Citizen science: Simulation of a neutrino signal at CERN’s LHC with its uncertainties
It was a good long break we had for this collaborative project on Hive, but we're back on track. It was great to know that I am still familiar with what we did from the previous episode of this project since this week's tasks are an extension to the simulation we've done a month ago.
This project is headed by @lemouth, our professor 🧑🏻💻 and resident particle physicist in the StemSocial community. The focus of this work is the simulation of a signal typical of neutrino mass models at CERN's Large Hadron Collider (LHC). In the Standard Model of elementary particles, neutrinos are considered massless; however, as observed in experiments, these particles are massive. And that is what we're trying to address in this project, there must be new particles responsible for the origin of the neutrinos' masses. We look into these new particles as they yield specific signals at particle colliders. Our reference article that is also authored by @lemouth has considered such signal for collisions producing a pair of particles called (anti)muons. We extend this by considering other pair of particles such as electrons, positrons or even by a mixed pair including one muon and one electron or one antimuon and one positron. There's a lot of exciting work to do! And if by any chance, this has caught your interest, it would be great to have you onboard. :)
Just a recap on what we have done so far:
- Installation of the tools [MG5aMC] necessary for particle physics simulation
- Using the MG5aMC to simulate top quark production at CERN's LHC
- Installation and use of MadAnalysis 5 for detector simulation and event reconstruction
- Investigating top quark production at CERN's LHC using MadAnalysis 5
- Exploring a neutrino mass signal at CERN's LHC using MG5aMC.
And for this week's tasks, we go back to the process we have considered, whereas protons are collided inside the LHC. At high energies, the constituents of protons or the quarks scatter during collision. These initial quarks emit a very energetic W boson by virtue of the weak force. The two W bosons interact with each other by an exchange of a heavy neutrino N, which is responsible for generating the masses of the neutrinos of the Standard Model as proposed in our model. This exchange produces a pair of leptons of the same electric charge, as mentioned, the reference article considered the case where these two leptons are either two muons or two antimuons.
The calculation of the production rate associated with the above signal is a perturbative calculation. From the earlier episodes of the project, it was mentioned that our calculations will concern infinite series. Calculation of an infinite series is impossible to do, at some point, we only need to consider some terms. The first term is the dominant one, which was what we have calculated from the previous episode. We call this leading-order calculation as we have ignored all the terms except the leading one. Our work for this week is to determine the uncertainties due to missing higher-order terms.
The next installation of citizen science will be the performing the laborious next-to-leading-order calculation, which is not easy to handle numerically, as it deals with infinities that cancel each other. In doing this, we include more terms and in return, we expect that this will reduce the uncertainties we have calculated this week.
Let's get started!
We start by running MG5aMC in the terminal with
./bin/mg5_aMC assuming that you're already on your working directory. The commands below were the similar ones we use from the fifth episode.MG5_aMC>import model SM_HeavyN_NLO
MG5_aMC>define p = g u c d s u~ c~ d~ s~
MG5_aMC>define j = p
MG5_aMC>generate p p > mu+ mu+ j j QED=4 QCD=0 $$ w+ w- / n2 n3
MG5_aMC>add process p p > mu- mu- j j QED=4 QCD=0 $$ w+ w- / n2 n3
MG5_aMC>output espresso_lo
The next step is to recalculate the leading-order production rate associated with our signal and this time, we include the estimated uncertainties inherent to the calculation. Similar with how we used MG5aMC previously, we will configure the neutrino model we considered by tuning the parameters necessary. By launching the model, we modify the param_card.dat and run_card.dat as specified in this week's tutorial blog
Here are results I've got for the first run, where the mass considered for the heavy neutrino is 1000 GeV. The additional information we got here are the two uncertainties, scale variations and PDF variations. Calculating for the total uncertainties, we add these number in quadrature, thus getting the results of 0.01393 pb with an upper uncertainty of 12.32% and a lower one of 10.76%.
