One of CERN collaborations, the LHCb, has reported observation of direct CP-violation in the decays of charmed mesons at the Hadronic Collider Physics Symposium 2011 (HCP 2011) in Paris today. This is a fantastic news! While I am not at HCP 2011, kind folks at LHCb let me know about this fantastic measurement — since charm physics is my specialty.
So, what are we talking about here?
First things first. CP (or Charge Parity) is a set of (discrete) transformations performed on a theory’s Lagrangian — a function that describes what particles we have in a theory and how they interact. If your Lagrangian is symmetric under this transformation, then particles and antiparticles — matter and antimatter — have the same properties. If not — interactions of matter particles are different from interactions of antimatter particles. This possible difference is a crucial property of a theory because, according to three Sakharov criteria, the Universe could evolve in what we see around us only if matter and antimatter have different interaction properties. Otherwise, at best, we’d have big chanks of antimatter floating around — or at worst would not not exist at all.
This is why many huge experiments built to study CP violation. Big national labs’ flagship experiments were designed to search and study CP-violation (BaBar at SLAC, Belle at KEK, LHCb at CERN), with hopes to see glimpses of New Physics that could explain matter-antimatter asymmetry in the Universe. This new result from LHCb can in principle provide one.
So, what did LHCb see? The reported analysis looks at the difference of a difference — i.e. a difference of CP-violating asymmetries in kaons and pions. The CP-violating asymmetry is defined as the difference between decay widths (roughly speaking, decay probabilities) of a neutral D-meson to decay into a final state, say positive K-meson and a negative K-meson and the same quantity for the D-anti-particle to decay to the same final state. This quantity is also defined for the final state of two pions — and it is CP-violating!
The structure of this CP-violating asymmetry, aCP, is not that simple. Because D0 is a neutral particle it can, in principle, mix with its antiparticle (see here) — and this antiparticle can also decay into the same final state! This process can be also CP-violating (this type of CP-violation is called indirect CP-violation). So the result would depend on both types of CP-violation!
Moreover, experimentally, the asymmetries like this are not easy to measure — there are experimental systematics associated with D-production asymmetries, difference of interactions of positive and negative kaons with matter, etc. For this reason, experimentalists at LHCb decided to report the difference of CP-violating asymmetries, in which many of those effects, like productions asymmetries, would cancel. So, here is the result:
ΔaCP = -0.82 ± 0.21 (stat) ±0.11 (syst) %
In other words, this quantity is 3.5 sigmas away from being zero. The first question that one should ask is whether this quantity is consistent with previous measurements. The biggest question, however, is whether this quantity is consistent with Standard Model expectations.
There is a bunch of previous measurements available for aCP (KK) and aCP (ππ) separately. The thing is that
aCP (KK) = – aCP (ππ)
or approximately so. So by subtracting those quantities we not only subtract the experimental uncertainties, but also enhance the signal! However, looking at the table on page 6 of the talk, one can immediately realize that this measurement is at least consistent with the previous ones.
Is it a sign of something beyond the Standard Model? This one is hard to answer. I usually put an upper bound on the SM value (that is, absolute value) of asymmetries like aCP (KK) at 0.1% — which would make ΔaCP to be about 0.2%. Is it consistent with LHCb findings? Maybe. The size of this asymmetry is notoriously difficult to estimate due to hadronic effects. Maybe it is a sign of New Physics — this could be an exciting conclusion, as we have never seen CP-violation in up-quark sector.
It is interesting that the first “big” result from LHC comes in the realm of charm physics, not Higgs searches. Moreover, all “big” results in the last decade were from the experiments searching for New Physics indirectly, in the “intensity frontier” (this is lingo of US Department of Energy) — with most of them coming from charm physics. Maybe at the very least LHC-b should be renamed as LHC-c?
We have a job… or two! October 21, 2011Posted by apetrov in Particle Physics, Physics, Science.
Depending on how the budget for the new year looks like, we (the high energy particle theory group at WSU) will have two new postdoc positions. Please apply, if you are interested! Here is the ad.
The high energy theory group at Wayne State University ( http://www.physics.wayne.edu/heptheory ) anticipates making TWO postdoctoral research appointments to start September 1, 2012, subject to budgetary approval. The initial appointments will be for one year, and may be extended for one or more years depending on the performance and availability of funding.
