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Studying the Coulomb State of a Pion and a Muon

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Studying the Coulomb State of a Pion and a Muon
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Afternoon coffee at the physics department of New York City’s Columbia University once resembled a think tank where excellent theoreticians and experimentalists developed brilliant new ideas. One day in 1959, for example, the hypothesis that two different kinds of neutrinos existed was discussed. Tsung-Dao Lee (NP in Physics 1957) asked: “All we know about the weak interaction is based on observations of particle decay, and therefore very limited in energy. Could there be another way towards progress?”[1] Could it perhaps be possible to produce high-energy neutrino beams? Yes, said his colleague Melvin Schwartz, while others remained skeptical, and worked out an experimental concept and set-up. A few months later, in February 1960, he submitted a short paper to Physical Review Letters suggesting how such beams could be produced at one of the new particle accelerators.[2] If protons from the accelerator hit a target, they produce pions, which shortly afterwards decay into muons and a beam of neutrinos or antineutrinos of relatively high energy. In an extended form, the practical application of this idea at the Alternating Gradient Synchrotron in Brookhaven by Schwartz, his thesis advisor Jack Steinberger and his colleague Leon Lederman led to the discovery of the muon neutrino and hence to the proof that a second family of elementary particles exists.[3] Lederman, Schwartz and Steinberger were awarded with the Nobel Prize in Physics 1988 „for the neutrino beam method and the demonstration of the doublet structure of leptons through the discovery of the muon neutrino“. It was the first Nobel Prize dedicated to neutrino research. In this lecture, Melvin Schwartz talks about „the manufacture of atoms made of particles that don’t exist very long“, namely by coupling charged mesons like pions and muons. He is motivated by the interest to find out whether there are any interactions that are not anticipated by the normal course of events. “These days, just about everything in this world is anticipated by the standard model and I begin to wonder if there is any more business left for people who do experiments, but I guess in the long run there’ll always be something left for us to do”. The major source for his experiments are neutral K-long kaons that are abundantly generated in accelerators and, amongst others, decay into a pion, a muon and a neutrino. Because charged pions have a coulomb interaction between them, they may be “stuck together as an atomic bound state” if they come out of the decay close enough to each other. Schwartz discusses the conditions for producing and detecting relativistic hydrogen-like atoms in such a way in much detail. Some twenty years before, he had succeeded in observing 155 such events at Brookhaven and Fermilab. Melvin Schwartz was a scientist and a businessman. In 1970, parallel to his tenure at Columbia and Stanford, he founded the Silicon Valley start-up Digital Pathways Inc. together with a colleague. Between 1983 and 1991 he devoted himself full-time to his company as its CEO, before selling it and returning to academia. Perhaps he would have staid in business, if he had not declined the request of two of his Stanford students. In the winter of 1975/1976 they had shown him a prototype motherboard for a personal computer and asked him for an investment from Digital Pathways in the company they were planning to found. Yet Schwartz replied that “personal computers won’t go too far and that Apple is a bad name“.[4] Joachim Pietzsch [1] Samios NP and Yamin P. Melvin Schwartz. A biographical memoir. National Academy of Sciences 2012, p. 3ff. http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/schwartz-melvin.pdf [2] Schwartz M. Feasibility of using high-energy neutrinos to study the weak interactions. Phys. Rev. Lett. 4:306-307. [3] for more details cf. http://www.mediatheque.lindau-nobel.org/research-profile/laureate-schwartz#page=all [4] Samios and Yamin. l.c., p. 13 f.
