1 00:00:00,000 --> 00:00:06,660 Hello, everyone. And my talk is going to be about the issues related to the 2 00:00:06,660 --> 00:00:12,240 application of the effective field theory in the search for new physics in vector 3 00:00:12,240 --> 00:00:20,250 boson scattering processes at the LSE. What I am going to show is based on 4 00:00:20,610 --> 00:00:27,060 studies and work done by several people, including CMS physicists, such as myself, 5 00:00:27,450 --> 00:00:32,010 and as well as theorist. I'm not a theorist. So it's maybe too much to say 6 00:00:32,010 --> 00:00:38,730 that this is a theory talk, but it will be somewhere in between the experiment I hope 7 00:00:38,730 --> 00:00:44,370 that will be suitable for everybody. So let's move on to the second page. I have 8 00:00:44,370 --> 00:00:49,530 one slide of introduction about the vector boson scattering, which I don't really 9 00:00:49,530 --> 00:00:54,840 think I need to go through in the details, but let me just say that in terms of the 10 00:00:54,870 --> 00:01:00,630 EFD expansion, in principle, we can say that in vector boson scattering processes 11 00:01:00,630 --> 00:01:07,260 we can probe. The dimension six operators that affect the triple gauge couplings, 12 00:01:07,260 --> 00:01:13,920 the Higgs to gauge couplings and at least some of them affect only also the quartic 13 00:01:13,920 --> 00:01:19,260 couplings. And we can probe the dimension eight operators that affects only the 14 00:01:19,260 --> 00:01:24,720 quartic couplings. Now, traditionally VBS analysis are focused on the dimension 15 00:01:24,750 --> 00:01:30,540 eight operators and the related quartic couplings because they are the best 16 00:01:30,540 --> 00:01:39,420 processes to study them. And I am not going to discuss this issue of how much it 17 00:01:39,420 --> 00:01:47,190 is justified to to omit dimension six and go directly to dimension eight because 18 00:01:47,220 --> 00:01:53,280 opinions differ already at that point, but for for the purpose of this talk, I will 19 00:01:53,280 --> 00:01:58,440 just assume that we are interested here in the quartic couplings and the associated 20 00:01:58,440 --> 00:02:07,170 dimension eight operators Okay. And yes, so let's go to page three. And of course, 21 00:02:07,170 --> 00:02:11,850 the important issue that we immediately have to face is the problem of unitarity. 22 00:02:11,850 --> 00:02:18,780 So let me just briefly recall that there's been two main philosophies that has been 23 00:02:18,900 --> 00:02:24,540 been in used by by experimental groups, how to deal with this problem of 24 00:02:24,540 --> 00:02:33,630 unitarity. In GPS data analysis. The first approach is what we what we used to do in 25 00:02:33,630 --> 00:02:39,630 CMS, at least up to now, okay, which is simply to disregard the unitarity limits. 26 00:02:39,630 --> 00:02:47,130 So, so to to, to apply the EFT expansion as if the unitary It was not a thing. And 27 00:02:47,130 --> 00:02:52,470 of course, as long as what we want is to have some some mathematical tool to to 28 00:02:52,710 --> 00:02:57,900 quantify the precision the relative precision of the data and the degree of 29 00:02:57,900 --> 00:03:03,930 agreement or disagreement with the status The model this is fair enough, but 30 00:03:04,110 --> 00:03:10,200 unfortunately in this way we give up the physics interpretations the numbers we get 31 00:03:10,320 --> 00:03:14,760 do not have the right physics interpretation in the EFD framework. Of 32 00:03:14,760 --> 00:03:19,380 course, there would be no difference then no no problem at all. If the if the 33 00:03:19,380 --> 00:03:24,510 unitarity limits were so far away that we would not see them anyway, but this is not 34 00:03:24,510 --> 00:03:32,010 the case unfortunately, in within the range of parameters that we are sensitive 35 00:03:32,010 --> 00:03:38,280 to unitarity violation happens well within the measure branch, okay. And the other 36 00:03:38,280 --> 00:03:43,740 philosophy was to apply some kind of unitary