 Welcome everyone. This is our second webinar for the fourth season of the Latin American webinars. Today we have Philip Tanedo from the University of California at Riverside. Philip is a professor there and he was previously postdoc at I-Bind and he is a PhD. From the University of Cornell University. And Philip, today we will talk about a very hot topic in physics right now. It is the fifth force possible we found. And well, it's better if Philip talks indeed about that. Okay, welcome Philip and well, go ahead. Great, thank you very much. So now let me share screen and then we'll go to full page. Okay, so thank you very much for having me. I've been a follower of Latin American webinars since the very beginning. So it's an honor and a pleasure to be here. So I'll be talking about work with colleagues at UC Irvine. And actually before jumping in, let me just give the quick picture. So the quick picture is if you go back eight months ago, so in January of 2016, actually this December of 2015, this paper was put out on physics review letters. And one of the big claims in the paper was this 6.8 sigma deviation from expected behavior. And the expected behavior was in a particular nuclear transition of a particular nucleus, a beryllium 8. And you can see in the title here that they said this is a possible indication of a light neutral boson. So this is what some people are calling a fifth force. So if you think back eight months ago, there's perhaps a lot of people were thinking about 750GV, so maybe this is something which slipped under the radar. The other thing is that this is coming from the nuclear experiment community. So this showed up on nuclear EX. And this is something where I think a lot of particle physicists weren't quite checking. So let me just give references. So the main paper explaining the experimental result is this first one here by Krasnohoké et al. So this is from the group at the Atomke nuclear laboratory in Hungary. And so it's this paper, a possible observation of anomalous internal pair conversion in beryllium 8. If you're really going to dig into this though, it's also very important to look at the second paper by the same group. And this is the instrumentation paper that really explains what it was that the experiment did, how it was set up, what the calibration was. So the two really go together. And here is a photograph of the Krasnohoké group. The work that I'll really be presenting is mostly from this first paper here from our theory collaboration. So this is a group of phenomenologists. We were all at UC Irvine this past year. Susan Gardner was on sabbatical from Kentucky. And I'm now at Riverside. And this upper paper here is the one that really is, it's a bit hefty, it's 40 pages, but this is the one that I think really summarizes the phenomenological status of the anomaly and how one could begin to play games to build models for it. And then we also give two explicit examples of models that actually work. The second paper here is earlier, this is a PRL, where we started talking about the initial phenomenology. How would you take the experimental result and map it onto a model of particle physics, and then how do you compare that model of particle physics to existing bounds. And so for those with a bit less of a physics background, we also have a science explainer down here at particlebytes.com. This is north level of the general public. And that's just explaining, again, summarizing the anomaly and what's going on. So jumping into the physics, the general principle here is you can use nuclear physics to search for beyond the standard model physics. And this is not a common thing that we think about these days. These days we think about high energy experiments looking for high energy and new physics. But actually the idea that you could use nuclear physics to look for beyond the standard model is it's old, it's from the late 70s, from very famous people, as you see on the bottom. And there are two really nice features about nuclear physics. So, nuclei, just like atoms, have excited states. And we know a lot about these excited states. You can go to these nuclear tables and learn more than you ever knew there was to learn about these nuclear states. But two things in particular are very nice. One is that you can excite nuclei resonantly to an excited state. So from the particle physics language this is just saying you can produce an excited state on shell. So you can really produce tons of them. And that's great because you can have really high statistics experiments to look for very weak coupling. The other thing which is very nice is that one of the things that we know about a lot of these excited states are the transitions. So we know, for example, that the state that we're really excited about is the 18.15 MeV state of beryllium-8. We know that this thing transitions to the ground state with that splitting energy. And so we know all of the kinematics of a lot of processes that we care about. And this is again to be compared to the LHC where a lot of the hot searches involve missing energy and trying to find ways to go around the particles that you don't see. It's the opposite case here where you know exactly what the energy transition was. So more specifically, the excited nuclei can decay in many ways. Sometimes it just falls apart into a different nucleus. A smaller amount of time you have electromagnetic transitions where you decay into a photon, like a gamma ray that you can detect. And an even smaller amount of the time you can de-excite by an off-shell photon. So this off-shell photon is called internal pair creation because the off-shell photon turns into an E plus E minus pair. And the properties of this E plus E minus pair, one are in part fixed by the kinematics. Once you know what the transition energy is, you know what the energy of the E plus E minus is. But the opening angle, for example, tells you about what this internal particle was. So if you go back 40 years, this is what people were thinking about. Okay, so let's now focus in on internal pair creation. So this is now a textbook example in advanced quantum mechanics. So if you're going from an excited state to a round state through an off-shell photon, you can categorize these transitions by parity, so whether they're electric or magnetic, and also by the partial wave, so by orbital angular momentum. And the important thing, and so this is something that students can do as a long homework assignment, you can map out what you expect from ordinary electrodynamics. And depending on the particular type of transition, and that depends on the quantum numbers of the nucleus, you get different spectra of opening angles. So this plot here shows the, let's say, the