Ivana Hristova: you're well.
Thomas Teubner: So Hello everybody and welcome to the seminar from my side speaker i'm.
Thomas Teubner: very happy to that you are having me here I realize checking my records that is more than 11 years ago they don't pay you a visit last time, so this time it's not in person, but I hope it will work with assume as usual.
Thomas Teubner: So I will talk about the standard model prediction of T minus two of the new one.
Thomas Teubner: And when I arranged the seminar I wasn't entirely sure in the beginning, what you want it, because, as I.
Thomas Teubner: point out here with my logo is while i'm a theorist at the University of Liverpool theoretical physics group i'm also a full member of the T minus to experiment.
Thomas Teubner: But of course as a theorist I should not talk too much about the experiment and I have been informed that you have a talk next week from one of our real experts on the experiment.
Thomas Teubner: So the plan of my talk will be I start with a with a short introduction very general, but just to set the stage and to remind us about a few basics.
Thomas Teubner: And then I will really talk about the standard model prediction SS done by the mulan T minus two theory initiative, so, in principle, there are many groups, I have my very own.
Thomas Teubner: mini collaboration of theorists doing doing this with me and my own number, but what the theory initiative has come up with.
Thomas Teubner: Is a number that I would call agreed and consolidate it with conservative areas, and I want to explain you why I believe this is the case.
Thomas Teubner: and in doing so I will concentrate on the electronic vacuum polarization and to a much lesser extent on the light by light.
Thomas Teubner: scattering contributions and I, it will become clear why in a moment, and I will then end with a discussion what all this means and given out look into part two of you chop progress.
Thomas Teubner: Now, new ones are, of course, like electrons, but they are 200 times heavier and dedicate.
Thomas Teubner: And, like other metal particles, they have intrinsic angular momentum, there has been one our party, because we all know this.
Thomas Teubner: So they also charge means they have a magnetic moment they are like little typo and the formula is given here.
Thomas Teubner: Where the magnetic moment is connected to the spin and then there are constants of the charge divided by two times the mass and the chief actor.
Thomas Teubner: And the director, the equation not only implied that there I antiparticles which was at the time sort of revolutionary, but it also tells us that this girl magnetic factor cheat is exactly to.
Thomas Teubner: me if you would just take into account the erotic equation now if you put a new on in the magnetic field, then it processes it's like a spinning top.
Thomas Teubner: And they're very important feature here is that this procession can be measured very precisely this will be a scarce talk next week, and it can also be calculated very precisely, and this is what this talk will be about.
Thomas Teubner: The whole story started, of course, with the Iraq equation, but especially for measuring and calculating the T minus two.
Thomas Teubner: In 1947 even small deviations from predictions in hydrogen and helium is defined structure were observed and, at the time, cushion for a proposed an explanation saying well if the CIO is not exactly to that has a small deviation then everything will be fine so that was, of course.
Thomas Teubner: An explanation, but just by factoring a parameter, that was not satisfying unless you have a reason to believe that this is what comes from from the theory.
Thomas Teubner: And in 1948 when I calculated the famous radiative correction, which is also engraved on his tombstone.
Thomas Teubner: And this is from the one loop diagram the photon that sticks out here is always the photo and couples to move on to the electromagnetic external field.
Thomas Teubner: And then we have as a one loop correction one photon one virtual photo an exchange here.
Thomas Teubner: And in the language that we are using here the anomaly is then defined as the deviation of the chief actor from two divided by two, and this is his famous alpha over two pi.
Thomas Teubner: correction which I have given here with numbers, and this at the time, explained the discrepancy and was really a crucial step in the development of patrol but if quantum field theory and qed.
Thomas Teubner: Why am I saying so well we'll see, especially with a bit of my short explanations later on the qt corrections, but it was really one of the first quantities, where you needed.
Thomas Teubner: This sort of higher order correction in order to explain an experiment and it kick started the whole industry of doing high Roi calculations first acuity and later in the other sectors.
Thomas Teubner: And then T minus two, we will see the whole story unfolding in all the sectors now in terms of an effective lagrangian the anomaly comes from what is called a poly term and.
Thomas Teubner: It is a term which capitalist why I spin flip.
Thomas Teubner: Left handed and right handed field components, so there is a stigma new new term here and the F new newest electromagnetic field strength 10s or so this provides the coupling with electromagnetic field, and then they are constants in front and yea.
Thomas Teubner: High you should know it and there's also if you interchange left and right indices here there's a second term.
Thomas Teubner: And I want to make the note that this is, I said I mentioned five operator, not to normalize and not part of the fundamental acuity lagrangian so it's not just a perimeter of the standard model that we can measure but.
Thomas Teubner: On the other hand, it'll cause through it radiative corrections, as we have seen with the one look graph already, and this calculable in perturbation theory, well, I have been to Beijing in brackets, because most of the talk will have to go beyond, otherwise we wouldn't have a good description.
