 Okay, so, thank you very much, and thank you very much for the invitation to come and lecture here. It should be fun. Okay, so, broadly speaking, the topic I'm going to talk about is how to use experiments beyond the traditional collider programme, which at the moment is represented strongly by the LHC, to look for physics beyond the standard model. So, I mean, I'm sure you've heard already in various lectures The reasons why we think such physics beyond the standard model must be out there, we have just to go over it very briefly. We have dark matter which you had an introduction to in the last lecture. We've got a load of stuff out there which pretty much can't beat any of the normal math that we know about but nevertheless makes up a large fraction of the energy in the universe. We've also got various problems with the standard model. Mae'r bwysig o'r problemau yma o'r ffordd, oeddwn i'n gwneud o'r bwysig o'r modd yn ymgyrch. Felly y Llyfrgellwyrwyr Cymru, y Llyfrgellwyr Cymru, ac o'r bwysig o'r problemau o'r bwysig o'r cosmologiau. Felly mae'n fwy o'r unrhyw ymddiad yma, yn ymgyrch ar y mawr, o'r mawr yn ymgyrch, ymgyrch o'r unrhyw o'r unrhyw o'r ffordd o'r gael gael, a o'r ffordd o'r cyfrwyr, The need to create perturbations through something like inflation, the need to create the observed matter-antimatter asymmetry through barrier genesis, but we can't make work just with the physics we know about. And then, somewhat beyond all that, there's the question of how to include gravity in a theory in a self-consistent manner that works up to all energy scales. So, there are various reasons we know, well, that something else, other than just the standard model, should be out there. Okay, but what form could that take? So, if we plot things out on sort of an extremely rough graph, so this is, and then things like the LHC collider programme are pretty, are for the most part, searching for things around the electri-we scale with this axis is going to be coupling, say to the standard model, with decent-sized couplings to the standard model, somewhere around here, with the standard model matter sitting, and this is certainly a well-motivated place to look by considerations such as various models of dark matter, issues of the electri-we hierarchy problem, various models of barrier genesis, things like that. But in many models of new physics, there can also be new stuff looking at very different places. For example, there can be new physics at much higher mass scales. For example, unified theories, so what are called gran unified theories, explanations for neutrino masses, other things sitting up at energy scales significantly beyond what the LHC has access to, so you can't try and find them just by banging stuff together and looking for the new stuff to be produced. Similarly, though we've explored pretty well normal energy scales, it's always possible that there's new stuff around that's light, but it's just weakly coupled enough to us that it's very hard to see. We didn't see neutrinos for a very long time even though their masses are very small, it's very easy in some sense to produce them, it's just very hard to detect them. And there's lots of theories of beyond standard model physics where you also have things down here. For example, the QCD axion solution to the strong CP problem, you get naturally light particles there. Sorry, just to make sure. I should probably write bigger, shouldn't I? Can people see these words? Okay, that's a good start. There are various models in which there are extra forces arising from extra dimensions, various things like that. And so generically, as well as the collider problem looking up here, there's a strong motivation to look both down here at low masses and weak couplings and up here at much larger mass scales and see whether there's any observational evidence we can get. So, yeah, basically my lecture will be talking about these two parts. Today, we're going to be looking at this regime, so large masses above collider energy scales. The rest of the lectures will talk a bit more about looking for stuff which is light but very weakly coupled. Okay, so how can we try and look for something if it's so heavy that even our highest energy colliders can't actually produce it? So that they'll see you're hoping to bang particles together and actually produce new supersymmetric particles or whatever, which will then decay and you can see the decay products and what have you. Here, we don't have that option. What they will do is that if we have some new stuff in addition to the standard model, then at low energy scales, we've got the standard model Lagrangian, which is all of the usual terms up to dimension 4. So, kinetic terms plus our Yukawa terms. And these are all things which are part of the renormalisable theory. If we had extra states of high energies, then their effects in low energy experiments can generally be summarised by writing down some higher dimensional operators. So, operators which are suppressed by some higher energy scale, say, and are still made up of standard model fields, because those are the things that we're actually doing the experiments with, and so on. And so, in order not to have seen these yet, this new scale, so this is a scale of whatever new physics is coming in with couplings, et cetera, this should generally be significantly larger than the scales we've probed. So, electro-weight scale, et cetera. Now, if you just write down some random operator like that, looking for it's going to be kind of hard, you want some systematic way of going about it and a good systematic way of, well, one way to start is asking what can't happen in the standard model but could happen if we added extra stuff in. So, looking for things where you know that you're not going to get it if it's just the stuff we know about, it has to be new stuff in order to make it happen. And the first thing I'll talk about like that is nucleon decay. So, in the standard model, we have baryon number, which is so each quark carries baryon number, so a baryon number of each quark is one-third, baryon number of each anti-quark is minus a third, so protons and neutrons have baryon number one. And anti-protons and anti-neutrons, baryon number minus one, et cetera, et cetera. OK. So, in the dimension four standard model of grantian, baryon number is an accidental symmetry. We just look at all the terms and we find that we've got quark, anti-quark, so that's minus a third plus a third, doesn't violate baryon number. These ones again, quark, anti-quark, anti-quark, doesn't violate baryon number. If you want to get terms which are violating baryon number, you're going to have to write down things like three quarks to keep SU3 colour invariants, and those just automatically turn out to have higher dimension. So, we have the chance that in the standard model we're not going to get violation occurring, and in particular that means that if baryon number is a good symmetry, then the lightest b equals one state, which is the proton, is stable baryon number concept. Which is good because we don't see protons