1 00:00:00,230 --> 00:00:14,959 Some of these. Okay. 2 00:00:14,960 --> 00:00:19,220 Thanks, Dave. Um, yeah. It's a great pleasure and indeed an honour to be here. 3 00:00:19,610 --> 00:00:26,210 So celebrate, uh, Don's career. And it's lovely to see so many, uh, old friends here in the audience. 4 00:00:26,780 --> 00:00:28,009 Um. Special thanks. 5 00:00:28,010 --> 00:00:36,140 Go to Bill Scott, of course, both for the the collaboration over many years and for specific recollections, um, that he passed on to me for this talk. 6 00:00:36,980 --> 00:00:42,350 So, um. Uh, Don retired, I think, in 1992. 7 00:00:42,380 --> 00:00:53,470 And from 1994 to 2002, Don and I and Bill Scott collaborated on five phenomenal phenomenology papers, uh, which, uh, 8 00:00:53,510 --> 00:00:58,969 we we attempted to understand the the large array of, um, uh, 9 00:00:58,970 --> 00:01:04,370 neutrino oscillation data that was started to come in and put, know, impose some sort of order in it. 10 00:01:04,880 --> 00:01:10,250 So of course, the only people to do to attempt to do that, but I think we had some success and, 11 00:01:10,280 --> 00:01:14,929 um, I hope to convey some of the interest of that and also, 12 00:01:14,930 --> 00:01:19,430 um, some of the impact that that had in terms of perhaps the feedback that we've received and whatever. 13 00:01:19,940 --> 00:01:25,520 So, um, I don't firstly, I'm Mark prepared the ground very well for me. 14 00:01:25,550 --> 00:01:31,430 Um, I didn't meet Don until 1994 when he was already retired. 15 00:01:31,790 --> 00:01:37,940 Um, and so, uh, I've enjoyed very much hearing about what he did before I was born and when I was still in short trousers. 16 00:01:38,420 --> 00:01:43,550 And so, uh, I was asked to cover a little bit of what happened at the beginning. 17 00:01:43,610 --> 00:01:48,350 And as Mark said, he worked on these proton decay experiments to don one to shoot on to. 18 00:01:48,680 --> 00:01:55,790 And he really championed the importance of the atmospheric neutrinos, um, as the background, uh, in proton decay. 19 00:01:55,850 --> 00:02:02,389 And so as part of that, he pioneered and helped helped, uh, push the calculations of atmospheric neutrino fluxes, 20 00:02:02,390 --> 00:02:06,440 which became very important, as Marcus alluded to, for other reasons. 21 00:02:06,890 --> 00:02:17,330 Um, a quote here from this, uh, proton decay experiments, um, review, which Mark already mentioned from 1984. 22 00:02:17,750 --> 00:02:21,889 Um, the dominant background of proton decay experiments is due to atmospheric neutrinos, 23 00:02:21,890 --> 00:02:26,330 which the ultimate limiting factor determining the sensitivity to proton lifetimes. 24 00:02:26,780 --> 00:02:33,230 It's become abundantly clear that a proper understanding of this background is at least 90% of the battle to discover a proton decay signal. 25 00:02:33,410 --> 00:02:37,220 You can kind of imagine him saying that over coffee to to mark at some point. 26 00:02:38,120 --> 00:02:51,109 Um, so the context before, just before I met Don, uh, towards the end of 1993, say was we'd had, uh, something like 25 years of the Homestake, uh, 27 00:02:51,110 --> 00:02:53,450 solar neutrino, uh, experiment, 28 00:02:53,450 --> 00:03:00,160 which I remember as an undergraduate being told there's only a third as many neutrinos coming from the sun as expected. 29 00:03:00,170 --> 00:03:03,680 And that was, uh, that was in the late, uh, that was in the early 80s. 30 00:03:04,160 --> 00:03:13,000 Um, so it was already known then. And, um, uh, these, these experiments went on and on, of course, and proved to be perfectly correct. 31 00:03:13,010 --> 00:03:17,960 And they've, of course, took a major part in proving that they were correct. 32 00:03:18,380 --> 00:03:26,720 Uh, but, uh, later in the early 90s, the gallium experiment started, uh, producing results sage and galaxies and, uh, candy. 33 00:03:26,720 --> 00:03:33,080 Candy, of course, the, uh, the water tank off detector and they all or they also saw deficits, 34 00:03:33,080 --> 00:03:40,190 although they rather than seeing about a third, they saw some something around point six of the expected flux. 35 00:03:40,520 --> 00:03:47,090 The generally accepted theoretical solution, uh, for this was the small so-called small angle MSW effect, a very, 36 00:03:47,540 --> 00:03:53,570 uh, subtle and intricate effect to do with the the interactions of neutrinos in the sun as they're coming out. 37 00:03:54,440 --> 00:03:58,970 Um, so the first signs of issues with the atmospheric neutrinos. 38 00:03:59,390 --> 00:04:07,110 Uh, there's this paper from 1988 here. And you can see that the, um, this is as a function of momentum, the, the the, uh, 39 00:04:07,130 --> 00:04:11,780 block histogram is the, the prediction from Monte Carlo, and the data points are clear. 40 00:04:12,200 --> 00:04:17,089 The electron seems to be propagating perfectly fine and uh, on suppressed. 41 00:04:17,090 --> 00:04:22,900 But the mean once again you sort of thinking about 0.6, although the errors are very large. 