 Welcome to this new edition of the a lot of physics webinars a Just well this week we have a manuela Becky from University of Sao Paulo Well, she's working actually in some Carlos the Institute to the physical the St. Carlos in Brazil well, Manuela a dts phd in Rome in And in France two of them and one in Taiwan, although I think she spent most of the time in in CERN and she got this a permanent position in In Brazil in Sao Paulo. Okay. Well, I Would like to remain Remind you that you can post questions here with this hashtag low OP And also if you are watching this through YouTube you can post your Comments and in the comment your questions in the comment section. Okay. Well, welcome Manuela Thank you Thank you very much for the invitation and Okay, so I Can start sharing the screen Okay, thank you here we go So Are you still there? Can you see the screen? Yes, you can hear you perfectly on the slides are there So, let me start by Explaining that the Results I am presenting you today Are the results the the the the fruit of a very fruitful collaboration between experimentalists and theoretical physicists and We are a very wide group that we dubbed the crack standing for cosmic rays alpine collaboration and This group includes physicists working mainly in France and in Brazil so This presentation is based on this work That was posted in archive in December last year and it is currently under review So in the slide three, can you see the slides moving? Yes, we can see everything So the main points about this work are Let's say three So first of all we provide an updated estimation of the secondary positron flux Based on a semi analytic method over an extended energy range and this is very important because we can cover Entirely the energy range of the measurements of the AMS experiment between from 0.5 GV up to 500 GV Moreover, we are able to solve the full transport equation taking into account all the effects that positrons undergo when they propagate in the galaxy and Moreover Once we have our secondary positron flux We can combine the secondary positron flux with the AMS positron data and we investigate the possibility That the excess of positrons with respect to the astrophysical background originates from the annihilation of that matter particles Okay, so This is very beginning Slide and just to summarize for those of you who are not familiar with this cosmic rays are high energetic particles produced outside the solar system, so in When talking about cosmic rays in the energy range between the GV and the TV we consider that the most likely the sources that are most likely to produce and Accelerate these particles are supernova remnants once the cosmic rays escape the production and acceleration region they propagate in the interstellar medium Where they undergo diffusion processes convection processes Re-acceleration processes and as a funk as a consequence of this propagation they can Occasionally produce other particles that we call secondaries so What about us in this picture Secondary and primary particle can be detected at hurt or Next to the atmosphere using Spaceborne or ground base detector and in particular today we will talk about the comparison with the data collected by the AMS experiment Space the tech a particle physics detector operating on the International Space Station Okay So back to the secondary positrons. What are the main ingredients for the production of secondary positrons? These particles are created by the interaction of primary cosmic rays Mainly hydrogen and helium nuclei on the interstellar medium. That's it also Composed mainly of hydrogen and helium. So as a consequence of this interaction as you can see here schematically Explain we have for example the interaction of a cosmic ray proton with the proton of the interstellar medium producing something and for example charged pylons and As a consequence of the decay of the charged pylons we can have positron To obtain the secondary positron flux prediction we have to take into account several Ingredients namely the spectra of primary cosmic rays the interaction cross-section between the cosmic rays and the interstellar medium The description of the galactic environment the solar modulation and the propagation so Following the work by David mohan and other collaborator since 2001 more or less and a lot of We did a lot of bio a bibliography We assume the galaxy to be axi-symmetric and we describe it by the two-zone model in this Model the first zone is the galactic disc and the galactic disc has a size of about 200 Parts x the disk is essentially made of 90 percent hydrogen and 10 percent helium and it is embedded in a much Larger second zone that is called the magnetic halo This magnetic halo Has a size capital L that is not clearly Whose side lies between one and 15 kilo parts as can be let's say inferred from the bottom to carbon ratio measurement Then in the cosmic ray transport equation that we see in the middle of slide six we have Several processes that occur to The cosmic rays once they are produced so the cosmic ray transport the question includes the space diffusion coefficient This k that is a function of e that has that depends on two parameters k zero and delta that can be Inferred from bottom to carbon ratio Then we have the energy