Transapient Musings of an S6 Archailect

This week in the arxiv: superconductivity update
src

Summer writing and travel are eating my blogging time a bit, and I've also agreed to write the occasional nano-related blurb for the ACS. While my posting rate has taken a hit, science has continued to march forward, with a lot of exciting new preprints concerning (relatively) high temperature superconductivity. Here's a sampling....

arxiv:0805.4463 - Matsumoto et al., Superconductivity in undoped T' cuprates with T_c over 30 K
This paper is a perfect example of why materials growers are (unfortunately often unsung) heroes in this field. The authors have come up with a new method for growing cuprate compounds of the form T'Re₂CuO₄, where T'Re is a rare earth from the series (Pr, Nd, Sm, Eu, Gd). Historically these compounds were found to be antiferromagnetic insulators - no superconductivity. In this new work the authors argue that these old results were due to interstitial oxygen leading to pair-breaking. Instead, with the new growth + annealing technique, these compounds are found to exhibit superconductivity with transition temperatures as high as 30 K. These subtleties are why one should always be very careful when looking at suggested compositions in new compounds....

arxiv:0805.4630 - Rotter et al., Superconductivity at 38 K in the iron arsenide (Ba_1-xK_x)Fe₂As₂
This is the first paper I've seen (though I may have missed one) that reports superconductivity in a compound related to the new iron arsenide systems but with two iron arsenide layers per unit cell rather than one. Back in the heyday of the cuprates, the same sort of thing happened - people went from compounds with single copper oxide planes to those with multiple planes per unit cell, and transition temperatures went up. Once again we see how rich the materials landscape can be.

arxiv:0806.0063 - Wang et al., Very high critical field and superior J_c-field performance in NdO_0.82F_0.18FeAs with T_c of 51 K
Other exciting features of the new iron arsenide superconductors are their extremely high critical fields and critical currents. If the transition temperatures could be raised a bit (say past 77 K) and the compounds could be made in wire form (certainly not easy in the cuprates; unlikely to be simple in these either since like the cuprates they are brittle), this could be a huge deal for high field magnets and other applications of superconductivity.

arxiv:0805.4616 - Chen et al., The BCS-like gap in superconductor SmFeAsO_0.85F_0.15
arxiv:0806.0249 - Matano et al., Spin-singlet superconductivity with multiple gaps in PrO_0.89F_0.11FeAs
These two papers examine two related compounds with different techniques, trying to figure out how the charge carriers in these iron arsenides pair up to form the Cooper pairs that make up the superconducting condensate state. In the former, measurements of Andreev reflection (a process where an electron in a normal metal approaches a superconductor, two electrons actually cross into the superconductor, and a hole is "retroreflected" back into the normal metal, leading to a pronounced feature in the conductance of the metal/superconductor interface) strongly suggest that the samarium compound acts like an ordinary BCS superconductor. That is, each Cooper pair has zero angular momentum (s-wave pairing); this implies that the superconducting gap is uniform in momentum space, with no nodes. In contrast, the cuprates exhibit d-wave pairing, with a superconducting gap that has a four-lobe structure in momentum space and that goes to zero along four particular crystallographic directions.

The second paper uses NMR measurements of the Pr compound to argue instead that there are multiple gaps, and further that the pairing symmetry is p-wave (which has been seen in superfluid ³He and in strontium ruthenate). At first glance, these two results seem to disagree, though (a) they are talking about different materials, and (b) the Andreev measurements are particularly sensitive to the surface, while the NMR measurements are nontrivial to interpret, at least for nonexperts. Well, this is the fun part - stay tuned, and we'll see how this shakes out.

posted at: 11:37 | path: /sci/physics | permanent link to this entry

I wish to offer you, my dear reader, the chance to play the part of the experimenter and confront you with a simple measurement setup, wherein a subtlety is hidden -one the experimenter needs to realize if he is to perform his experiment correctly. I will describe the setup and the equipment, and give maybe too much detail, as per my typical style. Then I will formulate a question, giving you one day to ponder on it. I am going to try to make this post so simple that you are not expected to know anything about particle physics in order to participate. All is needed is the knowledge that muons decay, with a lifetime of about two microseconds, producing an energetic electron; but you just acquired that knowledge by reading the last sentence.

The experiment seeks to determine the muon lifetime by stopping muons from cosmic rays inside a thick bar of aluminum, and then measuring the time it takes for an electron to emerge from it. A simplified view of the apparatus is as shown below.