The remaining part of this week's tasks is to consider different masses of the heavy neutrino. Again, I have used the same mass values and let my computer do all the hard work of calculating the cross sections rates and uncertainties.
Signal rate dependence on the neutrino mass at 13.6 TeV
| Neutrino mass (GeV) | Cross section (fb) | Error |
|---|---|---|
| 50 | 3.843 | ±0.00892 |
| 100 | 8.576 | ±0.0237 |
| 150 | 12.23 | ±0.0405 |
| 250 | 16.14 | ±0.0560 |
| 500 | 17.80 | ±0.0578 |
| 1,000 | 13.91 | ±0.0455 |
| 2,500 | 5.69 | ±0.0167 |
| 5,000 | 2.02 | ±0.0038 |
| 10,000 | 0.57 | ±0.0014 |
| 20,000 | 0.15 | ±0.00019 |
The plot below shows the signal rate dependence on the neutrino mass. I have included error bars, it looks like the error bars in the x-axis, but it's actually the caps of the error bars in the y-axis.
Estimated uncertainties of the production rate for neutrino masses at 13.6 TeV
| Neutrino mass (GeV) | Scale variation | PDF variation | Total uncertainty |
|---|---|---|---|
| 50 | 2.56% -2.67% | 5.87% -5.87% | 6.40% -6.45% |
| 100 | 3.87% -3.73% | 5.78% -5.78% | 6.96% -6.88% |
| 150 | 4.89% -4.56% | 5.82% -5.82% | 7.60% -7.39% |
| 250 | 6.34% -5.69% | 5.72% -5.72% | 8.54% -8.07% |
| 500 | 8.57% -7.40% | 5.71% -5.71% | 10.30% -9.35% |
| 1,000 | 10.80% -8.99% | 5.72% -5.72% | 12.22% -10.66% |
| 2,500 | 13.50% -10.90% | 5.90% -5.90% | 14.73% -12.39% |
| 5,000 | 15.00% -11.90% | 6.02% -6.02% | 16.16% -13.34% |
| 10,000 | 15.60% -12.30% | 6.16% -6.16% | 16.77% -13.76% |
| 20,000 | 15.90% -12.50% | 6.15% -6.15% | 17.05% -13.93% |
As I end this report, with the estimated uncertainties we got and calculation of the total uncertainty, I remember this thought from a journal I read a long time ago. My memory is failing me a little and I can't seem to find the paper from the keywords I vaguely remember, but here's the thought: It's not that physicists don't want uncertainties, what they aim is to quantify those uncertainties and reduce it further.
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Nice job! good to know that you are back to track! What is your background, just curious!
Cheers,
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I studied physics 😅 although I'm only learning about particle physics now, through citizen science.
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As I mentioned to @agreste, today was a big day: two reports. Not one; two! This made me super happy and even if I wanted to keep their review for the train trip to Amsterdam of tomorrow, I could not resist and dealt with that tonight.
The calculations you did were correct, but I don’t understand the final plot. There is something weird with the error bars, and I think that I understand what exactly. But before dealing with this (I will propose a few paths to explore to solve the issue), let me first go with two minor comments.
I must add a small clarification here. What you mentioned is the case for the process that we consider in this project, in which two quarks or two antiquarks scatter. However, in general, we should keep in mind that not only (anti)quarks can scatter, but also gluons.
What a nice folder name! I totally like it!
I have the impression that you took the numerical error associated with the calculation (that is indicated in the first table) as the error to include in the plot. This error, which is of a few permiles, has however nothing to do with the one that originates from the truncation of the perturbative series. The latter is of the order of 10%.
The numerical error is instead related to the fact that our calculation involves a highly-dimensional integral that is computed through a Monte Carlo method (involving random numbers). The method itself therefore returns an error, that we must keep as small as possible. Such an error (less than 1%) is however much smaller than the theoretical uncertainties inherent to the calculation, and can thus be neglected.