Thomas Teubner: Now the stand up model comes in, in T minus two with all it sectors that's just the sketch of the standard model, of course, we know it has deficiencies we don't know why they are three.
Thomas Teubner: Generations, we also don't know why br in the world at all because there's CP violation provided within the corporate sector, it seems not to be enough to explain our existence.
Thomas Teubner: There are the deficiencies, Sir, and maybe there are hidden already, yes, we will come, of course, to later that also the experiment see is.
Thomas Teubner: Something that deviates, how can we do this well through quantum.
Thomas Teubner: Effects actually all the sectors of the standard model contribute to this anomaly of the moon, so the standard model prediction of a new consists of acuity part part from the weekend direction part of the electronic in directions.
Thomas Teubner: And all this contributes now, before going into a new, I want to make a quick remark about a.
Thomas Teubner: Now, why are we actually looking at a new at all when a he the anomaly for the electron is measured with a sort of table top one electron quantum cycle for an experiment to an impressive really impressive.
Thomas Teubner: accuracy of point two four parts per billion, when the p&l restarted achieve Point five four parts per million so that's more than three orders of magnitude between.
Thomas Teubner: So on the right is a picture from the NL that's not fermilab so that will be talk next week so here i'm not going into details of the formula experiment of course now.
Thomas Teubner: For the electron to experimental measurement is 2000 times more precise, but the loop contributions for the electronic come from very, very small photon virtual realities.
Thomas Teubner: There is the new one, we are still dominated by low photon virtual realities, but we see, we have a glimpse into ios games.
Thomas Teubner: With a simple dimensional analysis this theorists like to do we can phrase the sensitivity to a new physics at some scale of new physics Lambda and be.
Thomas Teubner: in the following way there is then the new physics contribution really typically there is no hard and fast rule but in many models, this is the case.
Thomas Teubner: scales, like the leptin mask read over the new physics scale, if this is a larger scale, and here the new one wins by a vector of 43,000.
Thomas Teubner: And therefore, we can see the electron anomaly as a determination of alpha it's a super precise test of Q amp D and very low scale physics, but not for what people are typically looking at when they're searching for new physics.
Thomas Teubner: Now let's look go back to a new back to the future let's have a very quick wrap up what was the case.
Thomas Teubner: What was the picture long time ago, when the whole thing started well the early measurements Mayor of course with a very large uncertainties, but and so on, so on was.
Thomas Teubner: sort of the prepared for for more precise experiments and the most precise experiment and was p&l and p&l measured with positive and negative new ones and converge over the years.
Thomas Teubner: To a number, which is still the number today, unless you take into account the very reason precise from formula which I will only show in the very last slides.
Thomas Teubner: Now so i'm started this 40 years ago brookhaven deliver Point five ppm and the formula experiment, together with the Jay park experiment, they are happening, and they should give a certainty what is happening here.
Thomas Teubner: So the blood is taken here from Fred vehicle a nice book and his motto is the closer you look the more there is to see we'll see what this means in a moment, what I want to stress, with this is that always.
Thomas Teubner: This discrepancy has been here from the very beginning, the moment we had some some good experimental measurement it was clear that there is some gap to fill.
Thomas Teubner: But this plot here and already already more than 10 years ago so let's have a slightly more up to date picture and the slightly more up to date Victoria blood from provided by Mark Lancaster.
Thomas Teubner: And this role is now.
Thomas Teubner: The value from brookhaven, which of course hasn't changed, then there is the expected improvement from fermilab if the main value would stay the same, and then some more reason unlabeled stand up model estimates, many people have contributed to this endeavor.
Thomas Teubner: And we have, if you take as the baseline and I will explain in this talk this baseline the standard model prediction from the theory initiative.
Thomas Teubner: Then we have a 3.7 Sigma gap to fill so that's the discrepancy that we have here in some units of 10 to minus 10 and that could be provided by new physics.
Thomas Teubner: So if the two don't match then maybe something is missing in the standard model if we can really trust our theory evaluation.
Thomas Teubner: And the experimental numbers, so there is of course the discovery potential for new physics, but it's also a call for better and more consolidated predictions and not only measurements.
Thomas Teubner: This plot here is again taken from critique ELENA and I don't want to discuss all the bars here, but what it shows is how over history it's a nice blood to look at, but I don't want to spend too much time on it.
Thomas Teubner: What it shows is how over history we got more and more sensitive to the different contributions and it shows us that, with the current with with existing.
Thomas Teubner: brookhaven and now with the formula results we are really hitting, of course, the accuracy limit that comes from the head trauma contributions, but that we are saved with respect to the electromagnetic corrections.
Thomas Teubner: uncertainty and also for the week corrections uncertainty so really there is a need to control the electronic contributions, this is the message, and this is why the new on T minus two theory initiative was established in 2017.
