 OK, so I think you're live now. So hello, everyone, and welcome to the Latin America and Webinars on Physics. Today, we're super happy to have Sara Tabrizzi. So Sara just finished her first postdoc at the University of Sao Paulo in Brazil. And she's about to move to Virginia Tech to start her second postdoc. And meanwhile, she's spending some month in Castaway, right? So Sara will talk about re-acting oscillations as constraints on effective field theory. So are you there, Sara? Yes, hi, everyone. Let me share this screen. Thanks, Nicholas, for the great introduction. So as Nicholas said, today I'm going to talk about the constraints we can get on effective field theory using not to know oscillation experiments. So I will talk about this work, which was in collaboration with Adam Falkowski and Martina Lonso. So in the first part of the talk, I will briefly explain not to know oscillation in the standard model. Then I will talk about effective field theory ladder and different Lagrangians we have in different energy scales. Then I will explain how this effective field theory modifies the oscillation of not to know. And we will look at the application at reactor experiments. Then we get the constraints that reactor experiments. And we compare them with non-oscillation constraints we have from other experiments. And at then I will conclude. So as you all know, at the standard model, neutrinos appear in the charge and neutral current interactions. We don't have right-handed neutrinos in the standard model. So neutrinos are predicted to be messless. However, we know from several decades of several neutrinos experiments that neutrinos oscillate in nature. And therefore, to explain this oscillation, they have to be massive and they have to mix. The oscillation of neutrinos in the standard model is explained by the elements of this 3 by 3 mixing matrix, the so-called PMNS matrix, which relates the flavor eigenstates electron, mon, and tau neutrinos to the mass eigenstates in nu1, nu2, and nu3, which means that, for example, in a given mass eigenstate of, for example, nu1, how much of it is electron neutrino, how much of it is mon neutrino, and how much of it is tau neutrino. This unitary matrix has three mixing angles, theta 1, 2, 1, 3, and theta 2, 3, and one CP-violating phase. Therefore, in the standard model, at least in the vacuum, the oscillation of neutrinos is explained by the elements of these PMNS matrix and also the mass squared differences delta m squared kj, which is the difference between the square of masses. Using all these neutrino experiments, several different kinds of neutrino experiments, we have very good constraints on all the three mixing angles, theta 1, 2, theta 2, 3, and theta 1, 3. And we know with a very good accuracy the values of delta m squared. We don't know the value of the sleepy phase yet, and we don't know delta m squared 3, 1 is positive or it's negative. However, we have very good information about the other parameters of the neutrino physics. So the idea is we use all this broad range of neutrino oscillation experiments to use them as an ingredient in the precession measurement program, and we use all this data to constrain effective filtering parameters. Apart from neutrino masses and mixings, this oscillation phenomenon of neutrinos is also a function of how neutrinos interact with matter. So in the standard model, they can interact with matter through charge current or neutral current interactions. If we have some heavy physics, we can modify, we can have new effective for fermion interactions between leptons and quarks. And these effective interactions can have effects in the production, propagation, and detection of neutrinos. And they are observable phenomena. So in this way, perhaps, we can constrain the whole heavy new physics. But with precision measurements at low energy experiments, perhaps we can have a feeling on where is the tail of the new physics. So that's the idea. We want to study effective filtering parameters in the neutrino oscillation experiments. Why effective filtering? Because we have very different low energy observables which can probe different particle interactions, but all within the same consistent framework of effective filtering. And then all these different constraints can be compared with each other in a meaningful way. And finally, once we get these results, we can translate them to some new physics, some new complete new physics. And so we can constrain our new physics models. So that's the workflow. Our neutrino oscillation experiments, that the ones at least we want to consider here, the reactor experiments, they are at the few MEV. So they are at very low energy. So we study our effective filtering observables within the weak effective filter in Lagrangian. Then if our new physics is much heavier than the Z boson mass, their relevant effective filter is the standard model effective filter. There is the one-to-one matching between the weak effective filter and the standard model effective filter. So once we get the constraints at our weft, we can get the constraints again on our SMF. And once we have these constraints on our standard model effective filter, we can translate them to different BSM model number one, BSM model number two, or so on. So let's go down to our EFD ladder to explain better what we want to do. If our new physics is much heavier than the Z boson mass, then the effective filter that we consider is this standard model effective filter. Here, the particle content and the symmetry is the same as the standard model. The only difference is that apart from the standard model Lagrangian, we can have all these different higher dimensional non-renormalizable operators. So we can have, for example, at dimension four, we have our standard model. Then we have dimension five interactions, which are the Weinberg operators which give masses to notrinos. And we have several