.

Electroweak precision measurements

Even though we understand the theory of the electroweak interaction pretty well, there are plenty of interesting measurements to be made, especially regarding the weak boson mass. Since it is the main mediator of the weak force, lots of particles' decay rates depend on this mass, so the better we can calculate it, the better we can determine the decay parameters. These parameters are involved in checking the standard model for internal consistency, and certain extensions of the standard model (like MSSM) will require a precisely known W mass to check.

With the latest calculation of the W boson mass based on Tevatron data, the global uncertainty is reduced by about 30%, and the preliminary new world average stands at $80385\pm 15\ \si{GeV}$ .

$\alpha_s$ status

Arguably the most fundamental parameter in QCD is the strong coupling, $\alpha_s$ . As the most fundamental parameter, it can't be predicted theoretically; it needs to be measured, and there are continual research efforts underway to determine what the value (at any given energy) actually is. The worldwide average stands at $\alpha_s(m_Z) = 0.1184\pm 0.0007$ , mostly determined by lattice QCD calculations. That's very precise, but there are definitely some discrepancies to investigate. Other methods of determining the strong coupling include various methods of analyzing $\tlp$ decays, the angular distributions of $\elp\ealp$ collisions, and the parton distribution functions from hadron scattering (like DIS), and not all of them agree. It's hoped (and expected) that LHC data can soon start contributing to this determination as well, which may help clarify some of the discrepancies.

Theory developments in QCD

On the theoretical side, much of the recent progress in QCD has centered on two fronts: automating NNLO calculations and computing resummations.

NNLO

In perturbative QCD, all important quantities are expressed as power series in $\alpha_s$ . The individual terms in the series are quite complicated to calculate, so it can save a lot of time if we get computers to do it for us, but unfortunately it can be as hard to define an efficient procedure for a computer to calculate the terms as it is to just do it by hand.

Right now we've been able to program computers to calculate the leading order term in the series, $\orderof{\alpha_s^0}$ , and the next-to-leading order term, $\orderof{\alpha_s^1}$ . There are a bunch of different programs you can use to do this (MadGraph and MadLoop respectively, among many others). So the frontier of this programming is now on calculation of the NNLO $\orderof{\alpha_s^2}$ term. A few selected results are already available, and we're close enough that a general framework could be implemented within a couple of years.

Resummation

Alternatively, there are efforts underway to resum the series by organizing the terms in a different way — instead of writing a cross section or decay rate as a series in $\alpha_s$ , make it a series in $\alpha_s\ln(E_1/E_2)$ . You still need to calculate term by term, but with this different organization, more of the contribution is hopefully shifted into the early terms in the series, so if you stop at, say, third order, the pieces you're missing aren't as significant.

2012

Mar

What is Deep Inelastic Scattering?

Posted by David on March 25, 2012 — Comments

Since I'll be writing about the Deep Inelastic Scattering Workshop this week, I was planning to make a pre-conference introduction post explaining in some detail what DIS actually is. But as it turns out, one of the plenary talks tomorrow is devoted to exactly that subject — plus I'm really tired after traveling for about 18 hours and walking around the city for another four or so. So I'll start with a quick introduction and update this with more information tomorrow.

Deep Inelastic Scattering

Deep inelastic scattering itself is a particular type of physical process that occurs when a hadron (a particle made of quarks and gluons, such as a proton) collides with a lepton (a particle that, as far as we know, has no constituents).

It's "deep" because the lepton has very high momentum as measured in the proton's reference frame, so the way it behaves in the interaction can depend on very small features of the proton's structure.
It's "inelastic" because some of the kinetic energy of the original two particles is lost. In modern DIS, that energy goes into splitting the proton into many outgoing particles.
It's "scattering" because the lepton is deflected and comes out at a different angle than it came in at. Measurements of that angle can be useful in characterizing the collision.

DIS processes were used to make the first measurements of the number of quarks in the proton, among other things. (A favorite of mine among those other things is geometric scaling, which is related to what I'll be talking about at this conference — but the details will have to wait for another blog post.)

Higgs boson search update

Tevatron combined Higgs signal

Tevatron combined relative cross section At the Moriond conference on electroweak physics, CDF and D0, the two major experiments from the (now closed) Tevatron, reported an excess of collision events between about $\SI{115}{GeV}$ and $\SI{140}{GeV}$ , peaking at $2.2\sigma$ . This could be a very weak signal of the Higgs boson, but it wouldn't have been much to get excited about if ATLAS and CMS hadn't already detected similar (but stronger) signals in the same energy range.