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Transcript: English(auto-generated)
Thank you very much. Ladies and gentlemen, it's a real pleasure to be here. And what I'm gonna be talking about today is a little bit of an unusual field. It's one where I did some pioneering work. It's probably one that will end with whatever I end up doing because I have never discovered anybody else
who's interested in the same subject. But it's intrigued me and I'll tell you a little bit about it. The subject is basically the manufacturer, if you like, of atoms that are made of basically particles that don't exist very long. For example, a pion, which decays normally in two, say, two times 10 to the minus eight seconds,
coupled to a muon that might decay in the order of a microsecond. You might wonder how you can take a pion and a muon and put them together and then do some experiments with that combination. Of course, what we're looking at is exactly a hydrogen atom on a small scale and the interest, of course,
is to discover if there are any interactions between pions and muons or between, as you'll see, muons and kaons, things of that sort, any interactions which are not anticipated by the normal course of events. And in fact, these days, just about everything in this world is anticipated by the standard model
and I begin to wonder if there's any more business left for people who do experiments. But I guess in the long run, there'll always be something left for us to do. Okay, now, how do we make such atoms? Okay, it's actually simpler than one might imagine.
I started worrying about it some 20 years ago and then in fact came up with some ideas but discovered that I had been beaten by a gentleman, lovely gentleman named Leonid Nemenov in the Soviet Union who in fact had written a paper showing how one can make such atoms, indeed he did a lovely experiment
in which he made such atoms out of electrons and positrons and I'll talk about it a little bit later. If you take a K long, which is a well-known elementary particle produced in great abundance at most accelerators, the K long decays as one of its major decay modes
into a pion, a muon and a neutrino. And in its own center of mass, those particles come out more or less at random with typical relative momenta of the order of 50 MeV over C. Now whenever things come out together, there's always some probability that two of them may stick together
if there is in fact an interacting force between them that allows them to stick and obviously a pi plus and a mu minus have the Coulomb interaction between them. So if somehow or other they came together close enough, so to speak, they might come out in fact stuck together
as an atomic bound state. Now it's actually quite straightforward to calculate the characteristics of such a state. The reduced mass is 60.2 MeV over C squared. The internal momentum, which is of course alpha times C times its mass is about a half MeV over C.
The ground state binding energy is 1.6 keV. Later I'll talk a little bit about the level structure and how one might conceivably make a measurement of the Lamb shift in this unusual atom. But it's rather simple to make an estimate of what the rate of production of such atoms would be.
I mean basically it depends of course on the extent to which the pi and the mu overlap. Okay, or at the same place at the same time because the decay itself takes place at a point the pi mu nu decay. And the simplest way of estimating it
and gives you an awfully good answer is to say let's compare the volume of phase space contained by a half MeV over C cubed with a volume of phase space contained by the typical hundred MeV over C cubed if you like that are available for all the possible configurations.
And that comes out to be of the order of 10 to the minus seven, which is in fact more or less what the rate is. It's actually as you'll see about four point something times 10 to the minus seven. The actual calculation again as I said
is not difficult to do. And it turns out that the rate at which these atoms come out relative to the production rate of a pi and a mu in a neutrino is four point three one plus or minus point oh eight 10 to the minus seven. The theoretical uncertainty is largely because there is some uncertainty
in understanding the relative spectrum of the pi and the mu as they come out in a normal decay. The so-called form factor is related to the decay itself. And to the extent there's a slight uncertainty there to that extent this uncertainty will be there.
Now, how does one actually see such atoms? Of course, you imagine there are kaons coming along and those kaons break up. And somewhere, right, there's now an atom going this way, neutrino going some other way. How does one observe such an atom? Well, it's very simple actually.
You just break it up with a very thin foil because the binding is so small compared to the typical sorts of energies that are involved in collisions of elementary particles. You put a little foil in. It turns out about 10 thousandths of an inch or so
would be quite adequate to break these things up. As they make their way through the foil, they suffer a sufficient number of collisions so that the pi and the mu are basically ionized. And from that point on, they proceed as two independent particles
but of course along the same line more or less as the atom was traveling along. Actually, it might be easier if I get one of these lasers here. Might as well go over to high technology. Okay, well, here it breaks up. I have a pi and a mu coming out forward of this foil.