diffusion coefficient this k ee That depends on the alpha and velocity that is also a parameter that can be inferred from bottom to carbon ratio the diffuser acceleration and the convection that is Parameterized with the VC that is the speed of the galactic wind produced in the supernova by the supernova in the disc So the five propagation parameter L k zero delta VC and VA Can be constrained by the bottom to carbon ratio and in our study We use the sets of propagation parameters that are allowed by the bottom to carbon ratio analysis made By David Mo et al in 2001 so in the little box on the bottom right you have the three benchmark Sets of propagation parameters that are usually gold mean met than max depending on the sides of the magnetic halo So mean is the one with the smallest sides of the magnetic halo and max is the one with the larger Magnetic halo sides of 15 kilowatts x Okay, so Concerning the source term for the secondary positrons this Capital Q the source term is given by this integral that you see in slide 7 Where we have the dependence on the cross-section between the cross-section of interaction between the cosmic rays and interstellar medium As well as the dependence on the primary flux so We can see in our study We use the parametrization of the interaction cross-section from kamai et al And we have checked that the effect We have checked the effect of other parameterization But we found that this is the most conservative. So we use this one In the slide 8 We can see The another important ingredient that is the flux of primary cosmic rays. So we are Very lucky because we can use the precise data from AMS and cream and using AMS and cream Proton and helium fluxes. We have an idea of the primary fluxes between Let's say 1 giga from G1GV up to several tens of TV So we use this data with parametrizations of this data where we can see that Our parametrization has a power law with the transition in the spectral index that arrives around occurs, sorry around 300 Jeff Okay So another important thing is the solar modulation The solar modulation affects the the propagation of a low-energy Charged particles let's say below 20 GV and the simplest model to link the Let's say the fluxes in the interstellar space to modulated quantities Affected by this the magnetic field of the Sun is the so-called force field approximation that you can see describing here where We can relate the unmodulated to modulated flux by this Potential that we call Fisk potential that is that depends on the time Where for example a solar cycle has a period of about 11 years so in our case we rely on the analysis made by Gelfietal published in 2006 and 16 that is based on AMS proton and helium fluxes and Voyager data Okay, so now let's go back to the propagation in the trans for the transport equation in the steady states Can be written Here as it's written in a slide in the box in the slide 10 So there you have all the ingredients that I told you before we have the convection We have the space diffusion. We have the energy losses and we have the diffusive acceleration and energy diffusion So we assume that the diffusion as well as the inverse Compton and synchrotron radiation take place in the halo Then on the other hand the diffusive Acceleration the Bremstra long and other low energy processes take place only in the disk where the matter is Concentrated so what we do is that we split basically the energy losses into disk and and halo to study the effect of this Phenomena separately and this is very important as you will see in a moment So let's focus a little bit more on these effects So besides energy losses as I said other relevant processes are the convection the diffusion and the diffusive Acceleration so on the left plot of the slide 11 you have the Flux of the secondary positrons Rescaled by the energy to the power 3.3 as a function of the positron energy So let's start with the light blue dashed curve that indicates for a given set of propagation parameter in these cases mad the flux of secondary positrons only in the case of diffusion Process only when when only diffusion is taken into account Then if on top of diffusion we consider the high energy losses taking place in the disk Sorry in the halo We see the dashed red curve and you can see that of course at high energy the the the energy loss is larger The flux is smaller Okay, then when we consider the diffusion plus the the Diffusive reacceleration we have the orange Dashed curve So you have an enhancement of the low energy say below 100 gv flux What happens now if we compare we combine diffusive diffusion plus high energy losses plus diffusive reacceleration Well, we get the purple curve That is a little bit shifted to low energies because we have high energy losses if we Switch we substitute so we consider diffusion plus high energy losses plus Convection for instance, we have the green curve Where the low energy part is the low energy flux is lower Okay, so long story made short if we combine all together we get the black solid line where diffusion Convection and diffusive reacceleration and energy losses are taken into account This is for one particular set of propagation parameters While on the right you have what happens if we combine For example, we will compare sorry not combine