ization technique, like for 37 00:03:43,740 --> 00:03:51,090 instance, the favorite technical class was was the K matrix, the technique that 38 00:03:51,090 --> 00:03:56,550 assumes amplitude saturation at the unitarity limit, and this is usually sold 39 00:03:56,550 --> 00:04:02,640 as the physics significance of this is described The maximum possible signal 40 00:04:02,820 --> 00:04:09,270 related to a given operator. The problem is that there is no unique prescription to 41 00:04:09,270 --> 00:04:15,120 the unit unit derive the amplitudes. And again in the parameter range that we are 42 00:04:15,120 --> 00:04:23,490 sensitive to your result is driven mainly by whatever you assume. Extra. Okay, so so 43 00:04:23,490 --> 00:04:30,600 it's like part of a more complex model. So the first question that I would like to 44 00:04:30,600 --> 00:04:35,820 address in this talk is how to render the experimental numbers more difficult, but 45 00:04:35,820 --> 00:04:42,900 at the same time to keep them as model independent as possible. And the next page 46 00:04:42,900 --> 00:04:43,410 please. 47 00:04:45,660 --> 00:04:52,290 So first, let me focus on on some facts about the EFT validity catalog. So by 48 00:04:52,290 --> 00:04:59,490 construction, EFT validated stops at the scale of lumba, which is supposed to be 49 00:04:59,490 --> 00:05:05,880 the scale of new physics, and lambda is not equal to the unitarity limit, but it's 50 00:05:06,060 --> 00:05:12,030 rather it may be maximally equal to the unitarity limit, but it may as well be 51 00:05:12,210 --> 00:05:18,540 arbitrarily lower than that theory actually does not predict the value of 52 00:05:18,540 --> 00:05:24,510 lambda n the only way for us to get to know the value of lambda is to deduce it 53 00:05:24,510 --> 00:05:33,390 from the data. So, that is one thing, then I will not insist on whether lambda is one 54 00:05:33,390 --> 00:05:37,860 value for all the higher dimension operators or there can be different 55 00:05:37,860 --> 00:05:42,300 lambdas for different operators. I mean this I guess it depends on the underlying 56 00:05:42,300 --> 00:05:49,110 physics. But I will insist because this this follows from from construction that 57 00:05:49,110 --> 00:05:56,040 for a given operator, lambda is just one value and it applies to all the individual 58 00:05:56,070 --> 00:06:03,090 amplitudes that are affected by this given operator. Even if the individual unitarity 59 00:06:03,090 --> 00:06:09,390 limits of the single amplitudes are are much larger than that and this is relevant 60 00:06:09,390 --> 00:06:14,700 for instance to to the to the individual amplitude of the different Felicity 61 00:06:14,700 --> 00:06:21,000 combinations of the initial and final state as I will show in the next slide or 62 00:06:21,000 --> 00:06:27,270 maybe the next to next and this is also relevant to different processes if they 63 00:06:27,300 --> 00:06:35,610 probe the same coupling and if, if they are sensitive to the same set of higher 64 00:06:35,610 --> 00:06:39,870 dimension operators. Why is this important? Well, because for instance in 65 00:06:39,870 --> 00:06:46,230 the WWE process, we have the same sign WW and we have the opposite sign that the 66 00:06:46,230 --> 00:06:51,120 process experimental is may be more interested in the same sign process 67 00:06:51,120 --> 00:06:56,850 because it's it has much less background, but it happens that both of them probe 68 00:06:56,850 --> 00:07:01,830 actually the same coupling and it is the opposite Same process that breaks 69 00:07:01,830 --> 00:07:07,110 unitarity faster than the same same process. Here we have three examples of 70 00:07:07,110 --> 00:07:12,900 that and you can see that the difference is actually quite large. And even the from 71 00:07:12,900 --> 00:07:17,700 the experimental point of view, we are only interested in the same same process, 72 00:07:17,730 --> 00:07:22,650 we have to consider the unitarity limits that follow from the opposite sign 73 00:07:22,650 --> 00:07:27,870 process, which are the limits that are relevant for us. And by the way, the same 74 00:07:27,870 --> 00:07:36,420 also goes for w z and z z, because both processes probe the same quartic coupling 75 00:07:36,420 --> 00:07:44,850 ww z z and usually zz brakes unitarity faster than w z. So, this defines the 76 00:07:44,850 --> 00:07:52,290 unitarity limit that is relevant in this case. Then on the next slide, this is 77 00:07:52,290 --> 00:07:59,880 slide five now, I am showing here the the energy dependencies of the cross section 78 00:08:00,000 --> 00:08:06,930 In the same sign WWE scattering process this is calculated for on shell W's in the 79 00:08:06,930 --> 00:08:12,180 presence of an anomalous Quark the gauge coupling for different dimension eight 80 00:08:12,210 --> 00:08:18,750 operators and for for each dimension eight operators there are several values of the 81 00:08:18,750 --> 00:08:21,510 corresponding Wilson coefficient depicted here. 82 00:08:23,040 --> 00:08:29,130 The standard model is of course, this this purple curve which is which is falling all 83 00:08:29,130 --> 00:08:36,210 the way down okay and the relevant unitarity limits are marked here with 84 00:08:36,450 --> 00:08:41,550 ethical lines for for every value of supply efficient and what we observe here 85 00:08:42,210 --> 00:08:49,680 is that the whenever the cross section starts to deviate from the Standard Model 86 00:08:49,680 --> 00:08:56,250 value in a in a measurable way so to say we immediately hit the unitarity limit so, 87 00:08:56,280 --> 00:09:02,760 the measurable bsm effects are confined to A very narrow origin which is just before 88 00:09:02,760 --> 00:09:08,100 the unit article and essentially either you measure nothing by nothing I mean the 89 00:09:08,100 --> 00:09:12,690 standard model in this case or we immediately run into trouble with the 90 00:09:12,690 --> 00:09:19,650 unitarity limit. So, already at this point, we see that the we may we may have 91 00:09:20,250 --> 00:09:26,700 a difficulty here, then the next plot I would like to show on page six is this is 92 00:09:26,700 --> 00:09:34,920 again the energy dependence of of the same sign WWE scattering process, but in the 93 00:09:34,920 --> 00:09:41,220 presence of the FT one operator for some arbitrary bug to have it, but this time 94 00:09:41,220 --> 00:09:47,220 this is decomposed into the individual Felicity combinations of the initial and 95 00:09:47,220 --> 00:09:53,310 final state. So, in principle we have three to the fourth come in fellas and the 96 00:09:53,310 --> 00:09:58,260 combinations which is a the one that if you consider all the symmetries related to 97 00:09:58,260 --> 00:10:03,510 the fact that it's for identity apart because we ultimately end up with certain 98 00:10:03,570 --> 00:10:08,550 amplitudes that are really independent of each other. And they are listed on this 99 00:10:08,550 --> 00:10:15,780 table here on the right hand side. So what we see here is that the individual energy 100 00:10:15,780 --> 00:10:20,490 dependencies are very different from each other. And also from this table we see an 101 00:10:20,490 --> 00:10:25,740 important fact that the individual unitarity limits for this individual 102 00:10:25,740 --> 00:10:31,710 amplitudes vary quite a lot. Okay, so if you were to unit there is every amplitude 103 00:10:31,710 --> 00:10:36,570 separately on its own, you could even end up with a completely different signal 104 00:10:36,570 --> 00:10:41,610 estimate which is however, not consistent with the principles of the EFT which 105 00:10:41,610 --> 00:10:48,630 requires to make a one cutter for them all. In this particular case, the 106 00:10:48,630 --> 00:10:56,220 unitarity limit calculated from t matrix diagonalization is marked by this vertical 107 00:10:56,220 --> 00:11:02,190 line on the plot which is just below three TV and this is the value that is relevant 108 00:11:03,210 --> 00:11:10,530 everywhere here in this case, five minutes. So, yes okay. So the fact