And of course, they have the same velocity which means that their momenta are in the ratio of their masses. And so now if I just put a magnet over here and measure the momentum of the pi and the mu, I will find in fact or should find in principle a peak corresponding to this situation
in which the ratio of the momenta is equal to the ratio of the masses. Well, we did this experiment back in the mid 60s at Brookhaven and we saw about 44 events which turned out to be about a factor of three less than were anticipated on the basis
of the theoretical calculations. But it was a terribly difficult and a very poor experiment in the sense that it had a very poor calibration. It was built in such a way that it was virtually impossible to calibrate adequately. And so, none of us believed that that factor of three was real.
But if there is a factor of three or if there's any factor of discrepancy, it can really be due to two alternative possibilities. One is, of course, that you make fewer atoms than anticipated for one mechanism for one reason or another. And the second is the possibility that the atom disappears more rapidly than anticipated.
The disappearance in principle should be just at the rate more or less that the pion decays. In fact, the disappearance should be predominantly a disappearance in which one gets an atom turning into a mu and a second mu
and a neutrino just from the decay of the pion. On the other hand, it would be interesting to see if there's any alternative to that particular type of reaction. We then began an experiment at Fermilab, one which I'll describe to you in some detail because it has a number of elements that are rather nice
and it's a very pretty experiment as experiments in high-energy physics go. And it only had 10 people involved in it, not 1,000 or so. So it was one that was actually fun to do. So that's not to say that there's anything wrong with 1,000 people in an experiment. You just have to have it if you're building
a large piece of equipment, but it's not my style. Okay, anyway, this experiment was carried out from 1978 to 1980. And it was designed from the very beginning to allow for a very complete calibration against the standard decay mode, K long into a pi and a mu and a neutrino.
May I have the first slide? Okay, let me turn this. I hope you can see all of this. But basically you start by, of course, producing a beam of K long. Now, those of you who can read this will see that we're out here at 470 meters.
That's 470 meters from the place where the K longs were first produced. So way, way, way down over there, we have a target. Actually, it's about 30 centimeters of beryllium. And from that target come all sorts of particles, but it's very easy to filter down to the point
where you have only neutral particles. And those neutral particles are predominantly neutrons, gamma rays and K longs. The gamma rays are relatively easy to filter out and they also don't do very much to hurt you. Neither do neutrons for that matter. The K longs are the particles that we're interested in
and they come down a long, long, long vacuum pipe. The vacuum pipe itself was close to 500 meters and it began at the 250 meter point and ended way out in the yard so as to avoid any particles scattering against the air and causing background. Now, as the particles make their way down,
the K ons that is, some of them, of course, decay and those that decay may have, will have some probability of sending their decay products up. And that's essentially how our detection takes place. You see a view from above here
and this is a view from the side. Let me just run through the various elements in this and then show you in somewhat more detail exactly how the detection takes place. The first point that you must realize is that the biggest background are just the normal decays of K long
in which the pi and the mu are coming close together but not in a Coulomb bound state. For every one, obviously, that is in a Coulomb bound state if I double the relative momentum and have it just two particles going parallel to one another, then I will have almost an order of magnitude more
in the way of that sort of background than I have of atoms. So there are huge numbers of pi mu pairings coming this way and I must do something to keep those from being counted because they have essentially the same velocity, not the same momentum but the same velocity and because they're coming together,
one would normally expect that these can confuse things. So we begin with a vertical magnets. This is about several meters of magnetic field here and the magnetic field at this point is horizontal. In other words, normal magnets have their magnetic field
at least at Fermilab vertical. This one was turned on its side and so it would take a pair of particles entering this way if they had opposite charge and bend them apart. So they no longer appeared to be coming parallel to one another from this foil.