Thomas Teubner: to map out the strategies for obtaining the best theoretical predictions for these electronic corrections in advance of the experimental results, so we did this.
Thomas Teubner: In in close dialogue with for me, let me we made sure that we publish our White Paper before they come up and then it was a was a bit of a delay in the experiment.
Thomas Teubner: took longer to analyze the difficult run one data that will be explained next week, and here I just give you the.
Thomas Teubner: Few numbers, so we had six International workshops an extra one online will will come up and have children.
Thomas Teubner: We published a White Paper with hundred 32 authors from 82 institutions in 21 countries it's really an international initiative and we published.
Thomas Teubner: As a as a physics reports so that's a picture from the last time we could meet in person and you see my collaborator Alex casual RC you see my collaborator dies can nomura you see our Chair persons.
Thomas Teubner: are either Aida and Christopher leaner and they and you see many other people here who contributed.
Thomas Teubner: And if you see later on abbreviations TNT that is for elec styles can myself, who worked over the years, a lot on the head trauma contributions.
Thomas Teubner: Now if you're at half not my time then just this is the upside slide for including the new metrics so we have Q amp D contributions we have the contributions.
Thomas Teubner: And then we have the head 20 contributions which come into versions vacuum polarization that's a block with two photons connected to it and light by contributions that's a block connected to had chronic block connected.
Thomas Teubner: To for for tons So if you just cut off from you in line and twist one lake around you could talk about two photons in two photons out that's why we talk about light by lights kettering.
Thomas Teubner: And here are their positions with which these have been calculated with respect to the total number and you'll see.
Thomas Teubner: The numbers for the individual contributions and we immediately see that acuity is basically everything but with nothing to the arrow.
Thomas Teubner: Various be contributions are as the names as very small and come with a much larger arrow but still very small because look at the numbers that are they are for the electronic contributions.
Thomas Teubner: light is formally higher order more photon couplings here involved so it's not surprising that they are smaller, so the arrow is.
Thomas Teubner: The percentage wise very big bite is now less than the arrow that I will explain you we still have to deal with our vacuum polarization correction contributions.
Thomas Teubner: So the uncertainty is completely dominated by electronic contributions, and this is why the theory initiative concentrates on this.
Thomas Teubner: Now still one slide on qed and Beak I can't stop but but showing at least some of these five flow diagrams that kinoshita has.
Thomas Teubner: Calculated numerically so he calculated T minus two or 1234 and five loops and there are 12,672 five loop diagrams they had to write code which generates code, including right normalization.
Thomas Teubner: Then the Multi dimensional numerically integration sleep to an uncertainty that comes just from the amount of computer power, you can throw it.
Thomas Teubner: But the number gets a green checkmark because it's really so precise and for the mulan there are no worries that very small changes in the last digit with any could change anything you know I pick a picture that's different for the electron but it's not the subject of today.
Thomas Teubner: For Beak contributions I did pick just one loop diagrams here.
Thomas Teubner: And they're all already 1600 52 Luke diagrams I don't want to to dive into discussing them, but what I want to point out here that, of course, the hicks.
Thomas Teubner: With a small you Karma coupling to the mulan gifts a tiny, tiny contributions Maris they said, and the w both sons give sizable contributions, with a very important constellation between them here.
Thomas Teubner: And in an ir E for you at the higher order corrections.
Thomas Teubner: The dyno and the folder to looper then you're getting this number slide dependence on the arrow of.
Thomas Teubner: The geeks MARS and things like this, but it's really known know very well and check between different groups, including recently a normal purely know American calculation, which also agrees.
Thomas Teubner: With the same year, and a bit of calculations provided here so again, the green checkmark i'm not worried about the weekend directions.
Thomas Teubner: So let's comes to the bad guys, the non operative Atlantic contributions, which are the limiting factor of this and not wanting prediction.
Thomas Teubner: So that's the two diagrams for head chronic vacuum polarization and leading order.
Thomas Teubner: And one of the higher order contributions here, which is not a vacuum polarization polite polite with this slightly different display of the diagram.
Thomas Teubner: So question is what's in the electronic vacuum polarization and light, but I it's kettering books, the answer is well anything hydroponic the virtual photons here can couple to.
Thomas Teubner: This quarks clue ones, but also underlying to your photons so there may be photons in here, leading to something that even in the limit of.
Thomas Teubner: Of master squawks with lead twice has been breaking it will be important, when we discuss very briefly lettuce later on and, importantly, if you do that loop integral you to the structure here of the photon propagate us very low Q square photons dominate.
Thomas Teubner: And this means we cannot calculate this with corks in a normal protocol, but if way, this would give you a very, very.
Thomas Teubner: rough estimate only a know precision, because the real degrees of freedom here are their headphones and not the quarks at low virtuality.
Thomas Teubner: So there are two very different strategies we can use a wealth of electronic data and this I call the data terrific dispersal methods, this is where actually the number comes from that I showed you.