The group consists of faculty Gil Paz and Alexy A. Petrov, as well as a postdoc and several students. Research interests of the group include particle phenomenology, physics beyond the Standard Model, effective field theori es, heavy quark physics, CP violation, Dark Matter phenomenology and particle astrophysics. The group has close ties to the nuclear theory group of Sean Gavin and Abhijit Majumder. The WSU Department of Physics and Astronomy offers a unique opportunity of close interaction with experimental high energy particle and nuclear physics groups.
Applications including CV, a list of publications, a brief statement of research interests and three letters of recommendation should be submitted to Academic Jobs Online at http://academicjobsonline.org/ajo/jobs/1128
or by mail to
Prof. Gil Paz
Department of Physics and Astronomy
Wayne State University
Detroit, Michigan, 48201
Prof. Alexey A. Petrov
Department of Physics and Astronomy
Wayne State University
Detroit, Michigan, 48201
or electronically to firstname.lastname@example.org or email@example.com. The deadline for application is January 15, 2012. Later applications will be considered until the positions are filled. Informal inquiries are welcomed.
Wayne State University is an affirmative action/equal opportunity employer. Women and members of minority groups are encouraged to apply.
2011 Physics Nobel Prize and related matters October 4, 2011Posted by apetrov in Uncategorized.
4 October 2011 is a day to remember. And I’m not talking about unveiling of the new iPhone, although it is also quite a remarkable event. Today, a 2011 Nobel Prize in Physics was awarded. As expected, in its annual failure, Thompson Reuters got it wrong in predicting 2011 Nobel Prize in Physics (to give them credit, they do put up the names of the right people, but always in the wrong year; this year they were predicting people from quantum entaglement). Anyways, this year’s Nobel Prize is totally deserving. The Nobel Prize in Physics 2011 was awarded jointly to Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess “for the discovery of the accelerating expansion of the Universe through observations of distant supernovae.”
This Nobel Prize is for the 1998 analysis of data from two collaborations, Supernova Cosmology Project (SCP), headed by Perlmutter, and High-z Supernova Search Team, headed by Schmidt and Reiss. The analyses centered on the the so-called Ia-type supernovae that have consistent peak brightness, which makes them “standard candles” of the Universe. This is an important property, which allows unambiguous measurement of distances (via the Hubble relation between the distance and the redshift) to the galaxy hosts of those supernovae. Using this data, they concluded that the Universe is going through the stage of accelerated expansion! This is a very interesting fact, especially taking into account the fact that the gravitational interaction is attractive!
This led to reevaluation of what we know about the Universe. It is widely accepted now that Dark Energy (i.e. something that permeates space and tends to increase the rate of expansion of the universe) accounts for about 74% of the total mass of the universe! Recalling that Dark Matter is responsible for about 22% of total mass gives us a fact that we really know almost next to nothing about the place we live in…
What is Dark Energy? This is a very good question. The simplest possibility is that it is the old good cosmological constant introduced by Einstein in the beginning of the last century. This leads to a particularly simple model of the Universe called Lambda-CDM model. Whether or not it is true remains to be seen. At any rate, Dark Energy/Dark Matter are currently one of the most exciting avenues for research in astrophysics (which is, of course, my subjective opinion!).
Meanwhile, the annual 2011 Ig Nobel Prizes were awarded on September 29, 2011. Among the most remarkable are
“PHYSICS PRIZE: Philippe Perrin, Cyril Perrot, Dominique Deviterne and Bruno Ragaru (of FRANCE), and Herman Kingma (of THE NETHERLANDS), for determining why discus throwers become dizzy, and why hammer throwers don’t.” As expected, for a work of this magnitude, the prize-winning research was published in the widely-read physics journal Acta Oto-laryngologica.
“MATHEMATICS PRIZE: Dorothy Martin of the USA (who predicted the world would end in 1954), Pat Robertson of the USA (who predicted the world would end in 1982), Elizabeth Clare Prophet of the USA (who predicted the world would end in 1990), Lee Jang Rim of KOREA (who predicted the world would end in 1992), Credonia Mwerinde of UGANDA (who predicted the world would end in 1999), and Harold Camping of the USA (who predicted the world would end on September 6, 1994 and later predicted that the world will end on October 21, 2011), for teaching the world to be careful when making mathematical assumptions and calculations.” This prize is quite timely, as the world once again is predicted to end 21 December 2012, although, frankly, they could have waited one year for this one.