relative frequency at which you measure the electrons at a given opening angle shown on the horizontal axis. E0, for example, means it's an electric transition, that is S wave, E1 is electric, that's P wave, M1, which is something we care about, is magnetic and P wave. The most important thing to take from this plot is that all of these processes that are from ordinary QED are smooth and they're monotonically decreasing. So any combination, these guys, you also expect to be smooth and decreasing. And this will become important later on when we talk about backgrounds. So these guys are the backgrounds to a search for new physics. Okay, now let's introduce the player. So the main player here is beryllium-8. So beryllium-8 is a particular nucleus with a particular proton and neutron content, 4 and a 4. And it has many excited states. So some of the excited states are shown here as horizontal lines. The ground state's on the bottom. And the two that we care, well the one that we care about the most is the red one. This is the 18.15 MeV state. What I've indicated here is that it decays to the ground state through an M1 transition. M1 just because the parity and the angular momentum of the state is such that if this thing decays to the ground state, it goes through the M1 multipole, if you want. There's another related state, which is nearby. It's this 17.6 MeV state, which I've shown in blue. It's close in mass, and it also transitions through an M1 transition. So these look very similar, except for the fact that there's this one here. And that one means that this lighter state is an isospin triplet. So isospin is a symmetry that separates protons from neutrons. And the lighter state is different from this isospin, with respect to isospin. I will remark later that isospin is actually a red herring. And in fact, the fact that this thing can decay from an isospin triplet to an isospin singlet actually tells you that isospin is not a good symmetry, which we know is not a good symmetry. So this will come up later on, so I just want to introduce these two excited states to you. Alright, now let me give you a little bit of prehistory. To go back to 1996, you know, back to the Atlanta Olympics, there was another paper which came out way back then that claimed an excess in beryllium 17.6. So this is the blue state, not the red state, the blue excited state. And what they did was they looked at the spectrum of opening angles for this decay of the excited state to the grand state, and they found that it didn't quite match their background prediction. And so on the right panel, you see their signal, their measurements versus the solid lines background. On the bottom panel is their residuals, and it's indeed, the residuals are non-zero. You compare this to the left where they look at a similar transition, that's E1 in carbon-12, so it's a similar energy, and there the residuals are spot on. So this guy from Frankfurt, Fok De Boer, who isn't the nuclear experimentalist, said that, oh, this looks like it's really the observation of a new particle. But unlike what I had just told you, this excess here is broad, it's smoothly decreasing, and it behaves like background, this is not a bump. And in fact, one of the results of the Hungarian paper that I mentioned at the beginning is to rule out a new physics interpretation of this 1996 result. And they in fact gave an explanation that if you include some of these additional states, some small fraction of those states, you get pollution from other transitions that actually can give you this De Boer excess from 1996. So this is not the anomaly that we're thinking about. Okay, so the old anomaly is gone. Let's talk about the new anomaly. Here is a schematic of how the experiment works. So what they did at the atom key lab is they took a chunk of lithium, so as far as we need to know, it's a chunk of lithium-7 nuclei, and they bombarded it with a mono-energetic beam of protons. So if you really control the energy of this proton beam, then you can excite the lithium nuclei into a particular, brilliant, 8 excited state. If you excite it with more energy, you can access higher excited states. But because this is a resonance, you can really get a lot of statistics for producing lots of these particular excited states. Then you let these excited states decay. So the proposal is, in addition to the ordinary decay through a photon, an off-shell photon, some of the time this thing can decay into a new particle X. So here the excited state goes into the ground state, and a new particle X, which eventually decays into electron and positron. So unlike internal pair creation in ordinary electrodynamics, this is an on-shell massive particle going into E plus E minus. And so the effect of that shows up in the kinematics of the E plus E minus. So here they have this, what I've shown here is in the transverse plane, they have a spectrometer which they use to measure the energy and the angle of the E plus E minus pair. So this is all you need to know about the experimental setup. And here is what they see. Again this is now my favorite plot of on the X axis is the opening angle between the E plus and the E minus. The Y axis is the distribution of frequency, if you want. The black lines are background and the different colored crosses are data. And the colors correspond to different energies at which you're hitting the lithium with a proton. So if I hit the lithium with a high energy proton, then I'm producing higher excited states. If I hit it with a lower energy proton, I'm producing lower excited states. A brilliant mate. And what you see here is that there's a bump around 140 degrees, only for a certain range of energies. And the interpretation here is that this bump appears to be coming from a new particle. So this is kind of our particle physics brain. Every time you see a bump you think it's a new particle. But the bump goes away when you excite at different energies. So there's something about the particular 18.15MV state that is accessing the new particle that you cannot access for other excitation energies. So it's really the particular 18.15MV state which is giving you the new particle. So this is the part where you start getting a bit excited. There's actually two measurements but these are very correlated. Let's start from the right. The right is the same measurements but mapped onto invariant mass. So going from opening angle to invariant mass is a nice exercise and special opportunity. But what you see here is something which looks like a bump right around 16.6MV. And here they've simulated signal and background for us. On the left is really the same data but from the opening angle point of view. And you see that the black lines, the black dots