dimension six operators. So here, we neglect the dimension five operators because the notrino masses are negligible at these experiments. And they don't have any effect on the production and detection amplitudes of notrinos. But however, these dimension six operators have a very strong effect. So we just want to study them. If we go one step down, the energy is relevant to our experiment at a few MEVs. We can integrate out all our heavy particles, WZ, Higgs, and top quart. And then the relevant charge current interaction, we just consider charge current interaction because that's the relevant interactions for reactor experiments. Then in this case, our weak effective filter, Lagrangian, is given by all these different interactions. So for the case of the standard model, we just have this U bar gamma mu PLD L bar gamma mu PL notrino. So this is our standard model part, which is a V minus A interaction. In the presence of the new physics, we can have all these five different possible new interactions. We can have a standard model-like new interaction. Of epsilon L, we can also have new right-handed scalars to the scalar and tensor interactions as well. We can match the two theories, the weak effective filter, that we show the Wilson coefficients with these epsilon. And we can match them with a standard model effective filter. And the matching is given by these equations. So it's very important to see that, first of all, at the order of lambda to the minus 2, which is the last order that we consider, all the five new interactions can appear at the same time. So they are equally important. And second of all, the right-handed interaction is the only one which has only diagonal elements. So there is no off-diagonal elements contribution from the standard model effective filter from a smet to the right-handed epsilon C. It's proportional to delta. The relevant degrees of freedom for the experiments are not really quarks, but they are protons and neutrons. So once we do the matching relevant for the effective filter of protons and neutrons to the weak effective filter lagrangian, we get to this so-called linear lagrangian, which is of this. So here, protons and neutrons are our degrees of freedom. These couplings, Gv, Ga, Gs, Gt and Gp are our nuclear couplings that we can fix them by lattice and by theory considerations. So we fix these couplings. We use the best fit values given here for our analysis. At the reactor experiments, the exchange momentum is much, much smaller than the masses of protons and neutrons. So we have to go one more step down to the EFDA ladder, and we have to write our non-relativistic linear lagrangian, which is given in this way. So here we have our degrees of freedoms are these non-relativistic styphils for protons and neutrons. We have only two matrix elements here, the so-called Fermi matrix element and the so-called Gomoff-Deller matrix element. And since we are at the non-relativistic limit, we see that there is no dependence to the pseudo-scaler epsilon here anymore. So at the non-relativistic limit, the pseudo-scaler contribution is suppressed, and we have only left-handed, right-handed, scalar and tensor interactions. It's very important to note that these right-handed and left-handed interactions, they are always next to Ud and this axial coupling. To explain it better, it means that once we go to the diagonal elements of alpha and beta, for example, to EE here and EE here, and we consider the charge electron and electron latrino here, what happens is that we can always redefine this epsilon L and epsilon REE into VUD and GA. So in fact, the same effective interaction, which appear at not-to-know experiments, is also responsible for constraining this element of the CKM matrix, Ud element of the CKM matrix and axial coupling. So we can redefine them into VUD and into GA, which means that at the end, our non-relativistically young Lagrangian is not a function of the diagonal epsilon L and epsilon R anymore, and at no level at the Lagrangian, and we can see it even at the level of Lagrangian, that at no level of the perturbation theory, we cannot constrain the diagonal elements of the left-handed and right-handed interactions. So that's one of the most important results that we get. So let's see now how these new interactions affect the oscillations of neutrinos. In the standard model, the neutrino oscillation is explained by this PMNS, the product of the PMNS elements, and the mass squared differences, the LMS squared KG. Now, in the presence of our new interactions, which can modify production and detection of neutrinos, instead of just the product of these PMNS elements, we have the product of the amplitudes of the production and amplitudes of the detection of neutrinos. So these A's here are the production and detection amplitudes of neutrinos, and they are in the standard model, it's just the PMNS matrix times some factor which depends on the kinematical considerations. And once we have the new physics, we have our Wilson coefficients times kinematical considerations for the production and for the detection and also the PMNS matrix elements. So to calculate the oscillation probability in the presence of these new interactions, we need to calculate the production and detection amplitudes carefully. Just let's expand these elements of CJK. We see that again, for the standard model, we get four products of the PMNS elements, very similar to what we had before. So at the standard model, we recover the usual formula. In the presence of the new physics, we have these coefficients Px and dx, which give the contributions from the production and detection. So to calculate the oscillation formula, we need to calculate these parameters. We know the elements of the PMNS matrix and we have our Wilson coefficients as epsilon x here. So let's just focus at reactor experiments. We know that in reactor experiments, neutrinos are produced. We