is that 109 00:11:10,530 --> 00:11:17,820 the page seven please So the fact is that the FT does not provide any predictions 110 00:11:17,820 --> 00:11:22,920 for above lamda. So the best thing we can do is not to use this region if we want to 111 00:11:22,920 --> 00:11:28,830 do EFT description. So what does this imply in practice for zz it's relatively 112 00:11:28,830 --> 00:11:34,170 easy because the invariant mass is known it is measured so we can simply place a 113 00:11:34,170 --> 00:11:39,960 cut on the data remove events, which light above the assumed cutoff value and either 114 00:11:39,960 --> 00:11:48,780 set limits or feed bsm accordingly for w z and wV Well, here the situation is tricky 115 00:11:48,780 --> 00:11:53,940 in principle, we can recover, try to reconstruct the invariant mass of the 116 00:11:53,940 --> 00:12:01,470 system but there are two problems to deal with somehow one is the the The jet PT 117 00:12:01,470 --> 00:12:08,730 resolution that that limits the resolution of the environment mass determination. The 118 00:12:08,730 --> 00:12:15,690 other one is that the kinematics of the neutrino, which was the reconstruction, it 119 00:12:16,110 --> 00:12:22,080 has a quadrat is subject to a quadratic ambiguity. So, there are some ideas how to 120 00:12:22,080 --> 00:12:27,030 solve this ambiguity and this is under progress now in CMS, but as long as we 121 00:12:27,030 --> 00:12:32,250 don't have that, then the situation becomes similar to what we have in WWE 122 00:12:32,250 --> 00:12:38,370 here that this problem is serious, because we have two new trainers with which means 123 00:12:38,370 --> 00:12:43,050 no experimental access to the invariant mass. So, the measured signal is in 124 00:12:43,050 --> 00:12:49,470 general always a sum of the region below lambda and above lambda where one region 125 00:12:49,470 --> 00:12:55,020 we can apply the EFT in the other region you cannot. Okay and the only way to 126 00:12:55,020 --> 00:13:00,840 correctly use the FT to apply the data is to make sure this the second region does 127 00:13:00,840 --> 00:13:05,010 not contribute significantly to what we measure you never know it from the data, 128 00:13:05,010 --> 00:13:11,370 but you can verify it from the simulation. Next page and this is this is what happens 129 00:13:11,370 --> 00:13:18,570 for for the same sign w for the for the WWE process in general. So in general, 130 00:13:18,600 --> 00:13:23,910 normally what we do is we measure the distribution of some physical observable, 131 00:13:23,910 --> 00:13:28,200 which is not the invariant mass because we don't have access to that, but which is 132 00:13:28,200 --> 00:13:33,000 whatever variable offers the best sensitivity to new physics. And we can 133 00:13:33,000 --> 00:13:38,760 define the DSM signal as the enhancement over the standard model prediction in 134 00:13:38,760 --> 00:13:40,380 terms of this distribution. 135 00:13:41,910 --> 00:13:50,160 So, what we measure is always a sum of the regions from zero to lambda and where the 136 00:13:50,190 --> 00:13:55,380 which is the EFD control region and from lambda to infinity, which is some tail. 137 00:13:55,680 --> 00:14:00,000 Okay, we don't know what to expect, but realistically there will be some signal 138 00:14:00,000 --> 00:14:06,420 There, but ideally what we would like in order to apply the EFT is what was called 139 00:14:06,420 --> 00:14:14,160 here the EFT signal which is defined by analogy but only restricted to the EFT 140 00:14:14,160 --> 00:14:19,890 controller engine above lambda, you put no additional signal which means only the 141 00:14:19,890 --> 00:14:27,480 Standard Model distribution and the two must be indistinguishable within 142 00:14:28,050 --> 00:14:34,980 statistical errors in order for the EFT description be viable for for what we 143 00:14:34,980 --> 00:14:41,010 measure and this is only true in a very restricted range of f lambda. So, if we go 144 00:14:41,010 --> 00:14:50,610 to the next page one minute. So, if