It's worth keeping in mind that the Tevatron has been shut down, so these latest results aren't based on new data (like the LHC results); they're based on a new analysis of the same data that had already been collected as of last year. The main reason they were able to discover this excess where they hadn't seen it before was an improved technique for b-jet tagging; that is, identifying processes where the Higgs boson (perhaps) decays into a bottom quark and anti-bottom quark.

ATLAS Higgs exclusion and signal suppression

ATLAS combined results Speaking of the LHC expreiments, at the same conference the ATLAS collaboration presented their latest results, in which they have found... well, mostly nothing. But in part, this is a good nothing. What I mean is that the cross sections observed by ATLAS are $2\sigma$ below what would be expected from the standard model Higgs boson at most energies other than this little window around $\SI{125.0}{GeV}$ . So we're basically 95% sure that there is no Higgs boson with a mass less than $\SI{122.5}{GeV}$ or greater than $\SI{127.5}{GeV}$ . This is actually half the battle in finding the Higgs boson directly: we have to not only show that it does show up at a particular energy (which corresponds to its mass), but that it doesn't show up at other energies.

On the other hand, in this energy range around $\SI{125.0}{GeV}$ where we suspect that the standard model Higgs is showing up, the latest ATLAS data have actually decreased the significance of the peak. You may remember that back in December, ATLAS and CMS announced that they were seeing a pretty tall peak around $\SI{126}{GeV}$ , which they took as a possible first indication of the Higgs boson. The hope was that if that really is the standard model Higgs, as more data came in the peak would get taller, which would mean that we could be more confident that it's not a fluke. But the opposite actually happened; when you take the new data into account, the peak is smaller than it was before. It's still enough to qualify as a region of interest, though, so the overall situation is much the same: there might be a Higgs boson at $\SI{125}{GeV}$ or so, we're just not sure yet.

CMS diphoton Higgs signal enhancement

CMS combined results CMS, on the other hand, didn't have much to add to their presentation from December. The main improvement they did make was a better analysis of the events in which they detected two photons that might have come from a decaying Higgs boson. In contrast to the ATLAS results, this new analysis increased the height of the peak, which means CMS is a little more confident that they are seeing something real.

The Last Neutrino Mixing Angle

In other news, the Daya Bay neutrino experiment has announced a measurement of the neutrino mixing angle $\theta_{13}$ . This one deserves a bit more explanation, but I'll still have to be brief for now. (I am happy to do a more detailed and/or less technical explanation of this if people would like to see it — leave requests in the comments.)

If you've studied neutrino physics in any detail, you know that neutrinos have flavor eigenstates and mass eigenstates, but the two are not exactly the same. What this means is that if you produce or detect a particular type of neutrino, such as an electron neutrino, it is actually in a quantum superposition of different masses, and if you are dealing with a neutrino with a particular type of mass, it is in a quantum superposition of different flavor states. This is how neutrinos are able to oscillate: they are created in a particular flavor state, for example $\ket{\enu}$ , travel through space as a superposition of mass eigenstates $U_{e1}\ket{\mathrm{\nu}_1} + U_{e2}\mathrm{\nu}_2 + U_{e3}\mathrm{\nu}_3$ ("rotating" through different flavor states in the process), and then are detected in some flavor state which may differ from the initial one. The matrix $U$ which relates the two bases to each other is called the neutrino mixing matrix, or the PMNS matrix, and it can be written as a product of three 2D rotation matrices (sort of):

$U = \begin{pmatrix}1 & 0 & 0 \\ 0 & c_{23} & s_{23} \\ 0 & -s_{23} & c_{23}\end{pmatrix}\begin{pmatrix}c_{13} & 0 & s_{13}e^{-i\delta} \\ 0 & 1 & 0 \\ -s_{13}e^{i\delta} & 0 & c_{13}\end{pmatrix}\begin{pmatrix}c_{12} & s_{12} & 0 \\ -s_{12} & c_{12} & 0 \\ 0 & 0 & 1\end{pmatrix}$

I'm using Wikipedia's abbreviations of $c_{ij} = \cos\theta_{ij}$ and $s_{ij} = \sin\theta_{ij}$ . The $\theta_{ij}$ s are the mixing angles which quantify the overlap between the flavor states and the mass states.