are the data we care about. And the different colors are different ansatzes for a new particle mass. And you see that 16.6MV seems to fit relatively well with the data. So the proposal then is that this could be a new particle with a mass around 17MV. So let's think about sandy checks. Okay, so the first most important thing is that this thing is a bump. These distributions show a bump, something which goes up and goes back down. And the point that I had earlier was that the backgrounds for this process coming from ordinary QED are all monotonically decreasing. So at least at that level there's no way for the ordinary background to give you a bump. The other thing is that the opening angle and the invariant mass agree. So as I said this is not, these are actually correlated observables but this tells you that this is a cross check that this is not for example some systematic effect from cosmic rays or something strange like that. The third point to remind ourselves is that this bump disappears off resonance. And that's just again reminding us of this statement that you only get the bump when you're tickling the beryllium excitation, the beryllium nucleus at exactly the 18.15MV state. This special excited state is the one which is producing the case that can go into this purported new particle. And the bump goes away if you look for different excited states. Okay fourth, the bump disappears for asymmetric energies. So let me explain what that means. So let's look at this left plot in this slide. If you really had a 16.6MV new particle being produced from an 18.15 transition from the excited to the ground state this 16.6MV new particle is non-relativistic. The rest frame of that particle is basically the lab frame. So the opening angles are large which we see here, 140 is large. In fact I should note that one of the new things about the Hungarian experiment is that they could go to very large opening angles. Previous experiments couldn't do this. And the other result of the new particle being non-relativistic is that the energies of the E plus and E minus coming from this decay are relatively symmetric because you're basically in the same frame. And so the black dots on this left plot are selected with some cut on symmetric energies. So the black dots are the ones that show the bump. The complementary set of data are these white dots that have been scaled down. These white dots are E plus and E minuses that have very asymmetric energies. So maybe the electron is very energetic but the positron is not. Those cases you don't expect to come from a non-relativistic new particle because the rest frame of the two particles is boosted. And so indeed you don't really see a bump in the asymmetric case. So that's at least a consistency check with the new particle interpretation. Okay, so finally, number five is kind of a Sandy check. You could ask, okay, there are tons of nuclei out there and tons of excited states for each nucleus. How is it that this beryllium 8, 18.15 NAD states, how is that so special that this is the only one that is seeing evidence for a new particle? And this is actually consistent. Beryllium 8, 18.15 turns out to be the largest transition where we could make this measurement and calibrate against the gamma transition. Meaning to say, this is actually the system where you can look for the largest transition. It's the only place you'd be able to look for a 17 MAV particle. That sounds surprising but if you take some much bigger nucleus, take your favorite nucleus xenon and take some excited state of xenon, the excited state, so for very large energy, large nuclei, the splitting energies are very small. And for other nuclei, it's a really high excited states. You don't go directly to the ground state. You go into a cascade of lower excited states. So this splitting between the beryllium 8, 18.15 excited state and the beryllium 8 ground state is actually fairly unique for being a large splitting where you can look for these sorts of things. So these are all at least consistency checks with a new particle interpretation. So this is me giving the optimistic look that this is really something to be considered. Let me now go to the phenomenological side and start by being pessimistic. So let me talk about what this thing cannot be. So one thing that is highly unlikely to be is a scalar particle. So something like a dark Higgs. And the reason is actually fairly simple. This is just our favorite selection laws from quantum mechanics. So this 18.15 state is spin 1. It has angular momentum. It's parity even and the ground state is spin 0 and parity even. So in order to conserve angular momentum, if the new particle were a scalar, you need to have orbital angular momentum 1, which means the parity picks up a minus sign from the orbital angular momentum. And because the other guys are parity plus, the net parity for the system is odd, for the transitions odd. So this decays forbidden in the limit of parity conservation, which is a fairly good symmetry at low energies. So it's unlikely to be a spin 0 particle. It is also unlikely to be a parity odd spin 0 particle, an axion-like particle. The reason for this comes from the pseudoscalar to photon decay, which you generically get from loops of standard model particles. And this range is ruled out, so this is a dimensional coupling. This range is ruled out from searches for axion-like particles. And in fact, this mass range goes all the way down to 1 over the Planck scale. So this is also very difficult to do. But Hermann actually just let me know this morning that there is a recent paper proposing a pseudoscalar new particle. So if it's not spin 0, and you're saying that you have a light, weakly coupled particle around 20 MeV, maybe it's been 1, and now we have a favorite candidate, the dark photon. So some new gauge boson that kinetically mixes with the photon so that all of its coupling is proportional to electric charge. And so we go to one of these exclusion plots. So on the x-axis is the mass of the dark photon. The y-axis is the extent to which it mixes with the ordinary photon. And the first thing that you see is that the ballpark range that would explain the beryllium anomaly is ruled out. And it's very ruled out. So this red vision is an exclusion from this Na48-2 experiment. This is the one which is most ruling it out. And what this thing does is it looks at decays of neutral pions into a photon and a dark photon, or this x-spin 1 particle. And that decays a thing which is really throttling us. So the first result that we have is that this thing is not a dark photon. This is not the nice, theoretically very well-motivated, easy to construct new physics that you would expect. And in fact, it's also not a