you draw this plane f versus lambda or lambda 145 00:14:50,610 --> 00:14:55,590 versus f from from the top you have origin which is forbidden due to the unitary 146 00:14:55,590 --> 00:15:03,300 condition from the left hand side, you have a region where The bsm signal is not 147 00:15:03,300 --> 00:15:09,480 significant enough to be detected and in addition, this EFD consistency criteria 148 00:15:09,510 --> 00:15:16,290 imposes an additional bond. So, from the right hand side we have a region where yes 149 00:15:16,290 --> 00:15:24,330 we can measure VSM signal but we want to be able to describe it using the EFT 150 00:15:24,330 --> 00:15:29,880 because there is too much coming from this from the region above lambda. And this has 151 00:15:29,880 --> 00:15:34,860 been the sub the subject of a detailed simulation work and I will just just 152 00:15:35,460 --> 00:15:43,050 quickly flash the result on the next page this is so what is left is some what I 153 00:15:43,050 --> 00:15:48,150 call EFT triangles mainly because the region is bound from from three sides but 154 00:15:48,150 --> 00:15:53,040 of course the shape can be more fancy than that. So for the individual dimension 155 00:15:53,070 --> 00:15:57,450 eight operators, it looks like that so there are some ranges where this is 156 00:15:57,450 --> 00:16:02,040 possible, but they are rather narrow and better. mind that this is just a generator 157 00:16:02,040 --> 00:16:07,770 level study. So the sensitivity is still bound to degrade significantly once we 158 00:16:07,770 --> 00:16:14,820 plug in the full detector simulation. Okay, and now the second the next page. 159 00:16:15,570 --> 00:16:20,190 The second case is one more related to what we're currently doing CMS because we 160 00:16:20,190 --> 00:16:26,640 have not observed any bsm signal so far. So how to set limits on vsms so that it's 161 00:16:27,240 --> 00:16:33,360 useful to the theory community consistent with the EFT. And here again, the EFT does 162 00:16:33,360 --> 00:16:38,670 not predict what's happening above lambda, but only the most conservative signal 163 00:16:38,670 --> 00:16:43,230 estimate will provide the limits that are guaranteed to be true. Anything else we 164 00:16:43,230 --> 00:16:47,610 assume might not be true. And the most conservative signal estimate is what is 165 00:16:47,610 --> 00:16:52,170 given by this, this so called clipping technique that maybe I don't need to 166 00:16:52,170 --> 00:16:57,660 explain because it's or you can ask me if you like, but since I am running out of 167 00:16:57,660 --> 00:17:05,310 time, I will only show them Next page which is page 12. Okay, in the brand new 168 00:17:05,310 --> 00:17:11,430 paper coming from CMS that appeared like two weeks ago or so, the clipping 169 00:17:11,430 --> 00:17:17,010 technique for the first time was was implemented okay here, we use the events 170 00:17:17,010 --> 00:17:22,350 clipped at the respective unitarity lemons This is a combination This is a new 171 00:17:22,350 --> 00:17:29,220 analysis of the same sign w W and W see the channels and their combination from 172 00:17:29,220 --> 00:17:34,380 data collected during the entire run to and the novel feature is the 173 00:17:34,410 --> 00:17:41,160 implementation of this clipping technique. Not unexpectedly the impact on the results 174 00:17:41,220 --> 00:17:48,420 of considering the unitarity limits is quite large okay because in this range of 175 00:17:48,420 --> 00:17:53,550 parameters that we are sensitive to the unitarity limits are rather low of the 176 00:17:53,550 --> 00:18:01,440 order of 1.5 TVs. So that's well be well within the measured range. Okay, let me 177 00:18:01,440 --> 00:18:07,410 very quickly just show the results page 13. Here you have the the current limits 178 00:18:07,410 --> 00:18:14,430 on dimension eight operators on top you have using using this standard CMS 179 00:18:14,430 --> 00:18:19,080 procedure which is disregarding the unitary condition on the bottom you have 180 00:18:19,080 --> 00:18:22,260 the same table but with the clipping 181 00:18:24,090 --> 00:18:29,280 applied at the unitarity limit as you can see, the difference is really large. 