Once again, the biology prize went for sexuality-related research. This time, among certain type of beetles and certain types of beer bottles (which should make a nice commercial of the type “Fosters is Australian for beer” (C)):
“BIOLOGY PRIZE: Darryl Gwynne (of CANADA and AUSTRALIA and the UK and the USA) and David Rentz (of AUSTRALIA and the USA) for discovering that a certain kind of beetle mates with a certain kind of Australian beer bottle.”
And my personal favorite is this year’s literature prize:
“LITERATURE PRIZE: John Perry of Stanford University, USA, for his Theory of Structured Procrastination, which says: To be a high achiever, always work on something important, using it as a way to avoid doing something that’s even more important.”
I would like to remind my readers that so far, there is only one “Grand Slam winner” — a person who got both Ig Nobel and a Nobel prizes: last year’s recipient of the Physics Nobel Prize Andre Geim.
Why do physicists go to Aspen? September 1, 2011Posted by apetrov in Near Physics, Particle Physics, Physics, Science.
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While the most obvious answer to this question is “to ski”, it is, nonetheless, not the correct one. Yes, skiing is great here in the winter (and hiking is great in the summer), but most of the time physicists come here to work. The reason is Aspen Center for Physics. I write “here” because I’m currently participating in one of the programs organized by the Center (the program is called “Flavor Origins” — it brought together theorists working on the problems of neutrinos, heavy and light quarks, CP-violation, etc.). The Center, which exists here since 1961, organizes workshops and conferences. But the main reason that theorists (and occasional experimentalists) come here is to talk to other theorists. In short, it is as if you are visiting a huge theory group — you can work individually or with your colleagues, but you can always knock on an office door and bounce your ideas off someone else visiting the Center, etc. It is great to have such a concentration of theorists of different trades. And it leads to breakthroughs and simply good papers. As it is said on the Center’s website:
“Many seminal papers have been written in Aspen, which has grown to be the largest center for theoretical physics in the world during its summer sessions. Among many other subjects, the theories of superstrings, chaos, evolution of stars and galaxies, and high temperature superconductivity have all made large strides in recent Aspen seasons.”
There is almost always someone with an expertise in a subject that you have a question about. And that makes this Center great. And, of course, hiking and skiing is also good. The only “downside” (note the quotes) is that you can meet a real bear (even at the Center) or other wildlife. Today a snake came to check out a lecture on conformal field theories…
P.S. Also check out my blog on Quantum Diaries…
Congratulations Dr. Yeghiyan! July 26, 2011Posted by apetrov in Near Physics, Particle Physics, Physics, Science, Uncategorized.
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Today my third graduate student at WSU, Gagik Yeghiyan, defended his Ph.D. thesis. Congratulations Dr. Yeghiyan! Good luck to you in your new life as an Assistant Professor at Grand Valley State University!
As I blogged some time ago, Italian government decided to fund a new accelerator for precision studies of New Physics in decays of heavy-flavored mesons, the so-called SuperB factory, a high-intensity B-factory, which is designed to look for glimpses of New Physics in rare decays of B- and D-mesons (for professional description of the physics case, see here; for Conceptual design Report (CDR) see here).
Last week a decision was made for a location of the site of the new machine. It will be built on campus of the University of Rome ‘Tor Vergata’. Here is the picture of the proposed site (shamelessly taken from the talk of Roberto Petronzio, President of the Italian National Institute for Nuclear Physics at XVII SuperB Workshop and Kick Off Meeting – La Biodola (Isola d’Elba) Italy):
The (“green”) site is located reasonably close (4.5 km) to another well-known Italian National Lab in Frascati, Laboratori Nazionali di Frascati (LNF). The new lab will be a CERN-like consortium. The name for the lab was proposed: Cabibbo Lab, after the great Italian physicist Nicola Cabibbo whose name is associated with some of the most important objects in flavor physics.
The new lab will bring lots of talent from all over the world and, besides experiments in high energy physics, will be used as a light source for other physics experiments. It is great that even at the time when finances are tight, European governments realize that fundamental physics is important for the future of their countries. These are exciting times for the European physics!
Update on the situation at Japan’s Fukushima nuclear plant March 15, 2011Posted by apetrov in Near Physics, Physics, Science, Uncategorized.