dark Z because at this mass range you have a lot of tension with atomic parity violation experiments. So now things are looking a little bit grim. And you need a handle for how do you attack this problem. So the path that we took was to do gross violence to the theory. So let's take a phenomenological model, which means it's not a model at all, not a model of particle physics, but just take a spin 1 particle and give it arbitrary couplings to the different types of standard model fermions. So it couples to the up-cork with some strength. It couples to the down-cork with some independent strength and the electron with some independent strength. And then let me see if, even if I break the theory and give it that much wiggle room, can I explain the anomaly? So at this point you should worry. You should say, okay, that's a nice game to play, but this is not a model and I would agree. The moment that you do this, you generically run into a lot of trouble with the internal consistency of the theory. So this is anomaly cancellation. Which I'll comment on later, but at least to diagnose the experimental result, let us use this phenomenological model and see what kind of couplings you would need and see what that takes us. All right, so the big problem is this decay. Pion's going to a photon and a dark photon, or this x goes on. So we know that pion's normally go to gamma-gamma, but if you have another dark photon like state, you can go into gamma-x. And the trick to avoid pion decays, to avoid pi to x-gamma, is to pick the charges of the up quark and the down quark, the qu-prime and qd-prime, the charges with respect to the x-force, such that this triangle diagram cancels. And that's actually fairly easy to do. You know that this diagram is proportional to this product of quark couplings. And so since the pion is the anti-symmetric combination of uu-bar and dv-bar, it's a superposition, as long as the two superimposed pieces cancel, so that's this equation here, then you avoid this bound. And then you get that the charge of the down quark is minus twice the charge of the up quark with respect to the new force. If you think about this, you'll quickly note that this means that the neutron has a charge, but the proton does not. So this is where the funny word protophobia comes from. If the x boson does not talk to protons, then the pion cannot decay into it. As a little side note, on the right half, there's a very subtle way of thinking about this, where you can think about an effective theory where all you have are pions, protons, and neutrons. And in this case, the thing running in the loop is a proton, because only the proton talks to the proton. And then it's quote-unquote obvious that if the x doesn't talk to the proton, then there's no particle in the loop that can give you this diagram. This is actually a very subtle thing to say, even though this is how Jack Steinberger actually calculated pi to gamma gamma in the 60s, but there's a fantastic discussion of this in Howard Georgia's book. It's a cute argument, but it comes with a lot of caveats. Okay, so now let's take this limit. Now we have a trick. As long as we're willing to do gross violence to the charges of the theory, so as long as we're willing to accept this and accept this protophobic limit, maybe we have a chance. So let's go to phenomenology. Now we need to know how big the couplings have to be. So to diagnose this, we need to know what's the rate we're actually producing this x goes on. And a very convenient way to report what the rate is is to take this ratio, so the rate at which the excited beryllium goes into the ground state plus a new particle divided by the rate at which the excited beryllium goes into the ground state and an ordinary on-shelf photon. There's a reason why this is a nice ratio to take, and the reason is that what you end up with here is an expression which depends on the couplings and momenta, but not any nuclear matrix elements. And the fact that that happened is not a surprise. So because the x and the photon are very similar, they have the same parity, they have the same spin, you can go into an effective field theory of nuclear states. So you treat the excited beryllium and the ground state beryllium as fundamental particles, and you can use parity and Lorentz invariance to write down an effective operator to mediate this decay, and it's the same effective operator. And so when you take the ratio of these branching ratios, these nuclear matrix elements will cancel, the beryllium matrix elements, and we'll show that in the next slide. The result is that this production rate goes like the proton plus electron charge squared, we're taking a limit where the proton charges small, times the ratio of three momenta. So what's important about the ratio of three momenta is that the more massive x is, the smaller the numerator is. So this thing is actually phase-based suppressed by momentum cubed. That'll be important later. And here is a target value that's being reported by the Hungarian experiment. So let's run with that. Let's now talk about understanding this ratio. Why is it that these nuclear matrix elements cancel? It makes, as a particle physicist, that makes our lives really, really easy because we don't have to worry about nuclear physics that's hard. Okay, so this is a bit of a technical slide, but let's walk through it. This Jn mu is the current to which the exposon couples. So whatever is here, this is what the exposon is talking to. And what I've written down here is that it talks with some charge to protons. So here's the proton current. And this is how strongly couples to protons. And here is the neutron current in red. And this E epsilon n is how strongly it couples to neutrons. Now, that's nice if you're thinking about electric charge, but it's actually more useful to go into an isospin basis. So let me rewrite the proton and the neutron current in terms of the isosingulate and the isovector nucleon currents. So here capital N is just the proton-neutron doublet. And so this thing is like the proton plus the neutron current and the isovector is the proton minus the neutron currents, which is all I've done here in the next slide. Okay, so you have some linear combination of isosingulate and isovector currents. And let's take the approximation where isospin is conserved. This is a bad approximation, it turns out, but it's illustrative. In that case, because the beryllium-excited state and the beryllium nuclei are isosingulates, then the isotriplet matrix element cancels. It's zero, which means in this matrix element which shows up in the decay rate, I can forget about this yellow piece, I can forget about this yellow piece and just look at the green pieces. And then we're