three sets of propagation parameter for instance the benchmark Sets mean mad and max then you have a dashed line Well, only high energy limit is taken into account And the solid line includes all the effects both the effects that happen in the disc In relevant at low energy and the effects that are That take place mainly in the halo and they are relevant for the high energies So in the end the solid red curve in the right plot Is the same as the solid black curve in the left except the scales are a little bit different Okay, how do we Get these curves In a minute. I will tell you so what we did is a very tricky and smart thing That was mainly from the theoretical point of view developed by matthew budo Under the supervision of pierzalati The transport equation is written here again in the case of posidrons and electrons It can be solved analytically only in the high energy regime because we neglect the low energy But we wanted to have the both disc and galactic and the halo energy losses So what we did we know that it's hard to solve the propagation equation when energy losses do not take place in the same region So to solve this issue we developed a method that allows us to consider the halo energy losses to take place in an effective way in the galactic disc So we want To reproduce this effect assuming that the positron lose energy only in the galactic disc But to so to do this we need we just we seem I mean simply not simply but we Boost the intensity of the energy losses processes occurring only in the disc in order to obtain the same effect on the positron so As a matter of fact we replace in the equation the energy loss term In the disc by a function That is an effective energy loss term that ensure that the solution of the transport equation Is the same both in the disc and in the halo. So the key factor is This function psi That you see in the slide 14 for as a function of energy for different Sets of propagation parameters and you can see for example that the scaling factor is larger for The large halo sides because we need to boost more the energy losses in order to have the same Result so equipped with our pinching factor and our method We're able to solve analytically semi analytical the full transport equation Taking into account all the effects that positrons undergo when they propagate in the galaxy both in the disc And in the halo and this is uh the very important result because using semi-analytic methods. This is the first time That such a result is achieved Okay, so once we have this Important result we use it to Study to To address two questions First question is what can we say about the galactic environment? And second thing is what can we say about dark matter? So first of all Let's focus on the galactic environment So In general by measuring secondary cosmic ray particles We get information on the galactic environment And in particular Cosmic ray secondary cosmic ray particles are also positrons that are Produced as a consequence of the interaction of primaries namely protons and helium with the interstellar medium So, uh, we know that actually positrons can be considered secondaries Let's say only below 10 gp. And in this case We can use them to constrain propagation parameters following Any idea that was developed by julien laval et al in 2014 That consists essentially of comparing the flux of secondary positrons with the ams data and Excluding so only allowing so setting cosines Excluding all the models That produce a secondary positron flux that overshoots The ams data So we did we we followed a similar approach in our case We know that the low energy part of the spectrum is affected by the solar modulation And to be conservative, we apply the maximal effect of the solar modulation Producing secondary positron fluxes using 1623 sets of Propagation parameters allowed by the boron to carbon analysis of 2001 And we test this set of propagation parameters by comparing the Corresponding secondary positron flux with ams data So in this plot in slide 15, we have the secondary positron flux Rescaled by the cube of the energy as a function of the positron energy So the black dots indicate the positron ams data And this envelope corresponds to The secondary positron flux is obtained For each individual set of propagation parameters So our idea was the following in order to set constraints on the propagation parameters We compare for each individual energy bin of the ams measurement. We compare the data to the model and we We exclude the models who Overshoot the ams data by more than three sigma Okay, so out of 1623 sets of propagation parameters. We only keep 54 as you can see in the slide 16 and if We Look at the corresponding propagation parameters. We see that They allowed Models that are the one indicated in pink in magenta in the plots in slide 16 The allowed model are let's say Are more Correspond to large halo sides Let's say larger than eight kiloparts x and small diffusion coefficient So in this case, we are basically excluding the mean and med Models, okay So this is also a very important test in order to constrain the propagation parameters And In slide 17 you see again this 54 Propagation, I mean the the positron flux rescaled by the energy to the cube of the energy as a function of the of the energy