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A Mathematical Search for the Mass of the Standard Model Higgs Boson

fair higgs boson lambchopz physics science

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#1 LaMbChOpZ

LaMbChOpZ

    Lead Particle Physicist and Musical Orchestrator

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Posted 14 March 2013 - 09:39 PM

Well, I've been pretty inactive lately thanks to what you are reading about now. For those who don't know, I'm into particle physics and am also involved in a few science-related activities (Pennsylvania Junior Academy of Science and a few science Fairs) where I devise my own project and test it. This year, my 5th year in PJAS, I have been able to follow my passion and create a project I could only have dreamed to complete.

My project looked for a way to mathematically track the data collected for the Standard Model Higgs Boson search at CERN (European Organization for Nuclear research):




A bit of Background on the matter:

Standard Model Higgs:
  • Made up of a subatomic particle (Higgs Boson) and a ubiquitous field (Higgs Field)
  • Predicted by a group of physicists led by Peter Higgs (where the name comes from) in the 1960's
  • Field is responsible for giving electrons and other subatomic particles masses (like quarks, protons, leptons, etc) through Higgs Mechanism (the more a particle interacts with field, more mass it acquires)
  • Boson will provide proof of the Higgs Field existing



Now, it may seem easy to think "oh, that doesn't seem like a hard thing for a particle to do, create mass", but it is. This boson fits in to a gigantic theory called the Standard Model. The Standard Model is like a gigantic puzzle, trying to fit all the known particles together and explain how they interact with one another. This theory is not only based on conceptual thinking, but complex mathematics called the Lagrangian. I won't go too far into detail, but these PDF's explain in detail how the equations are formed, what they do, and etcetera. The equation basically breaks up into creating a particle that is massive, scalar, and self-interacting, fitting the description of the SM Higgs.

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This particle is found via the the Large Hadron Collider at CERN (LHC). This is a gigantic particle-accelerator that collides millions upon millions of protons together every second.





Now, the experiments at CERN that search for the SM Higgs are the ATLAS Experiment and CMS. I was able to email and get in contact with a member of the ATLAS Experiment. He provided me with hundreds upon thousands of graphs to use. Within the links below, the GIF graphs show the accumulation of data. Some of this data was used in my project for analysis.

https://twiki.cern.c...cale-Short2.gif
https://twiki.cern.c...cale-Short2.gif
https://twiki.cern.c...e-NoMuProf2.gif
https://twiki.cern.c...e-NoMuProf2.gif

The actual graphs used can be found somwhere in here: https://atlas.web.ce...SICS/CONFNOTES/



So, after combing through these graphs, choosing the 8 I wanted to use, and asking for their data plots, I ended up having to estimate all the data points myself due to legal issues with giving me the plots. These graphs ranged from January 2011 to December 2012. (I will upload pictures of the graphs used in a little bit)

After this was done, I tried to create a Java/HTML5 program that I could put the data coordinates in, have them show up on a virtual graph, and have the equation graphed with the equation. However, the program took a turn for the worse as I ended up struggling through it and was not able to fix the issues there were with the data manipulation and accumulation, so it was trashed. However, my school's laptop has a graphing program (LoggerPro) where I was able to input the data coordinates, graph it, and get the equation. With the equation used, it gave me the estimated sigma value and estimated mass.

(Graphs are uploading and will be included later)

(Data table is being uploaded and will be included later)


In conclusion, it was found that I could mathematically track and predict the mass of the SM Higgs Boson using the ATLAS Experiment's data for the SM Higgs Boson search. If I am able to get this program working (maybe with someone's help on here), I would be able to use it at the fair I am going to in the beginning of April as well as send it to my CERN contact.



At my PJAS meet, I received a First Award Perfect Score, only one of 4 from the 42 members from my school to participate, and only one of a select few from the entire meet. At the local science fair I participated in on Sunday-Wednesday (March 10-13), I won 1st place in high school mathematics and was a candidate for best in fair. Although I did not receive best in fair, I did win a Society of Professional Engineer's award for Mathematics. From winning 1st place, I am moving on to the Delaware Valley Science Fair in the beginning of April. At this fair, I could win partial/full scholarships to Drexel Univeristy, University of the Sciences, as well as many other colleges, and take home a small portion of the over $1,000,000 given away in scholarships that evening. If I do win at the Valley fair, I may even be able to go to the Intel International Science and Engineering Fair!


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It stood out above the rest :P
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The candidacy for best in fair was realized with this (just one of 4 people to receive this).
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Coincidentally enough, CERN announced they are almost certain they've discovered a Higgs Boson, but they still need to do more work to determine if it is indeed the SM Higgs. This won't happen, however, until 2015 when the LHC is finished repairs. CERN's Announcement about Higgs

If you have any questions (other than when I will be uploading graphs and such), ask away! If you are interested, I can also send you the 70 page paper/report I wrote for the science fair that covers the topic in much more depth than I did here.

Edited by LaMbChOpZ, 14 March 2013 - 09:47 PM.


Member of a few physics experiments; Orchestrator and/or Copyist for a few musicals.