done. Then we say the nuclear matrix element of the thing that the X goes on couples to, this current, is proportional to couplings times this green hydronic matrix element. I don't know how to calculate. However, the exact same thing is true of the electric current. The photon also couples to something proportional to this exact same nuclear matrix element. And so when I take the ratio here, these two nuclear matrix elements cancel. And that actually makes life much, much, much easier. So one thing which is difficult with different spins is to actually make a prediction for what the coupling is. So this slide here, we have a very clean equation that relates the couplings to the, a number that is measured. Now this approximation had to do with isospin conservation. It turns out to be, for the purposes of talking about nuclear matrix elements, this turns out to be pretty close. So in our paper, we go into the details for isospin violation. But there is one qualitative thing about isospin violation that I want to point out. Because isospin is violated, the 17.64 state can also decay through an M1 transition to the ground state. So remember, the red excited state is the one that we care about that has an anomaly. The blue excited state does not. But there is nothing prohibiting the blue state from also doing the same thing. And if the blue state has this mass, why haven't we seen anything? And this is now one of the words of the problem, one of the ugly things. One of the things that you have to appeal to is this phase-phase suppression. Because the lower your mass is, the closer your mass splitting is between the X particle and the progenitor particle, the smaller the phase-phase suppression is. And because it's cubed, the suppression can be very different. So an X particle produced from an 18.15 state has a much smaller suppression here than an X particle produced from a 17.64 state. So that is one of the caveats for model building here. You have to figure out why the 17.64 state does not give you any anomaly. Okay, so now the top line we understand. The top line now just tells, gives us an equation for how to determine what our target coupling is. On the bottom, I'm also saying that you have a bound, a lower bound on the coupling of the X particle to electrons. And this is just simply because you want the electron to decay inside this apparatus. Otherwise you would never have seen anything. So this turns out to be around 10 to the minus 5. Alright, so now let's look at what this target space looks like. So these are kind of involved plots. The X axis is the proton coupling. So here is zero, this is the protophobic limit. And the Y axis is the coupling to neutron. So these are two independent parameters in our phenomenological model. The different colors correspond to production rates. So this is this nice normalized rate at which you produce the expos on divided by rate at which you produce gammas. And the most important thing is that the dashed black lines here corresponding to 5.8 times centralized 6, the dashed black lines are your best fit. Okay. The bounds from pion decay, NA48, are this white shaded band. So you have to live inside the white shaded band in order to avoid pion decay bounds. And this black vertical line is what happens when you have a protophobic age boson. And here you see that there's a region right there where the protophobic limit matches intersects with the best fit. The dark photon, which would have been certainly my favorite choice for a new particle, intersects at the contour in the bottom left. But this thing is very far away from the bounds from NA48. So this thing is very much ruled out by pion decay. So this is now the parameter space for the production coupling, so the quart coupling, so the new boson. So it has to live around here. It has to have a coupling to neutrons that are 10 to the minus 3 and a coupling to protons, which is really small. Or sorry, 10 to the minus 2. Okay. What about the coupling to leptons? So the y-axis here is a coupling to electrons. And we already said that there's a lower bound coming from the decay length of the new particle. It has to decay inside the detector. There's also an upper bound, as you would expect, coming from experiments like Chloe II, which are E plus E minus collisions going to a photon and an X boson. And these things, you tag on the photon and you can even just look for miss energy or whatever the X goes into. There's also another lower bound coming from beam dump experiments. So we have a particle beam that hits a target, say a thick lead target. And if you have new weekly coupled particles like a dark photon, those can propagate through the lead and can be detected on the other side of the dump. The only way to avoid these bounds, like this here for example, E141, is if you force the X boson to decay inside the dump. So that gives you a lower bound on the coupling. So now this white space here is where you can afford to live. The X axis is a neutrino coupling. So here are bounds on the diagonal coming from neutrino electron scattering. And you can say, oh wait a second, we never needed neutrino couplings. In fact, neutrino couplings are very problematic because the X boson can decay into neutrinos then. But the point is, in the back of my mind, at this point even, that the new particle, if it couples to electrons in a vector like way, it almost certainly couples to neutrinos. So I need to worry about what my underlying theory would predict an neutrino coupling to be once I have a consistent theory. So this is important to also plot. And so you end up with some target region of up quark and down quark couplings, or equivalently neutron and proton couplings, and electron and neutrino couplings. So now you have a phenomenological target that appears to avoid constraints. And the game is can you produce a reasonable theory that is at least mathematically consistent that can realize this parameter space. And so this is the question of UV completions. So we have a couple of these in our paper. I'm not going to go into the details, but let me just give you the general idea. I'm not going to go into the details, the general idea. You might worry that this idea of a protophobic coupling is very arbitrary. But in fact it's not. And you can get the protophobic couplings to quarks automatically if you couple to electric charge minus baryon number. So for example, you can gauge baryon number and then kinetically mix with electromagnetism, which is what the photon does, the dark photon does. And if the kinetic mixing is large and if it's tuned to the right value you can get exactly protophobic interactions with quarks. Turns out though one of the problems with this is that the electron