So those particles were given then a slight kick and they would make their way in here and if they came in essentially on top of one another, they would come out above one another in this detector array. On the other hand, the particle which was a true atom would break up in this foil right here,
leave the foil right parallel, the two particles parallel to one another, enter a magnet whose magnetic field was vertical and so they were separated at that point and then enter another magnetic field which exactly canceled out the momentum kick
that was given by this so that the two particles leaving here were in fact parallel to one another but some distance apart. Again, to go up to this view, coming from this foil, there would be a pair of particles that would be separated at this point here,
separated apart and then made parallel and then passed through this array. Finally, there were a large number of multi-wire proportional chambers here to track the particles and an array of counters to allow you to trigger. And the triggering was very specifically organized
so as to pick out only tracks that were more or less parallel with respect to one another as seen from above. Next slide. Okay, this gives you a picture of the various orbits through that magnetic system.
A Pi Mu atom that's coming along here splits at this point, looks as though the two tracks are originating at a point on the foil. They get separated, they get brought together. The muon of course is passed through a muon filter which is some meters, I guess it was about five meters of steel.
Anything that passed through that was bound to be pretty much a muon. Just in front of the apparatus, just in front of the steel was a shower counter detector that was able to decide on whether we were looking in fact at an E plus, E minus pair.
Why so? Because it's clear another major background and one which originates in a foil is an E plus, E minus pair that would be produced from a gamma ray which in turn is produced through the K of a K long. So we need to be sure when we detect a pair of tracks that the pair of tracks doesn't include two electrons
or in fact includes no electrons at all. On the other hand, here is a situation as seen from the side, two tracks that are almost together, they get bent apart by this horizontal magnetic field
and then I see a mu and a pi and those of course even though they count will show up as two tracks in the side view of the apparatus instead of like one track in the side view. Next. Okay, one of the, as I said, one of the major backgrounds and one that we needed very much to worry about were the electron pairs that came from that foil,
from gamma rays which converted in the foil. The simplest way to separate the pions or muons for that matter from electrons was basically to make a graph of the fraction of energy observed in the shower counter,
as a function of the number of events. The number of events is a function of the fraction of energy in the shower counter. Now it's clear a pion, until it begins making pi zeros and showering, gives you predominantly a very small release corresponding just to the ionization loss as it makes its way through the counter.
Whereas electrons of course shower and they come out up here and you have essentially all of the energy visible in the shower counter. And so by making a separation, essentially at this point, one can eliminate essentially all of the electrons
but still keep essentially all of the pions. Next. Okay, this gives you, well let me just preface the next series of slides by a very simple statement. The key to this experiment is not just the running of the accelerator but as an extensive amount of Monte Carlo calculation
in order to understand exactly what's going on in the various pieces of geometry. I think most people in high energy physics today realize that the Monte Carlo calculation generally will occupy at least as much time as the running time on the accelerator.
And that's because the geometries are complex, the calculations to understand what you're doing depend very much on understanding those geometries and understanding the rates that one should receive in each of the various detectors. So we've done a series, we did a series of complex Monte Carlo calculations
and compare them with the predictions for both the Pi Mu atoms and for the Pi Mu pairs where they started out really as individual tracks. Okay, this one for example is the Monte Carlo against the atoms transverse momentum
and it compares it with what we, I haven't shown you the atoms yet but this is a typical result. Next, okay, this is the momentum of the atoms that were finally detected. By the way, the interesting thing is their momentum is about 550, sorry, GeV over C. And that's very relativistic.
So, you know, think in terms of this little atomic bound state moving along with velocity that's awfully close to the velocity of light and with enormous gamma of the order of, I guess it must be 100 or so. Anyway, this is a Monte Carlo versus actual on that.
Next, the same on predictions of the longitudinal positions of the events where they appeared to come from. You can of course reconstruct where an event came from because you know its momentum, you know its mass, you know where it's going, and you know exactly where it has to in fact
have intersected a counterbalancing neutrino going the other way, going down. Next, okay, the transverse momentum of the pion and the muon in the K Mu 3 events. Those were constantly monitored as a standard against which all of these measurements were to be made.
