Derrick2011

[|My Many Eyes Account]

[|Excel with Cuts 12/7/2011] Final Project

The Getting Started Milestones

The CMS- Compact Muon Solenoid is a detector built to investigate a wide range of physics. It has the same scientific purposes of the atlas experiment looking into the Higgs-Boson, dark matter, and extra dimensions. Higgs Boson- This is the elusive object the particle physicists have been searching for. It is our theoretical source of mass within the Universe. We are in an exciting time, because we are on the verge of either discovering the Higgs, or it doesn't exist at all, at which point we will have to turn to our theorists to make a new conclusion

Dark Matter- The Universe is vast, really vast, in fact we have only observed 4% of it with all our technology. Dark matter seems to make up at least 72% of the Universe. It is the source of the vacuum effect throughout the Universe and maybe why space is so cold. This is another big goal of Particle physics

Extra Dimensions- One of the more ambitious searches, if not crazier ones, many know that there are 4 dimensions. That we know for sure exist. However, some physicist speculate about gravity, and how we don't feel the everyday aspects of gravity, and that there may be up to six more dimensions in which the true force of gravity is felt. I have some serious questions about this one

Know Your Detector

CMS why is it so big?- It is the same weight as 30 jumbo jets or 2,500 elephants. This detector is an immensely huge piece of machinery built to measure the tiniest events in the Universe. It's size comes from necessity, as the bigger it is the more accurate it becomes. The CMS also must withstand the high energy caused by the collisions and still be able to measure them. Al lot of the size also comes from the iron needed to offset the massive magnetic forces within the detector thus making it a very large machine that runs like a Swiss watch.

Detectors and Sub Detector etc...

The Superconducting Magnet- it looks to be located right in the dead center. It creates a field of 4 Teslas, or about 100,000 times the magnetic force of earth to help measure the events.

The Tracker- this is the very center of the detector and it is the part that tracks the paths of events down to the width of a human hair. The Hadronic and Electromagnetic Calorimeters- the Hadronic measures the forces of the protons while the electromagnetic measures the forces of the electrons.

The Muon Chambers- the measure muons, which are like heavier electrons, and who can also penetrate the steel of the other chambers.

The Properties of the Proton

The Proton- the proton can be broken down into quarks which interact with each other in the detector and cause the events. Through this we can analyze the data and come to conclusions within the large hadron collider Detecting Indirectly- through analyzation of the directly detected events we can sometimes see events that were not picked up the detector and thus we indirectly realize that they happen and study them

Working With Excel and Matlab

I have been pretty familiar with Excel, having taken two years of Computer apps (about half the class was Excel), and Matlab is slowly coming to me. With the help of the unofficial textbook I'm slowly seeing the similarities between the programs, but more importantly the differences. MATLAB is a giant program with tons of variables, it would probably crash my crappy computer. However, this vastness comes with a really large learning curve to get over, but I'm gonna be working on that. Hopefully by the time this project has concluded I'll be competent at it.

I've been looking into the Higgs- Boson lately and the news that we might just have to go back to the theorists. A lot of the alternative theories sound much more complicated to Higgs. With my knowledge of Particle Physics right now I couldn't make heads or tails of the specifics, but I did get a broad overview of each. Although every theory as different wrinkle or variable, they all seem to share the concept that there is no God particle but maybe a string of events causing the effect that the Higgs does. This all except for one theory the Top Quark Condensate theory which is the one I have the hardest time understanding. To satiate my curiosty I will be looking into the diffrent particles types more in depth, to obtan a better understanding.

I have managed to get the posts back up. The wiki was storing them as drafts, becuase they weren't going through properly and I had logged off before they were properly uploaded and saved.

The detector and the particles that go through them

The Tracker: Picks up anything that has a charge, the middle of the detector. Electron Calorimeter: Picks up electrons and photons (light particles) Hadronic Calorimeter: Quarks, Protons and particles with positive charge Muon Chambers: Picks up the muons that go through the other parts of the detector.

We can use the CMS detecotrs many different parts to discover what particles and events were in the detector. By seeing that a particle appears only in the electron calorimeter we can discern that the particle in question is a photon, because it doesn't appear in the tracker it has no charge, therefore it must be phoon if it shows up in the EC. I was also able to use the CMS visualization to get all the different angles or viewpoints. By using this I found that you must do this to analyze many of the different things that going on withing that event. It also helps that they have the meausre of energy and amount of the events going on within that simulation also.