for ams data and the Yellowish maybe band Is the band that includes the that shows the 54 Propagation parameters that are allowed by our scheming method that I showed you before in this case We use the maximal. We maximize the effect of the solar modulation So in this case you can clearly see that ams data are incompatible with pure secondary hypothesis And in order to let's say Fill this gap between the model between the prediction and the data We need a primary source of positrons nearby the solar system In general, how can we solve this? puzzle which kind of Sources can produce Positrons high energy positrons in general there are let's say the most Common there are three Solutions to this puzzle Namely the fact that these particles are produced in galactic pulsars Or in the shocks of supernova remnants or as a consequence of the annihilation or decay of dark matter particles I apologize because here I just give a few references But there are a lot and I could not include them all but this is just to give you an idea In our paper we focus on the last Hypothesis that is the fact that these positrons can be produced as a consequence of the annihilation of the dark matter particle in the The vicinity of the solar system So in slide 20 we have a little reminder of how we do so basically we compare The measured anti-matter flux means the positron flux measured by ams And we compare it to the expected to the to the model And in order to build the model we need three main ingredients We need the propagation study as we did it before and on top of this we need the Primary positron and in this case the primary positron comes from dark matter annihilation So we need the particle physics information the annihilation channels the and the the different Particle masses as well as the dark matter density so In the slide 21 we have a sketch of this Dark matter source term and how we study it We have Our dark matter particle that can annihilate into For example standard model particles which may have Given lifetime and then they can produce Final positrons as a final product So the dark matter source term that is described in this slide depends on the astrophysics as I said So in particular, we have the dark matter density profile And it depends on the particle physics the particle physics term so the The positron spectrum at the source that is Obtained by the micro omega package version 3.6. So in our study We scan over the mass of the dark matter particle on the average annihilation cross section As well as on the branching ratio of the different channels as you will see in a minute To fit the ams data using the minute package They so have a let's have a look at the dark matter source term a combination of We use a combination of a five annihilation channels electrons mu on tau b and w Where the branching ratio Are considered as a free parameter So in this left plot, we have the primary positron fluxes For a dark matter particle with a mass of 100 gv and on the right We have the primary positron flux for a mass of one hand one tv so The our choice of combining just five annihilation channel And relies on the fact that this five channel describe quite well the various spectral shapes And avoids introducing too many free parameters So let's have a look at the result. We are equipped with a semi-analytic method to reproduce the Secondary and primary flux of positrons between 0.5 and 500 gv And the semi-analytic method is very flexible and fast So this allows us to test to make to perform a scan over a large parameter space Where we test seven models of this solar modulation 54 sets of parameters allowed by our scan and 20 Masses of the dark matter particle between 100 gv and one tv So in total we scan over more than 7 000 Models and this is on the slide 23 This is our result of the chi square of the models as a function of the chi square of the Dark matter particle mass in gv You have three bands because each one of these bands correspond to the envelope for a given value of the For a given case of the solar modulation Effect where we we actually tested seven, but we only showed three for otherwise is too Too too much confusion in the plot. So the red band is the maximum solar modulation effect the Green band is the average solar modulation effect and the blue band is the smallest Effect so you can see that our best fit occurs around 264 gv and the chi the corresponding chi square degrees of freedom is 1.5 The associated annihilation velocity average cross-section is About 300 times larger than the thermal Anni annihilation cross-section Then we did another test Instead of Dark matter annihilating into standard model particles we tested the hypothesis that the positron excess is Produced by leptophilic dark matter annihilating into four leptons through a light scalar mediator phi that we Took from the reference indicated in the case of this Dark matter leptophilic dark matter Anni annihilating into leptons only we only use three branching ratio As a free parameter electrons new ones and tau. So in the same scheme we Are able to Fastly scan over a large set of parameters. So we tested again the seven solar modulation Parameters the 54 propagation parameters and the 20 values of the mass of the dark matter particle Again here you have the chi square