coupling ends up being a little bit too big. A bigger problem is that this, the baryon number is an anomalous symmetry. Which means you have to give some additional matter content to make this theory consistent. And so all I'll say at this point is that there exist models that you can kind of take off the shelf garden variety models where there are UV completions with additional fermions that have not yet been ruled out. Okay, so maybe anomalies are something that you want to focus on. Then a simple way to extend this in an anomaly free way is to not mix with baryon number but baryon minus leptanum. So b minus l is anomaly free. And this also realizes protophobic couplings to quarks because all you're doing is changing the couplings to leptons. So that looks really great. But now you get the offset problem. Because now the charge of the electron is canceling between this q and l. So here you have q plus l and the electric charge and leptan charge are the opposite. So now you kind of have to play with things to make the electron couple a little bit too big. So maybe this q minus b minus l maybe there's a small factor here or 1.1 or 0.9. The bigger problem is that leptan number talks to neutrinos as well as electrons. And now this forces you back to having a neutrino couplings. And those tend to be very constrained and you end up having to do additional model building. So you have to have separate modules of new physics to cancel those couplings. Let me just add as an open question a third possibility that I've actually been really curious about is to have an axial vector. So an axial vector the operator structure would be completely different but the axial vector automatically avoids piondowns. So remember this whole schtick about protophobia if you had a spin plus 1 plus particle you don't have any piondowns because the pion won't go into a 1 plus and 1 minus. The problem though is that the axial vector we don't know what the matrix elements are. We can't play this game anymore. And so it's unclear how to write down what the target couplings ought to be. So you can look at our recent paper for details about these models because this is really qualitatively what the game was. And I noticed that today in the archive there are actually two new papers for model building for this anomaly. So what is the next step? So really the most important and the most critical next step is independent verification or ruling out of this anomaly. So what would be really great is if you could really just redo the same experiment independently. For example, I think the nuclear groups in triumph and maybe at the Berkeley lab are actually set up where it would not be too expensive to redo this type of experiment. There are also complementary types of experiments that you can look for that are typically looking for dark photons. So here I'm plotting the dark photon plane so x again is the mass of the dark photon or u-particle and y is the kinetic mixing which in our language is effectively the coupling to electrons. This solid black band here is the target region for beryllium. So it's around 17 MeV and it has this range of couplings to electrons. And here all the colored regions are future experiments that will probe this region. And I'd just like to focus on two. One is the mu to three experiment and the flavor experiment and at the end of phase two which begins in 2018 you should really be able to completely rule out this region. The other experiment that I want to point out is LHCB and so there is a proposal earlier this year to use LHCB to look for dark photons through D-meson decays and so this is a search that will happen during run three and that's happening in 2021 to 2023. But LHCB really can probe this entire swath of dark proton parameter space which is actually very interesting independent of beryllium. So that's the path forward. That's what the immediate future looks like. Let me now just mention so popping back out of it maybe the broader lesson is that there could still be new physics hiding at low masses and at very weak couplings and what I've presented here is an anomaly in beryllium eight but there actually are several anomalies right around that same ballpark the most famous of which is the mu on G-2 an almost magnetic moment and in fact the a protophobic gauge goes on in this mass range might even be able to help but I don't think it can explain it by itself but I think it might be able to help. There's the proton radius problem which has also been of recent interest because of recent deuterium results and people have thought about this as something which could be identified with MEV scale force but models are difficult. Generically a 20 MEV particles are really interesting to dark matter the dark matter community because if such a particle had strong interactions large interactions let's say with dark matter then you can solve a lot of small scale structure anomalies so this is something which is actually very curious but again taking the simplest model that we have and applying it to dark matter you end up with conflicts with direct detection and finally there's also this little known K-tev anomaly look at neutral pi and decays into E plus E minus and my colleagues recently have been thinking about this and it turns out if you had an axial vector of just the same roughly the same ballpark mass and roughly the same ballpark couplings you could explain this K-tev anomaly so again maybe all these anomalies are nothing maybe these all come from some systematic effects but maybe one of these things stick and it's actually interesting just to know where the limits of our exclusions go there's a ballpark where you really could have new exciting physics and it can interact with the standard model in dark matter in novel ways so with that thank you very much for your time and attention as a summary there is an anomaly in beryllium 8 in the 18.15 in the state it's high statistical significance it's a bump and the fact that it's a bump so it's in the angular spectrum like it goes up and down makes it difficult to explain through conventional backgrounds but what we've seen is that the types of couplings that you need to explain this while avoiding current bounds require that the model is actually a lot more exotic than a dark photon so this is not the type of new physics at the scale that you would have expected to see so UV model building a UV model is a challenge I've also mentioned a few other anomalies in the ballpark not necessary to say that you can connect these but at least to say that there's a broader thing to appreciate that at low energies and weak coupling there could still be surprises for us to go beyond the standard model and finally and really most importantly