produce electron anti-neutrinos and we detect them through inverse beta decay process. Here, a neutrino anti-electron hits a proton target and gives a positron and a notron. The positron annihilates and gives some photons and the notron is later captured and the difference and also gives some photons. The time difference between the annihilation of positron and the notron capture is a hint of the inverse beta decay process. We know this process very well at the standard model, so it's very easy to calculate the amplitude for this case. The left-handed and right-handed parts of the amplitude are constants. However, the scalar and tensor parts will have a constant part, which is the function of the nuclear coppings, as well as a part which depends on the neutrino energy. And the pseudo-scalar one is suppressed. The production of neutrinos at reactor experiment is much more complicated and it's a lot more involved. In fact, we have hundreds of different beta decays which contribute to the production of neutrinos. And we don't know very well these contributions even at the standard model case. What we know is that more than 70% of these fluxes of neutrinos are due to gum off-teller transitions. They are of the gum off-teller type. So as a first assumption, we assume that we neglect all the first four with an decays and we consider only the gum off-teller type transitions. This means that the only new physics we can consider at the production side is the tensor new physics because of the gum off-teller nature of it. The left-handed and right-handed ones are constants and the scalar and the pseudo-scalar ones either don't contribute or they are suppressed. So let's see one by one adding these new interactions how the probability changes. In the case of the standard model, the survival probability of the electron-antinotrinos after distance L from the source is given by these two parameters, the mixing angle theta-1-3 and delhame-square-3-1. And here b nu is the energy of neutrinos. If we just add a left-handed interaction on top of our standard model, a new left-handed interaction, what we see is that this effect will be re-observed into a redefinition of theta-1-3 mixing angle. So the change in the probability is just putting theta-1-3 till the nested of theta-1-3 and since this theta-1-3 is observable at these experiments, which means we have to measure theta-1-3 here, there is no way to distinguish between the standard model theta-1-3 and the BSM theta-1-3 till the here. And therefore at reactor experiments, we cannot be sensitive to V minus A new physics at all. We add new physics at the detector side. At the detector, we can have both Fermi and Gomoff-Teller, we can have Fermi interactions. We can have both a scalar and tensor new physics. So the real part of it changes the definition of theta-1-3, but with new dependence to neutrino energy, the imaginary part of it adds a new term to the probability for a portion of the sine of the theta-m-square-3-1. Once we also add the new physics at the production side, which is just of the Gomoff-Teller kind transition, we see that we can have just a tensor interaction here. So the tensor new physics can appear at both production side and detection side through the real and imaginary parts, but the scalar one, which also has the real and imaginary parts only appears at the detector side. It's also important to note that all these epsilons which contribute to our oscillation probability are the off-diagonal elements of the epsilons. So by studying the oscillations of neutrinos, we can be sensitive to the diagonal parts of these new interactions, at least at the linear order with respect to epsilons. Also, once we put L2-0, we won't have any non-oscillatory terms, which means that the zero-distance effect which usually appears at a standard interaction of neutrinos is absent in this language, up to first order with respect to epsilons. So here we are showing the ratio between the probability at the distance of the far detectors over the probability of the distance of near detector, because this is the observable we will consider for analysis. The orange curves are the curves we get for the standard model case in the absence of all these scalar and tensor interactions. The blue and purple curves are the same curves are after considering the new interactions. Either considering the real part, putting my generic part zero, or putting the real part zero and just having the imaginary part. And we see that in the presence of the new physics, both the amplitudes will be shifted to up or down, and also the energy spectrum will be distorted. So that instead of having, for example, the minimum here, we will have the minimum at some other energy defense. So far I completely neglected talking about the right-handed interaction here, and that was because since all these coefficients are only off-diagonal coefficients, and the off-diagonal right-handed interactions are absent in the standard model effective filter Lagrangian. So we don't have any right-handed interaction if we care about SMF. However, this weak effective filter can be consistent by its own. If our new physics is not necessarily at very high energy, we can consider WEFT as a consistent theory. And in this case, we can also have the right-handed interactions as well. So the real part of it, similar to the left-handed interactions, since it's just a constant here, there is no dependence to not really know energy. It's, again, we observed into Tata 1.3, but the imaginary part, it just gives a constant term, and we can probe the imaginary part by studying from these experiments. In the traditional NSI formalism, that it is considered in the not-to-know literature, the way we study the new physics is assuming whatever new physics we have at the source or at the detector, what it does is just changing the not-to-know flavor so that instead of having a pure flavor of alpha,