decaying. Baryons which are heavier, such as a neutron, can certainly decay, you can get a neutron decaying into electron neutrino, but the proton can't decay then. A quicker side, it isn't actually true that, strictly true, that in the standard model, even at renormalisable level, baryon number is strictly conserved. Though all of the terms in the grantian don't violate it, it's actually anomalous. So, if you write down triangle diagrams with w bosons and hypercharge bosons, then you find out that the baryon number current is violated where, so this is the number of generations, because you have all the different generations going round in these things, and you get some expression which involves gauge field strengths. So, and if you work out the consequences of this, then it turns out that non-perturbative processes called electro-weeks failure-ons can actually give you violation of baryon number from this anomaly. However, because of this number of generations thing in here, all of these baryon number violating processes occurs with delta B equals three times some integer. You can't get, yes. Oh yes, absolutely, sure. Which bit in particular? Okay, that's just, this part is somewhat details, but just put it out there. So this is just writing out the non-conservation of this due to the Chiara anomaly, the gauge field terms here. But the point is that once you do all of this, so you need to be careful about normalisation in everything, which is much more detail than going to here, but once you've done all of that, you find that because of the number of generations part in here, you have always, you've got to do up, charm, top or whatever if you're going round in the circle, and then you can only violate baryon number by multiples of three units through these. So even though we have baryon number violation, we can't violate baryon number by one. We can't say go from a proton, which is baryon number one, to some set of lighter standard model things with baryon number zero. So even taking this into account, we are safe in the standard model. Protons shouldn't decay. However, if we go to high dimensional operators, then, well, if we just naively write down something like this, then, well, baryon number may not be conserved, but this was very schematic. Can we actually get an operator that will do this? So let's try writing one down. So we've got, this is just an exercise to illustrate how you go about it. So in the standard model, we've got hypercharges for our various things. We've got that q has hypercharge minus six. We've got our up and down. Hypercharges two third. This is taking a particular convention, but as long as we take a consistent convention, everything is OK. We've got our lepton, multiplit minus a half, and we've got our right hand to the electron minus one. OK. So we want to try and put together some set of all these things which preserves all the standard model gauge symmetries. We don't want to violate those. Violating gauge symmetries is bad. Violating some accidental symmetry is naively fine. OK. So let's take combinations of the SU2 singlets to make things simple. So we're going to want three quarks, such that the SU3 indices work out. So let's take say our down, up and up. One has minus a third hypercharge. This one has plus two thirds. So this is plus one overall. So we see that if we stick in our right hand to the lepton minus one, we get no hypercharge overall. So this expression would be invariant under hypercharge. So what it's telling us is that we can write down some expression of the form. This is a dimension six thing, so the terminal of the branch should be dimension four. It's suppressed by some mass scale squared. So then we take this, and this is a valid term in the Lagrangian, which will be there with appropriate kinds of new physics, which will give us barion number violation. So we have barion number one here, zero here. OK. So, and just very directly, this kind of thing will allow us to take protons and cause them to decay. So just writing that out. We've got a proton, which is made of up, up, and down. If we have some four core co-operator here, so up, up, and now we're going to have a positron, and down. We started with a proton, and now we've got a positron, and this is going to be part of a pi zero. If we write out, you get the other part of pi zero, we can take up, down, and down. We get the other part of pi zero, we can take up, down, up this part. So this kind of operator will give us the ability for the proton to decay to a positron and a pi zero, and the pi zero will then decay to two gammas. OK. So this is interesting, and it's also, of course, somewhat dangerous, because we don't see protons decaying yet. It's certainly in normal life. So it better be that this process is very suppressed. Or to turn it around, because we don't really see protons decaying, we can put strong constraints on the kind of physics that can lead to such things. So what are the kind of experimental limits on how much protons can decay? So the best come from things which are used for neutrino detectors. So these are giant tanks of effectively water, where the walls are lined with lots and lots of sensors looking for high-energy photons. When a neutrino comes in, it will come in and bang into something, create high-energy photons, which you will see. But similarly, for proton decays, it will create high-energy photons from the positron and from the pi zero, which will then go out to the walls and we can see those. So what kind of constraints can we get from this? Oh, yeah, sorry. No, go for it. OK. I'm not quite sure I know what you mean there, but it's certainly the case that if you have these kind of operators, then you can also get decay of neutrons through them. In free space, neutrons decay much faster through the weak interactions, but like you said, in a bound state they don't. So in a nucleus, you can get neutrons in the nucleus decaying through this kind of thing in exactly the same kind of way. So I'm just saying proton decay because that's the sort of what happens in free space, but in a nucleus, certainly you can get effectively neutron decay through exactly the same kind of thing. Was there any other part of that question? Oh, yes. So in order to translate, you would so properly, one would need to take into account the protons are part of a bound state, et cetera, et cetera, et cetera. However, this is all physics, which is happening at very short distance scales and high energies, in particular high energy compared to the binding energy in a nucleus. So to a pretty good approximation, you can treat the fact that it's in a nuclear bound state as not particularly relevant and just do this calculation. Theoretically properly, you'd need to take into account it doesn't make much difference because the energy scales are quite separated. OK. So what kind of bounds can you get from this kind of thing? So there are about five times 10 to the 4 tonnes of water in one of these neutrino detectors. Like, for example, the best bounds come from super cameaicandae detector in Japan. And this is around something