the next step the way forward is experimental cross verification so thank you very much for your time okay thank you very much Philip it was very interesting very illuminated and webinar on this hot topic at least for me it was very clarifying well now we are going to questions let me remind people that we have this hashtag where you can put questions on Twitter or on Facebook low physics and well let's start with people here on the table any of you guys Roberto or Nicolas questions or Philip yeah I have a question that is not in the in the list but just to take advantage so one of the it was very nice to talk thank you is it possible that this the X boson interpretation is basically could be a kind of nuclear resonance I mean a new kind of like state or composite state just behave like in this weird way protophobic way yeah this would be very difficult so I'm not a nuclear expert one of our collaborators Susan Gardner actually is but just off the top of my head I would say the pions are the lightest hydronic states that we have around and for good reason there's a symmetry reason why the pions are light and to say that maybe there could be some hydronic state at the 10 MAB scale it seems a little bit strange to me and then you could say maybe it's not actual QCD maybe you have something like a pseudo goldstone Higgs or something like that then I go back to the argument that if it's a dark Higgs or if it's an axiom like particle spin and parity just tell me that it's very difficult to make it work there are other balance on new particles of that with those properties yeah in fact but in any case if it is a weird composite state or whatever it would be indication of new physics yes from new physics like particle physics or nuclear physics something that is not expected that's right I have more questions but I don't know if maybe other people want to ask first just to make a round of people we have a small question something that you about this possibility of having a scalar it means this possibility very fast at the very beginning but there are this new paper on where they say that could be absolutely a scalar so could you please repeat the argument oh yes yes for the parity conservation yes okay so I can even go back to the slide maybe that's the easiest okay so now I go to the screen share desktop okay so here I say it's not a dark Higgs so by this I really mean it's not a parity even scalar and the reason for this is that the excited state this 18.15 state is spin 1 and so if I'm decaying into a scalar and a scalar ground state the angular momentum of the the final state is 1 okay so the parity of the final state has to be even because parity is even but when I do the calculation for the parity it's minus coming from the p-wave and then plus from the ground state beryllium and then plus from the assumption for the dark Higgs so this decay would violate parity if it's a scalar it's spin 0 plus and okay so parity is actually violated but then the violation occurs so this we would think is very suppressed so maybe there are ways around that but that's the initial argument for the pseudo scalar it's phenomenological now I say that here's if I have a goldstone or if I have something that's parity spin 0 parity odd it's all going to look like this axiomite particle and very generically I'm going to have a loop of standard model particles to gamma-gamma that's even independent of anomalies the word axiom doesn't even have to mean anything just pseudo scalar I can draw a triangle diagram and I can have an effective gamma-gamma coupling phenomenologically this gamma-gamma coupling for a 20mm state is ruled out for a large range of couplings again so completely naively I would say that you can avoid that but I would come from incredible tuning of what's running in a triangle diagram that being said I haven't read the papers that came out recently so they might have some clever things that they do okay I think we should go to the question of the Q&A system sorry there's a question here so thank you for the talk it was very very very nice I was asking I would like to ask about the mu23e what are you doing because you have to say something about the flavor structure ah okay yeah so good so everything that I've said I've kind of assumed flavor universality but that's not something that I've dug too deeply in so if you want to play with the flavor structure how much can you get away with that I have not thought too carefully about I see so then the the new particle what does it couple to then couple through a loop with W I don't understand where I think this would just be radiated from an electron or possibly even the mu it's tree level yeah so there's a flavor change the mu decay is through a flavor changing interaction but the new particle doesn't touch that flavor change I see I see okay well then in Q&A we have a question by Nicolás Rojas he's asking well this new gauge falls on X interact with electrons do I have those particles being almost unnoticed in collider experiments ah good question the coupling is just way too small so I think probably I didn't emphasize this you know whenever we're talking about new physics at the MAV scale or very light scales that's exactly the correct question to ask if you talk about dark photons or axions why have we not seen this at colliders you know MAV scale we're already at 10 TV but for these things the couplings are very very small so we were talking about 10 to the minus 3 couplings and it's actually it's at some point when you go to very high energies it's actually very hard to look for light new physics okay well we have another question by Roberto it is possible to say something on the total decay width in principle one could expect that the X boson could decay to neutrinos yes ah okay so good and that's exactly a problem so there's problem two ways if you can talk to neutrinos one you have a whole set of bounds from neutrino electron scattering okay so then you have to make sure your couplings aren't too big but the second problem as you pointed out is that if you couple to neutrinos at all neutrinos are light and so you can decay into two neutrinos and you can decay into all three flavors let's say and then your branching ratio to electrons is actually small so producing the X boson you know more than two thirds of the time it's going to go into neutrinos then your rate for producing it for seeing this in the Hungarian experiment goes down so then you have to increase your core couplings and reduce more of the X boson so you can see the same number of electrons and then that pushes you deeper to the region where you're excluded from other experiments so but you're right the moment if you actually find the model that