Thomas Teubner: which relies on a data combination from many experiments and where we have to care about radiative corrections, maybe that's something like.
Thomas Teubner: I think you have questions or their people may see a bottleneck coming if we push it even further, but.
Thomas Teubner: I will talk about this a bit in a moment, various the second completely different method is that you simulate the strong indirection last photons on a democratized Euclidean space time and that's like the skews idiot.
Thomas Teubner: And here, it is, in principle, first principles, but then you have to ask questions like well, you have.
Thomas Teubner: To do the simulations in the finance is on a finance ice let this with the financial aid, the spacing their artifacts from latest democratize agents, all this should go away if you go to the large size and.
Thomas Teubner: And and in and and continuum limit, where we have no like the spacing, but these are of course limits that you must take and the simulations are always living on a on a on a limited great.
Thomas Teubner: And then we have to include curiosity plus Q ED because in these blocks here that can be four times as well, and there is no way to separate this out and to do it with activity calculation because it's do you ED effects in electronic systems.
Thomas Teubner: And in addition the numerical Monte Carlo methods require really large computer resources so only recently, things have become competitive here.
Thomas Teubner: Now.
Thomas Teubner: let's say a few words about the basic principles i've already dropped the bird dispersal methods, and let me, let me explain briefly what this is for the electronic vacuum polarization.
Thomas Teubner: First, so if we have this block here, and if we don't know what it is really we still want to do the integral there is this trick to bring the daytime it involves first.
Thomas Teubner: Relating the whole vacuum polarization operator or function, which has a real end an imaginary part to its imaginary part of.
Thomas Teubner: This works, based on very, very basic principles causality implies analytic city of this vacuum polarization function and this allows us to formulate a dispersion relation or a dispersion integral.
Thomas Teubner: From which means we can obtain the full electronic vacuum polarization function from its imaginary part only, why is that useful well in turn the imaginary part can be obtained from something that is measurable.
Thomas Teubner: So unit parity that's another sacred principle in our quantum field theories, we get the optical theorem and the optical theorem allows us to relate the imaginary part of the fall let's get during.
Thomas Teubner: To the some over all the cut diagrams what yellow square So if I take scissors cut the thing and off switch it over then that's the modulus square here.
Thomas Teubner: And I have to take into account all states that they could be means I have to some over all things that are allowed in the face space if i'm looking at the Cross section, so this relates.
Thomas Teubner: Therefore, the vacuum polarization the whole vacuum polarization can just be obtained from electronic cross section measurements, but we have to take them all.
Thomas Teubner: Now.
Thomas Teubner: The real formula that we then work with is this one dimensional dispersion integral where we calculate from threshold to infinity so some alternative cures, it will sneak in later on, but only far out and if we integrate unknown carnal function.
Thomas Teubner: With Atlanta cross sections, a debate function here of this kernel function divided by us, this is really an order one over us and really this means low energy is our most important, as I have said before.
Thomas Teubner: And in the language of veterans, this means that the final state, which consists just have to pions is dominating with about 73% to the total electronic mccune polarization contribution here.
Thomas Teubner: There are more than hundred data sets from about 35 or more electronic final states and the uncertainty of our calculation here.
Thomas Teubner: is then coming from the statistical and systematic uncertainties of the data particular city is used only at large rudeness and know modeling of the electronic cross section is really apply it, so we call this maximally data driven.
Thomas Teubner: Now there is a similar.
Thomas Teubner: dispersion relation or dispersion relations, but only much more complicated for light polite so I just want to flesh the slide.
Thomas Teubner: and tell you that huge progress has been made here because years ago people rely completely on models, I think it's fair to say that these models were sophisticated, they are not naive.
Thomas Teubner: But at the same time it's hard within the model approach to quantify arrows and to make them conservative.
Thomas Teubner: Because you could cook up another model with other mean values and other uncertainties and then it's hard to make a decision, because you don't have a systematic expansion.
Thomas Teubner: Now for light by light it boils down to understanding that there are dominating and SAP dominating thesis.
Thomas Teubner: And the dominant pieces are now in very good control and this up dominant are not in such good control, but they are sub dominant and because light bulb is already stopped bleeding that's not a spoiler anymore.
Thomas Teubner: And what I want to stress here is that with the new results which have become available during.
Thomas Teubner: The time the theory initiative face has pushed this and help facilitating the progress here huge progress has been made and light the light can now really be reliably predicted.
Thomas Teubner: And before coming to more on the vacuum polarization I flesh the overview slide here now, the value paper 20 this is sort of our our.
Thomas Teubner: Agreed standard model prediction and the contribution from the light by light here.
Thomas Teubner: Is in the moment completely dominated are completely but it's dominated by the data driven disperse evaluation for the light by light.
Thomas Teubner: And there was already available at the time and be compiled the White Paper.