42 00:04:22,970 --> 00:04:31,580 So Don of course was involved in this. He did some calculations and he wrote this paper, uh, the atmospheric neutrino problem, a critique. 43 00:04:32,000 --> 00:04:38,840 And from the abstract he said interpretations in terms of neutrino oscillations are correspondingly dubious. 44 00:04:39,380 --> 00:04:43,130 So what happened to turn that situation around in Dong's mind? 45 00:04:44,120 --> 00:04:50,240 Uh, so really, this was when I started getting involved in the business, summer 1994, the turning point. 46 00:04:50,360 --> 00:05:00,260 Um, so Bill Scott and I had been discussing, uh, actually, uh, mixing, um, theories about mixing for, for donkey's years, actually. 47 00:05:00,590 --> 00:05:09,919 And in 1994, we published our first paper, phenomenology paper proposing, uh, quite uh uh, it was, 48 00:05:09,920 --> 00:05:15,860 it was quite out there, really try maximum mixing of the corks and I'll explain what tri maximum mixing is in a minute. 49 00:05:16,310 --> 00:05:26,030 Um, but the idea was, would be that the all the mix angles were equal, essentially, and that the low energy mixing that we see today is to do with, 50 00:05:26,030 --> 00:05:32,600 uh, with radiative corrections and running, essentially running coupling constants with driving the small mixing angles down. 51 00:05:33,080 --> 00:05:36,970 Anyway. Um, so that was where I came into business. 52 00:05:36,980 --> 00:05:46,620 And then at the end of June. There was the neutrino 94 conference in a lot, and they were updated solar neutrino results from several experiments. 53 00:05:46,620 --> 00:05:54,090 And these firmed up these measurements that seem to imply that the suppression was down to about point six of expectation. 54 00:05:54,870 --> 00:06:00,450 And so shortly after that conference, really, uh, Bill and I realised that, uh, 55 00:06:00,750 --> 00:06:05,489 tri Maxwell mixing could actually rather be applied to the neutrinos rather than the quarks. 56 00:06:05,490 --> 00:06:10,740 And that that would be a much more sensible thing to do, because at least there was some sign of large mixing angles, 57 00:06:10,740 --> 00:06:14,880 potentially both in the solar neutrinos and in the atmospheric neutrinos. 58 00:06:15,330 --> 00:06:22,590 We weren't the first people to suggest that about 4 or 5 authors in the previous 20 years had suggested that perhaps, 59 00:06:22,620 --> 00:06:27,090 uh, neutrinos or leptons could have large rectangles, maximum mixing angles. 60 00:06:27,270 --> 00:06:30,870 But we were the people, I think, at the time who picked that up and ran with it. 61 00:06:30,870 --> 00:06:34,170 When the when the data started saying something exciting was happening. 62 00:06:34,950 --> 00:06:41,939 Uh, so then we came to the conference here in the UK, Glasgow, and Don was there, I was there, Bill was there. 63 00:06:41,940 --> 00:06:51,599 And of course we actually got talking. Uh, I'd never met Don before bill introduced me and uh, we got talking of course, about the neutrino results. 64 00:06:51,600 --> 00:07:00,450 There were new atmospheric neutrino results. And, um, there was this fantastic result, which, you know, I still remember, just like it was yesterday. 65 00:07:00,840 --> 00:07:01,070 This. 66 00:07:01,110 --> 00:07:12,210 So this what this is it's the ratio of the muon to the electron, uh, rates, um, in data divided by the expectation of that ratio from Monte Carlo. 67 00:07:12,390 --> 00:07:16,530 So of course this should be unity everywhere. And it's plotted as a function of cos theta. 68 00:07:16,530 --> 00:07:22,080 So one is the downward going neutrinos. They just travelled about ten kilometres from the upper atmosphere. 69 00:07:22,440 --> 00:07:25,590 Minus one is the upward going neutrinos. They've travelled through the Earth. 70 00:07:25,950 --> 00:07:28,620 They've gone about 10 or 15,000km whatever. 71 00:07:29,220 --> 00:07:36,180 And of course, the ones that are travelling a long way are suppressed away down with, with pretty good errors. 72 00:07:36,450 --> 00:07:43,229 So no longer was there any kind of, uh, there wasn't a serious, uh, dependence on normalisation. 73 00:07:43,230 --> 00:07:48,030 This is a self normalising curve because the one is fixed by the right hand end of the curve. 74 00:07:48,720 --> 00:07:54,810 Okay. So Don said, and I remember him saying, I've become more convinced maybe there's neutrino oscillations. 75 00:07:54,810 --> 00:08:00,730 So this was the first part of the turning point. Um, Kyoto relaxed conference. 76 00:08:00,730 --> 00:08:04,170 So many talks. He gave the latest results from Sage and Calix. 77 00:08:04,710 --> 00:08:08,940 Um, we've been saying to Don, well, you know, I'll try maximal mixing scenario. 78 00:08:09,270 --> 00:08:14,190 The suppression of the, uh, CO2 emission should be five nights. 79 00:08:14,190 --> 00:08:19,169 They should be suppressed to 5/9 of the original. Right. And Don said he looked at the this table. 80 00:08:19,170 --> 00:08:22,200 And there are two possible it's data over expectation. 