Starting in the 1960's, we've been able to determine values for two of the angles: $\theta_{12}\approx\SI{34}{\degree}$ from measuring how neutrinos produced in the sun oscillate on the way to Earth, and $\theta_{23}\approx\SI{45}{\degree}$ from the oscillations of neutrinos produced by cosmic rays striking the atmosphere. But $\theta_{13}$ proved to be a lot trickier because there wasn't a natural physical situation that allowed for a precise measurement of that one angle without involving the other two. The best that previous experiments were able to determine was that the angle is very small. It could have even been zero, which would be unfortunate because that would completely ruin our best chance at measuring the phase $\delta$ . That phase controls CP violation in neutrinos, which in turn is related to the origins of matter in the universe, so... you might say it's kind of an important number.

Recently, there have been three experiments (that I know of) trying specifically to measure $\theta_{13}$ : T2K, Double Chooz, and Daya Bay. It turned out that Daya Bay was the first to come up with a definitive nonzero value of around $\SI{5}{\degree}$ . The measurement comes at a significance of $5.2\sigma$ , which means they can say $\theta_{13}\neq 0$ with less than a one in a million chance of being wrong.

Antihydrogen Spectroscopy

In other news, the ALPHA experiment at CERN (not affiliated with the LHC) has measured the spectral lines of an antihydrogen atom for the first time. Their measurement isn't yet precise enough to compare with the spectral lines of hydrogen to see if they match, but it is a key first step. Comparing the spectral lines is one of the best ways we have to establish whether the electromagnetic force works the same way on antimatter as it does on matter, and that in turn could shed light on possible violations of CP symmetry.

The 230% Efficient LED

Physicists at MIT have developed a light-emitting diode that operates at an efficiency of 230%: it outputs more than twice as much energy as light as the electricity it takes in! That sounds rather crazy at first, but it actually works without breaking any physical laws, because what it really does is convert vibrational thermal energy into thermal radiation. In this sense it kind of acts like a refrigerator, in that it uses a certain amount of input energy to transfer a larger amount of energy from one thermal reservoir to another. Usually the output of a refrigerator is considered wasted energy, like when it gets vented off the coils at the back of your kitchen fridge, but the MIT group has basically found a way to make that "waste" heat actually useful: just let it be emitted as light.

Information and Thermodynamic Entropy

Another group collaborating between multiple institutions has experimentally demonstrated for the first time that the loss of information in any physical system produces heat. This effect was quantitatively predicted by Rolf Landauer in 1961. It's actually fairly simple to understand: the minimum number of physical states of a system that stores $N$ bits of information is $2^N$ , and the entropy of a system with that many states is $S = Nk\ln 2$ . So if a system goes from storing, say, one bit to none, it has to lose an amount of entropy equal to $k\ln 2$ . But in order for the second law of thermodynamics to be satisfied, something in the system's environment has to increase its entropy by at least that much, and doing so requires a heat transfer of $\Delta Q = T\Delta S = kT\ln 2$ .

Despite the simplicity of the theoretical argument, nobody had managed to experimentally observe this effect until now, because the amount of heat being exchanged is tiny, around $\SI{e-21}{J}$ at room temperature. Besides, the way that most common systems store information is highly redundant, so when you lose one bit of the information you thought you were storing, you might actually be losing many bits of physical information. This is intentional, of course, because you don't want a random thermal fluctuation wiping out half your hard drive! But it tends to get in the way of physics. So the team which performed this experiment had to construct a device which actually stores one and only bit of information, using an optical trap between glass panes, and measure its energy changes very precisely. When they did so, they found amounts of heat being dissipated that satisfied the Landauer bound very cleanly.

Upcoming events

The Moriond conference continues this coming week, with its focus shifting to QCD, so perhaps there will be more exciting news from the LHC or Tevatron experiments, or who knows what else. I'll definitely be watching to see what comes out of it, and I'll be posting any interesting results from Moriond or elsewhere to my Twitter stream, so keep an eye on that to stay informed! Otherwise, perhaps I'll have to write another summary blog post if it turns out to be another big week.

P.S. I should acknowledge that I grabbed the images in this article from Résonaances, just because I'm lazy (the original source is, of course, the relevant conference presentation).

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