per degrees of freedom as a function of the mass of the dark matter particle for the three solar modulation Regimes and you can see here that the best fit Is found at 183 gv, but the best fit Has a chi square per degrees of freedom of 18 So you're maybe curious of having a look at the best fit and here They are in the slide 25. So these two plots show the positron flux Rescaled by the cube of the energy as a function of positron energy on the top you have our best fit For the case of the direct annihilation into standard model particles So and on the bottom you have our best fit with the one with the chi square reduce chi square of 18 In the case of the annihilation Via light mediators for the leptophilic dark matter Okay, so what can we see we can see that Let's say for the top plot that is the one corresponding to a chi square of 1.5 for the dark matter mass of 264 gv You can see that the data Are in fair agreement with the the model except for the first and the last two points While for the leptophilic dark matter the agreement is not very good. We have a chi square of 18 Moreover you it should be Notice a very important thing That if we require the dark mass the dark matter mass to be larger In order to accommodate these last two points Let's say larger than 500 gv This turns out to be much worse It as you can you would see also in the previous plot because what happens is that The the chi square is much worse because what happens is that the low energy part that is very precise Cannot be described consistently Okay So If I have a couple of minutes Okay, thank you If I have a couple of minutes I and so I do have a couple of minutes. Thank you very much Um, I would like to talk about one particular Kind of a test we did in order to validate the robustness of our study that is Most more focused on the effect of the cosmic ray primary Experimental uncertainties on the secondary positive on flux. So in the previous sorry in the previous slide 25 We have the best fit for our dark matter results and now I show you some Um, let's say a systematic study to test our the robustness of our results. So in particular The uncertainty on in the slide 27 We can see that the uncertainties on the primary cosmic ray flux Implies an uncertainties on the secondary positive on flux. Here you have the Source term for the secondaries as I showed you at the beginning And in order to assess this effect We could simply use the uncertainties of various parameters that are derived by the fit to our model However, this strategy has several weak points First the correlation between parameters is not taken into account Second the statistical and systematic uncertainties cannot be treated in the same way Because while statistical uncertainties are uncorrelated And follow a normal distribution the systematic one can be correlated and follow a non-normal distribution So in order to assess this we developed a Monte Carlo method To take both effects into account. So what we did for each ams and cream Proton and helium flux data point We generate a new random value according to the following strategy To take into account the statistical error It follows a normal distribution centered on the data point and its standard deviation Is equal to the statistical uncertainty To take into account the systematic error We assume that the systematic uncertainties are totally correlated and we generate a random value following a uniform function Centered on the primary flux and whose width is twice the systematic uncertainties Of both ams and cream However, we generate two random values Independently for ams and cream since they are uncorrelated So each in this way we get a lot of randomized fluxes and each randomized primary flux is fit to our model So we get a pdf for each individual parameter of the fit As you can see summarized in this slide 29 So we randomize on the left you have the proton on the top and the helium on the bottom Fluxes you see the actual fit to the ams and cream data in red And this band indicates all the randomized fluxes that we fit with our initial model That is the single power law with the the transition of the spectral index occurring around 300 gv So we have seven parameters and we fit each one of these fluxes to the model And instead of having a fixed value of the parameter, we have a parameter pdf So with this parameter pdf we can actually have an envelope of Secondary positron fluxes and this is just to give you an idea the fit parameters distributions in slide 30 That shows how eventually these parameters are correlated between them So for example the c is the constant For the proton flux the phi is the solar modulation parameter gamma is the spectral index of the Single power law rb is the rigidity of Where we observe the transition in the spectral index let's say the break rigidity Delta gamma is the transition between the the the the the the variation of the spectral index s described the smoothness of the transition and alpha is an effective parameter that we use To describe the low energy shape So combining all this together we have the results in the slide 31 Where we have an envelope for the positron flux as a function of energy in this case This envelope is for a given set of propagation parameter Okay, before I show the envelope