81 00:08:22,200 --> 00:08:27,209 There are two models, the expectation. So there's a little bit of difference between the middle column on the right hand column. 82 00:08:27,210 --> 00:08:31,410 But basically Don said yep, the Gary Max fronts are really shouting five nights. 83 00:08:31,410 --> 00:08:36,090 And you can hear him saying that I think anyone who's, uh, spent much time with Don. 84 00:08:37,390 --> 00:08:41,170 So we go back to the, the the timeline, if you like, of 1994. 85 00:08:41,170 --> 00:08:46,200 So we realise the opportunity uh, the of the Glasgow conference and we agree. 86 00:08:46,210 --> 00:08:52,450 We talked a lot. It was very exciting. We agreed to form this collaboration, uh, after Donald retired. 87 00:08:53,110 --> 00:09:01,929 So he, he remains a busy physicist. Certainly. Um, the collaboration was to try and show or demonstrate that they were actually large rectangles. 88 00:09:01,930 --> 00:09:07,030 In fact, the try match more mixing might be the right answer. And we have, of course, a vested interest in that try. 89 00:09:07,030 --> 00:09:14,770 Maximal mixing is a very symmetric, uh, maximal anything uh is a sign of a symmetry in principle in physics. 90 00:09:15,190 --> 00:09:21,239 So the rest of the year we work together on this, uh, on, on a paper and on brought to that, uh, 91 00:09:21,240 --> 00:09:27,730 a deep knowledge of atmospheric neutrino fluxes and his healthy scepticism having only just been converted to the cause. 92 00:09:28,780 --> 00:09:36,400 So, um, what are our goals? Uh, well, of course, to fully embrace three flavours of neutrinos, most of the early work have been done. 93 00:09:36,760 --> 00:09:45,100 A lot of work has been done with two flavours of neutrinos in the solar effect, and two flavours of neutrinos in the atmospheric situation. 94 00:09:45,100 --> 00:09:49,390 Some people, of course, Roger Phillips included, had worked on three flavours neutrinos. 95 00:09:49,870 --> 00:09:53,500 But this was the way to go. Of course, they were three families of neutrinos. 96 00:09:53,950 --> 00:09:59,860 We wanted to understand all the essentially all the data on neutrino oscillations in a single unified framework. 97 00:10:00,370 --> 00:10:04,330 Keep it as simple as possible, but not simpler. So what did that mean? 98 00:10:04,360 --> 00:10:09,909 Of course, a three by three neutrino mixing matrix and two independent mass squared differences, 99 00:10:09,910 --> 00:10:14,230 the third difference obviously being just the sum of the other two effectively. 100 00:10:14,950 --> 00:10:18,400 And so we wanted to work within this theoretical framework. 101 00:10:18,850 --> 00:10:21,970 We wanted to interpret the the theory visually. 102 00:10:22,420 --> 00:10:29,620 And I'll discuss that in a few minutes. And also to be aware of the possibilities of new symmetries. 103 00:10:29,620 --> 00:10:34,449 Everything in physics today has been governed by symmetries. Perhaps there were new symmetries in particular. 104 00:10:34,450 --> 00:10:38,410 Try maximal mixing would need new symmetries. 105 00:10:39,220 --> 00:10:45,160 So what is trying Maxwell mixing? The basic idea here is you have this uh, p m and s matrix. 106 00:10:45,610 --> 00:10:49,710 The columns are labelled by the neutrino mass eigenstates one, two, three. 107 00:10:49,720 --> 00:10:55,180 The rows are labelled by the flavour, the flavours E, mu and tau, and the omegas. 108 00:10:55,180 --> 00:11:02,680 Here are just the complex cube roots of one. So of course you've got the one itself, Omega one and the number three. 109 00:11:03,040 --> 00:11:06,880 Uh uh, distributed around the circle 120 degrees to each other. 110 00:11:07,060 --> 00:11:10,690 All of them are of magnitude one. They simply have different phases. 111 00:11:11,290 --> 00:11:16,450 And so the matrix, every element has got a magnitude one over root three and modulus one over root three. 112 00:11:16,780 --> 00:11:22,330 And they all have different phases in such a way as to keep the rows and columns mutually orthogonal as they must be. 113 00:11:23,390 --> 00:11:31,010 So that was the idea. What were the predictions of that? Well, essentially that there are universal survival probabilities for all flavours. 114 00:11:31,370 --> 00:11:37,729 So the probability of each new we going to new E, which will become a function of L over years, 115 00:11:37,730 --> 00:11:43,040 will seed minute should be the same as the probability of uh mew mew mew mew. 116 00:11:43,470 --> 00:11:46,670 That's to say, the ones which don't oscillate uh, are equal. 117 00:11:46,670 --> 00:11:50,900 And you know, the probability for new targets, new, tough, eminently testable. 118 00:11:51,980 --> 00:11:56,850 So what is this? This is just a cosine squared off on a little bit of a pedestal. 119 00:11:56,870 --> 00:12:01,459 That's the prediction from um try match mixing threes. 120 00:12:01,460 --> 00:12:04,730 All right. So mixing as we call it in those things. And it's not very helpful. 121 00:12:05,150 --> 00:12:12,110 And it looks pretty horrible. And the one of the problems is we're going from not 50,000 in kilometres per GV. 122 00:12:12,140 --> 00:12:15,830 And that doesn't cover all the possibilities for all the experiments. 