silly big, three times 10 to the 34 nucleons in this tank. So if we watch it for a period of order years or so, and if we're sensitive to any one of them decaying, we'll get a bound on the lifetime of this thing, which is the lifetime has to be greater than the order this many years. And the actual bound is pretty close to that. The bound is greater than the order two times 10 to the 34 years. So what does this mean for the kind of physics that can give rise to a baryon number violation? So extremely schematically, just dimensionally here, we've got the rate of proton decay. It's going to depend on 1 over lambda to the 4 here, and then the other energy scale we've got in our problem is the mass of the proton. Of course, they have all the one factors and everything, but dimensionally speaking, it's going to go like that. And if you put in the numbers, then if we take lambda to be this very high energy scale, so more than 10 to the 16 GV, then we get that the lifetime is around the experimental bound. Putting that in. So this is showing us how even just an experiment which is operating at standard model energy scales can by putting a ton of stuff there and by monitoring extremely precisely such that we see even one decay among all of the atoms sitting in this tank, you can get sensitivity to new physics at extremely high energy scales. So if we had that, say, these operators in the high energy theory were actually coming from the exchange of some heavy particle, which we're ignoring here because it's so heavy that we can't produce it or whatever, then the lambda that we get is going to be of order the mass of this new particle over its couplings, et cetera. So we see that we're probing the kind of mass particles that occur in granunified days, things with extremely high energy scales. So this is one example of how vapors like experiments allow us to try and probe way up in this high mass region and look for different kinds of new physics. OK, so that's one example. Another, which let's start over here again. So another example of very much the same kind of thing is electric dipole moments. Before we talk precisely about those, we need to talk about why these are going to be interesting things to talk about, and the point is another symmetry-based one. Low energies, so below electric week scale, the standard model is at least at the lowest dimensional level is C and P symmetric, so under charge conjugation and parity. Both QCD and QED respect these symmetries. Now, parity symmetry is broken by the fact that the weak interactions have a handedness. The left-handed and right-handed fermions couple differently. But so Cp symmetry is less badly broken, so it's broken by the phase of the quark mass matrices, so the CKM matrix, which I've seen that you'll have done in the flavour lectures. Seen familiar? OK, and also the equivalent in the lepton sector, the PM&S matrix, the Neutrino mass matrix, but those effects are suppressed by small neutrino masses as well. OK, so all right. Well, we've got that Cp symmetry is something that only gets broken by effects of the electric week scale, but that's not necessarily enough in itself. Well, so this is the point at lowest dimension, the neutrinos just don't couple at all of those things. Their couplings are all high dimensional. So if we write down a low-energy standard model process, then we've got that the electrons and quarks interact through photon, through blue-ons, et cetera, but neutrinos will interact through processes which will be, in this theory, things like dimension six operators. So they'll be suppressed. It's something which is suppressed by one over the electric week scale squared. The point is simply that the things which violate CMP are suppressed by the electric week scale. Yes, exactly. They don't interact except through these things. OK, so this is fine, but essentially by looking at Cp symmetry we get an even more drastic suppression. So if we want to look at effects in the low-energy theory which violate Cp, say we have some four-quark operator, which we're going to want to be Cp violating, then we need two things. We need both that all three quark generations participate in whatever the expanded version of this diagram is because the CKM matrix on only two generations doesn't actually have any complex phase. In order to have the complex phase be meaningful, you need all three generations to participate. So we need this diagram to be something along the lines of we have, say, some loop here, say this is, I don't know, strange down or whatever, and then in the loop we have to sum over all the possible up-type quarks that can run through the loop. And because we need to do that, we need to incorporate the off-diagonal CKM matrix terms, which are small. So the CKM matrix has got mostly diagonal with small terms of diagonal. So Cp suppressed by both the off-diagonal CKM mixing terms and also the fact that if it were the case that you had any quark mass degeneracies, say the up was the same mass as the charm or the down was the same mass as the strange or whatever, then you'd again have a symmetry which you could use to redefine your fields, take away some of the freedom from the CKM matrix and leave yourself with no physical phase, so no Cp violation. So at small quark mass splittings, so the fact that M up squared minus M charm squared and M down squared minus M strange squared are much, much more than the electro-week scale. So taking all this into account, what we get is that the coefficient for this kind of operator, the Cp violating part of it, is one over electro-week scale squared as it has to be, but with some small numerical parameters up here which come from the smallness of the quarkicawas, the off-diagonal CKM matrix terms, et cetera. And this is useful because let's say we're going to try and look for new physics which is going to introduce some Cp violation beyond the standard model. Then that could also give, if it's heavy, it'll also give high-dimensional operators and the effect of those will be one over new physics scale squared but if it doesn't have these special symmetry properties which are suppressing the Cp violation from the standard model source from the CKM phases, then this now, the coefficient on top of this could be order one or at least order one over four pi or whatever. So you stand the chance of, even if the new physics scale is significantly higher than the electro-week scale, the new physics Cp violation is strongly competing with the standard model because of this small factor. Okay, so coming to electric dipole moments now, the reason to look at them is that they are pretty much the simplest Cp violating observable. So just a reminder, what is an electric dipole moment? So we look at the interaction of a photon with some Dirac fermion, then we can expand the amplitude for this so this is whatever the amplitude is once you take into account all the things that can be happening inside here. Then you've got the usual, so this is just we take, we've got a term that looks like the usual coupling which is basically the charge of this