Next, reconstructed K lab momentum for the K Mu 3. Sorry, the momentum of the KL, the K long. Again, this is the spectrum of the K longs that we were looking at as they were reconstructed firstly from the Ks and secondly from the Monte Carlo.
Next, and of course distance from the target for the reconstructed K Mu 3 decays. Next, okay, now we get to the real data. Those previous slides, their purpose was to show us
that everything in the beam was well understood because unless we were at that point, we really couldn't make a prediction of what to see in the case of the atoms. We next made a plot, and this is the key plot in the entire experiment.
We made a plot of a parameter that we call alpha which is the difference between the pion and the muon momenta divided by the sum. And of course, as I told you before, you must have the same velocity so the ratio of the momenta must be in the ratio of the masses. It turns out then at 0.14,
you should see a peak corresponding to the atoms and indeed there was a peak of some 300 or so events that went by all, that passed all of the criteria and indeed a very small background, residual background of things that had randomized values of alpha all the way across.
So this was in fact a demonstration that we were indeed looking at these atoms. Next, okay, one interesting thing I talked about earlier was what if these atoms decay away more rapidly than one might expect on the basis of the pion decay alone?
Well, unfortunately, we're not terribly sensitive to that. This is an illustration of what the proper time is in the atom's frame of reference. Okay, and it turns out that because these atoms are so fast, so to speak, we really only look at them
over less than one-tenth of their lifetime. In fact, 0.08 of a lifetime is the typical time and that means that a fairly substantial fluctuation in lifetime will make very little difference in our measurement rate.
So it turns out that's one thing that we're not at all sensitive to. Next is the last of the slides and we'll get back to the view graph. While we're taking data, of course, on these atoms, we also take data on the gamma rays that come out of the beam and convert in the foil and that's useful for a measurement, for example,
of the rate k long into two gammas. And this is, in fact, the transverse momentum spectrum of these gamma rays as we measure them and indeed you can see an extremely good fit to the Monte Carlo, including also this particular set
of data, which is what we expect. That's the Monte Carlo data for the k long into two gammas. As you can see, the Monte Carlo data isn't just one beautiful smooth line. It takes time to make a Monte Carlo calculation and you're limited by the time it takes on the computer system.
Okay, let me get the lights back. We'll go back to this again. Okay, I can go on. Okay, what's the result? By the way, the one thing that we were very careful of was to be sure that the foil thickness wasn't a big issue in trying to determine the rate
of the reduction of these atoms. And so we took half of our data with a 20 thousandths of an inch foil and the other half with 35 thousandths. The calculations that we did told us that about 10 thousandths is quite adequate to fully ionize these atoms. And indeed we saw no real difference
between the two batches of data. The overall measurement then, the ratio between the production of atoms and the k going into pi mu nu was measured to be 3.90 plus or minus 0.39 times 10 to the minus seven. And the agreement with theory was adequate.
About one standard deviation away from the expected or the anticipated value. But as I said earlier, it's not sensitive at all to the lifetime of the atom. Now where do we go from here? Okay, if this were the end,
I think probably it wouldn't be worth talking about. But in fact, there are a number of very intriguing things to do. First of all, the possibility of exploring energy levels. It sounds like a formidable job in the course of this very short time that you have to look at an atom to make any measurements at all. And it is formidable, so I'm not going to say it'll be done within the very near term.
But there's some interesting things to do. Firstly, unlike the hydrogen atom, the Lamb shift has the opposite sign because it's predominantly, in fact, almost entirely vacuum polarization. And the 2p 3 halves, 1 half states are above the 2s 1 half state.