123 00:12:16,010 --> 00:12:23,600 So you put it on a log scale, log scale. You can go as far as you like to infinity, but of course your solutions get bunched up on the right hand end. 124 00:12:23,600 --> 00:12:28,790 We were the first people to do this, so this is quite well known in the literature from the early 80s, 125 00:12:28,790 --> 00:12:36,290 is full of plots like this from Roger Phillips and others. Um, what thing we think that I think was, was very important. 126 00:12:36,290 --> 00:12:40,910 Here is all the experiments have a resolution that the blue curve is just the theory. 127 00:12:41,220 --> 00:12:44,690 Experiments have a resolution I put on here three Gaussians. 128 00:12:44,690 --> 00:12:48,200 They look asymmetric because the log plot, they're all 30% width. 129 00:12:48,590 --> 00:12:53,270 But the point is when you measure the energy, your error is in a is a percentage. 130 00:12:53,270 --> 00:12:56,959 So the width on the log scale is constant. Okay. 131 00:12:56,960 --> 00:13:01,790 So you can see that the nice yellow one that doesn't even enclose the whole oscillation, 132 00:13:02,300 --> 00:13:07,490 um, a whole oscillation cycle, the red one on the other hand is enclosing dozens. 133 00:13:07,820 --> 00:13:13,600 Okay. So the oscillations are completely washed out by the resolution at the right hand end, but not at the left hand. 134 00:13:13,610 --> 00:13:16,640 And so what does that do? What it means. 135 00:13:17,240 --> 00:13:20,090 And I've expanded the yellow scale here a little bit. 136 00:13:20,450 --> 00:13:30,500 You've got a threshold here, uh, a single uh, reduction to a new to a plateau in try maximum mixing with plateau 5/9 height. 137 00:13:31,730 --> 00:13:36,740 Um. So the top bar of this is, I don't know. 138 00:13:36,950 --> 00:13:42,770 Yeah. The top that measures the mixing angles in some function of the mixing angles and the position along here. 139 00:13:42,980 --> 00:13:48,290 It's reciprocal. Is the delta m squared for the neutrino mass squared difference. 140 00:13:48,710 --> 00:13:54,140 So these are the observables potentially that can be a second threshold for the second squared difference. 141 00:13:54,440 --> 00:13:55,730 Going to a new plateau level. 142 00:13:56,060 --> 00:14:03,469 And that second plateau level also measures a function of the the mass square differences I mean try by Maxwell is five minus methods. 143 00:14:03,470 --> 00:14:08,810 So that's what I've drawn. Okay. So here's the data confronting the theory. 144 00:14:09,470 --> 00:14:16,610 And on this plot, essentially all the neutrino oscillation data in 1994 are shown. 145 00:14:17,720 --> 00:14:23,510 Um, you start off with the accelerators. Yeah. So this is also a function of l overy so small. 146 00:14:23,750 --> 00:14:29,330 E goes to the right and largely goes to the left. So your accelerators at the right, the subtle ones. 147 00:14:29,840 --> 00:14:34,129 Sorry. Yeah. Accelerator neutrinos are on the left. So the neutrinos are on the right. 148 00:14:34,130 --> 00:14:38,270 Partly because they're low energy, but partly also because they have very low. The sun's a very long way away. 149 00:14:38,810 --> 00:14:44,300 Then you have the reactor. So the accelerator mostly will be muon neutrinos, the reactors. 150 00:14:44,630 --> 00:14:52,040 Electromagnetic neutrinos. Atmospheric. Well, there's it's actually the double ratio that's plotted here with some corrections. 151 00:14:52,610 --> 00:14:56,600 Um, so that's mu over three. So muon and electron neutrinos essentially. 152 00:14:56,900 --> 00:15:04,639 And so of course the solar neutrinos, electron neutrinos and they all fit except this one point, this triangular point here. 153 00:15:04,640 --> 00:15:09,200 That's the the third from the home state, the longest standing one. 154 00:15:09,770 --> 00:15:12,860 Um, so we took the view here. 155 00:15:13,070 --> 00:15:18,320 That is, a lot of physicists took the view that this might actually be be not right. 156 00:15:18,320 --> 00:15:20,510 It would have been going for 25, 30 years. 157 00:15:20,930 --> 00:15:28,010 And we essentially took a gamble, I suppose, that there would be no energy dependence here, that this would be a long plateau. 158 00:15:28,040 --> 00:15:33,230 Eventually that would be another threshold going down to a third. But that the data didn't. 159 00:15:33,470 --> 00:15:38,270 Once you go down to a third here, at least in vacuum oscillations, you can't go back to five nights. 160 00:15:38,660 --> 00:15:44,150 So that's why we discounted this point essentially. And the chi squared excluding that point was a very good fit. 161 00:15:44,180 --> 00:15:47,300 20.5 over 28 for all the points. 162 00:15:48,110 --> 00:15:54,469 So. Well it worked. Uh, that was our first fit of the neutrino. 163 00:15:54,470 --> 00:15:59,990 A massive difference in difference. And delta and prime delta m prime squared was unresolved. 