thing. We've got a term which is going to give us a magnetic dipole moment which for a simple Dirac fermion we can calculate. This is what's generally called F2. But then we also have another term which just by the Leven structure we can always put in there which has an epsilon in it. Details not particularly important but we get some extra term which is allowed and can have some other coefficient. This is going to turn out to be the electric dipole moment of how I think. So, okay, at low energies, what this gives us is some interaction. Let's say we're going to a situation where our fermion is normal relativistic. We have an interaction which is what you'd expect from an electric dipole. We have the external e-field dotted with the dipole moment of this thing which is going to be the magnitude times the spin direction of our fermion. Okay, and by looking at the transformation properties of this we can see that this is going to be Cp-violating. So under charge, our electric field which is sourced by charges and stuff goes to minus e. The spin of our particle is to minus s. You can verify just doing the fermion stuff. Under parity our electric field is a vector. So also goes to minus e but our spin is a pseudo vector so goes to s. So our interaction term is invariant under charge conjugation. It changes side under parity so it's a Cp-violating interaction. What that means is as we discussed over here any contributions in the standard model are going to be extremely suppressed. If we take the electron EDM as an example both because that's very easy to do measurements on and because it also has to talk to the quarks in order to feel any Cp-violation so in standard model EDM at four loops it only comes in at four loops. You need to connect to the quarks which need to have some loop diagram to give you things there. And the value that you get is 10 to the minus 27 sorry, let's just check that. That sounds a bit wrong. Yeah, no, that's correct. Good. It's 10 to the minus 27 times the bull magneton, which is the natural sort of value. This is the parametric value of the electron's magnetic dipole moment. The electric dipole moment is 10 to the 27 times smaller than parametrically it could be. The units that are experimentalists in this field like to use this is 10 to the minus 38 electron charge times centimetres. If you imagine the electron having some tiny deviation from being spherical more negative charge on one side positive charge on the other that deviation is 10 to the minus 38 centimetres big. It's incredibly tiny. Okay, so the standard model of contribution is very small. How big could a contribution from some new physics be? So if we just write down sort of dimensionally the most naive thing we can so we have some heavy particle which is going to couple to the electron to have some CP violating phase contributing to the loop where we're not going to worry about where this comes from. I don't know the answer. I have not gone through the details of that so I don't want to give an answer based on no more knowledge than you. But you'd need to worry a bit about what you mean by things there. I mean you have some strong coupling set up on whether or not this kind of thing is a sensible quantity to evaluate what you need to think about. But yeah, I'm not sure. So for a theory where we're looking at this for electric charges. So we're not in any kind of strong coupling situation where we've got my name on a pulse, nothing like that. This for electric charges, everything is nice and normal and weakly coupled. I would expect that you shouldn't get some kind of hierarchy there. Once you introduce the monopoles into the system then something weird might happen. Basically I don't quite know what the correct formulation of that question is either. Anyway, okay. So we have our generic new physics here which we're just taking to be introducing some kind of CPU violation parameterised by some phase phi. Then the magnitude of the CPU of the electric dipole when we get from this loop we just get from dimensional analysis. So the parametric thing will be the Bohr magneton so this is expanding out is electron charge over twice the mass of the electron. So we've got the coupling of whatever this new thing is to the electron, some kind of pi's thing here. We've got to be suppressed by 1 over mx squared from the propagator. So dimensionalising that we've got some 1 over mx squared there. And then we've got to depend on the imaginary part, so the sign of whatever this CPU violating phase is. Okay, so if we just put in order one numbers for all of these things then if we have new physics around a TV we find that one loop unsuppressed electric dipole for the electron assuming some order one CPU violating phase will be much, much larger so in the units that experimenters like using 4 times 10 to minus 26 ECM. So much, much larger than the standard model contribution. So this is telling us that if you can push sensitivity down then you'll potentially see new physics at plausible scales well before the standard model will come in and make things more difficult to disentangle. So what have people actually achieved experimentally? So the best bound, best current bounds on the electric dipole model to the electron come from something called the ACME experiment and this place of the bound that the magnitude of this thing has got to be less than of order 10 to the minus 29 ECM. So putting that back in MUB units that's around 2 times 10 to the minus 15 of MUB. So this is telling us that we've measured the electron to be having no deviation from CPU violating to an extremely good precision here and in particular a precision which though it's not near the standard model value is in the regime where you're probing interesting scales for potential new physics. So the experiment itself is of course a very complicated thing but schematically how do they actually do that? So and this is quite a nice neat experiment that illustrates a few themes that are important in actually trying to build experiments that will work and will be completely dominated by systematics on things. So the first theme is that we need to make our effect as large as possible. The most naive thing you might try and do. So we have, remember, our interaction Hamiltonian which is our electron spin direction dotted with the external E field. So the most naive thing you might try and do is make a sort of big capacitor in a lab or whatever, set up a big E field and run some electrons through it or whatever. However, the E fields you get in a lab are most of order. So by the way, you can set up if you're doing pretty well around sort of mega volts per metre before bad things happen like your air starts to ionize and lightning bolts start flying and everything goes to hell. So to get round that what they do is they use electrons in polar molecules. In particular the molecule they use is thorium oxide but that's somewhat irrelevant. So we have one of our atoms here, another atom here. This one is positive this one's negative. So an electron which has got some orbital cloud which is around the