There is a 8-inch shield of lead on top (the blue rectangle), which stops the so-called soft component of cosmic rays (three thin lines ending inside it are shown). This is due to protons, pions, electrons, and photons - all secondaries produced by the high-energy interaction of a cosmic proton in the upper atmosphere or subsequent decays in flight. Those particles are largely absorbed by the lead, while a good fraction of muons -also secondary products of the cosmic ray- pass it rather easily.

Muons are special: they can traverse large amounts of matter with only minor modifications of their momentum. Those that manage to punch through the lead cross a pair of scintillation detectors (read out by photomultipliers labeled A,B at one end), and then enter an aluminum bar (in red). While most muons also exit the aluminum at the bottom, leaving a signal in the other scintillation counter (cyan layer read out by photomultiplier C), a small fraction of them stop in the aluminum, where they stay and then decay with a typical exponential law.

The stopping of muons can be identified by requiring that there is no signal in the lower counter in coincidence with the two on top. This anti-coincidence also determines the start of our clock $t_{start}$ : we want to see how long it takes for the stopped muons to produce an electron, which yields a delayed signal in one of the counters surrounding the aluminum bar (the one labeled C in the plot above). The delayed signal is the stop of the clock $t_{stop}$ : so the time the muon sat in the aluminum bar is simply determined as $\Delta t = t_{stop} - t_{start}$ . Once a stop signal is seen, the value of $\Delta t$ is stored, and the experiment is reset to its initial state, looking for another start. If instead 20 microseconds pass without a stop signal occurring, the event is discarded and the experiment reset, getting ready to catch another stopped muon.

In the experimental setup, you work with a multichannel analyzer (MCA) which converts the time interval $\Delta t$ into a number T from 1 to 256. T=1 corresponds to $20 \mu s /256 = 0.08$ microseconds, while T=256 corresponds to 20 microseconds. Every time a start and a stop occur, the histogram is filled with an entry corresponding to the bin $T=256 \times \Delta t /20 \mu s$ . After a long enough exposure, one should obtain a histogram showing the typical exponential decay law, proportional to the function $N(t)= e^{-t/\tau_\mu}$ , where $\tau_\mu$ is the decay constant, the muon lifetime we want to measure. Are you still with me ? Well, the math is basically over.

Now, all this is nice and simple, but the Devil created backgrounds to keep physicists busy. In fact, during those 20 microseconds while our apparatus waits for the muon to spit out an electron, our counters may be crossed by another particle. This will cause a stop, and the MCA will be filled with a random entry. This entry, it is important to stress, has absolutely no correlation with the arrival time of the muon ( $t_{start}$ ). So we may expect them to be distributed with a totally flat distribution between 0 and 20 microseconds: each one of our 256 channels will be ridden with some background hits, after any given exposure.

Now the question for you is the following. Given that muons produce stops with a falling exponential law - whose decay constant is equal to the muon lifetime (2 microseconds), and thus much smaller than the 20 microseconds during which we keep our system receptive of a stop signal- while background hits produce stops at random times, what is the kind of histogram one expects after a long enough exposure if the overall number of decay and random stops is roughly equal? I give you five options below, and one day to think about it.

A falling exponential distribution with time constant equal to the muon lifetime
A falling exponential distribution with time constant equal to the muon lifetime, on top of a flat distribution
Two falling exponential distributions one on top of each other, one with time constant equal to the muon lifetime, the other with a longer time constant
Two falling exponential distributions one on top of each other, neither of which with a time constant equal to the muon lifetime
A flat distribution

Of course, the problem can be solved analytically, but the math needed is not totally trivial, and I bet you have rather use your intuition. Good luck! Please type your answer in the comment box before reading what others may have answered, to make things more interesting!

Post-scriptum: just before going to bed, I realized that some of the more knowledgeable among you might be misled by the fact that positive and negative muons do quite different things when they stop in aluminum or other materials. Please disregard this detail - or rather, keep it in mind, we will discuss it tomorrow; it has no bearing on the answer of the question I posed above.

The feeling I have when deciding what to discuss next about this year’s American Astronomical Society meeting is like what I get in a good used bookstore. Where to turn next? We’ve already looked at several stories with exoplanetary significance, but the arrival of a new type of star entirely seems to vault past even these in significance. If, of course, the so-called ‘quark star’ is real, a question sure to remain controversial as the study of extremely bright supernovae continues.