164 00:16:00,230 --> 00:16:04,490 And as I promised, I wanted to, uh, illustrate some of the impact we had. 165 00:16:04,790 --> 00:16:13,400 Um, Luciano Mariani at the. It's, uh, we contractions of neutrinos conference in 1997 dubbed this this wonderful plot. 166 00:16:13,760 --> 00:16:16,790 So, of course, we don't usually hear what people think of your work, 167 00:16:16,790 --> 00:16:21,860 but if you happen to be in the audience, you sometimes, you know, that's nice to hear. 168 00:16:22,250 --> 00:16:26,600 Okay, we got some more nice feedback now. This was one was interesting, joked Harrison. 169 00:16:26,600 --> 00:16:33,500 This was, uh, I didn't know John Bacall. John Bacall was the father of the standard Solow model, essentially, 170 00:16:33,710 --> 00:16:43,190 and he spent many years of his career calculating the rate of solid neutrinos, which form the denominator for all the solar neutrino experiments. 171 00:16:43,670 --> 00:16:48,860 And he said, I think you must have just addressed it to me, because mine was the first name on the paper and he knew Don. 172 00:16:49,310 --> 00:16:53,060 He's like me, and I didn't know if you wrote me your preprint with Perkins. 173 00:16:53,060 --> 00:16:57,410 Scott is extremely interesting to me. It's a very nice idea, well argued and presented. 174 00:16:57,800 --> 00:17:01,220 I don't think he really liked it because he liked the Mass Effect. 175 00:17:01,220 --> 00:17:05,810 And of course we said there's no Mass Effect, but he was being very polite and very, very proper. 176 00:17:06,230 --> 00:17:10,880 Um, so we wrote back and in fact, we had quite a correspondence with him, and Don wrote to him. 177 00:17:11,210 --> 00:17:15,440 Um, and that was all very nice. So just as a sort of interlude. 178 00:17:15,440 --> 00:17:20,510 So a little bit about working with Don, I don't remember getting emails from Don. 179 00:17:20,720 --> 00:17:23,990 Maybe I got some I haven't looked because I've moved universes. 180 00:17:23,990 --> 00:17:30,590 I can't get his email accounts. I do have an archive somewhere, but I got letters from Don. 181 00:17:30,800 --> 00:17:37,220 Loads of letters, letters and faxes. Okay, we have mobile phones in those days. 182 00:17:37,550 --> 00:17:46,670 So, um, gentleman to Paul and go gentleman his his, uh, my offering on the paragraph on atmospheric neutrino oscillations in his inimitable hand. 183 00:17:46,970 --> 00:17:52,320 And this one, this is my favourite one over here. I'll. You stand an extra chance of being sued. 184 00:17:52,620 --> 00:17:56,880 Was with was his reaction to one of our drafts. 185 00:17:57,060 --> 00:18:00,180 He felt that we hadn't given due credit to one of the experiments. 186 00:18:00,330 --> 00:18:07,830 Well, I'm sure he was right. And Don was very good at holding our feet to the fire and, uh, keep us focussed while keeping us on the ground, actually, 187 00:18:07,830 --> 00:18:14,280 because Bill and I have a tendency to to go off into more, uh, more theoretical directions, which perhaps weren't warranted. 188 00:18:15,030 --> 00:18:18,570 So I learned. Of course, I learned a vast amount from Donna. 189 00:18:18,840 --> 00:18:24,629 It was a great thing. Um, so our second paper was this no mystery. 190 00:18:24,630 --> 00:18:28,500 So no matter of fact, in Maxwell mixing, actually, specifically in two fold. 191 00:18:28,500 --> 00:18:30,890 Maxwell mixing, uh, in the sun. 192 00:18:30,900 --> 00:18:39,390 So we were saying that if, uh, Tri Maxwell mixing was correct, there would be no matter, in fact, in the sun and there would be no dip. 193 00:18:39,990 --> 00:18:42,389 And the one on the right looks a bit like the one you've seen already, 194 00:18:42,390 --> 00:18:48,420 but it's actually plotted as delta m prime squared every, not all over it, because the distance the sun is fixed. 195 00:18:48,420 --> 00:18:52,080 We know that. So you just put L fixed and then you can make the plot. 196 00:18:52,410 --> 00:18:59,580 So what we did we did a computer program and we uh, we simulated essentially we we integrated the propagation equations, 197 00:18:59,580 --> 00:19:06,450 including the matter of fact and um, starting off with actually in vacuum with no much effect. 198 00:19:06,840 --> 00:19:14,880 And the physics here is that because the mixing angles, theta 12.79 is, uh, one over three value for the mixing angle. 199 00:19:15,330 --> 00:19:19,229 And uh, this one is a smaller angle and this one is a bigger angle. 200 00:19:19,230 --> 00:19:24,870 And you see that three of those, you get less suppression. So Maxwell mixing had the most suppression. 201 00:19:25,530 --> 00:19:33,030 But if you have a small angle, if you're coming out of the sun and the density is changing slowly as you propagate out of the sun, 202 00:19:33,540 --> 00:19:36,809 then essentially the, um, the mixing angles change with time. 203 00:19:36,810 --> 00:19:43,440 You get this dramatic, uh, change of electron neutrinos into into muon neutrinos, and you get a deficit here. 204 00:19:43,650 --> 00:19:48,389 And this deficit can actually go to essentially as close to zero as you like the smaller mixing angle, 205 00:19:48,390 --> 00:19:57,120 the lower down this gets and there's an inverse deficit, uh, an increase if the angles get bigger than actually, uh, sine one over root three. 