molecule will see some effective electric field from the nuclei which is of order atomic strength. So parametrically the effective E field will feel is of order kv squared. That's the sort of length scale that is relevant to the molecule and in normal units that's about 100 gigavolts centimetre. So it's many odds of magnitude bigger than the largest E field you can sensitively make over a decent scale in a lab before all your equipment starts flying and going to hell. So first thing, we want our effect to be as big as possible so we want to make our thing rolling out here the external E field as big as possible. OK, so then but what are we actually going to do to measure this effect? So just like a spin in a mag field if we put some spin perpendicular to our external electric field then what it will do is it will process and in particular of its angle will be equal to the E dot E times d plus or minus depending on which direction we're going to go which direction the E field is in. So what ideally we do is we'd have our molecule and we'd set up our electron spin perpendicular to the effective E field and then try and look for its procession. Now in terms of actually trying to measure say the field of the electron, shifting a bit that would be hellishly hard. Trying to measure the sort of large scale effect on this will be very difficult. So what you want to do is you want to do some kind of interference experiment. You want to do some experiment where you're effectively preparing them in one state and then measuring how much they've changed in one state later. So physically what happens is we use some kind of laser setup to polarise all the electron spins in this direction. We wait a while and then if they have any DM they'll have moved round a bit so they're now in this direction and now if we apply the same laser field again it gets a different response than if they'd all stayed in the same direction. Now even that is going to be prone to all kinds of systematics so what we want to do is have something we can easily change about the experiment while keeping all the other surrounding things in the lab etc. the same and that'll change the size of our effect so we can look for some small change over some backgrounds that we're not going to be able to control very well. So what we can do is if we have all this within our box and we've got all our experimental apparatus complicated stuff around here this is going to give various many fields various whatevers that are going to cause the electron spin to process as well as the effect we're looking for we have two handles on this we can change both the direction of the spin we started in and we can change whether we're making the molecules go in this direction or in the direction so electric field this way and both those things can be done just by basically hitting them with lasers of various kinds so we can flip the sign of our effect while keeping all the rest of the apparatus and hopefully all the extraneous may fields etc etc pretty much the same. Okay let's assume that we've done our experiment and we've kept all the nasty noise to a minimum how good a measurement can we actually hope to get from this kind of thing so let's calculate this we have our DE let's say we're at the experimental limit that they get which is 10 to the minus 29 ECM or so and we had our effective E field which was our 100 gigavolts per centimeter or so at this limit DE times the effective E field is minus 18 EV so even with this very large E field this corresponds to an extremely tiny energy split between our up spin and our down spin so if we let the molecules go for some amount of time so let's say that we take what they actually do in the experiment is a millisecond and that implies that the phase change we get which is T times DE times E effective multiplying all these things together comes out to be about 10 to the minus 6 so even with all this we only have a very small phase change so a very small difference from the initial spin state we started at it okay but while you obviously couldn't measure this with one electron it's almost certainly just going to be measured to be in the same state that it started in if you have the same experiment done on many many molecules then in the usual way the error on the phase that you can measure goes as one over the square root of the number that you do so this is basically time of flight across the apparatus so you're making these molecules quite cold this is certainly a lot slower than the usual things you get from some kind of hot source but you can't so far in these kind of experiments they can't keep them like static in a trap these things in some beam which is moving across the thing and has some travel time which is of all the milliseconds or so various people are looking at trying to do EDM experiments with molecules or atoms or whatever actually within some kind of static system either some kind of optical trap or some kind of solid matrix where they're very insulated from all kinds of disturbances but you really you want as few disturbances as possible and ideally that is when something is freely sailing through space not talking to anything else but if you have that it only sails across for a certain amount of time before it hits the other wall so that's what's driving that here more is of course better okay so if we're going to try to take this kind of thing then purely through systematic error we need to send at least 10-12 molecules through and the actual flux in this thing is about 10-13 molecules per second so they're not limited most strongly by this kind of statistics so one thing this is telling you is that unlike in the case of say the nucleon decays we were talking about earlier actually how many nuclei can you cram into your detector we can't sort of win by doing clever things other than building an even bigger detector which they are doing of course here we see that the numbers are such that there's no fundamental reason why we can't just either spend more time or send more molecules through or whatever it's telling us that sort of fundamentally there is quite a lot of headroom here if we do experiments in a more clever way we won't come in and stop us from getting that improvement and indeed these people and the sort of competing experiments hope that within the next sort of decade or so they will have brought this bound down by quite a few odds of magnitude sort of depends how optimistic they're feeling when you ask them but four or five-ish maybe so this is and we can see why that is on some level just from doing this kind of very rough calculation we're not hitting the sort of physical bounds of how many molecules how much time, whatever there's still a lot of improvement which is there if you can use it cleverly enough so that is a actually one other comment to make on EDMs there's also in the standard model another potential source of CP violation other than the CKM phase the strong CP term which I don't know if it's been introduced in the lectures yet it could be in the BSM lectures at some point everyone's heard of strong CP so