When I say bright, I’m talking about three events in particular, each of which produced one hundred times more light energy than normal supernovae. The events, designated SN2006gy, SN2005gj and SN2005ap, have been under intense scrutiny, among the researchers a team from the University of Calgary, who point to the lack of a satisfactory explanation of these events. The hypothesis they defended at AAS is that neutron stars are not the most compact solid objects known to exist. That honor belongs to still denser quark stars.

Take an average neutron star, maybe sixteen miles across but 1.5 times as massive as the Sun. Produced by the catastrophic collapse of a massive star (and thus associated with the accompanying supernova explosion), neutron stars could theoretically be packed tighter still, the same mass being squeezed to an object just twelve miles across. At this point, the neutrons dissolve into quarks and vast amounts of energy are unlocked, causing the aforementioned super-luminous events. The researchers — Denis Leahy and Rachid Ouyed — are quick to point out that competing explanations of these supernovae cannot be ruled out without further observations of these exotic phenomena.

All of which is highly speculative but a stunning possibility just the same. What’s happening to the Milky Way itself is also a bit of a surprise, for at the same AAS meeting, a team led by Robert Benjamin (University of Wisconsin, Whitewater) used new imagery from the Spitzer Space Telescope to re-examine the galaxy’s structure. The result: There appear to be not four but just two major arms to our galaxy, a possibility neatly captured in the image below. Benjamin notes how tricky studying a galaxy from within can be:

Image (click to enlarge): Like early explorers mapping the continents of our globe, astronomers are busy charting the spiral structure of our galaxy, the Milky Way. Using infrared images from NASA’s Spitzer Space Telescope, scientists have discovered that the Milky Way’s elegant spiral structure is dominated by just two arms wrapping off the ends of a central bar of stars. Previously, our galaxy was thought to possess four major arms. Credit: NASA/JPL-Caltech.

Earlier radio surveys and the infrared surveys that followed them had revised the initial model of a spiral with four major star-forming arms, but Benjamin’s software has gone to work counting stars and measuring stellar densities, employing a vast Spitzer mosaic that takes in some 110 million stars. The Milky Way now appears to be like other galaxies we have observed with a central bar of stars (the latter a discovery made in the 1990s). The two major arms are now seen to be the Scutum-Centaurus and Perseus arms (although the Perseus arm is not visible in the field of view covered by the new Spitzer images).

The Sagittarius and Norma arms are now considered to be minor, with the Perseus and Scutum-Centaurus arms showing the greatest density of both young, bright stars and older red giants. Bear in mind that our own small star is currently found near the partial arm known as the Orion Spur, located between the Sagittarius and Perseus arms. But as this JPL news release points out, stars tend to move in and out of arms as they orbit the galaxy’s center. In fact, our Sun would have made sixteen circuits of the Milky Way since its formation four billion years ago.

Wed, 28 May 2008

I am preparing the slides for the PPC08 conference, which will be held in Albuquerque next week, and I thought I would post here two slides that show how present Tevatron data is increasingly wiping off the board one Supersymmetric model after another - yes, I regard a choice of parameters as a single “model”, since the phenomenological implications of varying the >100 SUSY parameters are just too varied to call it a single model: instead, SUSY is a framework, and points in the parameter space are models.

The models we kill today belong to a version of the minimal supersymmetric extension of the Standard Model which has “minimal SO(10) soft-SUSY breaking boundary conditions“. No, I am not going to tell you what this is: you will have to read it on hep-ph/0506233 if you really must. Instead, I will show the present limit that CDF has obtained on a particular decay of the $B_s$ meson, which is heavily suppressed in the standard model, but which could be enhanced by up to three orders of magnitude in SUSY models. Because of this enhancement, and because we could be sensitive to it, the matter is intriguing: by measuring the decay, one would instantly achieve two things: 1) prove the SM is wrong; 2) favor some SUSY models among the various possible interpretations of the effect.

$B_s$ mesons are hadrons composed of a b and a s quark. They are electrically neutral, and have a long lifetime because the b-quark is unwilling to turn into a 2nd generation charm quark (decays across generations are suppressed). But they do, in about a picosecond. Blitzing fast for our senses, but quite slow for 5 GeV unstable subatomic bodies. What happens is that the b-quark emits a W boson, changing into the charm quark. The W boson is virtual, because it has a mass way below its nominal one of 80.4 GeV, and it immediately turns into a pair of light quarks or a lepton-neutrino pair.