#2 amagzi24

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Posted 14 March 2013 - 09:45 PM

Well I would, but I don't understand 99.5% of this, so... but seriously though, this is some serious, awesome stuff. The fact that you became proficient in this field and then found a way do do something in it that no one has done before, at your age, it amazing. This is national science far quality. Maybe even international, as far as I'm concerned. Fantastic job!

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#3 commando

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Posted 14 March 2013 - 10:12 PM

I'll give it a shot, I too have an interest in sub atomic physics, yet I doubt my understanding is on the same level as yours. Fermi-lab is 30 minutes away from my place and I keep meaning to sign up for a tour one day. I would have a really cool opportunity through school to see the place but band got in the way. Just out of curiosity, what field do you want to go into?


#4 TheSUCKCrew

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Posted 15 March 2013 - 02:36 AM

Yeah sure, send in to me!



#5 BGTKing

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Posted 15 March 2013 - 05:29 AM

Sounds like Matlab would be a good program to use to hold and process your data.


#6 Witting

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Posted 15 March 2013 - 10:28 AM

If you have any questions (other than when I will be uploading graphs and such), ask away! If you are interested, I can also send you the 70 page paper/report I wrote for the science fair that covers the topic in much more depth than I did here.

if you want you could send me it because i'm learning a bit about sub-atomic physics because in may i'm going to spen 2 days in the LHC myself.

Edited by Witting, 15 March 2013 - 11:46 AM.


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^ thank you CCI

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#7 RCT2123

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Posted 15 March 2013 - 04:47 PM

Sounds like Matlab would be a good program to use to hold and process your data.


Ahh Matlab. The lazy engineer's language (so by that I mean every engineer's).

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#8 Maxlaam

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Posted 15 March 2013 - 05:55 PM

Had a course about MATLAB today, pretty annoying language syntax wise.


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#9 commando

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Posted 15 March 2013 - 08:22 PM

Ahh Matlab. The lazy engineer's language (so by that I mean every engineer's).


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#10 BGTKing

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Posted 16 March 2013 - 06:29 AM

You can do some pretty awesome things with Matlab & Simulink. We use it extensively at work.


#11 RCT2123

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Posted 16 March 2013 - 02:19 PM

You can do some pretty awesome things with Matlab & Simulink. We use it extensively at work.


Oh for sure. Everything is very easy to do in Matlab. That's why I was making fun of Engineers for using it.

BTW, where do you work BGT?

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#12 Jogumpie

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Posted 17 March 2013 - 07:35 AM

Max, Matlab is awesome.


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#13 LaMbChOpZ

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Posted 24 March 2013 - 10:04 PM

So, results of my county fair:

First place in High School Mathematics (9th-12th grade)
Special Award by the Pennsylvania Society of Professional Engineers in Mathematics (get to go to a dinner and get awarded $$$)

This means, I move on to the next fair - the Delaware Valley Science Fair! It's April 2-4th where students from PA, Delaware, and New Jersey who won in their county fairs come and compete. I will be in the 11th grade mathematics category and will compete against several other 11th graders in mathematics (there could be just a few, or almost 20 people competing against me...). I feel that I have a good shot this year judging from what a lot of people have told me about my project, but there's no way to really tell. Like I've said earlier, I have a chance of getting amazing awards this year. I could get full or partial scholarships to Drexel University, University of the Sciences in Philadelphia, and a few other places. I also could win money, special awards, and/or a category award (1st, 2nd, 3rd, Honorable Mention) in my category.

The DVSF fair will follow the same process as the county fair, but our interviews can last much longer. Typically, interviews are 5-10 minutes long, but some of these can be 10-15 minutes long and you could be interviewed several times by category and special awards judges. Last year, we were interviewed from 11-2pm, then had to wait for 2-3 hours for the judges to make decisions and special awards judges to make their rounds and interview. At 5-6pm, we find out who should show up to the awards ceremony/ceremonies, depending on which type(s) of awards you've won. You find out by a mad dash to 6, 8.5 x 11 inch papers posted on the walls with the winners names and which type of award(s) they've won. Here's a picture from last year:

https://sphotos-a.xx...460245560_n.jpg


It can be a mad-dash to find out....
https://sphotos-b.xx...348038031_n.jpg


Anyway, the real point of this post was to inform those of you who were interested that my research paper for this upcoming fair is finished. It is actually uploaded to this post. Now, the PDF itself is not all 121 pages. Along with the other two attachment below, I have 2 research papers by CERN from July 5th and March 14th that are about the Higgs Discovery. It takes up a good 40 pages, but really goes in depth about the findings better than I could. Now, if there are any of you who are into physics, remember, I am just in high school with no real experience with this type of physics. Granted, I'm still in pre-calc and honors physics, so it may not be perfect. If you have any questions or suggestions, post them!

Enjoy!

As for the MATLAB, I am looking in to it now. I may not be able to finish the program by next week. However, if I can start it, I will try my best to finish it.


EDIT: Well, the upload didn't work. If you are interested, PM or post your email and I will send it to you as soon as I get it.

Edited by LaMbChOpZ, 24 March 2013 - 10:19 PM.


Member of a few physics experiments; Orchestrator and/or Copyist for a few musicals.


#14 Witting

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Posted 27 March 2013 - 01:52 PM








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