the QCD theta term and things like neutron EDM measurements are especially interesting in that they allow you to probe what that how small that term is so there's certainly lots of other things to be said on EDM experiments which will have to wait to you going and looking at a review or something anyway, ok so then the other thing I want to talk about in terms of looking for high scale new physics is a neutrino so neutrino less double base of decay so even with things at the level they're at oh actually yes, sorry I should say at this point so if you take the naive one loop kind of calculation here we saw that for a TV mediator here then we had a electric dipole moment which was significantly larger than the experimental limit so if you put in the actual bound then in the one loop model the scale of the new states should be larger than about 30 TV so in things with no protection at all from CP violation you're already probing quite a large range of say models which are focused on hierarchy problem kind of things what you'll do by going beyond that is probing ones which have some structure which suppresses it say that it's suppressing the angle there or it comes in at higher loops or whatever but if you take it to another few order of magnitude you'll make it an even more stringent problem for all of the theories which postulate new physics somewhere near the electric week scale this lambda will go up to 10 to the 3 or whatever TV or something and you'll need to build in more protection in order to not get to these bounds there's also as well as Susie models or composite models etc of the electric week scale there are I think some models where this was talking about CKM phases here but you also have some input from the PM&S phases if the new machine mass is whatever so some models of neutrino mass are also probed by improving the limits here so how is this people going to do that like the overall thing is uncharged right it's a molecule no no this is the molecule the whole molecule goes through and the electron is an electron within the molecule sorry if that wasn't clear so yeah we're saying the whole molecule through which is a good thing because the molecule is overall neutral and rejects all kinds of disturbances that charge particle would so the whole molecule goes through and we polarise one electron within that molecule so we've tuned some laser to be at the energy splitting such that it flips it to the correct thing but we're just sending a beam of cold thorium oxide molecules through our experiment and again it's this thing that you want it to be insensitive to disturbances in order that you don't get lots of sorts of error but that also means that it's harder to control any other questions on any of the topics so far okay well so then on to the last topic for today will be neutrino less double laser decay and this is basically coming from the question of neutrino masses as I'm sure you learned from neutrino lectures we don't know what the form the neutrino mass is within the standard model so first people thought the neutrinos were massless in which case it's just a massless spin half particle we have one state which is our neutrino and it's right handed the spin has a particular relation to the menton direction and then the anti neutrino right handed spin the opposite relation so in that case everything is simple but then there was the discovery of neutrino oscillations and that means that the interaction eigen states in which they're produced have to be different from the propagation eigen states in order for the oscillation to happen so we need some kind of non-diagonal mass matrix the PM&S matrix okay now the problem is so like for normal particles like an electron or whatever we can sort of probe them everything's fine neutrinos the masses are very small so from cosmology bounds the sum of the masses of all three mass eigen states is less than around 0.1 ev and basically because neutrinos have interactions which grow in strength as you go to higher energies below the electrical scale we only really see the effects of neutrinos which are at MEVA energies and above so they're always extremely relativistic and that means it's rather hard to tell the differences between different forms of neutrino mass that we're going to go over okay so the possible mass terms we could write down for a neutrino or for any fermion are myerana mass terms in two component notation this would just be some mass and then the spinner times itself or we can have Dirac mass terms where we have where we have the left-handed neutrino coupling some other species some other spinner so we introduce new states now in general we could have the mass let's say that we've got our introducing some new states, the right-handed neutrinos then we can have mass terms both of myerana form schematically Dirac and Dirac form for these kind of things so it could be that the neutrinos are purely Dirac so if I have no myerana mass terms then we just have our Dirac mass terms it would be like the electron quarks whatever in the standard model so in that case we then have four states we'd have spin states for the to have our usual things so we'd have a neutrino we'd have an anti-neutrino and whatever but we'd also have the other spin states for the neutrino and the other spin states for the anti-neutrino so we'd have four states in exactly the same way as we have for electrons and positrons we've got electrons spin one direction electrons spin another direction positrons spin one direction and positrons spin another direction now ok we've got four states here so can't we tell the difference between that and two states the problem is not very easily at all because these two because the weak interactions they only interact with left-handed parts so if the neutrino is very relativistic the parts are the ones that actually interact with things whereas these parts hardly interact at all up to corrections expressed by the small neutrino masses so it's very hard to see the effects of these things if we're only dealing with very relativistic neutrinos ok now it's also possible of course that we just have my round of masses or the other point is that this is somewhat on the side but if you have a hierarchy in this matrix such that your left-handed mass is small you have some Dirac mass and you have some very large mass for the new states then diagonalising this we get a heavy neutrino which has mass of order this very large mass and then we get the light which have a mass set by Dirac mass squared over the mass of this thing so if you set say this to be weak scale which you can get by writing theories with interactions with the Higgs so and then you set this mass scale the high thing, this to be some high scale such as 10 to the 12GV or so then the light mass scale you get out here is the appropriate one for the neutrino masses we see evidence for so in this kind of theory where the you can get the light neutrino masses coming out as coming from heavy physics giving you a scale suppression then the light neutrinos will just be ignoring the integrating out the heavy