What is described above is the rule, but there are exceptions. In an exceedingly rare combination of circumstances, the standard model predicts that a $B_s$ meson will instead decay by emitting two W bosons, with a box diagram (see below, top) or a penguin diagram (bottom) whose end product may be a pair of charged muons: a striking signature of the decay! This, however, is calculated to happen only four times in a billion decays. That means we have to study several billion decays to observe it!

Searching in 2 inverse femtobarns of data, CDF has seen no signal, and a limit on the fraction of these rare decays has been set at 5.8E-8: no more than 58 in a billion. The search was done by looking for pairs of muons with an invariant mass compatible with that of the $B_s$ meson, and by training a neural network on the dimuon kinematics and purity to distinguish true decays from other backgrounds.

In the slide below you can see the neural network discriminator output for signal and backgrounds, in the top right graph. The scatterplot in the lower right instead shows the NN output versus the reconstructed dimuon mass: the two small boxes are the regions where the signal for $B_d$ and $B_s$ mesons were sought.

The result on the branching fraction has implications on the models of SUSY with SO(10) soft susy breaking, as was said at the beginning. In the slide below you can see that indeed, for a particular choice of the parameters describing the space of these theories, the area not yet painted with any color - indicating it was still not disproven by searches of Higgs bosons, charginos, or other constraints - has been fully excluded by the CDF limit.

In the graph, the green band is the one most favoured by cosmological bounds on the relic density of dark matter. The full black line is the lower limit on charginos found by LEP. That bound has also been updated by CDF, and from 104 GeV the lower limit has been brought up to 140 GeV.

As Veltman puts it, “SUSY is hiding just around the corner… It has been hiding there for a while” (I am quoting by heart… but the meaning is unaltered). So, as we continue turning corners and finding nothing but good-old standard model physics, one starts to wonder whether we are fooling ourselves.

Tue, 20 May 2008

Nuclear fission is the process in which a nucleus decays into two fragments. For large nucleii, this process is a complicated one in which the nucleus undergoes several stages of deformation before tearing itself apart.

In recent years, physicists have predicted that fission ought to be affected by the presence of electrons in orbit about the nucleus. That’s because any change in the shape of the nucleus naturally affects the electrons which tend to absorb energy making fission less likely. And the more electrons there are, the more energy they absorb. But the effect has never been observed because ordinary, naturally ocurring elements simply don’t have enough electrons to make this effect significant.

Today, Vlad Dzuba and Vic Flambuam at the University of New South Wales in Australia have calculated the strength of this effect for superheavy elements which would have more electrons. They say that although the effect is tiny for naturally ocurring nuclei with fewer than 100 or so protons, it would be hugely significant for these larger nuclei. In fact, they calculate that an atom with 160 protons would have double the expected half life because of this effect.

That could have significant implications for how much of this stuff we’re likely to find because elements that decay quickly tend to be rarer) . Last week, arxivblog reported on the potential discovery of element 122 (with 122 protons). Perhaps the groups looking for superheavies should be setting their sights much, much higher.

Good morning boys and girls. In keeping with Th’ Gausslings weakness (sickness??) for odd and specialized information, a quantity known mainly to nuclear reactor operators and other nukkenvolk is trotted out.

Neutron lethargy, or logarithmic energy decrement, u, is a dimensionless logarithm of the ratio of the energy of source neutrons to the energy of neutrons after a collision: u = ln(Eo/E), or, u2-u1 = ln(E1/E2). So, if you plot a curve of E vs u (E = Eo*exp(-u)), you see an exponential decay of energy per unit collision showing that the greatest delta E’s of energy result from the early collisions.

Basically, it shows that in order to obtain thermal neutrons from fission decay neutrons, you have to contain them so that they can rattle around and dump energy before they fly out of the area of interest. As to the number of collisions that are needed? Well, that is a different issue.

Source- Glasstone & Edlund, The Elements of Nuclear Reactor Theory, Van Nostrand, 1952, p 146.

In a recent post where I shortly discussed a rapidity distribution of muons produced in low-energy proton-proton collisions at LHC, I formulated a conjecture: given parton densities in the colliding protons which are monotonously decreasing functions of the momentum fraction (and they are, for small fractions), the rapidity y of the parton-parton collision has a maximum for y=0.