Thomas Teubner: And let this computation complete latest computation which agrees variable So this is the average of these two numbers and now very recently only.
Thomas Teubner: Just a few days, literally before the announcement of the formula presented a new lead this resolved became available and This again is in very good.
Thomas Teubner: Agreement and all of these sort of agree with the earlier with the earlier model based.
Thomas Teubner: Calculations and this gives us now really a very good picture and the confidence that this number compiled with this arrow here.
Thomas Teubner: is something we can trust, and it will get better once we include this in the leveraging, of course, and there is more improvements on the horizon, both from the data driven disperse if and also from the latest calculations.
Thomas Teubner: So we are not yet there where we want to be, we want to squeeze the arrow further, but this is definitely now in the making and it's not the biggest arrow anymore.
Thomas Teubner: let's come to the guys who contribute the biggest arrow, and this is the electronic vacuum polarization leading water but they're also next to leading all the diagrams when I have an extra photon or I could have a repetition of the bubble.
Thomas Teubner: and
Thomas Teubner: There are even calculations done with the same disperses methodology at next to next to leading order and they turn out a tiny bit bigger than expected, so be taken into account, now.
Thomas Teubner: But this area seems to converge very nicely if you looked at from leading to next to next to next to leading order.
Thomas Teubner: So here I show, for example, the the if I have three bubbles with in inserted in one virtual photon like the shrink diagram then this would be called next to next to leading order had chronic vacuum polarization.
Thomas Teubner: And this is calculated again with the dispersion relation, which is more complicated you then end up with a three fold integral, but it can be done has been done.
Thomas Teubner: The alternative here is like this ques ED but, as I already mentioned, we have to include acuity and ISIS been breaking and there has been lots of activity by several hoops the arrows are coming down and discuss in a moment.
Thomas Teubner: Now here I want no to stress the overall picture.
Thomas Teubner: That that we have here, let me have a cross section that is compiled from many different sizes it the lowest and he is the most important.
Thomas Teubner: i'm not showing you the Cross section, as such, but the Cross section normalized by the moon cross section also called our ratio and they are ratio that's for alpha squared over three s.
Thomas Teubner: The cross section so that's the normalization factor here but and, and this is this is sort of normalized cross section, but the most important thing is really the low energy region here further up, we have.
Thomas Teubner: So in chronic degrees of freedom that's things like the role and mixing with the Omega the fi, then we have of course further up the charm and then the blood domo in your.
Thomas Teubner: Bio in states and only had an energy, which is indicated by this dashed line, our group uses butter operative curiosity.
Thomas Teubner: The rest is completely data driven, but we must build the data driven thing up and on this slide I give you a glimpse into who are the main players in providing the electronic cross sections.
Thomas Teubner: Now, you may not have heard so much about them if you're not working in this field, but experiments like cm D3 and sad.
Thomas Teubner: At Novosibirsk there is still bb are contributing clore and for scotty best three and Beijing and there will be a massive opportunities for bell to coming up.
Thomas Teubner: As also cater to our at Novosibirsk at a slightly higher energies it's important to note that.
Thomas Teubner: This is a very mature field for more than 25 years experiments have provided cross actually inputs for the dispersion integrals.
Thomas Teubner: And the Cross section measurements come with a very different methods they come with direct can when the beams plus or minus even so attuned and with their ad ad for a time when.
Thomas Teubner: The Amazon factory we operated the Center of mass and achieve have initial state photon radiated which lowers the Center of mass and achieve.
Thomas Teubner: The effective Center of mass and achieve of our a blessing minus going into headphones.
Thomas Teubner: And this is really powerful powerful cross check not only across check it's now from the data quality and quantity, the.
Thomas Teubner: The the leader in the game, but it's completely different radiative corrections it's completely different setups.
Thomas Teubner: At the collider us so and detectors so we really have have trust that we are not far we cannot be far off with so many different experiments contributing in such a different way.
Thomas Teubner: I also want to mention that creative corrections already 10 years ago in a different working group, I have been involved in.
Thomas Teubner: We have worked a lot on the radiative corrections so while they are important and may need improving in the future, even further it's very well documented what is done here.
Thomas Teubner: Now cross section compilation.
Thomas Teubner: What are the main players, I mentioned two pi and then we have the high Roi on multiplicity is then carry ons come in and other things like eating pie hours are there.
Thomas Teubner: So we have basically now so many channels mesh they'd be do not rely on modeling using things like ISIS been relations for things that would be.
Thomas Teubner: would have escaped the measurements only above about 1.8 TV, we can use property few CD and, of course, of a from the resonance between have to add them by end.
Thomas Teubner: So the challenge here is the data combination locally in and achieve with the arrow inflation, if there are tensions.
Thomas Teubner: And then experiments measure off course in different energy ranges different energy bins there are correlations all this gets really tricky if you want to go below the percent level, and this is what we need, and have done.
Thomas Teubner: Now one further detail here is that when it comes to radiative correction somewhere in the formula, I had not seek my zero index here super script on the on the cross section, this means that we need to bear cross section.
Thomas Teubner: We don't want to have running coupling effects, which are intrinsically part of many measurements in there, we have to divide them out that's one radiative correction, otherwise you would have a double counting when it comes to iowa does.
Thomas Teubner: But we must include the final state photon radiation because remember in the electronic block that can be any amount of photons and if you cut through that block using our our principles, our set up.
Thomas Teubner: Then.
Thomas Teubner: measure the Cross sections, then this is real and virtual photons that go together with the headphones and they must be included and whenever something could have been cut away, it must be added, back in, so there is the issue of radiative corrections, but they are, as I noted.
Thomas Teubner: Very well studied and, in addition, we add a sizable uncertainty when we are looking at all the data sets where things are not that well under control, the very things that could have gone wrong.
Thomas Teubner: and devise an extra uncertainty, which is quite sizable if we come to the robot should in a moment.
Thomas Teubner: Okay.
Thomas Teubner: I don't have time to go over the 35 channels, this is just for reference and to give you a glimpse what is all out there, it may be too small for you to read anyway.
Thomas Teubner: But I give you instead the graphical representation here in the Nice I call it the T shirt blood, but we have never produced a T shirt which was done by my former PhD student Alex cash of our CEO is now in Manchester.
Thomas Teubner: And it shows the dominance of the two pi channel and then other channels are creeping up.
Thomas Teubner: In the legend, which is also very small, you can see all the channels and they all add up together to the light blue background here, which is the total cross section.
Thomas Teubner: Now a picture here that needs a bit more assuming in, especially when we look at the Employment pipe last pie minus channel we combine my than 30 data sets with more than thousand data points in this one channel alone.
Thomas Teubner: And this is now what people call the role and this is the role or mega mixing this shoulder here and on this picture everything looks beautiful.
Thomas Teubner: radiative return data sets from bar bar and floor dominate the game in the moment but actually these two don't fit perfectly together, there is some tension, the data.
Thomas Teubner: To counted for by a local Chi square minimum inflation, but also by of what I will come back in a second what we call the White Papers merging procedure between what different.
Thomas Teubner: Groups have done so, when I say groups can T that's what i'm involved myself in, and then there is another main player in the field, Michelle w and collaborators this comes with a abbreviation D hmm.
Thomas Teubner: How bad are the tensions, this is shown in the picture here, there is a tension between mainly bar bar and closer and the total compilation in our way of doing things still fits very well together and.
Thomas Teubner: But the arrow inflation leads to something like a 15% bigger arrow than you would expect, on the right hand side I show in a different blood.
Thomas Teubner: differently blood and the late here the road with the road America interference, I show how bad the bar bar data disagree from the rest, this is our way of plotting it, you can see it the other way around.
Thomas Teubner: And and see where that law ends up, which is shown here with Marcus, but this is accounted for not only wire, the Chi square inflation, but also by adding in addition.
Thomas Teubner: As soon as the metrics which takes into account what happens, not just on the level of combining the data locally, but what happens, or would happen if I would.
Thomas Teubner: make a new predictions leaving out either Bob or claw and what happens then has been has been taken is shown in this picture here and really leads to a very sizable additional uncertainty.
Thomas Teubner: of what we call the head chronic vacuum polarization contributions based on the dispersion religion now.
Thomas Teubner: Just to flesh, I will run out of time here is the the show here.
Thomas Teubner: Basically, the fly, but we don't parameter is a fire fire I don't even use the language but we integrate over cans, in the final state in charge and neutral mode, there are so many quality data that we have we could do this already in some time ago, and now it's getting better and better.
Thomas Teubner: I skip this this is how it looks at the higher energy region where we could use a particular city, but are still using data, there is a small discrepancy.
Thomas Teubner: So the other group that's basically putting up a diffuser do we are using data, and this is then one example where we compare the two approaches and whenever we are in disagreement we beef up the arrow.
Thomas Teubner: This is the blood that shows how the pushes and pulls in the main channels between our main competitors and our compilations go and while the overall results in Korea very well.
Thomas Teubner: There are quite some pushes and pulls in different channels, and this is all taken care of by what we call the merging procedure, so if we look.
Thomas Teubner: I I don't have time to do I don't want to cut discussion short, so the there's a bit more detail on the marching procedure.
Thomas Teubner: Given here I leave that for the discussion, but I use instead the overview slide here which brings us close to the final result it, however, the picture looks from the perspective of the different inputs in the total stand up model prediction coming from the electronic vacuum polarization.
Thomas Teubner: that's been a bit of a sentence, but hope I can make it more clear in the moment what goes in the White Paper prediction.
Thomas Teubner: is really the merging it's not a combination value with the arrow expect the arrow to shrink, but we are using basically the same data with different methodology.
Thomas Teubner: rethink that one could have done either one, so the arrow is actually bigger than the smallest arrow here it's about as large as what Michelle w and collaborators to but.
Thomas Teubner: The main value is slightly lower than us, because our resolve contributes, of course, in the merging procedure so that's the number for Atlantic vacuum polarization.
Thomas Teubner: that the White Paper from the theory initiative quotes and which goes into all the numbers that you have seen flying around.
Thomas Teubner: That takes into account these two it doesn't take into account others which would lie even lower, but there is more than mortal dependence in year.
Thomas Teubner: And importantly the White Paper does not use any of the latest evaluations of electronic vacuum polarization why.
Thomas Teubner: Well, at the time when this hell was compiled and it's not so long ago now, it was just last year we didn't have a published BMW is solid.
Thomas Teubner: And the other things were bouncing around very strongly so when we compiled an average of the published lettuce results they came with a very large arrow bar hinting that things first need more checks and further improvements before we can take it into any airbrushing.
Thomas Teubner: Now, this leads basically weekly to a very different picture if you would just pick, for example, this presented here for the electronic vacuum polarization.
Thomas Teubner: So I should say that everybody agrees that there has been impressive progress, but there is this large spread between the latest results.
Thomas Teubner: And they're always attention span looking at something that's called the UK region time window comparison, I have some discussion backup slides on this, if you want.
Thomas Teubner: And there are also large systematic uncertainties within these lettuce predictions they're not only statistics dominated some of them still are.
Thomas Teubner: But they're the most precise BMW resolve it, which came out which has only been published, officially, by nature, on the same day as the fermilab announcement, as you may have noticed.
Thomas Teubner: This is now dominated by the system ethics and the systematics comes from the non trivial extrapolations to the continuum limit and I think finance ice.
Thomas Teubner: extrapolating this tend to infinite side effects there.
Thomas Teubner: If you combine disperse different lettuce you end up with this purple marker here, which is in line with what we have done when the data driven frontier.
Thomas Teubner: The White Paper then Indian quotes this number one on my earlier slide with the numbers, this was on already.
Thomas Teubner: So the remarks here is that really, of course, the theory initiative White Paper number release based on the disperse if data driven evaluations, with a minimal model dependence, we have not use things which would be more model dependent.
Thomas Teubner: And the arrow or here is really conservatively estimated to embrace all sort of possible scenarios different ways of combining different ways of choosing data input.
Thomas Teubner: data input coming from very different sources so we trust that this is really a number that could not easily change outside its arrow boss.
Thomas Teubner: Now let me come say a few more words.
Thomas Teubner: On my second to last slide here about the white elephant in the room, which is of course that BMW, and you will be a BMW number.
Thomas Teubner: And BMW is the latest collaboration their version one was even have the paper on Dr which was on the archive.
Thomas Teubner: Early.
Thomas Teubner: earlier last year already.
Thomas Teubner: And this version one moved in to the iterations with the referees I guess move to beat down the value and the uncertainty is quite a bit thicker and now it's it's bang in the middle.
Thomas Teubner: between what sort of the experimental value is from bl I haven't talked about the formula number, and what we get based on the dispersion relation.
Thomas Teubner: So we have 3.7 Sigma between the pro cave number, and what is based on here, if you would take the published version of BMW face value.
Thomas Teubner: You would have attention with the data driven which would need explaining and you would have a slight tension still in the T minus two itself so it's not that we solve everything in one goal by just going to let us, but then we'll have to explain why things are so different.
Thomas Teubner: Interestingly, if you look at a comparison of the lettuce analysis from our BMW friends and colleagues.
Thomas Teubner: With what we do data driven and if you don't just look at the T minus two comparison, but there's something that's called a window quantity, I talked about before.
Thomas Teubner: Then the picture would be like showing on the right lower panel here, then you have a number coming out this work here is BMW, then you come out here.
Thomas Teubner: And then you come in comparison to the ratio here, so this isn't a new, but not the whole at for the called middle window.
Thomas Teubner: And this year here the discrepancy looks what rather mild, but if you look at something like this, you need serious explaining why all the data driven things should be so wrong.
Thomas Teubner: And it's worth noting that this number here is obtained from these very tricky limits where things like taste breaking corrections have first to be applied, otherwise you would have a completely different.
Thomas Teubner: Dependence on the letter spacing should have said this before, this is a blood that shows how the.
Thomas Teubner: How the limit to the continuum is performed, you can simulate the continuum he will simulate on a discrete lettuce so.
Thomas Teubner: Different lead the spacing have been calculated, then you apply different corrections and get very different continuum extrapolations.
Thomas Teubner: So this is large corrections and large systematic effects, which are taken into account by BMW, one should say in a very sophisticated way.
Thomas Teubner: But there are questions, what would happen if different collaborations with do this as shown here for the window quantity.
Thomas Teubner: So my take home here is our my my justification by I think at the time being, it is still fine be, can I just take their latest resources.
Thomas Teubner: That have been published face value and try to combine we first need to understand this big discrepancies here, which are much bigger than the discrepancies that we see between data sets that we use in our analysis.
Thomas Teubner: and with this I come, then, to the quick wrap up here of the of all the numbers but we don't need to go into the detail, this is only with respect to be an elevator I have bought it to 3.76 months already.
Thomas Teubner: Just to say that the accuracy of the total by paper result it stands now, at point three seven parts per million.
Thomas Teubner: Where their contribution is, of course, completely dominated by acuity but the uncertainty is completely dominated by the head trauma contributions.
Thomas Teubner: And now the vacuum polarization contributions dominate the light the light contributions, after all, that progress on light by light and my.
Thomas Teubner: Basically last contents like before I really come to the outlook is now this looks if I compare.
Thomas Teubner: Including formula i'm taking off course survey from next week's talk, but you're you have seen these presentations before.
Thomas Teubner: The purple mark or here is the p&l recited we have I have compared to the previous slides and now the formula presided is the lowest marker here and they are combined together and the experimental average is now that orange and here, and if I take the White Papers number.
Thomas Teubner: Then I quote, now the 4.2 Sigma discrepancy that we have with the combined Teresa.
Thomas Teubner: Now, what does this mean if you refer to my title, I of course can't give you a definite answer, because there will be huge progress from fermilab only 6% of the often anticipated total data has been part of the analyzed one run one data, where this result is based on.
Thomas Teubner: And there will be more progress here I mean course then if the main values don't change we could get a much bigger discrepancy if mean values would creep together.
Thomas Teubner: It could even with small errors still be below much sought after five six months now, if PM of all.
Thomas Teubner: If all the latest computation would agree at the BMW number, then we would have a headache to understand what doesn't fit together here, there could also be other headaches, but i'm leaving them.
Thomas Teubner: For another discussion.
Thomas Teubner: Just one note here that.
Thomas Teubner: How to check this independently and there is a proposal of new on the new on electrons kettering experiment at CERN where they had chronic vacuum polarization in the.
Thomas Teubner: In the TV channel scattering between new ones at electrons would be measured basically directly, and this would be completely different for measuring electronic cross sections, this would really be.
Thomas Teubner: A more direct comparison to what lettuce simulates and there, there has been a pilot run and and things are looking good that this will really happen in the future.
Thomas Teubner: This brings me to my summary and outlook, so there is still unresolved, new and T minus two discrepancy, which has triggered a lot of new experiments.
Thomas Teubner: For had chronic data but also, of course, most importantly, the experiments for T minus two and on the theory side has cricket the.
Thomas Teubner: Video and T minus two theory initiative coming together and much progress, I had no time to really talk on this has been made for light by light.
Thomas Teubner: which was previously seen as the bottleneck, so this is really good news here and somewhat surprisingly for people who claim that there would never be a data driven disperse if approach possible for this four point function.
Thomas Teubner: They have been proven wrong because the biggest numerical in the moment the biggest.
Thomas Teubner: gain here was from exactly such approaches and they allow reliably estimate and more work is in progress, but also a lot of lettuce progress, especially very recently, and in the future.
Thomas Teubner: Now for disperse if electronic vacuum polarization I have gone into some detail of the published and conservative and what I call robust consensus for the.
Thomas Teubner: Data based evaluation of the electronic contributions, but they are not at the end of the game.
Thomas Teubner: Because soon new electronic cross section measurement, especially for the most important to pi channel will come from bbar still and analyze data there from CMU three best three and hopefully from bell tool.
Thomas Teubner: and longer term I have shown you that there is this new on a proposal for someone which would provide a completely independent yet another completely independent check what's going on here like this has started to deliver really impressive for a solid sub percent precision now.
Thomas Teubner: And I take the point of view of the theory initiative and which is also underwritten by subset of the BMW authors that further work is needed here and it's actually ongoing to scrutinize check and improve.
Thomas Teubner: These different approaches, but once this is starting to be expected, things will fit together and then like and let the light blue light sector, and then the lettuce will have to play a massive role here.
Thomas Teubner: I stress the role of the immune to Minister theory initiative and we will continue to facilitate as work and to publish agreed and conservative send them what your predictions, if we can always prior to a new.
Thomas Teubner: Experimental resolved and well I leave you with the 4.2 Sigma us and I don't call them, yet the end of the standard model because we are very serious that for.
Thomas Teubner: About four Sigma is not yet the end of the standard model, but it has not gone away, things have been no stones have been left unturned and I call that discrepancy more intriguing than ever, thank you.
Ivana Hristova: Thank you very much to you, Thomas for this insightful.
Ivana Hristova: presentation on the on what's behind the theory of the latest G minus two result that has been in the headlines in the news.
Ivana Hristova: I stop the recording.