where each individual positron flux correspond to a set of to a given set of propagation parameter In this case here, we have one set of propagation parameter But each one of these positron fluxes is obtained with the different set of primary cosmic reflexes, okay, and And so this may look large because of the scale, but actually the flux relative uncertainty that you have on the right plot is Very modest and it is of the order of six percent in the last energy bin that is up to 500 gb So the uncertainty caused by the experimental error on the primary fluxes has no great impact on the study of the secondary positrons and So this is the result of of this test So I think that I am already to my conclusions And I Today I presented you the results of very fruitful collaboration that We in during this in this collaboration We provide an updating estimation of secondary positron flux based on a semi-analytic method Over an extended average range that entirely overlaps with ams positron flux and this semi-analytic method for the positron flux is In this way, we are able to solve the full transport equation taking into account all the effects that positrons undergo when they propagate in the galaxy So we also Equipped with the secondary positron flux comparing to the data We are we reinvestigate the origin of the positron excess in terms of annihilation of a single dark matter particle Over the whole energy range of the dark matter than the ams data As a result, we find that the annihilation of a single dark matter species Is not enough to Explain the origin of the positron excess And I think that I am done. I thank you for your attention and I Hope to hear the questions now Thank you very much. Manuela. It was very nice presentation And well now we are going for the round of questions First I think we are going for questions people here in the room I don't know if you have questions. I don't know Roberto Nicholas Have any questions Uh, hey, I have a question. So Nicholas Okay, go ahead Nicholas, please. So Manuela if you go back to your slide 15, I think Uh, if I would say I move back to my slide 15 What happened Uh Yes, exactly that one. So you say that you're excluding the models Like yes Because you're overshooting the data, right? But what about the others when you have less, uh, flux than the data? They are, uh, considered But why Okay, that's only for secondaries. That's only for secondaries. Ah, okay. I see Okay, so on these models where, uh, these models, uh, the models who pass, uh, our The allowed models we can eventually imagine that we can put, uh, on top of the secondaries family component. Yeah, because of the, yes. Okay. So there are components Okay, more questions Yeah, I have a couple of questions for for Manuela So one in this slide that I don't remember the number I gave was 23 or something like that when you are showing the the different uh result When you have single annihilation channels, you know No, what's after when you are comparing That for instance, you cannot have that matter heavier than Uh, 500 gb because these two last being you cannot reproduce And yeah, this one exactly that one. So my question was, uh, if you have tried with Making combination of different annihilation channels to in some sense because Particle models of the market all the time they give like not pure annihilation. So it's just a kind of Combination of quarks and leptons in some cases or yes. Yes. This is uh, I'm not sure if I understood Correctly your question, but this is actually exactly what we did Um, uh, I may be, uh, sorry express, uh, I didn't express myself correctly But I need what I mean direct annihilation. I mean that there is no mediator To differentiate with respect to the leptophilic case Okay, but we Study a combination of five annihilation channels. It's not a pure annihilation into, uh, I mean It can be pure if We study we also the case where each individual one is, uh, only one is 100 and the others are zero, but in general the branching ratios are Mixed Yeah, no, yeah, this part is sorry. I didn't yeah No, that was my question if you try this and another question because I was very amazed with this pinching method If if you have tried or it's in the plan to try to To compare this method this pinching method for example with observation with gamma rays or radio because This is a effect that is going to affect all the propagation in all the parts of the galaxy of the diffusion zone So, I don't know. I mean like a further test of this pinching method could be Try other type of servables a part of the cosmic reflexes so, um I'm probably not the most entitled person to talk about the project For the pinching method part, but I believe that because the the theoretical part Is more also developed in collaboration with a lot of colleagues Uh, especially matthew buddho From But I believe that this is in the in the list of of things to do However, we are also very interested in updating our computations using the Latest bottom to carbon Ratio flux ratios published by ams, but this is for sure Another another important thing to Yeah, for the reason I was thinking that this could be interesting but Like all the check from this pinching method. What is the the output for instance in galprop because also I mean, I guess for the