Of course, I was guided by experience: I know for a fact that unless you bias your data sample with requirements such as trigger selections or analysis cuts, any time you plot a rapidity distribution you obtain something symmetrical around zero. But one thing is having experience of the rule, the other is proving there are no exceptions.

So I was triggered to demonstrate the rule. I was helped by a grad student in our group, Nicola Pozzobon… Without him, I would not have gone past the long-forgotten rules of the delta function!

Demonstration: Take parton distribution functions in the proton to be monotonously decreasing functions of the momentum fraction:

$f(x)$ , $x \in [0,1[$ , $df/dx<0$ .

The rapidity of the collision can be defined as

$y=0.5 \log (x_1/x_2)$

and so to obtain the distribution of rapidity arising from a given distribution of the partons in the proton we have to integrate on $x_1, x_2$ as follows:

$G(y) = \int dx_1 dx_2 f(x_1) f(x_2) \delta(y-0.5 \log(x_1/x_2))$ .

The delta function, which is zero everywhere and equal to one only where its argument is zero, “picks up” the relevant values of $f(x_1), f(x_2)$ capable of contributing to a given value of y.

Now, if we solve $y=0.5 \log(x_1/x_2)$ for x_1 we find $x_1=x_2 e^{2y}$ , so we can substitute in the expression for G and integrate in x_1, to find

$G(y) = \int dx_2 f(x_2) f(x_2 e^{2y}) /(2x_2 e^{2y})$ ,

where we have used the property of the delta function which says that

$\delta(h(x)) = \delta(x)/|h'(0)|$ ,

and the fact that

$h(x_1, x_2)=y-0.5 \log(x_1/x_2)$

from which

$h'(x_1)=dh/dx_1=-1/(2x_1)=-1/(2x_2 e^{2y})$ ,

or

$h'(x_2)=dh/dx_2=1/(2x_2)=1/(2x_1 e^{-2y})$ .

If we had instead substituted $x_2$ we would have found

$G(y) = \int dx_1 f(x_1) f(x_1 e^{-2y}) / (2x_1 e^{-2y})$ ,

so we can generically write, using x with no subscripts:

$G(y) = \int dx f(x) f(x e^{\pm 2y}) e^{\mp 2y} /(2x)$ ,

with the agreement that both expressions implied by the sign swaps have to be true simultaneously.

Upon derivation with respect to y we find

$G'(y) = \int dx f(x)/x [ \pm x f'(x e^{\pm 2y}) \mp f(x e^{\pm 2y}) e^{\mp 2y}]$ .

For y=0, the derivative of G is thus equal to

$G'(0) = \int dx f(x)/x [\pm x f'(x) \mp f(x)]$ .

But these (the G’(0) with +- and the G’(0) with -+ signs chosen) are two expressions that must simultaneously be correct: and since they have opposite values for any x in the integration interval, they must be zero. If the derivative of a function is null, the function has an extremum there. CVD.

We have thus proved that the rapidity distribution has an extremum if the PDF f(x) are monotonous functions of x. It would be easy to show that this is indeed a maximum, but I will be content with the above result for this post.

So in conclusion, my conjecture is correct! If the parton distribution functions are taken to be monotonous, the rapidity distribution of the center-of-momentum of the collision is indeed maximum at zero… I prefer to use intuition usually, because the above demonstration took me more than an hour!

UPDATE: Hmmm, by thinking at the problem for a microsecond, rather than writing integrals and derivatives, I only now arrive at the following conclusion: Since the rapidity distribution is symmetrical around zero - from its very definition -, and since it must go to zero for y going to plus and minus infinity, it goes without saying that there is an extremum at zero, duh! However, it is still interesting to see how that arises mathematically. THis also proves what I know for a fact: a bit of analysis is worth more than a megabyte of programming - and the same can be said with thinking and computing formulas!

QED
src

I've read very few books twice. Unless a book is so jam-packed with neatness that every read is sure to introduce something new, I figure it's not worth the time. One book that is worth the time every time, however, is Richard Feynman's QED. I just finished my second run through this book, and it was absolutely 100% worth it.