stuff have looked like they have a purely myerana mass at low energies so we have these two things and because of the fact that we only see very relativistic neutrinos is very hard to tell the difference just an illustration of that you could think of a number of ways in which okay how can we tell what's going on here can we just try and look at slow neutrinos for example the cosmic neutrino background which is left over from the big bang in the same way that the CMB is the photons which were thermalised in the early universe these will be given the masses which we see some of them are probably non relativistic in galaxies today and the interactions you get with them will depend on whether they're myerana or Dirac however seeing the cosmic neutrino background is an extremely difficult problem in itself you generally require football field size worth of detectors all perfectly instrument is an extremely hard problem so trying to see slow neutrinos even in itself is extremely difficult you can ask okay well can we just try and see the effects of producing these things in the early universe even if we can't detect them now so if we write down our high energies we can get Dirac mass term from some coupling to the Higgs so we've got our say electron we've got our right hand neutrino and we've got the Higgs so in the early universe if we get collisions like this but it will produce the right hand neutrino are these kind of things enough to actually get you anywhere basic answer is no if we write it like this then our mass is going to be lambda times the electric week scale and we need lambda less than the order 10 to the minus 12 in order to get the correct neutrino mass scale and this number is small enough that when you plug things in you never produce anywhere near like the right number of these in order to actually see them so these kind of approaches are extremely difficult and not going to get you very far as before one of the best ways to try and look for the difference here is to ask what kind of symmetries are different in these two cases and what kind of standard model process can we find that will not occur in one case but will occur in another and the obvious point is that myerana masses violate lepton number we have lepton anti lepton whereas dirac mass terms don't they lead to lepton number conservation so in the same way that we were looking for baryon number violation earlier through proton decay in the neutrino case we're looking for lepton number non-conservation through decay processors and the one that turns out to be best for this is this double beta decay so beta decay is when a neutron decays so double beta decay is when two neutrons decay neutron is our up down down the wheat process so we have some w-bose on and this gives us our electron this is going to give us our proton here so we get lepton proton usual way and we have a neutrino we do the same for the other one electron out here now usually in a double beta decay both of these neutrinos from this one and this one will just go flying out into the universe as well so we get double beta would be so neutron neutron goes to proton proton e-minus e-minus nu nu but here if we have a myerana term which takes two lepton neutrinos and connects them then these two can as we are writing out diagrammatically annihilate each other we can write down a diagram such that we only get the two electrons out so ok what's the rate of this going to be? very roughly so extremely schematically we've got two powers of two electromate bosons here so we got gfermi to the fourth here we've got a term which has got to go like the myerana mass of the neutrino squared and then dimensionally we've got to have some energy to the power seven here so this energy scale is going to be of order MEV because that's what the energy difference here is obviously it's going to depend rather sensitively on actually getting the numbers right here but if we just plug all this in we get that this is 10 to the 31 years if we make this of order typical neutrino mass scale and we make this of order so actual calculations you get for this kind of neutrino mass scale about one over 10 to the 28 years we shouldn't be surprised by a few orders of magnitude difference here because we have large powers hanging around but schematically this is sort of showing you where the scale is coming from so we've got something that is a very very long time but as the example of proton decay illustrated isn't necessarily hopeless there we were getting bounds of 10 to 34 years or so so putting in actual numbers we need that whereas before we were looking at thousands of tonnes for proton decay here where a few orders of magnitude better so we need sort of tonnes scale samples in order to have this happen like a few times see them a year time and if we have that this will happen a few times within the lifetime of our experiment now of course unlike proton decay where pretty much nothing looks like a proton decaying here we have another process which looks almost exactly like it except for some neutrinos but we don't see the neutrinos so how do we tell that this has happened a proton a proton and two electrons versus a proton proton electron electron and two neutrinos what we need to do is to use the fact that the electron the neutrinos have taken away some energy so if we look at the energy of the two electrons that we get and this is like the number that we see for the double beta decay process some thing which has some distribution set by the phase space etc and cuts off whatever the energy difference is minus the neutrino mass scale with this process what you're going to get on top of that is you don't have the neutrinos taking the energy away the electrons take all of the energy away so you're going to have some small bump this is exaggerated of course what you actually get is something that's much much smaller and only just peaks out above you get some small bump at the end of the energy spectrum so this is telling you that you're going to need extremely good energy resolution in these things you're not only going to have to see all of these things with almost no background you're going to have to see them and measure the energy of each electron exquisitely precisely in order to tell that you have a tiny bump on top of this tail which has many many more events in overall so that is challenging but something that is currently being pursued very very sort of aggressively and for some models with neutrino masses in the wide range might actually be able to see stuff within the next sort of certainly the next decade so because there are no neutrinos exactly so if we look at the case with the neutrinos so what we've got is we've got our nucleus and it goes to double v to the K case it goes to nucleus which reacts a little bit we get two electrons flying away and we also get two neutrinos flying away so new new EU so it's most likely that because the energy that's involved is quite large compared is decent size compared to the mass of the electron and certainly large compared to the mass of the neutrino all of these