electron position. I'm not sure that it is included this type of No, but maybe they try to solve the full transport equation. Yeah, exactly in in In galprop and as well as other numerical Codes Like jagon in general you do not need to make this kind of Trick because you can solve the question numerically this kind of The pinching method is very useful to solve semi analytically because otherwise you just cannot solve the question analytically but So it is in galprop in general It's not it's not needed because they solve it numerically Yeah, and also it's going to take longer in galprop to do this analysis that you have done Yeah, I mean for us And so equip the with the pinching method we are able to do To solve the full equation and then the advantage and and also take advantage of the real peculiarity of the semi analytic method that is the fact that it's fast So with the to do this analysis just to give you an idea to scan over More than seven thousand sets of Parameters plus the sorry the 54 parameters plus the seven values of the physical potential plus the 20 mass of the dark matter If I remember correctly it took us 24 hours now very short Of course on multiple cores of of the Of course, it's not on a laptop, but anyway That you make on multiple cores and uh in in 24 hours. It's done in uh on uh, let's say numerical code Okay Yeah, no, I know it could take forever. Yeah Exactly So We have developed this this method because now we are able to make scan Scan very very fast scan Yeah, also can be done for doing this kind of the Of the propagation parameter No, because one of the stuff that is all the time complicated is like When you have the the the diffuser acceleration or over effect is kind of all the time is It's an unstable solution Let's say because one effect tend to increase your flags a low energy and the other effects tend to reduce your flags Yes, so it's very Yeah, but there is a very interesting this method of pinching because Can give you an idea what is happening there? Yes, but in the path was not included. Yeah So yeah, thank you. I guess there are questions for the others Are you so fast a second question? So, manuela, you are using this born to carbon ratio, but the results from 2001 or something like this, no? But a ms has measured this ratio as well, right? Yes, and now we are working on this. Okay. Okay. Yeah So you plan to update this with the new results Uh, so first of all we plan to publish this uh as possible and we are also working on Uh, first we need to study the new The sets of propagation parameters that are allowed by the new ms data Second we will update the result. Yeah, but first of all we want to publish as it is Yeah, but but do you expect this to to change dramatically results or not? I mean how this burned to carbon the new results compared to the old one Um, look, I prefer uh to tell you let's Wait because uh, it's more interesting to surprise Okay, otherwise you will not be interested in following the next paper if I tell you No, I don't know Okay And I have another one if I may Yeah It's about and on your slide nine. I think uh, you mentioned the solar modulation Mm-hmm. Okay. Just to have a uh an idea that that solar modulation Is only an overall normalization or I'm I'm kind of confused with that I mean, what's the effect of the most solar modulation? Okay, my computer is changing the the slides with its own Say criteria However, uh, no, I think now it's going. It's okay. Yes. Um, so the effect Of the solar modulation Is what you see in in this in this slide in a first Approximation because this model is very simplified Okay, but basically the effect of the solar modulation is to Modify the shape of the flux especially in the low energies Okay, and So this uh shape modification In a very simplistic approach is seen is described in this formula So the effect of the magnetic field of the sun depends on the z of the particle and on the atomic mass and that is of the proper of the cosmic ray and then on the this phi potential that can be estimated that they use a neutral morning in neutral Or also on The parameters and also comparing the what this is what Has been done in this paper Comparing the voyager data that are outside Heliosphere and so not affected by the magnetic field and in the data of a mess Well, you say that it affects most low energies low energies meaning what? Okay, so low energy. I don't have Let's say a definition, but I would say that May below 20 gb below 50 something like that Okay, I would say that above 50 gb the effect is negligible, but it's very small above 20 gb Thanks Okay, if there is no more questions, I would like to make a question and regarding the this this Statistical test or Monte Carlo test that that you did a My question is more. Well, you did this test to to Prove what will be the effect of primary flux and But I think also That kind of test can be done for for the feet itself No, when when you fit a dark matter parameters and all these things Yes I think well this sky square is kind of simple for this highly complicated model in which you You can I don't know if a chi square tells you something about what is happening there If you don't consider this kind of a correlation Sorry, I think that your question is very elaborate like this. I don't see