QED reduces nearly all physical phenomena to the movement and interactions of electrons and photons. Starting from the most common of phenomena (light reflecting from glass, light bouncing off a mirror, lenses), this book is literally a fascinating journey into the mysterious character of light. Feynman adopts the role of a specialist teaching the layreader the neat, intuitive way to solve physics problems, and describes the bizarre character of light with delightful whimsy.

The first half of the book is an exposition of the path integral formulation of quantum mechanics as it applies to light. The probability that light does a certain thing is represented by the square of the length of a vector that corresponds to the event. Movement of the light and reflection cause turning and shrinking of the "unit arrow" until a final arrow for the event in question is reached. Summing all the arrows for the way an event can happen gives a final arrow for the event. Although there are an infinite number of ways any event can happen, the ways close to the path of minimum time reinforce each other, while those that take longer cancel each other out. This is the principle of least action at work!

After going through several simplified problems, Feynman reduces all events to combination of three simple steps: a photon goes from A to B, an electron goes from A to B, and an electron emits or absorbs a photon. The arrow-length formulas for the first two events are functions of the distance traveled and the time the travel takes (photons don't have to travel at c, as it turns out). Fascinatingly, the arrow-length formula for emission and absorption is just a constant...the charge of the particle! Everything from optics to atoms can be analyzed using combinations of these three simple events.

I don't want to spoil the rest of the book, but it is chock full of amazing observations like this. Teaser: an antiparticle is just a particle traveling backwards in time!

posted at: 23:00 | path: /sci/physics | permanent link to this entry

Since I am currently preparing the slides of the talk I will give next week at PPC2008, a conference being held in Albuquerque on the interconnection between particle physics and cosmology, I have my hands full with material that would be perfect for this blog. The talk is a review of new results from the CDF experiment, and there is literally a ton of them! What makes it hard for me is to sort out the stuff that is really the very best and most worthy of being shown at the particular event.

I am however not posting here direct CDF results, but rather a plot that my friend Sven Heinemeyer was kind to produce according to my directives, which I meant to allow me to summarize in my talk the status of electroweak fits by separating the main contributions of experimental measurements. In the graph below, showing the dependence of the Higgs boson mass on the value of W boson and top quark masses, you can see several different regions highlighted with black, blue, and magenta lines. The black lines bracket the LEP II determination of the W mass; the blue ellipse describes the Tevatron measurements of the two parameters, and the magenta hatched “wing profile” area shows the allowed values of the two quantities according to electroweak fits performed using LEP I and SLD determinations of electroweak parameters.

Also shown in the plot is the SM-allowed range (in red), where the Higgs boson has a mass varying between the lower LEP II limit of 114.4 GeV (upper border of the red hatched area) and 400 GeV (lower border), and the SUSY allowed region (hatched green), which shows the zone allowed by different choices of some of the many SUSY parameters, in particular the mass of supersymmetric particles.

Now, let me make a few points concerning the plot above.

Although precise, the indirect experimental input shown in the plot is still incapable of discriminating between SM and SUSY - and it probably never will by itself, since LHC will soon rule out or find SUSY before it shrinks the ellipse sizably (ok, ok, I am neglecting the possibility of split SUSY…)
the celebrated LEP I / SLD data looks obsolete from this particular vantage point, in light of the more recent direct measurements; this would however be an unfair interpretation, given that electroweak fits have many more parameters than just W and top quark masses.
The LEP I / SLD data is obsolete as far as the top quark is concerned: in the plot it does not even appear to constrain it if compared with the ultra-precise (+-0.8%) Tevatron determination!
The top quark mass has been bouncing up and down a bit, although always well within errors, in the last 5 years, from 178 to 170 to 172.4 GeV. This has slightly moved up and down the preferred value of fit Higgs mass in the SM. However, as the ellipse shrinks, this is becoming less of an issue. In fact, to justify the effort of producing the best possible top mass measurement, we used to say that a 1 GeV precision on the top mass was equivalent to a 7 MeV precision on the W mass as far as the knowledge we would obtain on MH was concerned, based on the slope of the Higgs contours in the plot above. Now that the error on top mass is well below 2 GeV, however, it becomes clear that we will not gain much knowledge by increasing the precision much further. The W mass has become one of the main players in the game of precision SM fits now!
The ellipse includes 68% of the area of the two-dimensional gaussian centered on the Mw-Mt determination, just as much as the black bars do, but being two-dimensional it is deceiving: the single most precise determination of the W boson mass is in fact from CDF, and Tevatron and LEP II are basically at the same level of precision on that quantity!