The situation at Japan’s Fukushima nuclear plant remains fluid, but it makes sense to do an update. It turns out that the situation is more challenging then I originally thought. To recreate what is happening (based mainly on TEPCo’s press releases and Japan’s Nuclear and Industrial Safety Agency (NISA) press releases), let us take a look at the Mark 1 BWR reactor (for a short description of physics of the nuclear power generation and schematics, please see my earlier post):
This picture was modified (by me) from the materials provided by Department of Energy’s Nuclear Regulatory Comission’s (NRC) website. It is Mark-1 BWR-type nuclear power reactor supplied by General Electric.
The Fukushima Daiichi plant operates six reactors, Units 1, 2 and 6 are supplied by General Electric (Unit 1 is the oldest, built in the 70’s — I’ve heard it was supposed to be decommissioned this Spring), while Units 3-5 are supplied by Toshiba and Hitachi. So, what is happening there?
As you already know, the magnitude 9.0 on Richter’s scale earthquake hit Japan. The reactors at the Fukushima plant were designed to withstand the 8.2 magnitude quake. Nevertheless, the structures held (note that the Richter scale is logarithmic, meaning that 9.0 earthquake releases 10 times energy than 8.0). Since Japan is located in seismically-active zone, there exist provisions on what to do in case of one, especially for the nuclear power stations.Reactors 1-3 were operational at the time of the earthquake, while reactors 4-6 were in a shutdown mode.
So, first and foremost, control rods (containing boron, neutron-absorbing material) were automatically inserted. According to TEPCo’s press release, this was done successfully at all three units that were in operation. There was an alarm on Unit 1 that one of the rods was not fully inserted. The alarm then went away. It is now believed that all control rods were fully inserted and chain reaction in fuel assemblies was stopped. Even after this, one must keep circulating water in order to continue cooling fuel assemblies due to the heat produced by decays of nuclear reaction products in the fuel rods. It needs to be done for several days.
It appears that over the course of three days reactor cooling systems kept failing, which resulted in increasing steam pressure in the reactor pressure vessel (see the picture above). In this case you really don’t want to keep the pressure rising, as it eventually would simply blow up the containment vessel and you’d get pretty much what happened in Chernobyl. So, the idea is to gradually release pressure by disposing the (slightly radioactive) steam through the vent line (see above picture). The steam is only slightly radioactive because one is using purified water, which does not get activated by the radiation from the fuel assemblies. This was done at all three units. You have to still keep cooling the core, which was done at Units 1 and 3 with injection of seawater into the Primary Containment Vessel and at Unit 2 with seawater injection into the Reactor Pressure Vessel. Injecting seawater is a desperate move, as it contains salt and other staff that can get activated. Which means that the reactor will be decommissioned regardless of whether there is a meltdown or not. Along with seawater, they injected boric acid to capture neutrons.
Now, if the cooling is ineffective (as it appears is at Fukushima) and you keep disposing steam, you lose the amount of water you have in your reactor (think of a boiling teapot). This leads to water levels in the reactor dropping to the point that the fuel assemblies get exposed to steam. This is what happened at Fukushima. This is bad, because this drops cooling efficiency and fuel rods start to heat up (recall the decays of radioactive decay products that are still going on). At some point, zirconium in the ziralloy (the alloy of zirconium and tin that makes up the fuel rod casings) starts react with water vapor. Here is the chemical reaction:
2 H20 + Zr = 2 H2 + Zr O2 + energy
which means that you start producing hydrogen (H2), some of which will escape into the reactor building. Most likely, escaped hydrogen exploded in units 1-3, blowing off the roofs of the reactor building hosting Unit 1, 2, and 3, like this:
This picture is done by the local TV station and posted on Wikipedia. According to the power station owners, the containment vessels are still intact, which is precisely what they are designed to do. Let’s hope that this is an accurate assessment.
Now, if there is a meltdown (fuel rods are damaged), some of the reaction products might get into the atmosphere (the troubling news is that the monitoring stations did detect small amounts of iodine nearby the reactor). The most immediate concern are radioactive Iodine (half-life of 8 days) and Cesium (half-life is 30 years). Iodine can accumulate in human’s thyroid gland – so the first line of defense is to saturate the gland with non-radioactive Iodine. This is why the population around the station is given iodine tablets as a precaution. The detected amounts of iodine are not of a concern for the US West Coast (too far).