things take away roughly the same amount of energy whereas in the neutrinos case we have a nucleus and we get the nucleus recoiling a little bit and the two electrons taking away all of the energy so in this case the electrons going to have most of it's like half of the energy goes into the neutrinos most of the time here all the energy goes into the electrons all of the time so we get a situation where we have almost all of the energy going into all of the energy going into the electrons whereas here that's an unlikely thing to happen just through phase space reasons so we get a tiny bump that's the idea so we're not there yet in terms of probing realistic models but we will be one slightly pessimistic note is that this parameter M new here wasn't actually the mass of any given neutrino this was so we have some interaction eigen states here and this parameter which is generally called M beta beta is some appropriate sum of the neutrino masses and the mixing angles and phases in the PMS matrix so it's possible in certain configurations of that matrix that this parameter there could be cancellations that M beta beta could be small even if the neutrino masses are whatever their value is so it would be tuned yes but so well if you've heard the phrases normal hierarchy inverted hierarchy in the neutrino lectures then in the inverted hierarchy it is such that you can't get cancellations working out in a normal hierarchy it can be small so yeah but this isn't this is something that it would just have to be unlucky but you can be a bit unlucky and that can make it much harder to see it and then on a more optimistic note even if you did see this kind of thing there's the question of okay we've seen this is this actually due to neutrino masses all we've seen is that we get some process where this is happening but there are other lepton number of violating things that could happen we could put heavy states in here instead and can we tell the difference one thing that makes that somewhat less worrying is that the neutrino mass operator is the lowest dimension thing one can add to the standard model so if you add a term which is lepton higgs lepton higgs suppressed by only one power of some new scale that gives you your myerana masses operators which violated lepton number in a different way are going to be higher dimensional so they're going to be suppressed by more powers of whatever the new physics scale is and they're going to get decent size rates for this kind of thing so if we have some higher dimensional operator which gives us lepton number violation that means that lambda new physics should be of order few TV in order to actually get something of the right rate because we're getting more powers of it when we actually work out the decay rate and in that case you could hope that there would be some new physics around the TV scale or whatever which you'd see along with this at the LHC or other experiments so probably about the time to finish up on that and take any other questions but the general theme throughout this lecture has been how can we look for the influence of new physics which is at higher energy scales than we can probe directly through just banging stuff together by looking at the effects on standard model processes at much lower energies one of the best ways to do that and a theme going through all of these things is try and find some kind of symmetry reason why the messy standard model backgrounds that you'd otherwise have go away and you can look for some clean signal so in the other lectures we'll go on to more of the low, the lightweight couple of physics and that I sort of motivated in the first spreadsheet diagram but yeah any other questions? well so if so yes it could be that there's some reason why this doesn't occur I am well so for example if you did have a say B-L symmetry then you couldn't have that and you should have to be Dirac so having to be Dirac is a definite reason why this kind of thing wouldn't happen and the Dirac mask has come from various places in cases where you're left on masses in my arena I mean this is the easiest thing to make work so I don't know off the top of my head you could probably construct if you had to any, yep so if you gave barion number something has gone very wrong because like I said in the first part of the lecture barion number is violated even within the standard model by Svaloron processors so you would then have an enormous gauge symmetry that doesn't make sense if you're actually viewing it as a real symmetry what it does mean is that your barion number would need to be extremely weakly coupled if it's light because otherwise you'd have production processes which were of its longitudinal mode which blew up with higher energy now you can gauge B-L because Svaloron processes have delta B delta L equals minus 3 and things like that so that is possible and in that case yes you'd be required to have a Dirac neutrino mass because these kinds of things violate B-L so B and L individually bad because of the anomalous nature of the symmetry B-L is possible although one interesting point about that is that as I think Matt Rees has been talking to you about there are reasons from considerations around quantum gravity to be a bit worried about very weakly coupled forces and from bounds which we have on forces coupling to matter a B-L vector which was light would need to be extremely weakly coupled otherwise we'd have seen it already so there are potentially some theoretical reasons there to be like ok is that still compatible but those are a very different nature than this phenomenal logic could be that thanks so what about the electric dipole moments of say muon and tau is there any experimental bounds any coming up bounds I do not know what the bounds there are they'll be much, much worse than the electron because obviously you can't do these kind of precision experiments where you're having them hang around for a millisecond or whatever to measure it that's an interesting question these bounds will be from various collider type things I do not know what I expect I expect they'll be correspond to things at scales of hundreds of GV or something just because if you have extra stuff doing that then you would see it at very high energy things like LHC so maybe things like that any other questions there's a discussion session later as well so ok so the little bump at the end comes from the neutrino list double beta decay but is there so apart from regular beta decay what is the addition from neutrino full double beta decay due to the spectrum as in quantitatively like what's the comparison or maybe I didn't I mean is there any more topographical sort of characteristic that it acquires so you're asking like if you can measure things like polarization or whatever would there be any difference there or in other observables is that the question maybe or does it alter the spectrum at all the presence of the fact that you can have double I guess actually it's just two beta decay happening at the same time right ok never mind that no more questions so it seems so let's thank you ok