Why is the comparison deceiving ? Because if you have one single quantity, you determine the 68% interval by integrating a gaussian distribution from its center outwards, until you “cover” 68% of its total integral (from -inf to +inf). If you add a dimension to your single-variable gaussian, and make it a two-dimensional gaussian shape, the 68% bounds remain the same unless you integrate by expanding an ellipse, rather than a band, around the center. The ellipse encompasses values of the 2-dimensional distribution which have the same “probability”, but in so doing it “cuts the corners”, and to total a 68% of the 2-dim integral it now has to extend past the one-dimensional 68% boundaries in each of the two variables. A sketch will clarify matters:

Well, not exactly “clarified”… But I have no time to make the graph easier to understand. The point is that the ellipse “cuts” only a part of the band in each direction, and so the integral of the 2-dimensional curve it comprises is much smaller than the band. To make the ellipse include 68% of the 2-dimensional distribution constructed with the two gaussian curves, one has to widen it to a roughly double size.

So, paradoxically: if LEP II had a determination of the top quark mass too, the band bracketed by the two black lines in the plot by Heinemeyer would convert into an ellipse which would be about as wide in the vertical direction as the Tevatron blue ellipse.

Not convinced ? Oh well. Think at it this way: with a single measurement of the W mass, you say “the probability that the mass is between 80.35 and 80.45 GeV is 68%, because I determined it to be 80.4 and I have an error of 0.05 GeV”. Fine: the gaussian distribution, if integrated from -1-sigma to +1-sigma, provides 68% of its total normalization. The same goes if you claim that, having measured the top mass at $172.4 \pm 1.4 GeV$, there is a 68% chance that it lies in the interval 171-173.8 GeV. However, if you ask what is the probability that the W mass is between 80.35 and 80.45 GeV AND the top mass is between 171 and 173.8 GeV, this is much smaller than 68%, because independent probabilities multiply each other: it is, in fact, only 46.2%; but this corresponds to the square drawn around the circle in the graph! The probability that the two values lie in the ellipse with major axes equal to 1-sigma band widths is (if I recall correctly) about 37%.

The bottomline? Whenever you look at a plot with two measurements, one described by an ellipse and the other by a band, always regard the ellipse with more respect than it seems to deserve!

This week in the arxiv
src

A couple of interesting papers, two about graphene and one about a weird fluid mechanics effect.

arxiv:0805.1830 - Bolotin et al., Temperature dependent transport in suspended graphene
It's become clear over the last year that a lot of what was limiting the measured electrical transport properties of graphene sheets had to do with interactions between the graphene and the underlying substrate (usually SiO₂). Now multiple groups have started preparing suspended graphene membranes (supported around the edges by oxide) overhanging underlying gate electrodes. By ramping up the current through the suspended membrane, the graphene sheet can be resistively heated in vacuum up to a temperature sufficient to desorb residual contaminants, and electronic properties can be measured without substrate effects. In this paper the Columbia group demonstrates that extremely high mobilities are then possible (well over 100000 cm²/Vs), and by examining the temperature and gate dependence of the conduction they can understand the scattering mechanisms at work as well as residual disorder in the system. Very clean looking data.

arxiv:0805.1884 - Booth et al., Macroscopic graphene membranes and their extraordinary stiffness
The Manchester group has also been very busy. In this paper they show a cute technique to produce large (say 0.1mm in diameter) graphene sheets in a form that's easy to suspend and handle. Basically instead of abrading or cleaving graphite into graphene on top of oxidized Si, they do so on top of Si coated with a layer of e-beam resist. An additional layer of a different sensitivity resist is put on top and patterned, followed by metal deposition. The metal layer forms a frame that goes around the previously identified graphene sheet, and the metal is then used as a seed layer to deposit a more robust Cu layer via electrochemistry. Finally, the original resist layer is dissolved, freeing the graphene+Cu frame for manipulation. They then further study the mechanical properties of these suspended layers, finding that single sheets of graphene are indeed very stiff - much more so than you might think, since they're 1 atom thick. The technique is elegant, and there is one particularly impressive TEM image. Nice SuperSTEM that they have over there in Cheshire.