the so can you rephrase it? Well, the my point is well that you this test about Primary fluxes with this Monte Carlo why you did the perform kind of similar test for the dark matter feet Uh, so the question is why we did not Use this secondary randomized positron fluxes and then To in order to make a fit To the dark matter Primaries, this is your question Yes Well I think it's a Good question. However, the I we we actually tried In at the beginning of This study The effect was also very small. So, uh, we didn't We we did the check the very beginning. You see that actually the the effect of the uncertainties are negligible So in the end we didn't Go ahead because the effect is negligible Okay In the end the effect if you look for example in this slide In this right plot. You see that the effect The uncertainty caused by the primary experimental error On the second the ripositrons is In the highest energies Where of course everything every uncertainty is larger It is most of six percent, but this is the highest thing if you look Below, uh, the the the uncertainty is much smaller. So, uh In the end we did not consider it It was okay trying Okay, well, we we have a question in in the chat in youtube And this is by chi sheng feng and the question is if The fit to ams also are also consistent with the galactic center gamma ray observations By with fermilato or s well in this study, we only, uh, focus on the Depositron fluxes we do not Uh Make any kind of Correlation with the depositron with the other with other messengers. Okay We do not Compare with other With other messengers we do not compare with gamma rays in the galactic center But for instance the parameters of the dark matter That you get for the best fit are compatible with for instance gamma ray constraints Or are they Look in this very moment. I cannot remember. However, our fits are not Extremely good. So Even if they were compatible, they would not I mean In in this moment, I cannot remember. I'm sorry. Okay But what it's important is that the the the fit is not extremely Okay And well one final question is regarding well if you go to the The plot when you have the fittings is The what sorry the data you have the data and the fit with these two dark matter models I think it's a couple of slides before Yeah, right that one That that will be like the best fit In both cases, but well You are missing for example in the in the first scenario. You are missing the The high energy points the two And that would be any physical Phenomena that can explain this I mean like maybe you are missing some background Let's assume that this is the armatter and you have the armatter there You could you you will be missing Another background at higher energies. Maybe some another component appear They're Said these points or something like that It seems hard to imagine. I mean What I can I mean I don't know if I am able to speculate a lot in this moment, but I mean, let me just Let me just brainstorm a little bit So our best knowledge of the secondary component is expressed in The green light green sorry green line. Okay on the on both top and bottom plots This secondary component is Okay, this is a given benchmark model, but with some uncertainties But it's not it cannot vary in order to you see you saw it already in the other plots that is considering even In the between the seven thousand 600, I don't remember Propagation parameter models that we test There is no way we we achieve large Flux in order to cover the data then So the result of this Fit tells me that this dark matter pure dark matter Hypothesis is not enough Then eventually so to we can imagine Another background If I knew another background, I maybe in this moment we could have Included in in the paper, but instead maybe it can be possible that different dark matter Candidates or dark matter plus astrophysical sources can Accommodate can describe these last two points. For example, if you assume that at least the dark matter candidate of 250 64 gv is the responsible for this this data I don't know if I I hope I Yeah, I to clarify. I clarified your your point Okay, thank you very much my opinion. Yeah, I think this is the most conservative way Okay, interpret this And well, I think we are well, I have a question From our roberto has a question very very very short Manuela Do you which type of dark matter profile you use for the for this analysis because I would expect that The the the profile may have some impact especially if it is kind of Spike in the center or smooth No, we use the navarro frankenwhite. We did not check against other I Are there models? Okay. Yeah. Yeah, it's just the standard navarro frankenwhite just the benchmark one. Yes Okay, thank you Okay, I think we should thanks manuela for this very nice webinar and also, well, I would like to mention that a The video will be post on facebook and our On youtube in our youtube channel. You can see this As many times as you like and Also the slides we hope we will have those slides soon in our web page and Okay, we can Reconvenience in two weeks. We have another webinar by Tian Tian you I think it's the name and I think it's about Diet detection of dark matter And I hope Many of you can connect and thank you very much, manuela Thank you for the invitation. Bye. Bye Okay