In the case of a serious meltdown, the melted fuel will likely remain in the reactor containment below the rector pressure vessel. This would be bad, but still nowhere near Chernobyl’s explosion. BTW, I was on a school trip in Kiev when the Chernobyl power station blew up. I had to bury my shoes because the radioactivity levels on them were too high (dust)…
To add to the problem, rector unit 4 (which was not operational at the time of an earthquake) developed problems of its own. In particular, it appears that the personnel missed that the water level in the spent fuel pool came down. This exposed spent fuel rods that contain more long-lived radioactive isotopes. You want to keep spent fuel rods in the water to cool them, as the decays still produce heat. In this case, usual convection cooling (warm water is rising and is replaced by cooler water) is sufficient to keep them cool. That is, if there is water! There was report of a fire at the spent fuel pond. This might indicated that the water level in the pool went down and spent fuel caught on fire. This might be bad, as this would release radioactive material in the air. Japanese scientists monitor the situation.
I’ll try to keep you posted as well.
What is happening at Japan’s Fukushima Daiichi power plant? March 12, 2011Posted by apetrov in Near Physics, Physics, Science, Uncategorized.
This is a good question to ask — especially amid speculations about “possible Chernobyl-like nuclear meltdown” and pictures of explosions at the plant. Knowing a little bit of physics (and reading press-releases from TEPCo — Tokyo Electric Power Company), one can make some initial analysis. Clearly, a complete picture will follow in the near future.
So, first of all, what is the problem? To understand this, let me note that nuclear reactors at the Fukushima Daiichi plant are of the Boiling Water Reactor (BWR) type — quite different in design from Three Mile Island’s PWR-type reactor and Chernobyl’s RBMK reactor. In order to see the logic of what Japanese engineers are doing, it is useful to see how the BWR reactor works.
Here is the scheme of BWR-type reactor, taken from the Wikipedia page on BWR. The physics here is very simple. Fission reaction in the uranium fuel assemblies (2) heat water (blue stuff, 7), which turns into steam (red stuff, 6) in the reactor vessel (1). The steam exits the vessel and spins the turbine (8 and 9) that generates electricity. That steam is cooled down and returned into the reactor vessel (as water) and the process begins again.
Simply speaking, fission reaction happens when a slow (thermal) neutron is absorbed by a uranium (U-235) nucleus, which then splits into several (two) lighter daughter nuclei, and several fast neutrons (about 3), releasing energy that is converted into heat. In order to have sustained nuclear reaction one needs to slow down those produced neutrons so that they could be absorbed by other U235 nuclei to initiate chain fission reaction. Different reactor designs use different moderators to do that: water (BWR, PWR), graphite (RBMK), etc.
This simple excursion into nuclear physics tells us that the rate of power generation can regulated by controlling the flux of thermal neutrons. This is indeed what is done by the control rods (3) that are usually made of a material (boron) that absorbs neutrons.
What happens in case of an earthquake? Well, the automatic control systems first and foremost would kill the sustained fission reaction that is going in the fuel elements. This was done at the Fukushima plant immediately by inserting the control rods (notice that the control rods are inserted from below). So, what’s the problem then? Why is the water vapor’s pressure rising?
The problem is that during the fission reaction one also produces a lot of short-lived nuclear isotopes. Normally, if you would like to shut down a reactor (say, to refuel), you need to allow for some time (several days) for those isotopes to decay. During that time, water is still being circulated through the reactor core in order to take away the heat produced in the decays of those short-lived isotopes. This is done via pumps that are operated via electricity from (a) power grid or (b) diesel generators or (c) batteries. After the earthquake, the grid was knocked out and the diesel generators got damaged. The pumps are now running on the batteries and the water vapor pressure inside the reactor vessel is rising — by the way, the normal operating pressure there is about 75 atmospheres!!! TEPCo reports that the pressure there rose twice that, so the plant operators decided to release steam from the vessel. Now, to cool down the reactor (until those short-lived isotopes decay) they decided to flood the containment vessel with sea water.