206 00:19:57,310 --> 00:20:01,260 So for bigger mixing angles you get this anti MSW suppression. 207 00:20:01,860 --> 00:20:07,140 And we said look in the vacuum in the story in the three fold Maxwell mixing case alone. 208 00:20:07,590 --> 00:20:09,890 The third is completely unaltered. 209 00:20:09,900 --> 00:20:18,600 There is no match effect uniquely in Maxwell mixing actually two full much mixing and to some extent in the for Max Maxwell mixing as seen here. 210 00:20:19,230 --> 00:20:24,210 Um. So I didn't leave the conclusion. 211 00:20:24,720 --> 00:20:35,550 We also put in the paper little explanation of this as an analogy with the diabetic flip of a, um, a spin half magnetic moment and jump call. 212 00:20:36,150 --> 00:20:37,590 This time you send us an email. 213 00:20:38,400 --> 00:20:44,760 Uh, I was very surprised by the result, initially wondering if your computer program could possibly have been in error. 214 00:20:45,150 --> 00:20:50,070 No, it wasn't in error, but the analogy with the spin off dipole in the magnetic field is very convincing. 215 00:20:50,370 --> 00:20:54,510 Quite a remarkable result. So again we bank this. This was a nice thing to be told. 216 00:20:55,170 --> 00:20:58,800 Um, and you know, he liked the analogy, made it very clear. 217 00:20:59,820 --> 00:21:01,740 Um, that's just a picture of the analogy. 218 00:21:02,490 --> 00:21:09,900 So, um, we also made this prediction that, um, that there could be a five like one third, five months faster. 219 00:21:10,020 --> 00:21:14,100 We didn't say it applied to the data at the time. Probably we should have done it. 220 00:21:14,790 --> 00:21:16,049 Uh, it wouldn't have helped. Actually. 221 00:21:16,050 --> 00:21:21,390 It wouldn't have helped because we were still selling three fold, much more mixing, which turned out to be wrong as it happened. 222 00:21:22,170 --> 00:21:29,020 But I think all this, you know, the paper generated a lot of excitement, a lot of interest, and got people thinking about this and that. 223 00:21:29,040 --> 00:21:36,929 That's part of the legacy, I think. So, um, as I've said, I've just put on this these point data points weren't put on at the time. 224 00:21:36,930 --> 00:21:43,450 These are the, the modern, uh, the the modern points, the, the error bars are roughly comparable to the size of the points. 225 00:21:43,480 --> 00:21:48,870 I didn't it's just a sketch really, but it shows, um, that you've walked, uh, snow, uh, 226 00:21:48,870 --> 00:21:53,099 discovery essentially that we're in the large mixing mystery thing which which we kind of said, 227 00:21:53,100 --> 00:21:57,509 well, this is what the bathtub will look like in the bath. We didn't like the name Bath tub. 228 00:21:57,510 --> 00:22:05,280 I don't know who made who made the name bathtub, I have no idea. But anyway, um, we predicted at least a five nights, two bath tub. 229 00:22:06,660 --> 00:22:09,870 Um, so I'm not going to talk very much about these two papers. 230 00:22:10,140 --> 00:22:19,469 Uh, three and four. Um, the only thing to say is these are the four possibilities for what's happening at the solar scale, 231 00:22:19,470 --> 00:22:23,160 at the far right and end of the US, which is three for maximum mixing. 232 00:22:23,160 --> 00:22:27,990 Nothing interesting happening. These are the data points. Um, this is the small angle. 233 00:22:28,500 --> 00:22:32,670 As I said, it could go to zero and then come back up. This is the large angle of view. 234 00:22:32,670 --> 00:22:35,040 The five minutes to five nights bathtub. 235 00:22:35,220 --> 00:22:41,370 And this is the so-called, uh, this is blackouts just so oscillations that even he said was fine tuned when he published it. 236 00:22:41,850 --> 00:22:46,080 Um, but anyway, we felt these were fine tuned and say they were disfavoured. 237 00:22:46,470 --> 00:22:54,270 Don't have an anecdote. He was in the US some years before I met him, and he was giving a talk, apparently explaining the MSW effect. 238 00:22:54,600 --> 00:22:59,970 And Chandrasekhar was in the audience and Chandrasekhar says, yeah, leave that to you. 239 00:23:00,720 --> 00:23:06,960 So, um, I don't know if that influenced on, but we we, you know, the fine tuning seemed to be an issue at least. 240 00:23:07,740 --> 00:23:11,070 Oops. Coincidences do happen, but they don't happen so often. 241 00:23:11,820 --> 00:23:16,379 Um, and our prediction here of this third paper was spectacular. 242 00:23:16,380 --> 00:23:22,680 Effects will be expected. Long baseline reaction centre experiments choose Palo Verde, Minos, etc. 243 00:23:23,610 --> 00:23:28,409 Uh, no spectacular effect. So this is the two reactor results. 244 00:23:28,410 --> 00:23:33,690 It's um, uh, one kilometre three MeV energy. 245 00:23:33,960 --> 00:23:37,430 No spectacular effect. So this trial, Maxwell mixing is wrong. 246 00:23:37,440 --> 00:23:42,150 We were excluded from this point. Um, E3 squared has to be small. 