arxiv:0805.0490 - Amjadi et al., A liquid film motor
Hat tip to arxivblog for pointing this out to me. These folks at Sharif University in Iran have found that DC electric fields can make soap films flow in very interesting and controllable ways. They suggest a few possible mechanisms for this kind of electrohydrodynamic motion, but conclude that none of them are entirely satisfactory. The paper has a minor rendering problem with Fig. 4, but you should definitely watch the movies on their webpage. Very dramatic! Soft CM physics can be inspiring - here's a visually impressive phenomenon that might actually be useful in fluidic applications, and the whole experiment is simple, elegant, and inexpensive. No exotic apparatus required.

posted at: 22:43 | path: /sci/physics | permanent link to this entry

Mon, 12 May 2008

Windows/Mac/Linux (All platforms): Phun, a free open-source, cross-platform 2D physics simulator, makes you want to pick up blocks, or maybe crayons, and learn more about the way things fall and move under pressure. Written by a Swedish graduate student, the program teaches concepts of restitution and friction, so it's great to load up with the kids, but you'll probably find yourself sneaking a few turns by yourself at creating, and knocking over, shapes and lines. Phun is a free download for Windows, Mac OS X, and Linux systems; hit the link for instructions on using and having, well, fun in Phun.

Here is an excerpt of the latest LHC schedule for the following few months, as agreed in a meeting at CERN chaired by the Director-General, with the experiments and LHC machine heads.

Based on the good progress for the cool down of the LHC sectors, and on the powering tests from two sectors, the following planning was arrived at:

End of June: The LHC is expected to be cooled down. [...]

Mid of July: The experimental caverns will be closed [...]

End of July: First particles may be injected, and the commissioning with beams and collisions will start.

It is expected that it will take about 2 months to have first collisions at 10 TeV.

Energy of the 2008 run: Agreed to be 10 TeV. The machine considers this to be a safe setting to optimize up-time of the machine util the winter shut-down (starting likely around end of November).[...]

The winter shut-down will then be used to commissioning and train the magnets up to full current, such that the 2009 run will start at the full 14 TeV design energy.

The above means that the machine will deliver collisions from the end of September on, for at most nine weeks in 2008. More safely, one can assume 6 full weeks of data-taking. What luminosity do we expect to collect ?

A state-of-the-art estimate was made by a colleague, who used his past experience with LEP as well as the information on the current limitations of the RF system -which will make the proton bunches shorter than planned (RMS of 5.4 cm), and with a transverse size of 46 microns. At the lower energy the low-beta squeeze will also be loosened from 2 to 3 meters. These figures reduce the instantaneous luminosity, and the estimate for 6 weeks of collisions are of about 40 inverse picobarns of data in 2008.

If ATLAS and CMS will be fully on during the weeks of collisions, these 40 inverse picobarns will fruit, in my opinion:

A top pair production cross section with 10-15% accuracy
A sizable sample of vector boson decays to leptons, very useful for calibrations and checks of lepton efficiency studies
The first estimates of b-tagging and tau-tagging capabilities of current algorithms
no information on the Higgs
no SUSY discovery (of course!)

All the above will have a chance of being ready for the 2009 winter conferences, if all goes well…

Quantum dot based quantum logic gate proven possible
src

engineers and physicists from Stanford and the University of California at Santa Barbara demonstrate a potential progenitor of an essential component of quantum computers, "a logic gate" that enables interaction between just two particles of light.

"We have demonstrated a system composed of a single quantum dot in a cavity that can be used to realize such a gate, and we demonstrated that two photons can be made to interact with each other via this system," says Stanford applied physics doctoral student Ilya Fushman, a lead author on the paper along with two other doctoral students from the Vuckovic group, Dirk Englund and Andrei Faraon. "So we showed that such a gate is possible and demonstrated the first necessary steps in that direction."

The team has demonstrated that when the two photons are identical, a phase shift of 12.6 degrees is achieved. This is only a fraction of the 180-degree rotation required to make a full logic gate, Vuckovic says, but by combining several of the devices in a row, her team expects to attain the needed effect. Also, when the signal and control photons are allowed to differ, the phase shifts can be up to 45 degrees.

Other challenges include eliminating manufacturing imperfections and reliably placing the quantum dots right where they need to be within the crystals, but the team is optimistic.

"We are hopeful that these engineering challenges can be overcome to open the path to chip-based high-fidelity quantum logic with photons," Vuckovic says

Wed, 11 Jun 2008

Wed, 28 May 2008

Tue, 20 May 2008

Mon, 12 May 2008