So, as you see, the Chernobyl-type of explosion is highly unlikely at the Fukushima plant. I think the reactor will cool down in a couple of days. BTW, it appears that the reported explosion happened at the pumping system…
The only troubling news is that the monitoring stations appear to detect small amounts of iodine and cesium isotopes (to quote TEPCo’s press release “The value of radioactive material (iodine, etc) is increasing according to the monitoring car at the site (outside of the site). One of the monitoring posts is also indicating higher than normal level.”). Those isotopes are normally produced in the nuclear fuel rods. This might indicate that one or more rods are damaged.
Update (3/14/2011): It appears that water circulation systems in reactors 1 and 3 of the power station failed on 3/12-13. The reactor containment is now cooled by sea water (with added boric acid to further capture neutrons). Sea water is not an ideal coolant — purified fresh water is — sea water contains salt and other things that can become radioactive in the core of a reactor. Thus, the spent water will most likely be transferred to the spent fuel pools (place on the power station’s campus where spent fuel rods spend some time before being transferred to the permanent storage facility). It also appears that there were two hydrogen explosions in Units 1 and, recently, 3. Where did the hydrogen come from? It most likely came from the chemical reaction on the zircalloy’s casings of the fuel assemblies. Zircalloy, an alloy of zirconium, tin and sometimes other things, contains zirconium. That zirconium reacts with oxygen in water and releases hydrogen. It is, however, believed that in both cases the containment vessels held up. Those containment vessels did not exist at the Chernobyl’s power station.
Update (3/15/2011): I decided to put updates in the separate post.
I usually don’t comment about politics in this blog. But today I’ll make an exception. Maybe someone from Michigan Congressional delegation will read it. I’ll be happy to answer any questions regarding this situation.
Each developed country in the world has a stake in an interdependent triad that builds up its wealth and independence: fundamental research, applied research and industry. It is only the combination of excellence in those three fields that has kept the United States at the forefront of technological revolutions of the past 50 years. Elimination of one of those components will spell trouble for the remaining two: for example, defunding fundamental and applied science in the Russian Federation in the early 1990’s led to a quick demise of that country’s high tech industry.
The new Continuing Resolution (CR) bill announced on 02/08/2011 by House Appropriations Chairman Hal Rogers  imposes deep cuts on Department of Energy’s Office of Science (DOE OS), National Science Foundation (NSF), NASA and National Institutes of Health (NIH) that simply threaten US fundamental research. The cut to DOE OS’ budget of $5.12B is $1.1B. It is proposed to happen half way through the current budget year. To keep things in perspective, the amount needed to implement this cut would be equivalent to closing down all US National Laboratories for a continuous period of time this year.
Among other things, DOE’s Office of Science supports fundamental and applied research done by the University groups all over the country. In the state of Michigan that includes University of Michigan, Michigan State University, Michigan Tech and Wayne State University. This funding is neither redundant nor wasteful: each grant issued by DOE’s Office of Science, NSF or NIH is reviewed by several independent experts and expert panels. It is this funding that helps us train the next generation of scientists and engineers that will keep America prosperous in coming years. It is this funding that the new CR proposal would severely cut.
To compare, Chinese government’s spending on science and technology was slated to rise 8% to $24 billion in 2010, of which $4 billion is basic R&D . By contrast, the cuts included in the proposed Continuing Resolution bill reduce funding to basic and applied research made by DOE’s Office of Science by 18%. Liberal and conservatives commentators alike voiced concerns about how the US is losing its edge in math and sciences. This budget cut signals that there is no reason for young Americans to pursue careers in science.
The fundamental research done by particle scientists might not have immediate applications to industry. But not all basic research projects are “long shots.” The first Internet browser developed by high energy physicists at CERN (the site of currently running Large Hadron Collider) for the needs of the experiment designed to understand the basic building blocks of Nature in 1991 made possible creation of the World Wide Web and revolutionized the US and world’s commerce.
Balancing our country’s budget is an important and noble goal, but it should not be done at the expense of the future.
 House appropriation committee website http://republicans.appropriations.house.gov/index.cfm?FuseAction=PressReleases.Detail&PressRelease_id=259
A picture on a wall? February 12, 2011Posted by apetrov in Funny, Particle Physics, Physics, Science.
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I was moving old pictures from my camera to my computer today and found this image. Here is a funny picture of a reflection on my neighbor’s wall. What does it look like?
To a particle physicist, this is just a pair of Feynman graphs for 2 -> 2 scattering amplitudes… with the left one in an external field :-). Enjoy.