In the figure, we need to plot the second error (the one of order 10%), and on the Y-axis. It is the error on the cross section (or the rate), and not the error on then heavy neutrino mass (there is no error here, as it is fixed precisely in the paramcard).
Also note that in matplotlib, you need to provide absolute errors and not relative ones.
I am confident that with the above clarifications, you will manage to finalise the plot, which already looks good. Please let me know.
This is so true! This consists of an always on-going task.
Cheers!
Haha, the review didn't make it to the train ride. Thanks for the feedback! I'm not really if I got the right values to use for the plot. I hope I got it right this time, from what I understood, I'll need to show the error of the cross section (plotted in the figure) from value before it was truncated?
I didn't understand the above statement, and I therefore do not know how to answer the question. I am really sorry. What do you mean by "before it was truncated"? Do you mind providing some more details? Thanks in advance.
Oh, sorry. Let me rephrase my question. From what I understand in your previous comment here:
..is that what I need to include in the plot is the truncation error of the cross section?
I re-plot the figure with the new error values got from the terminal log. Can you confirm if this one is right? Thank you. :)
OK I think I got your point. Let me try to re-explain (if I am off, please let me know again), with the example of the 50 GeV mass point. I will also use approximate values for the errors, but this should not change the flow of the discussion.
The calculation has returned three types of errors, plus a central value.
The total error on the results is obtained by the combination of the PDF and scale uncertainties, and we get a total relative error of about 6.4% (cf. second table). This gives a corresponding error of about 0.25 fb, which needs to be reported as an error bar on the figure. I have the impression that your error bars (on the last figure) are too big.
Is all of this clearer?
Cheers!
Oh, I totally understand it now! Thank you. :) I replot the figure (again haha) and got this:
Excellent! Glad to see this (this looks OK).
Note that I will wait a bit before releasing a new episode, as some community members mentioned to me that they wanted to try the project out. Therefore, episode 7 should be released by the end of the month.
Cheers!
Oh, nice! That's really great. Your mention of the project during HiveFest sparked curiosity, I noticed it from the the live chat during the broadcast. :)
I have indeed done that, and I actually explicitly mentioned your work, as well as that of @agreste. I believe it was a fair thing to do.
For the rest, I still hope that @eniolw will catch up, so that we will have three up-to-date participants in the project, and that @itharagaian (and possibly others who mentioned it to me at HiveFest) will join us!
Cheers!
Gotta startup a specific machine, but as soon as I feel better, be sure I will join and try it out
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I am glad to read this. Good luck! ^^
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Really cool post and I think I'm going to have to go follow you so I can catch up on all of this interesting research!
Thank you very much for your extremely high quality physics content here!!!!
Thank you so much for your kind words, glad you enjoyed reading this blog. I think you'll enjoy reading @lemouth 's blogs too if you'd like to consume more physics content. 😀
Thank you very much and I clicked on the follow button for that account!
Hopefully you will have an amazing day today.
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Dear @travelingmercies,
May I ask you to review and support the Dev Marketing Proposal (https://peakd.com/me/proposals/232) we presented on Conference Day 1 at HiveFest?
The campaign aims to onboard new application developers to grow our ecosystem. If you missed the presentation, you can watch it on YouTube.
You cast your vote for the proposal on Peakd, Ecency, Hive.blog or using HiveSigner.
Thank you!
This is really great @arcange! This reminds me of the Complexity Weekend , I'm still not sure what the cohort covers but I got to know about it from people in the academia. The Hunt as mentioned in the proposal is somehow the same with how Complexity Weekend gives platform for participants to join or start new projects. (It was a bit intimidating but collaborative works are real exciting work).
Hoping to see this onboarding of developers from outside Hive and even the current users (like myself! ^^) see this materialize.
Thank you for your feedback and support @travelingmercies, really appreciate it! 👍
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STOPCheck out the last post from @hivebuzz: