Scientific Seminar: MicroBooNE finds no evidence for a single sterile neutrino

— Okay, welcome to Ramsey, and on behalf of the Colloquium Committee, I'm Tom Junk, and one of the reasons why we're here today is because of the scheduling of this result with the publication ended up on a Wednesday, so now it's a colloquium instead of a wine and cheese. And because the Quantum people took One West, here we are in Ramsey Auditorium, which is a really nice place. So many thanks, Young-Kee, for providing this, and it's great. So without further ado, let's introduce our very own Matt Toups, co-spokesperson of MicroBooNE, along with Justin. Matt? I don't see Matt. Yes, Justin, will you please be Matt? — I will be Matt. Matt's up there. Are you coming down, Matt? Can I hold fort for a minute while we bring you down here? Certainly, on behalf of myself and Matt, we're very pleased to see you all here today. Thank you for coming to see the release of this result. Matt, I'll hand over to you. — It's great to be here. Should I do another lap? Thank you so much for coming. We are so excited to share with you this result published this morning on Nature. Before we get started, I'd like to invite the lab director, Young-Kee Kim, to say a few words of welcome, and maybe something about neutrinos and the importance of this result for the lab. Young-Kee? — Well, I don't want to talk about neutrinos because the speakers will talk about neutrinos, but this is super exciting. I'd like to thank Justin and Matt to lead this collaboration and coming to this outstanding result. I have to look at it. I have to listen to it, you know, and judge. But this anomaly has been going on for many, many days -- decades. So I'm super-excited that we have some conclusive -- the conclusion. Conclusive conclusion sounds funny. And this is, again, very impactful to our science, and in particular, physics. So I very much look forward to listening, and congratulations to MicroBooNE Collaboration. And this is our 10th anniversary, so it's a perfect time, so well done. — Thank you very much, Young-Kee. [ Applause ] One quick note. We will have a reception following the colloquium. So we'll have the colloquium, then a Q&A, and then a reception afterwards, so please stick around for that. And so, on behalf of Justin and myself, I'd like to invite our first speaker, Hanyu Wei, professor at LSU, up to start our presentation. Thank you. All right. Good afternoon, everybody. I'm Hanyu Wei. I'm an Assistant Professor at the Louisiana State University. This is my colleague, Sergey Martynenko, from Brookhaven National Lab. We'll give today's talk together. Why doesn't it work? Okay. Good. As advertised this morning on social media and various venues, MicroBooNE has reported a landmark sterile neutrino search using the first-ever two-beam and one-detector setup. This result was published in Nature earlier today, and it's a pleasure and honor for Sergey and me to present this result on behalf of the whole MicroBooNE collaboration. Okay. Neutrinos, why study neutrinos? Neutrinos remain some of the most intriguing particles in the universe and are constantly challenging what we think we know and pushing physics forward. They open a unique window for probing some big questions, such as if the standard model of elementary particles complete, possible extensions, and why is there much more matter than antimatter in the universe? And how does a supernova and its energy, that feed the next generation star? And how does a black hole emerge from collapse of a massive core. And all beyond that, could there be an entire sector of the universe, dark particles, dark forces, that we've never seen and shape the cosmic evolution from behind the scenes? And neutrinos sit right in the middle of these mysteries. They interact rarely. Therefore, they are able to carry critical information from extreme environments in nature

and provide one of the cleanest pathways to new physics beyond the standard model. So that's why we study them and use them as the most powerful tool for discovering what comes next. In the standard model of elementary particles, neutrinos are fermions and matter particles coming in three flavors, electron neutrino, muon neutrino, and tau neutrino, and they are the second-most abundant in the universe. They have no charge, no mass, and interact. They are only weak forces, and one of the features that makes neutrinos especially fascinating is they oscillate, transform from one flavor to another as they travel. This implies they are not massless and inconsistent with what the standard model tells us. And this is a simple two-flavor neutrino oscillation probability, sinusoidal, as a function of L over E. And L is the neutrino travel distance or detector baseline relative to the neutrino source. And E is the neutrino energy. In the two-flavor picture, let's assume only electron neutrino and muon neutrino. Flavor eigenstates are superpositions of the two mass eigenstates, and mixing can be described by this two-by-two rotation matrix with one parameter, theta, a so-called mixing angle. And each mass eigenstate will pick up a different fifth value, M squared times L over E. And the fifth difference will be proportional to delta M squared times L times over E. That's the oscillation probability shown here. And this factor is the sine squared 2 theta. That is the mixing angle. Back to this plot, assume only muon neutrino is produced at the source, and the blue curve is the mu disappearance probability, and the red curve is the appearance probability of the other flavor; if the detector stays at the right baseline and right energy, it can observe either an excess -- one flavor showing up unexpectedly, or a deficit of the flavor produced -- at the neutrino source. Okay. This oscillation pattern can let us extract the mixing angles, and the amplitude gives us frequency lets us extract the underlying mass squared difference, which is the delta M squared term here. For example, the in SuperK experiments, the spectrum from atmospheric neutrino oscillation, so the 1 over 2 deficit let us extract the corresponding sine squared 2 theta value. And the NOvA experiments, the spectrum from accelerator neutrinos, and there's a dip here. And the position of the dip corresponds to oscillation maximum, you know, helped to review the underlying mass squared difference. The journal results, the first journal results released two weeks ago, there is also a dip, a different position, and we viewed a different mass squared difference. Okay. In the full three flavor picture, flavor states and mass eigenstates mixed, and can be described by a 3-by-3 unitary matrix, and we call it a PMNS matrix. And each pair of mass eigenstates contribute to a two-flavor mixing like parts, something like that. The SuperK, NOvA contribute to this part. And other experiments using reactor neutrinos and solar neutrinos, they map out the other two parts extremely well. Put them together, three mixing angles, one, three; one, two; two, three; and two distinct mass squared difference corresponds to these two characteristic L over E scales of 10 to 3 or 10 to 5 kilometer per GeV or meter per MeV. All right. Over the past decades, extensive experimental results align beautifully with the standard three flavor framework, observing oscillations at the two characteristic L over E scales we just discussed. However, a few experiments have reported anomalies due to possible oscillations at much, much smaller L over E. This reminds us of the solar neutrino anomaly 60 years ago, and where detectors observed a 30 to 50% deficit in solar neutrino flux, which led to discovery of neutrino oscillations; but what would this anomaly tell us? And let me briefly review them first. LSND and the MiniBooNE, V of e appearance anomalies, electron neutrinos showing up unexpectedly. And in this talk, the NuE may refer to both electron neutrino NuE or electron anti-neutrino NuE bar. But in this slide, I'll distinguish them. The LSND experiment was to measure NuE bar from a mu plus decay at rest assortment

and the muons come from the decays of the secondary mesons and generated by a proton beam striking target. But in this neutrino source, the flux, neutrino flux, is NuE or NuMI bar dominated, electron neutrino, red, and the mu anti-neutrino, the cyan part. And this muon energetic corresponds to mu neutrino from pion decay. So as we see here, and it's negligible, the electron anti-neutrino component. So, however, in the LSND experiment, this measurement, so it observed a significant excess of electron anti-neutrino, and this excess, where do they come from? So it can be interpreted as a NuMu bar to NuMI bar oscillation, where the NuMu bar comes from. And this excess covers the L over E range from 0. 4 to 1. 4 meter per MeV, much, much smaller than the two characteristic L over E scales we just discussed in our scenario. Okay, MiniBooNE appearance anomaly. So MiniBooNE experiment, motivated by the LSND anomaly, was to measure electron neutrinos from a different neutrino source, decaying flight source. So the neutrinos come from meson decays in flight, rather than at rest. So this neutrino has much higher energy, so GeV or sub-GeV scale. So this is the flux of the MiniBooNE experiment, which is also the flux used by MicroBooNE, which we'll discuss later. So the y-axis is log scale. So the red curve represents the NuE component, which is very, very small, just a sub-percent level, and the MiniBooNE observed a significant excess in this measurement. So the data represented by the dots, error bars, and stacked histograms represent the prediction of the expected number of events. And this excess covers a LV range and similar to the LSND anomaly, and also, can be interpreted as the oscillation from NuMu from the source to NuE. If we put together the NuE/NuE bar excess to prediction ratios from different energy bins, from different baselines of these experiments, and expressing them as an appearance probability, we get this plot as a function of L over E. And the black curve represents the underlying appearance, NuMu to NuMu appearance oscillation probability, right, something like this. And this angle makes the angle. Sine squared 2 theta NuE is dedicated to NuMu to NuE appearance channel. All right, so if we map these parameters onto a 2D plane of sine squared theta and delta M squared, that is what they look like. And we call these extended areas allotted regions, and they are extended because they reflect the uncertainties in the measurement. And a lot of regions of LSND in a MiniBooNE cluster together and at EV scale delta M squared. In addition to NuE appearance anomalies, there are NuE disappearance anomalies from gallium experiments or certain reactor experiments. The gallium experiments -- GALLEX, SAGE, BEST -- they use radiochemical detectors based on gallium that can only measure total reaction rate. So they measure electron neutrinos from some active sources corresponding to a few discrete sub-MeV energies. And they constantly observe a 20% deficit of the electron neutrinos produced from radioactive sources. And this deficit can be interpreted as a disappearance effect of the NuE produced at the source. And L over E values correspond to a few discrete points, ranging roughly from 0. 5 to 2. 5 meters per MeV. And the Neutrino-4 experiment, mirroring electron anti-neutrinos from the reactor core, observed an oscillation pattern in a similar L over E region. So this is a lot of regions from Neutrino-4 gallium anomaly, the X-axis, and sine squared 2 theta ee. So we use theta ee for NuE to NuE disappearance. If we put back the appearance channel, we notice that they point to a similar delta M squared scale, an ee scale. This is 0. 1. This is 10. So the oscillation hypothesis provides a plausible, testable, and very natural explanation for all of them. Okay, back to this slide, so several anomalies due to possible oscillations at a small L

over E, and it corresponds to a very high delta M squared, inconsistent with these two known mass splittings, and imply existence of extra, heavier, flavor, and mass eigenstates, and commonly called a sterile neutrino, which has no standard model interactions. And this talk will focus on such -- any scale, light sterile neutrinos, producing small L over E oscillations. And in the 3+1 framework, this is additional flavor, nu-s sterile neutrino, and this is additional mass eigenstates, M4. And the delta M squared we discussed in previous slides, is actually delta M squared 41, and ignoring the difference amount, M123, and they are very, very small, compared to N4. And if such a sterile neutrino can be found, it will be a beyond a standard model particle and reshape our understanding of mass generation, lepton number violation, that kind of thing, and profoundly impact particle physics, extra-particle physics, as well as cosmology. Okay, MicroBooNE, the focus of today's talk, has already contributed to the sterile neutrino interpretation of these anomalies, by searching for sterile neutrino-induced oscillations. This is our 2023 result, an old result, and we set a constraint in the 2D primary space. And this constraint corresponds to a exclusion curve, and meaning, the oscillation parameters to the right side of this curve corresponds to stronger oscillation signals, and would have stood out clearly in our data. But because we saw no oscillation in our data, this region was excluded, this exclusion curve. And in addition to this MicroBooNE old result, earlier experiments, mostly accelerator experiments and short baselines, or low L over E, had set their respective constraints in this 2D plot, because they saw no oscillation in their data. And as we see, this is the accumulative excluding curve, represented by a solid black line. As we see, the 3+1 sterile neutrino model is still an open possibility. And there is another channel, okay, new MicroBooNE result. So it'll be very exciting to see a new MicroBooNE result and see how much it can contribute to clarifying this picture. There's another channel, NuE to NuE disappearance channel, just to remember, and the constraints from the earlier reactor neutrino experiments, the PROSPECT, STEREO, have ruled out most regions allowed by the neutrino 4 and the gallium -- and with the most recent result from KATRIN. And KATRIN released its latest sterile neutrino search result earlier today in the same issue of Nature, together with the new MicroBooNE result, but used a different method. It's not an oscillation-based method. It's based on the beta decay spectrum kink. All right, but KATRIN is more sensitive to high stratum, four regions above the scale in this plot. But with this new KATRIN result, I think, if I'm not mistaken, the entire regions are excluded. So this channel is very interesting, a very interesting situation. But it will be also interesting to see whether new MicroBooNE results can see something on it using a very different neutrino source. Okay, where is MicroBooNE and what is MicroBooNE? So MicroBooNE sits on the Booster Neutrino Beam Line in Fermilab, the Booster Neutrino Beam, this 8 GeV proton beam with a target somewhere here, producing neutrinos and passing through our detector. And the MicroBooNE detector is 70 meters upstream of the MiniBooNE detector here along the same beam line. So it can provide a direct test of the MiniBooNE anomaly. But MicroBooNE uses a very different detector technology, liquid argon TPC, a combination of liquid argon perimeter, high-resolution, facing a 10-projection chamber. So liquid argon TPC enables a powerful neutrino flavor reconstruction and selection, and MicroBooNE's L over E ranges from 0. 2 to 2, so it can probe the EV-scale sterile neutrino oscillations for all the anomalies we just discussed. Okay, the strategies of the last known neutrino search at MicroBooNE 3+1. So one additional sterile flavor and full 3+1 analysis, meaning all detectable oscillation effects are considered in our data, including NuE/NuE appearance, NuE/NuE disappearance, this is what we just discussed, and also, NuMu/NuMu disappearance, and a NuE to NuMu oscillation, NuE/NuMu to mu-tau or new-sterile.

But these two channels are negligible in our data, and they correspond to a very small number of electron neutrino events or neutral current events. So the three main oscillation effects are considered here. We perform a simultaneous feed on all available NuE and NuE interaction channel in our data, and this way we can also reduce the shared systematic uncertainties and improve the sensitivity. So this is, actually, a multi-parameter problem, but we can project our result onto different 2D planes and directly compare it to the available, you know, a lot of regions reported by these other experiments. So in addition to the NuMu to NuE channel that we just mentioned, we also set constraints in the NuE to NuE channel, though this sensitivity is not very competitive. Okay, so the sensitivity of the old result, 2023, is much worse than expected, and mainly due to a degeneracy in oscillation parameters. And this is a challenge that we need to deal with and what it is. The basic idea is the appearance and the disappearance effect in NuE spectrum can cancel each other. So the oscillated spectrum is indistinguishable from non-oscillated spectrum. For example, this is non-oscillated spectrum, NuE, and this is the energy spectrum. If you only consider disappearance effect, a small fraction of NuE also is missing, so times Pee, that's NuE/NuE probability. If you only consider appearance effect, a small fraction of mu-neutrino oscillating to NuE is added on top of the NuE events. So if the appearance effect happens to offset the disappearance effect, that is what we have. The net oscillated spectrum is the same as non-oscillated. That is the region of the degeneracy, but we have NuMu spectrum, if you remember. We fit to all NuE and new NuMu, but here, the NuMu spectrum provides little help with this situation. And the reason is, even if the appearance effect is as large as the total NuE events from the beam, this p-MuE/NuMu/NuE oscillation probability is still a very, very small number, as there is only a tiny NuE component in the accelerated neutrino beam used through a microbeam. And also, in general, in an accelerated neutrino beam, the NuE component is very small. So that will result in, basically, invisible disappearance effect in the NuMu spectrum. All right, so degeneracy arises. These two effects cancel each other, meaning the ratio of these two mixing angles is equal to the beam NuE to NuMu ratio, which is almost a fixed value for different energies in a beam, meaning there's also no shape information that we can use to disentangle the disappearance of this beam. All right. So MicroBooNE has two beams, so this is where the MicroBoonNE's unique capability comes in. So in addition to the booster neutrino beam on access, we see neutrinos from a different beam. The neutrinos, that main injector, the degree of access, MicroBooNE gives a very different proton beam in respect to the target. These two beams have very different NuE component. So this is the flux from the BNB. Only about 0. 5% NuE, BNB beam, and for NuMI, about 4%. So if we calculate the beam, NuMu to NuMI ratio, BNB, 200, NuMI, 25, so one order of magnitude smaller. So meaning they have quite different degeneracy points if we use a single BNB or single NuMI beam to do the oscillation search. So we have two handles, lift appearance and disappearance degeneracy. Now what happens if we combine these two beams? So we made this plot to demonstrate this. So this is according to frame. X and Y axes are the ratios of oscillated and to non-oscillated NuE events in BNB and NuMI. So these two dashed lines mark the degeneracy point. This is for BNB. This is for NuMI. They correspond to different ratios. This is NuMI to NuMI ratio from the beam. So where do those mixing angles sit in this plot? Here we go. So we add some curves, and each curve represents a constant value of the oscillation parameter. For example, the red one corresponds to sine squared 2 theta ee dedicated to NuE disappearance effect. And this greenish curve represents a constant value for another angle, sine squared 2 theta NuE, NuE to NuE appearance effect. And the NuMI to NuMI disappearance effect mixing angle can be determined

if we know these two values, and they are correlated. Okay. So if you take a look at this intersection where we have sine squared 2 theta e 0. 1, NuE 0. 002, that is what we have. This set of parameters will produce a stronger appearance effect in the NuMI spectrum resulting in a net excess in the BNB/NuMI spectrum. The same set of parameters will produce a stronger disappearance effect, resulting in a net deficit in the NuE NuMI spectrum. But we don't need to do this calculation, we can directly read this information out from the coordinate frames. So here, the BNB sits at 1. 1, meaning 10% excess, and the BNB 0. 96 is a 4% deficit. So if we place the full 2D grid, including the values of the mixing angles, and X and Y-axis tell us the NuMI and the BNB excess or deficit with the corresponding solution effect, then we can, relatively straightforward to, sense how the degeneracy is broken. For example, we can scan along this line. It corresponds to BNB degeneracy point because the ratio is always one for these oscillation parameter values. The BNB, no change. The NuMI deficit, if you take a look at the Y-axis value, it rapidly grows with an increase in sine squared 2 theta e, meaning we can disentangle the disappearance effect from the appearance effect. And also, based on this plot, we can sense the BNB is more sensitive to appearance effect because the gradient of this curve is roughly along X-axis, and the gradient of the sine squared 2 theta ee disappearance effect is roughly along Y-axis. So NuMI is more sensitive to disappearance. The survey will discuss further about that. Okay. We can use the more accurate and predictive NuMI spectrum to cross-check this understanding. So NuMI spectrum, BNB/NuMI spectrum, NuMI, this is where we start, so no oscillation effect. So we scan different sine squared 2 theta ee, sine squared 2 theta NuE change accordingly. That is what we have. So the BNB/NuMI spectrum, barely shift, but NuMI develops a pronounced deficit with an increasing sine squared 2 theta ee, meaning we could use NuMI to constrain this appearance effect. Subtracting the disappearance effect in BNB, then we can probe appearance effect, so that is what we do. All right. So the new result, at least in today's Nature, used the first three years of BNB and NuMI data and combined these two beams together, unlocked the full power to test the 3+1 model and compared to a lot of regions by the reported anomalies. So the dotted blue curve represents the new sensitivity of today's new result, and we achieved 0. 1% sensitivity in this NuMI appearance channel capable of testing these anomalies, and in the NuMI to NuMI disappearance channel, we also achieved a competitive sensitivity compared to KATRIN and PROSPECT. But we used a very different neutrino source, so much higher energy; ee sub-GeV compared to MeV1 or sub-Mev are usually used in this. All right. I'll stop here and hand it over to Sergey. He will walk you through the analysis and the results. — Fantastic. All right. Thanks, Hanyu. Let's talk about MicroBooNE 3+1 result. But before talking about results, we need to discuss several pieces that are, actually, in combination, give us a better understanding of the results we have. So we need to discuss our data, our event selection, systematics, and statistical analysis, starting with our data. As Hanyu already mentioned, we do have two beams, and across two beams, we use half of available MicroBooNE data for this analysis. With BNB beam, we reached about 6. 4, 10 to 20 POTs, and for NuMI, we reached about 1, 10 to 21 POTs. The most important part about these two beams for our result is that BNB, it's almost pure NuMu, and it's very sensitive to NuE appearance. And NuMI, it has much larger NuE content and more sensitive to NuE disappearance. That's our data. For event selection, our event selection starts with our detector. And for a detector, we used a low-energy threshold, fully active liquid argon calorimeter, and a high energy and position resolution time projection chamber. This detector is excellent at identifying different species of particles

and reconstructing 3D images with fine-grained precision. Here on the right, you can see the event display from our detector. You can see a vertex of -- neutrino vertex very well. You can see a couple protons coming out, a shower from pion decay, maybe delta ray and pion, but one of the important qualities of the detector, it's our electron-photon separation power, which we do in two steps. First is dQ/dx, which is ionization energy loss. It is two times different between one electron and a photon. And also, we are looking for a gap between the vertex, neutrino vertex, and the start of the shower. This enables our high-performance NuE selection out of an overwhelming NuMu charge and neutral current events. All right. The reconstruction in our detector is performed using the Wire-Cell package in four stages. It starts with noise filtering and signal processing. Then it comes to 3D imaging, clustering, and charge-light matching. Then we do 3D trajectory and dQ/dx fitting and cosmic muon tagging. And lastly, we do multitrack fitting, 3D vertexing, and particle identification. For neutrino energy, we use calorimetric reconstruction, which means we sum the reconstructed kinetic energies of all the particles in the event. We add the rest mass values for muons, electrons, and pions, and we also add the average binding energies per nucleon for each proton we see in the event. With this, we achieve a good resolution of about 15% and bias of about 10% for our neutrino energy reconstruction for our NuEs and NuMus, and this performance is similar for both BNB and new medians. Right. With this selection, we can take a look at our target channels, which are obviously NuEs, and you don't see the data points just yet. We will put them on later, but what you can see here is the green colors, which is our NuE and anti-NuE CC selection for BNB on the left and NuMI on the right. You can also see these blue patches here. It's our NuMu and anti-NuMu CC selection. In the other shades of green, it's our CC pi-naught and NC pi-naught selection. So the main takeaway here is that we have very few selection of NuE's. and the main backgrounds are NuMus and pi-naughts. All right. But it's not just these channels that we use. We have a lot more, so let's walk through all of them. First of all, we split our NuE CC channel into fully contained and partially contained. The reason is based on particularly constructed particles of fully in fiducial volume and up, and that gives us an increased statistics channel. We also do have sidebands. That's our NuMus, also split and fully and partially contained. And our NuMu channels are meant to constrain our NuMI prediction, due to universality of cross-section modeling for CC interaction and common hadronic parentages. And also, we have three pi-naught channels, CC pi-naught fully contained, partially contained, and NC pi-naught, and pi-naughts are a major background for our NuMI search because it mimics the NuMI signature. All of these channels, which you can see seven of them here, but in total there are 14 because there are two beams, are fit simultaneously in our analysis. Let's go through these sideband channels one by one, starting from our NuMu's. So here on the left, I always show BNB. On the right is NuMI version of our NuMu selection, with good chi squares for both of them. But also, you can see that both of them have -- you can see under prediction, which is still consistent at one sigma level. I'll get back to the NuMI part of this slide later in the talk. But for now, let's move to our CC pi-zero selection, again with BNB and NuMI having a good data Monte Carlo agreement. And last but not least, our sideband, it's NC pi-naught. And again, BNB on the left and NuMI on the right have a good data Monte Carlo agreement. All right. That concludes our event selection. So let's talk about our systematics. We have three main sources of systematics. It's detector systematics, cross-section, and flux. Let's start with detector. So we have a range of tools that we use to characterize our detector.

It's a cosmic muons, protons, laser. Like an example, you can see here on the right, we can plot the reconstructed entry and exit position of cosmic muons. But then, we evaluate the range of systematic effects, like covering light yield, space charge, combination, wire waveform simulation. On the right, again, you can see the effect of space charge. So in a perfect world, the positions should lie nicely on the angle here, but they are not because of space charge. So we compare our data to Monte Carlo to assess the magnitude from each of the effects, and we use modified Monte Carlo samples to assess the impact of these uncertainties on the analysis. All right. The second one is the cross-section, but before the uncertainty, a couple words about our cross-section model. So for the cross-section model, we have a base cross-section model, which is GENIE v3, and it's shown as a blue line here on the plot. But when we do tune it to T2K, NuMu CC 0 pi cross-section, which are data points here on the right, that's how we obtain our base MicroBooNE 2 model, which is the red line here. Then we can use this model and various sets of cross-section parameters around it, like lines here, and the various set of parameters, which is a total of 57 of them. We obtain this one sigma band, and we can propagate the same parameter variation to the event rates to build the covariance matrices. And here, the example of, actually, a correlation matrix because it's easier to read, how you can read this, BNB correlations are bottom left and NuMI on the top right. And they split in NuEs and NuMus. And the one, which is yellow, is, basically, the highest correlation, right? So you can see immediately that NuEs and NuMus are highly correlated for both beams. And that's, as I mentioned, because of universality of cross-section modeling for CC interactions. We can leverage these correlations to constrain the cross-section model and its uncertainties. So as an example, let's take a look at our uncertainty band for BNB NuE selection, and here, only cross-section systematics. And we can constrain our BNB NuEs with our BNB NuMus, okay? And you can immediately see that due to high correlation, the uncertainties significantly shrunk. All right. The last but not least, systematics of a flux, and before talking about flux systematics itself, a couple words about our flux model that we updated prior to this analysis, why we started looking at updating it. So at 8 degrees of axis, the NuMI flux is quite different from the traditional on-axis. Here on the left, you can see BNB flux for NuMus, and on the right is NuMu flux for NuMus. For BNB, most of NuMus come from pi-models. But for NuMI, there is a higher fraction of kaons later on. The model must account for kaon production very carefully. But then, we started looking at available models. We understood that they disagree significantly. For example, here, there are some available models, which are Geant 4. 10, 4. 11, and 4. 9, shown in different colors, and there is not much data that exists to constrain the K+ production for a new medium. So what we did, we used the base model that agrees best with available data for us, which is Geant 4. 10. And we applied the very conservative uncertainty up to 40%, where there is no coverage based on the model spread. All right. This slide, basically, shows the summary of what went into our updated flux. We did update some inline geometry. We updated our baseline model. We introduced constraints from NA49 and others similar to NOvA and MINERvA, and we did very conservative treatment of uncertainties outside the data coverage. On the right, you can see the ratio of old to new flux for NuMu's on the left and NuE's on the right. With new flux, we can, again, take a look at our correlation matrix for two beams, for NuEs and NuMus, and the same thing here.

BNB is at bottom left, and NuMI is at top right. You immediately can see that between two beams, the correlation part here is basically zero because we treat them as uncorrelated, because they have different hydronic processes and beam energies, and also, for NuMI beam, correlations are much stronger because they have a higher fraction of K pluses, as we discussed, and it's also a dominant decay for NuEs. So that's why the correlations are very high. And also, for off-axis beam, there is a high number of re-interactions, which also contributes to this high -- So as I promised, we are kind of getting back to our NuMu sidebands, and there is a way how we can validate our NuMu flux modeling using our BNB data. So as we discussed, BNB and NuMI correlated in detector and cross-section systematics, but their flux matrix is uncorrelated. So what we can do, we can constrain our NuMI/NuMu selection with BNB NuMus, right? What it's going to give us, the detector and cross-section systematics would largely cancel out, leaving us mostly with flux. And also, the NuMu prediction will be updated based on BNB data. So let's take a look at this constrained NuMI/NuMu spectrum, which is here in blue. So you immediately can see that there is a good data Monte Carlo agreement. The updated prediction agrees well with data, and uncertainty here is dominated by the flux. So with that procedure, we consider our NuMI flux model validated. All right. So we kind of discussed these three pieces, all of them come into our statistical analysis. And to understand the result, we need to remind ourselves of this equation, which is the probability of oscillation at short baseline for different neutrino flavors. But the most important part for us here is this sine squared, 2 theta alpha beta, which, obviously, can be different based on what you are trying to calculate. For NuMI appearance, it's sine squared 2 theta NuE; and for NuMI disappearance, ee; and for the NuMu NuMu. In our analysis, we explore, actually, the right part of these equations. So we explore 3D parameter space in delta M squared for 1, sine squared theta 14, and sine squared theta 24. But all the results are given in 2D, in delta M squared for 1, sine squared 2 theta NuE, or ee. Right. So to do so, we do profiling over sine squared theta 24, which is, basically, minimizing chi squared over the one axis and calculating, then, the result in two dimensions. Right. This is the full chi square that we use. We discussed our measurements, we discussed our prediction, and the covariance matrix that's coming to it. It's also worth reminding that this chi square that we use, it includes all 14 channels simultaneously. And how can we use it? Here is the pipeline that we follow in our analysis. First, we can get best fit value for oscillation parameters in four new hypotheses. Then, with best fit, we can do a data consistency test against three new hypotheses using the Feldman-Cousins procedure. And after, we can set limits via Frequentist CLs method if the data consistency passed. Okay. So now, all these pieces come together into our results, and we can start with putting data points on our target channel, starting from the BNB. So I'll show the NuE CC channels here on the left and its NuMu counterpart for this beam on the right. This one is not new. We published it in 2023. But still, it's worth reminding us that we do have a small deficit here in the BNB NuE CC channel, and we do have access in NuMu CC. But the interesting thing that happens in our 14-channel simultaneous fit is that our NuMus will be constraining our NuE channel, updating the prediction, and potentially, pulling it up based on new data. Okay. This one is new. So that's our new NuMI selection. On the left, again, it's NuE CC channel.

On the right, it's our NuMus, and both of them has a small data Monte Carlo set. But in the same sense as BNB, in our simultaneous fit, NuMus will constrain our NuEs, updating the prediction, and reducing the normalization of that, as you see here. Let's, actually, illustrate how this constraining procedure works. Let's isolate these two channels, BNB NuEs and NuMI NuEs here. And without constraint, chi square is about 37. 9 for 40 degrees of freedom. But then, we can constrain it with all non-NuE channels that we got, and we have this blue line here. And with constraint, chi square increases a little bit to 41, which makes sense because the uncertainty is strong. But this pool of the prediction up is coming from NuMus, as we discussed, because most constraining power comes from NuMus, and that's how our constraining procedure works in our NuMI channel. The other interesting thing to look at here is how our fractional uncertainties change in our NuE CC selection, because after all, we are a statistics limited analysis with dominant systematics being in flux and cross-section, and what we really need is to reduce our uncertainties for better results. So here is fractional uncertainty without constraint for BNB and NuMI NuEs. Then we shrink the systematic uncertainties, and we get this black line, which is already significantly reduced fractional uncertainty. But also, as you remember, the prediction for both BNB and NuMI is pulled up, which is so that it reduces the systematic uncertainty, and higher for NuMIs because the pull-up is higher for NuMIs. Okay. So with this data, we finally can go and follow our statistical analysis pipeline throughout. So starting with best fit values, here it is. So our best fit value is here on the left, and we compare this best fit line, which is for new best fits, red line here, with non-oscillation prediction, which is, in fact, a histogram for BNB on the left and NuMI on the right. Basically, you can see almost no difference between them. The reason is because we got this very low delta M squared for one, which leads to negligible oscillation effect. With this best fit, we can get a test against a new hypothesis. To do so, we use the Feldman-Cousins procedure. So we throw about 10,000 toys and we get this nice distribution of delta chi squared, and we can put our data, delta chi squared, which is around 0. 2, very close to zero here, and that gives us a p-value of about 0. 96. What does p-value mean? It means that BNB and NuMI data is consistent with three new hypotheses. All right. Now we can go ahead and set the limits and know that the data is consistent with what we knew, and we can start discussing our limits with our -- in this channel. So first, there is our sensitivity. So we compare our sensitivity, which is this blue line here, with our previous BNB-only result, which is our red line here. So sensitivity, obviously, improves with respect to BNB-only case because we mitigated the degeneracy of oscillation parameters and also NuMI and NuE contributions in this channel. But now, where actually our data stands? So let's take a look at our data exclusion. So that's our data exclusion. This is solid red line here, and you can see that MicroBooNE at 95% confidence level in this channel excludes most of gallium-allowed regions and parts of neutrino-4-allowed regions. We also can put our data result in respect of our Brazil band around our median sensitivity. So here, blue line is median sensitivity. Green band is one sigma, and orange band is two sigma bands around it. So you can see that data exclusion is mostly weaker than the sensitivity and lays, primarily, inside the one sigma band. Why is that? So we need to remember that disappearance channel is more influenced by the NuMI because it has four times more NuEs than BNB. And NuMI, after constraint, data matches prediction very well.

But still, BNB data has this deficit that weakens the NuE disappearance limit. Okay. Now, we can go through he same logic with our appearance channel, first, comparing our sensitivity with our previous result. And again, our sensitivity improves with respect to BNB-only case because of degeneracy mitigation. But now, we can finally take a look at our exclusion limit at appearance channel, and that's how it looks. This solid line is a huge jump in chi delta-M square, and we exclude at 95% confidence level LSND 99% allowed region. And also, we exclude vast majority of minimal 95% allowed region. Right. Same logic with disappearance. We can put it in context of our Brazil band around median sensitivity. You can see, again, that our exclusion limit is stronger than median sensitivity, and it lies on the border of two sigma regions. Why this is happening? Let's take a look. Again, we get back to this constraint, NuE predictions for BNB and NuMI. And what we need to know about this appearance channel is that it's dominated by the BNB beam because it has four times less NuEs and two times more NuMIs. And this BNB, it has a data deficit that boosts the appearance limit, which basically favors smaller appearance angles. But also, there is another way to look at this result. For this, we need to step back and remember our BNB only result, so here it is. These red lines show BNB only full 3+1 result that considers appearance, NuE disappearance, and NuMI disappearance all together, the solid line being data result and the dashed line being sensitivity. And obviously, the data result is slightly stronger than sensitivity because of the BNB deficit. But what we also published back in 2023 is appearance only result. It is unphysical in our case because it disregards any effects from NuE disappearance and NuMI disappearance, this black solid line here, and it's obviously stronger than our full result because it doesn't have any degeneracy coming from this channel. But what it also shows, it shows, basically, the limit that can be reached with BNB only data if there would be no degeneracy of oscillation parameters coming from other oscillation channels. So let's overlay this appearance only result with our new two-beam full result. So you can see that they are almost similar except this small part around the -- squares. And the reason for this is that basically, NuMI provides the maximum degeneracy mitigation to the BNB-dominant appearance channel, and that's why we reach this limit. All right. So just to summarize what I've discussed right now. So we saw no evidence for 3+1 sterility in the model. We exclude, at 95% confidence level, the 3+1 explanation for LSND and MiniBooNE anomalies and exclude most regions allowed by the gallium and neutrino-4. And with that, we close the window for 3+1 model as an explanation for long-standing LSND and MiniBooNE anomalies. And here, I'll give the torch back to Hanyu to put these results into a broader perspective. — Okay. Thank you, Sergey, for the presentation. Good to see you again. So now, I'm going to wrap up today's talk with an outlook where this takes us next. So as Sergey just summarized, the 3+1 framework no longer provides a variable explanation for the LSND and MiniBooNE anomalies. But those anomalies, the observed access data, haven't gone away; so do the reactor and gallium anomalies, and they also remain unexplained. And these anomalies continue to draft a global program of current next-generation experiments

in that resolving the remaining possibilities. I just list some of them, not exhaustive, and many of these experiments can provide a direct test of these anomalies as they employ similar neutrino sources, similar detector configurations, or in a similar LRE range. And many of them incorporate more advanced detection techniques or detector technologies, so more sensitive investigation of these anomalies. And among these experimental efforts, a central program is a strong baseline neutrino program at Fermilab, which is an extension of MicroBooNE with two additional liquid argon TPC detectors at different baselines, so the near-detector SBN and the far-detector ICARUS. So the near-far detector configuration can substantially reduce systematic uncertainty in flux in the cross-section detector and improve sensitivity. And also, the SBND detector, in close proximity to the beam target and ICARUS is very massive, and both fully operational, and have already collected the largest statistics of data in the band L over E region. So this enabled the SBN program to provide a high statistics, low-systematic exploration of the last far neutrino oscillation. And not only NuE-appearance or NuE-disappearance, as we just discussed, but also the NuMu-disappearance channel, and to which the MicroBooNE alone has very limited assistance. All right. In addition to sterile neutrino oscillation search, the SBN program can provide a more comprehensive and sensitive preparation of a broader landscape of beyond-the-standard model physics as well, some of which will be highlighted in the following slides and with relevance to the LSND and the MiniBooNE. All right. For example, expanded sterile neutrino models, this includes possibilities like 3+1 plus additional sterile flavors, plus 2, for example, or 3+1 and augmented by new dynamics involving the sterile state. For example, non-standard interactions, decaying sterile neutrinos, and some other examples. So MicroBooNE has begun exploring the 3+2 framework and is actively investigating the 3+1 plus decay scenario. In addition to sterile neutrino oscillation searches, non-oscillation searches targeting photon final states are making significant progress towards alternative explanations for LSND and minimum anomalies. So because the electromagnetic signature in the excess events may arise from photon final states, which convert into a pair of electrons, a positron, rather a single electron from oscillated mu. And the excess photon final states may come from unexpected or underestimated standard model processes. For example, the delta-related decay, single photons, coherent single photon production from current interactions, and the MicroBooNE recent analysis saw no sign of excess in these two standard model processes, but we do see an interesting two-sigma excess in a model of agnostic inclusive single photon search, particularly in this zero-proton channel, as shown here. These two bins, 100 to 300 MeV, and this is a two-sigma. So this motivates further investigations in MicroBooNE and SBN. All right, another active frontier is a broader landscape of dark sector models. And for example, the neutrino-induced upscattering, dark matter product-induced upscattering, or heavy neutral decay generated from the same target, and many of these models predict photon final state or direct the E plus or E minus final state. So signatures that MicroBooNE or SBN can identify with high precision, as we just discussed in the photon studies. This is the event at play of an e plus/e minus signal from a dark sector model simulation in MicroBooNE, with the argon-TPC detector. And recently, MicroBooNE released the world's first direct search for dark sector e plus/e minus signal as a possible explanation to the MiniBooNE anomaly. This is the result. This is data with error bars. We saw no sign of excess of such signals compared to a green dashed, the histogram, representing typical e plus/e minus signal from a dark sector model.

All right, but alternative dark sector models, particularly those with very different characteristic angular distributions of e plus/e minus pair or energy distributions, may remain compelling targets for further investigation of MicroBooNE and the SBN program. All right. I'll finish up here and back to the main results discussed today. So using the first two beams, one detector search of it can -- MicroBooNE sees no sign of sterile neutrino-induced oscillations in the relevant L over E regime, and closing the 3+1 window associated with the anomalies. With this chapter settled, the path is now open for new ideas and discoveries in future theoretical and experimental efforts. More to come. Stay tuned. Thank you for listening. [ Applause ] — Great. Thank you, Hanyu and Sergey. Even though I've known about those results for quite a long time, it's still really nice to see them up there on the screen at last. And it's really nice, now, to actually get the opportunity to start hearing some feedback from all of you outside of a collaboration on these results and to get your questions. So I think we now have about 10 minutes to take questions, so please. I see one up there, three up this side. Go for it, Tom. Yes. — Okay. So first of all, a huge congratulations, and thanks for beautiful results and also beautiful talks. I really like the results in your talks. I have a question. So you said that you have very negligible detector systematics, regardless of, you know, you have the NuMI beam or not, right? Did you say that? You have small detector systematics? Negligible systematics for detector? — Not negligible, but not dominant. — They're not dominant, yeah, compared to the other two. So that's true even though you don't use any NuMI beam. So detector systematics is still small, no matter what you use, NuMI beam or not? — Yes. — Okay. So how did you achieve such good, you know, detector systematics? — It's a good detector. I think that the detector design, the whole collaboration, tremendous effort, with the KATRIN detector, we better understand detector response. We also produce some version samples, something like that, to help us to estimate detector systematic uncertainty in high precision. — Okay. So that's one thing we need to learn from you, and another one quick question is that, so the last slide of your -- Hanyu's talk, so you compared the sensitivity with 2023 and the current sensitivity. So I see that the bigger science care data values, so your sensitivity degraded with the NuMI beam, so why is that? [ Multiple Speakers ] — You mean at the bottom? — Yeah, bottom. Yeah, those, you know, higher UE. So you see the current sensitivity is degraded compared to the 2023? — Because it's not exactly an apple-to-apple comparison, right, because here we compare data results with the sensitivity results. — So 2023 is the data results? — The data, so it would be more fair to compare sensitivity -- — Oh, okay. I see. I thought it was -- — -- then they would be converging at this point and that's going to be fine. — Yes. It would be good to see some apple-to-apple as well. — But this is data, so it's kind of a little bit to the left. — Okay. So, okay. Thank you. — In the future on the SBN program where you have two detectors on the BNB beam, how useful will the NuMI beam be, or will you need it at all? — Right. To me, I think that NuMI beam will further boost the sensitivity in that beam program. ICARUS can see the neutrino from NuMI for sure. And also, though we have near-far detector, but there's still sort of degeneracy. NuMIcan help, but this degeneracy will be weaker as we have, you know, a near-far detector

and different devices still, but NuMI can help. — Another one up there, Tom? — All right. Thanks for the talk. This is great. It's great to use NuMI beam to do the searches. I had two quick but highly correlated questions. One is, what is the NuMu bar contamination in NuMI fluxes? — Do you have that? This is negligible. Let me find the flux somewhere. I'm not sure we have a breakdown for NuMu and anti-NuMI, but it's a small fraction. Yeah. Percent level? — Oh, percent level? — Yeah. — Oh, okay. — And in our selections, it's also very small. — It's bigger than NuE, but much, much smaller than NuMu. — Wait, but NuE contamination is 5%. So then, NuMu can't be a percent level. It needs to be like, what, 20%? I think my question is, if anti-NuMus are relevant for this, and if they are, how do you correlate the cross-sections, because the anti-NuMu cross-section will have a very different Q-squared dependence, and it will lead to very different topologies in your detector, right? So your NuMu sample may have a much larger contamination from the NuMu bar, which will change the efficiencies, I would expect, due to topology. — Do you have the NuMI spectrum somewhere? — We don't have a breakdown for NuMu anti-NuMu here, but our cross-section model, you know, treats NuMu and the NuMI bar differently, and that information will go into prediction, for example, in this predictive electron, as well as in the systematic uncertainty estimation. — Yeah, the key thing is that will be in the covariance matrix. — Right. — It will be accounted for. — We just did not distinguish NuMu/NuMI bar here in this plot. Yes, but in general, we do. — Yeah, okay, thank you. — Tom, there's a couple of questions down here. There's one there, and then Young-Kee has one over here. [ Background Discussion ] — Can I ask something? It's not directly related to MicroBooNE. — Go ahead. — Or KATRIN, how -- what's going on? Do we have any results with the mass, neutrino mass? — Yeah, that was the main goal for this. — goal. Yeah, but they did release something at Neutrino didn't they? Now, what is the new KATRIN result? — You mentioned about their -- — Well, yes. The paper that came out today was a stab on neutrinos. — I understand, but I was curious what's going on with their main goal. — Ah, yeah. Main goal is to do mass. — -- 0. 40. — 0. 45. — EV. — That is the current limit. — 0. 45 EV. — My voice may or may not support this question. I was watching as it went by. You showed us more than a dozen fit results with chi-squared over a number of degrees of freedom. They were all less than one. Statistics doesn't do that. So somehow, the errors are too big. — I know exactly where to go. I mean, yes, the errors are big. The errors are concerning, but what we are doing in the end -- — Your constraint plot? — Yeah, I'll show you a constraint plot. — Yeah, Far, far back. Yeah, here we go. This one. — Yeah. So, yeah, because after constraints, the uncertainty shrinks. So, yeah, we do have a concerted uncertainty that in a simultaneous 14-channel fit would be changing due to the correlations from our chi-statistic sidebands. — In many of these plots -- all of these plots are correlated with each other. They're all showing much the same distribution in different ways. So I think in a feature of a, you know, a somewhat systematically limited analysis

once one of your plots has a chi-squared degree of freedom below 1, given that a lot of these error bars are highly correlated across their length, any distribution you make on that data is going to be, sort of, similarly correlated in a way. — Even the top-left plot, is a little -- 9 out of 25, even by itself, all in one, is a little unlikely, but -- — Yeah. — -- we'll give you one. — Oh, yes. No, it's a systematically dominated analysis with a highly correlated bin-to-bin systematics. — Thank you very much for the nice talk. Could you go back to the slide with a neutral energy estimate? I have two questions. So, first of all, so what is the source of the binding energy value, the eight-point something, maybe, I think? And the second thing, if you could produce better energy estimate for neutrinos, including neutrons, could you also get further improvement in the sensitivity? — For your second question, the answer is yes, and I think there is some work on deep learning energy estimation for MicroBooNE that actually might go later in the analysis and potentially boost the sensitivity. And for the second question, I missed it. — The binding energy? — Second question. For the first question, I missed the first question. — Binding energy. — What's the source of the binding energy? Some paper. Some measurement. A test. Yeah. — Okay. I see. — Yeah. — Because the values keep changing, so I was curious about it. — Right. — Thank you very much. — But that one, we also did some study. We can vary that a little bit, so the impact is not very significant. — Oh, sure. Thank you. — Any more questions? Oh, there's one. — Thanks, Pedro. — Okay. Sorry for like dominating, but just one more question, I promise. Do you have sensitivity to NuMu disappearance? Because if you can do the appearance at 10 to the minus 3, and the NuMI disappearance at the 10%, it feels like you should be able to get NuMu disappearance at the percent level, right, so did you check? — Yes. We checked that. It's not that sensitive, but we can provide some results in print, but we didn't publish that result. — But is that, like, at the 10% level or the 1% level? — Ten-percent level. — Okay. — Yeah. So that is, basically, the uncertainty in the NuMu spectrum. But in the NuE, that is something different, because that sensitivity is basically shrank, because the NuMu to NuE ratio is very, very high. We measure the NuE, but it comes from NuMu, but NuMu disappearance is still in NuMu channel, so that sensitivity will correspond to that uncertainty. — Okay. NuMu disappearance is very hard with a single detector. It's a dead record of your spectrum. You don't have this NuMu to NuE constraint. You can't use that in the same way to shrink your uncertainty, so that is somewhere where you really need a multi-detector SBN program to do a good job there. All right. I don't think I saw any hands, but if there is one -- oh. — So if I'm following what you said earlier, then you have -- your systematics are correlated bin to bin, and you've not taken out a separate global systematic. If that's the case, then, in fact, if you had accounted for that as a global, you would have had much worse chi squares. That, in turn, would have decreased your sensitivity in each of your points. And, basically, it sounds to me, you know, that, in fact, what you've done is you have over-coverage, and your limits, actually, should be weaker. I'll leave that to you to think about. — Yeah, I mean, it's not clear why that would make the limits weaker at all, certainly to me.

I mean, the sequential CLS method that we do at the end, it takes into account all of the possible uncertainties in the covariance matrix, as opposed to fake data experiments, and that's how we calculate the exclusion region. — And, also, there's a strong normalization systematic uncertainty for something like that, but if you remember the preceding band of the sensitivities, and we add the one-sigma, two-sigma band around the median sensitivity, we do see, you know, where data exclusion result is consistent with any reasonable result or uncertainty. — The uncertainties are correlated. You did it the same way. That's fine, but I'm questioning whether the methodology is right, if you have a global correlated systematic, which needs to be accounted for only once. — But the constraint, basically, reduced the systematic. — It doesn't matter. There's still a global effect. If there's a global effect that's going to shift the whole thing up and down, then that should be counted once and not as part of a broader bin-to-bin. — So you can account for a global normalization shift in a covariance matrix. It just looks like a flat covariance matrix, but you can encode that type of uncertainty in a covariance matrix. And so, the normalization uncertainties that are a part of this analysis are encoded in that covariance matrix. You get the same result as if you took it out, so it's included. — I think one more question down here, and then, I think we have to wrap up. So we've got time for one more question, and then we, actually, have to leave and get to the reception. — Should we go online? — So if you want one more question, Tony, go for it. — Okay. So I just want to make sure that I understood you correctly. So the reason why you have much better, you know, sensitivity with the NuMI beam is not, actually, because of the NuMI beam. That's because you constrain with even the BNB beam. You constrain with the other in the channel, the disappearance channel to appearance channel, right? That gives a huge reduction. So this plot is a little bit -- I mean, not this plot. I mean, so 2023 versus 2025 results comparison could be a little bit misleading because the main reason could be due to NuMI beam, but it's not NuMI beam. Even the BNB beam, you know, you can reduce a lot with constraining; is that correct? — I would say mostly correct. I think the power of this channel comes from the BNB beam, but the question is if we just do a single BNB beam study, if we do 2D comparison, there will be degeneracy, but NuMI helped to break this channel. NuMI policy unlocked the power from BNB. As mentioned, so here this sensitivity comes from the very large NuMI-NuMI ratio, but that is only true for BNB, not NuMI. — Okay. Maybe I want to talk to you more later. — Great. Thank you. Right. So the reception, I think, is outside One West. So, yes. Yes, please do now all head up to the atrium, and thank you very much for coming. [ Applause ] — Thank you. [ Applause ]