The energy difference between the 2s 1 half and the 2p 1 half is .07 electron volts. And then higher than the 2p 1 half by .0053 electron volts is the 2p 3 halves. Now one intriguing way of making a measurement,
although it's a very poor way in the end statistically, but it's cute, is to observe that these atoms being highly relativistic, as they pass through magnetic fields, of course, see a very high electric field. So for example, the 2s 1 half state is I enter a magnetic field and I enter it adiabatically
so I don't have any changes in the states. Just changing the characterization of the state will develop a 2p 1 half and a 2p 3 half component. Now at the very beginning, when I make the atom, I make eight times as many in the 1s 1 half state as I make in the 2s 1 half state.
And that's because the wave function squared at the origin, in this case, is a factor of eight higher than it is for the 2s state, okay? So I begin, let's say, with one in nine atoms up in this state and eight out of nine in here. Now, if I enter a magnetic field, of course,
and I begin mixing in these states, then I can have transitions down to the ground state. And so it turns out after passing through of the order of a meter of, say, 20 kilogouts worth of magnetic field, and if I have a gamma of the order of 10 for these atoms, then indeed,
this upper state will essentially depopulate down to the lower state. So in principle, I could measure the rate of depopulation of the upper state. And the way I would measure it is observe that the 2s 1 half state ionizes with a much thinner foil than the 1s 1 half state. Okay, and so I now can have differential ionization depending, of course, on the relative population
of these two. It's not exactly what I would call an easy experiment. There are other variations upon this which we've played with, but I thought it would be sort of cute to describe some of the possible things. Finally, in the last minute or so
that I've got left here, one of the things that we probably will do relatively near term is to measure the lifetime of the atom. When the atom decays, you expect it to go into one muon which is the original muon and just keeps moving along, and then the other muon which is the result of the pion decay. Of course, the relative momentum then is 30 MeV over C
because that's the momentum of the muon in the center of mass of the original pion, and that's a relatively straightforward measurement and not terribly hard to do, but like all things, take some time. The other thing that's intriguing to me and become increasingly intriguing
is the possibility of making other combinations of elementary particles. Now, a lot of this becomes possible because of the construction in the near future of heavy ion colliding beam machines. This is not exactly what they built the heavy ion colliding beam machines to do,
but it turns out it's sort of a fun thing, and as long as I can find someplace where nobody will get in the way, it'll be worthwhile doing. If I take a collision between two heavy ions, and typically at the new RIC machine, you can get essentially head-on collisions of the order of 500 or so per second, if you like.
In the typical one of these, there are 2,000 tracks emerging from the collision region. The collision region is really quite small, obviously very small compared to the size of the atomic system, and so with 2,000 particles coming out, some of them are bound to stick together.
Okay, and so now, in fact, you can look then at all the possible combinations that might stick. Now, most of them just don't last very long. For example, a pi plus and a pi minus will essentially disappear pretty much immediately into a pair of pi zeros, if you like, and k plus and k minus will disappear very quickly,
but a k plus and a mu minus will, in fact, in principle, then last a fairly long time. Now, in order that a mu attach itself to a k, they have to be made more or less at the same place, so these cannot be muons that come from a decay of particles that travel some distance. They have to be very primary muons
that originate right within the quark-gluon plasma if such exists, and so that's a rather interesting thing in itself. If you look at a muon tied to one of the other particles you can be very sure that it originated essentially right in the primal collision. So this is one of the directions
in which I thought it might be fun to go. That pretty much covers it. It's an unusual field, but I hope someday somebody else gets an interest in it. I should just mention that Nemanov did do one lovely experiment. He looked at E plus, E minus pairs tied together,
basically positronium atoms, if you like, produced when the pi zero decays. Pi zero, of course, decays occasionally into a gamma ray, an E plus and an E minus, and every so often, namely one in 10 to the 10, the E plus, E minus will stick together. Now that's a fascinating system
because it is so fast, so to speak, has such a high gamma and has such a large structure that the detection doesn't require any foil at all. All it requires is a few hundred Gauss of magnetic field, and that ionizes the thing. So you have your atoms coming along, put them into a magnetic field,
and then they break up. Anyway, that's one of the areas in which this has been pursued. Thank you very much.