247 00:23:42,690 --> 00:23:47,219 Could be zero. Might be just. Just a small number. So that was the end of try. 248 00:23:47,220 --> 00:23:52,530 Max might say that they've worked. Sno collaboration came out with this again, 249 00:23:52,530 --> 00:23:59,910 a third confirming the Homestake third and putting the final nail in the coffin of Tiber Tri Maxwell mixing. 250 00:24:00,270 --> 00:24:05,250 So I mean Maxwell mixing excluded. Long live tri by Maxwell mixing. 251 00:24:07,200 --> 00:24:12,020 So the fifth and final paper I'm going to talk about today HP, S5. 252 00:24:12,540 --> 00:24:18,690 Um, so data is king. We made a virtue of necessity and put out a new mass matrix. 253 00:24:19,380 --> 00:24:27,990 Um, the the 5/9 to bath bathtub was in fact, uh, confirmed beautifully by snow. 254 00:24:28,200 --> 00:24:33,000 And, um, uh, so I'm going to just mark the data point speak for themselves. 255 00:24:33,510 --> 00:24:37,950 We originally had up to scratch the third. We still had u e2 square root of a third. 256 00:24:39,030 --> 00:24:44,820 The super K atmospheric neutrino was strongly pointing to larger values. 257 00:24:45,360 --> 00:24:51,210 Umu three and Utah three. I'll show you these on a actually on a on a matrix in a minute. 258 00:24:51,990 --> 00:24:55,380 And so we accepted the half here. We accepted the third here. 259 00:24:55,860 --> 00:24:59,130 And we accepted the previous zero, the very small number. 260 00:24:59,730 --> 00:25:07,410 And that of course dictates the form of the matrix. So we had here the reactor max angle the show limit. 261 00:25:07,890 --> 00:25:13,379 So this was either small or zero. If you got a number small in physics that could be anything. 262 00:25:13,380 --> 00:25:19,200 It's probably zero. Or you've got a symmetry. Make it zero or maybe have a slightly broken symmetry. 263 00:25:19,590 --> 00:25:22,860 The atmospheric new moon Utah maximal mixing here. 264 00:25:23,340 --> 00:25:27,210 This is the two three scale for the atmospheric neutrinos. 265 00:25:27,570 --> 00:25:30,870 The universal survival probability was no longer valid. 266 00:25:31,620 --> 00:25:37,710 Uh, we had a solar mixing angle here that we still was saying should be one over three on aesthetic grounds 267 00:25:38,160 --> 00:25:44,430 and a solar mass scale trials from one to square the five parameters of neutrino oscillations. 268 00:25:44,610 --> 00:25:52,329 And we put in a little, uh, a little legal clause here, smaller non-zero values of E3 and somewhat different values. 269 00:25:52,330 --> 00:25:57,150 If you if you use things that are more or less equally acceptable experimentally. 270 00:25:57,330 --> 00:26:02,130 So we're pinning all colours to this masked world, allowing the possibility that we might be wrong. 271 00:26:02,280 --> 00:26:05,970 It's a very sensible. Of course. Um. 272 00:26:07,150 --> 00:26:11,000 I promised you. This is the only really mathematical slide, I hope. 273 00:26:11,030 --> 00:26:13,689 Um, symmetries of tribal mixing, 274 00:26:13,690 --> 00:26:22,600 as we know that the mixing matrix exists because the mass matrices of the two charge states in the doublets of the weak interaction. 275 00:26:22,900 --> 00:26:26,050 Here the charged leptons and the nutrients have different forms. 276 00:26:26,200 --> 00:26:29,620 They can't be diagonalised at the same time. And that then gives you a mixing. 277 00:26:30,130 --> 00:26:37,150 And so what the way to build tri by Maxwell mixing here is you have what we call um a circulant matrix. 278 00:26:37,150 --> 00:26:40,120 So this is simply invariant under the discrete transformation. 279 00:26:40,600 --> 00:26:46,130 Generation one and two two goes to three and three goes to one cyclically doesn't change. 280 00:26:46,270 --> 00:26:50,650 Okay. And if you do uh if you flip a pair it's complex conjugates. 281 00:26:50,860 --> 00:26:54,850 This one it's invariant under one free interchange okay. 282 00:26:55,330 --> 00:26:58,740 If you want to diagonalise that you use the original tri Maxwell matrix. 283 00:26:58,750 --> 00:27:02,470 If you want to diagnose that, use A13 by Maxwell. 284 00:27:03,070 --> 00:27:10,510 And you know, find together. This is what how you build the mixing matrix from a modal and you get a mixing matrix out. 285 00:27:11,710 --> 00:27:15,930 Today's setting is a colloquium at CERN. 286 00:27:15,960 --> 00:27:22,080 You can find the video of this bill. Scots very fond of showing people the idea of this because he says it's a tremendous achievement. 287 00:27:22,580 --> 00:27:30,810 Um, I'm quite an exaggeration, I think, but, uh, although some, some, you know, we, we got we got people's attention at least. 288 00:27:31,850 --> 00:27:34,940 So the future. Um. 289 00:27:36,640 --> 00:27:42,310 This is, uh, the Juno experiment, which is another reactor experiment in China. 290 00:27:42,670 --> 00:27:45,640 It's about to start taking data this year, any time now. 291 00:27:46,120 --> 00:27:52,029 They are, amazingly, claiming that they're going to be sensitive to the atmospheric mass scale, 292 00:27:52,030 --> 00:28:00,430 these short wavelength oscillations, while at the same time being sensitive to the solar scale, this long wavelength oscillation. 