182 00:18:30,360 --> 00:18:37,560 Generally the bounce the limits become weaker by a factor like four or five Okay, 183 00:18:37,560 --> 00:18:43,530 so in some in some cases, the bounds are pretty weak I mean if the Wilson 184 00:18:43,530 --> 00:18:49,560 coefficient is much larger than one then of course it brings up other problems, but 185 00:18:49,560 --> 00:18:55,050 this is where we realistically are okay and this is the way that that we are going 186 00:18:55,050 --> 00:19:01,110 to follow. So I am ready to conclude now and what I was trying to show Is that the 187 00:19:01,110 --> 00:19:08,400 usefulness of the EFT to study in PBS? The data is rather limited for several reasons 188 00:19:08,400 --> 00:19:13,920 that I outlined here. But we are implementing the clipping technique, which 189 00:19:13,920 --> 00:19:20,100 in my personal opinion is the correct way of analyzing the data. If we want to go 190 00:19:20,100 --> 00:19:26,160 for for physics interpretation, eventually it would like to learn something about the 191 00:19:26,160 --> 00:19:33,060 underlying physics from it. I didn't say my Yeah, thank you. Okay. Yes, that's it. 192 00:19:33,060 --> 00:19:33,480 Thank you. 193 00:19:35,250 --> 00:19:39,900 Yeah, thank you. Me, huh. We have maybe time for one question. 194 00:19:49,980 --> 00:19:55,590 And the question and so I mean, I would like to know slide 14 how a mature Pareto 195 00:19:55,590 --> 00:20:09,060 analysis can overcome the Should that you show the slide the slide? The issue that I 196 00:20:09,060 --> 00:20:16,920 show once, I mean the fact that the space in which you can say even CFT in a 197 00:20:16,920 --> 00:20:21,990 sensible way, it's that limited how much you're very nice you can overcome because 198 00:20:21,990 --> 00:20:23,280 at the end you say that 199 00:20:26,340 --> 00:20:28,440 we want them with a very thorough analysis. 200 00:20:29,460 --> 00:20:36,300 Well, actually, well, a multi operator analysis is more flexible, generally 201 00:20:36,300 --> 00:20:40,830 speaking, I don't know if it will overcome this particular problem. Maybe it won't. 202 00:20:41,160 --> 00:20:47,910 But of course, in real life, it is more likely that if we observe bsm effects, it 203 00:20:47,910 --> 00:20:53,100 will be a combination of different higher dimension operators rather than then it 204 00:20:53,100 --> 00:20:57,300 will be driven by just one higher dimensional uppers. So in this sense, it 205 00:20:57,300 --> 00:21:02,700 is more flexible, simply I mean, we're more or less Likely to Succeed, but then 206 00:21:02,730 --> 00:21:08,190 for technical reasons this is only possible if we combine data from from 207 00:21:08,220 --> 00:21:13,260 different processes, because in a single process you end up with terrible 208 00:21:13,260 --> 00:21:21,570 correlations you get this flat directions and here you are bound to 111 dimensional 209 00:21:21,570 --> 00:21:23,700 treatment like one operator at a time 210 00:21:25,380 --> 00:21:30,600 I thought the namely that implement more operators it's just worse because you have 211 00:21:30,630 --> 00:21:33,450 the end of all the triangles, no. 212 00:21:37,980 --> 00:21:44,010 Well, in principle, you may imagine that you may find a combination of different 213 00:21:44,040 --> 00:21:55,230 operators that well for sure the area will be many dimensional okay. So, there may be 214 00:21:55,230 --> 00:22:01,410 some some places where you, you may end up with a measurable say No, but you will not 215 00:22:01,710 --> 00:22:09,780 violate unitarity anywhere. Maybe I am not saying that it will be like this, but you 216 00:22:09,780 --> 00:22:11,760 have more flexibility, I think. 217 00:22:15,599 --> 00:22:17,729 Oh, ah, thank you. 218 00:22:19,170 --> 00:22:26,370 Okay, so let's take me how again and we can maybe move to the next clip.