you're attached to and you have a non-zero neutrino coupling you have to redo the analysis and see what the new revised couplings are and see how bad it gets okay we have another question by Nicolas do you know where nuclei are? yeah this is actually rather subtle yeah good you could say that okay it's a 17 MV boson just find a nucleus where you have a 20 MEV splitting and then just look for that thing and it turns out this is actually really hard so we know of some nuclei like helium 4 where you have that splitting but for that case you don't have the gamma transition to normalize so for the examples where we have a large transition experimentally it's just hard to make a meaningful quantification because you can't normalize the rate then you can say well let me just take a big nucleus those must have lots of high energy but it's the opposite right if you take xenon the energy splitting is really small yeah maybe it's frustrating that helium 8 is actually special in this respect okay another question can I ask something yeah so you mentioned this helium 4 I think okay even if you cannot normalize with the gamma normal you can still have a bump right? I guess in principle that is true so I'm not sure if there have been experiments looking at this so yeah I'm also not sure how easy it is to at least it's actually a chunk of solid material that you hit with a proton of a beam I'm also not sure how you do this for helium so that's outside of my expertise probably has to be ultra cold but yes in principle yes okay the other question by Roberto is if there is any other experiment that is able to cross check this MEV mediator for this mm-hmm right now this instant I think not the two that I gave at the end of the talk so mu23e and LHCB are I think the two that are soonest to have a complimentary bound and to the best of my knowledge I don't think there are other people who are redoing the experiment but in principle it's doable it's not a difficult or expensive experiment and so again this is the complete being completely naive as a theorist perhaps Triumph or Berkeley lab would be able to do this okay well we have another question by Lewis and Tom Skull and is it understood what happened to the 13.45 MEV BAM previously reported by the same collaboration in 2012 oh okay so these are things I'm less familiar with so this may be a sociological question so the bump that we are looking at is the bump that was published in PRO and I think the statement is that there were bumps in conference proceedings that never made it to a published paper so the valuable yes I don't know what happened to them but our approach was go with what's in the peer review journal okay well we have one final question by Roberto it is possible to observe this anomaly in other really I saw to post or is it I don't think so I don't think you would have the same transition available so that's an exercise that one can do you can go they have these public nuclear tables where you can look just click on several boxes and see okay what's the biggest mass pudding energy pudding that you have there and it's hard to find one that's above 17 MEV okay well I have a very general question it's well more sociological framework well it's the first day that I but it seems that it's very tricky to come out with some model to explain this anomaly to something that you uncover to another part normally what happened at least we see this in this recent excess in LHC is that well maybe something experimental that we don't know is happening there so maybe the best thing to do is wait to see this anomaly in another place well from the theoretical point of view well I think well we came up with very sophisticated modeling about this but maybe to test the reality of this excess will be I don't know what's your opinion on that yeah I'm afraid to say to give opinions on recorded broadcast the facts that you say are absolutely right so there's a 6.8 sigma number but that 6.8 sigma number is statistical so that means I would not believe at all that this thing is some statistical fluke but it absolutely could be a systematic error or something that we didn't know and you can go down the list of the Fermi 130G the SAVEN 750G the things which went away and that's life I think doing the groundwork and seeing how could an anomaly fit is meaningful but you're right at some point you asked am I going to build how many epicycles of a model do you want to build to say ah okay this now can fit but okay theory time is unfortunately cheap so well do we have much questions here label yes I have one question I was wondering the axial vector case I mean in the sense okay for the vector case it's easy because the nuclear form factor disappears so it's easy but in the actual case it's not possible even to try to put an upper bound it cannot be the form the nuclear structure factor be so uncertain that you don't have any kind of idea in order of magnitude or something like that so there are a couple of things so for the nuclear matrix element I sway between I really have no idea and you can do the 0th order estimate and how meaningful was that and I think the nuclear the few nuclear theorists I've talked to are very they wouldn't want to really pin down to some reasonable range of numbers even order 1 the other thing which is kind of interesting about the axial case is that the operator so you're right for the matrix elements you don't know but suppose you could know the other thing is from the effective theory point of view there are two operators so for the ordinary spin 1 minus we said oh it's the same operator as the dark photon which is nice you almost expect that but naively there's no reason it had to be so because this new particle is massive so the gauge symmetry is broken maybe there's some gauge breaking operator and it turns out that the leading order doesn't show up for the spin 1 minus but for the axial the leading order operators include kind of a gauge invariant piece and a gauge breaking piece and these two in principle could have separate coefficients and could they cancel each other there's a lot of interesting things they have different momentum dependence there's some interesting things there and if you could tell me with certainty what the matrix element was right now that's what I'm going to go home and work on okay well well thank you very much it was very nice webinar I think we've learned a lot about this at least I did and well what's next in two weeks we have Mattia from NASA he will be talking I think about gamma rays anisotropy and dark matter and many other stuff and please let me remind you again if you have comments please our hashtag and I think we are done for today see you in two weeks I hope thank you very much