293 00:28:00,940 --> 00:28:04,810 This is the survival probability of the electrons and neutrinos. 294 00:28:05,200 --> 00:28:08,229 This is the appearance probability, the sort of complement of that. 295 00:28:08,230 --> 00:28:15,309 And this I think the blue and the redder than normal in the inverted hierarchy, which is something that just the way the, the uh, 296 00:28:15,310 --> 00:28:26,260 the mass uh eigenstates are ordered in the um for the neutrinos and they claim a 1% resolution Eui to del 21 squared and delta m three squared. 297 00:28:27,010 --> 00:28:31,630 And, uh, they could resolve the question of the neutrino mass ordering of three sigma. 298 00:28:33,040 --> 00:28:37,180 Uh, the Holy Grail for CP violation. Mark Thompson touched on this. 299 00:28:37,990 --> 00:28:43,150 As you know, E3 is non-zero. Um, and all the other angles and non-zero. 300 00:28:43,270 --> 00:28:51,370 That means you can have CP violation if the phase in the p, m and S matrix is non-zero and not equal to pi. 301 00:28:51,940 --> 00:28:57,730 And these two experiments hyper k, I don't. My apologies to anyone who works on these because I don't know anything about them. 302 00:28:58,300 --> 00:29:15,730 Um, but um, hyper K claim a five sigma level of sensitivity to CP violation over 57% of the range of the CP phase delta by after ten years of running. 303 00:29:15,730 --> 00:29:21,790 And this is a truly an almost. It's like Minos that Mike was talking about bigger and much more powerful beam in Japan. 304 00:29:22,420 --> 00:29:29,379 Mark. Mark mentioned June, of course, you guys involved in both these explosions, more in June and amazing. 305 00:29:29,380 --> 00:29:34,240 They also have a five sigma sensitivity over 57% of the possible range. 306 00:29:34,510 --> 00:29:38,620 Oh, for ten years. So this is a completely different experiment. 307 00:29:38,710 --> 00:29:41,860 Different beam lines, different, uh, path lengths. 308 00:29:41,860 --> 00:29:44,860 So they just happened to both come to exactly the same sensitivity. 309 00:29:45,250 --> 00:29:50,470 Um, uh, coincidence? No doubt. So, um, my time is nearly up. 310 00:29:50,500 --> 00:29:55,210 I just did want to say something about what I considered the legacy of this work. 311 00:29:55,360 --> 00:29:59,980 Um, that Don, um, Bill and I did. 312 00:30:00,640 --> 00:30:07,420 He decided to leave the collaboration on a high, um, making HB five his last publication with us. 313 00:30:08,170 --> 00:30:11,530 Um, TBM was finally executed ten years later. 314 00:30:12,400 --> 00:30:20,710 Um, so, um. Because as with the loud, the little pause for you is not to be zero. 315 00:30:20,950 --> 00:30:25,090 It was executed by Daya, by Reno and to take um. 316 00:30:26,750 --> 00:30:32,270 This single paper, Pierce five, has been cited by over 1500 phenomenology papers. 317 00:30:32,270 --> 00:30:35,899 This is the citation count inspires or inspire hope, as they call it. 318 00:30:35,900 --> 00:30:39,410 Now this is the paper. Yeah, this is about where we got excluded. 319 00:30:39,860 --> 00:30:44,389 I was so [INAUDIBLE] up a few dozen citations a year, nearly all from Phenomenologist. 320 00:30:44,390 --> 00:30:47,570 Why? Because they like the symmetric forms of mass matrices. 321 00:30:47,570 --> 00:30:57,080 They suggest deeper symmetries and they can build, uh, they can build models whose end result is matrices with these symmetries that we discussed. 322 00:30:57,380 --> 00:31:08,360 So I think that's that's an impact, as the politicians like to tell us, uh, it's purely an academic impact, but a very valuable one, I believe. 323 00:31:08,960 --> 00:31:20,060 Um. 120 experimental publications cited five, including several of the proposals for the experiments that I've mentioned. 324 00:31:20,750 --> 00:31:29,389 And um, I would say, uh, reflecting exactly what Mark said, I think when, when we when we started this in 1994, 325 00:31:29,390 --> 00:31:37,549 the UK, uh, experimental neutrino community had shrunk over the years, and they came and joined us and other people. 326 00:31:37,550 --> 00:31:43,540 And I think this work, many people have done a vast amount to build that up again. 327 00:31:43,550 --> 00:31:48,110 But I think this work had a little bit to do with encouraging that from the start. 328 00:31:48,890 --> 00:31:56,900 Um, this I love plot that we showed and variance of it, I think had a significant impact, as I think I've demonstrated. 329 00:31:57,830 --> 00:32:05,510 And, uh, Bill and I have published 25 further papers on topics very closely related to this work. 330 00:32:06,230 --> 00:32:12,350 And because you three square is non-zero, it does allow the possibility of CP violation in the future. 331 00:32:13,070 --> 00:32:22,640 So, um, uh, all I'm done, all apart from uh, saying, you know, I'm extremely grateful to have had the opportunity to do this work with Don and Bill. 332 00:32:22,970 --> 00:32:26,090 It was one of the most exciting parts of my career. 333 00:32:26,650 --> 00:32:27,380 Thank you very much.