Many Eyes Parameters Explanation Px1: The momentum, speed, mass of the first muon/ event. Mass, Speed, and Momentum are fro our purposes the smae thing. This is illustrated in the visualization it self. Phi1: The value of the first variable in the terms of the second event M1: the invariable mass Parent Rest Frame: The viewpoint of the particles if the detector was moving, not them Many Eyes really allows us to see the relationships between the partciles that we normally would not be able to. By just randomly sorting through the different parameters you can make many differentconclusions such as, the mass of red opposite signed particles hovering around ninety, are most likely deacay products of th Z-boson.

Concerning the neutrinos traveling a little faster than the speed of light, I believe that it might have been a simple human or machine error causing a mis-measurement. However, if the opposite holds true then we will have to all go back to the drawing board and rewrite what for many years has been airtight dogma of physics. In other words we would turn all of it on it's head and have to rewrite the textbooks. I know that intense analyzation is still ongoing, but I would still like to think that what is being taught in the classrooms is correct. It is a fascinating time for the science of particle physics however. With the possibility of the Higgs Boson not existing, and now this, we can be in a time of serious upheaval, or just more progress in the direction we have been going.

M1 vs. py1, This shows the mass plooted against the movement along the y axis of the first event. media type="custom" key="10990992" M1 vs. Py2. This shows the mass against the y of the second event

media type="custom" key="10991046" M vs E1. We can see that the events that are highlighted are condensed around the area of 90 mass. From this we can expect these to be decay products of the Z boson. media type="custom" key="10991132" M parent rest frame vs M. M is the invariable mass of an event and therefore does not change from movement or other factors. In other words M equals the energy of the parent when still. To prove this I put M against M in the rest frame to show the equality media type="custom" key="10991150" Eta1 vs. M. This is a good illustration of how more common lesser particles have the tendency to stay within a very close pack while those with more mass are more spread out and less predictable than their counterparts.

media type="custom" key="10991178" Pzsum vs. p 3d resultant. This is the view down the barrle of the detector plotted against the p 3d resultant. This is good example of what can be done with Many Eyes, since you can get many strange results such as this arrowhead looking graph. I have no idea what this conclusively means, but it looks interesting.

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PxSum parent rest framw vs PzSum parent rest frame. A good illustration of how small the energy is within these particles and just how closely ten thousand of them fit together. There are very few outliers and even most of those have less energy than the majority. media type="custom" key="10991252"

CMS Dimuon in Excel changes

Px1 + Py1 and Px2 + Py2: I thought this would be nice to show the total movement of the muons within the detector. It seems to be pretty effective and I was thinking of using one with the Pz's but I realize that wouldn't have worked as well.

M1-M and M2-M: By subtracting the Invariable Mass which is the parent cell when at rest by the mass in motion which is higher than jus M1, I hoped to find another way to see how much energy that the motion gives the particle. It helps that mass and velocity are interchangable in our studies

eta1+phi2 and eta2+phi2 : I made this one although I'm unsure if it is valuable at all. It does look a little strange on the Many Eyes and that is why I was wondering about it.

Cosmic Ray Detecting: Cosmic Rays are beams of particles that travel through space continuously and are actually very, very common within our everyday lives, even though we may not notice them. In the lab at Quarknet we can see the detector there picking up as many as 9.589 events a day, at least that the most I've seen. Since these are particle streams they can interfere with our calculations within the detector, we have to try and limit this. That is why we put our detectors underground, and for other reasons to. Even with this we still Cosmic Rays within our events and they can be counted in the data, at which point we have to cut them out. By making parameters and using our data we should be able to do just this. For Right we are using SumEta which is the sum of Eta1+ Eta2 and DeltaPhi.

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This is the Block Histogram for Delta Phi, It is showing us that it's is mainly centered around 0 with spikes around 4 and -4. As there are also a large number of particles both positive and negative around the zero we can see why we needed to give the data some leeway, because some of the Cosmic Rays do come in from a slight angle from 90 degrees. This is especially well illustrated in this graph.

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This is the histogram for SumEta. Because the particles are mostly centered around zero this is telling us that Cosmic Rays are mostly coming from right above, or an 90 degree angle like we predicted. There are also spikes around the positive and negative 4.5 to 5 area, as that must be a common angle also.

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Cosmic Rays Many Eyes Data SumEta against DeltaPhi.

media type="custom" key="11339920" DeltaPhi= Phi1-Phi2 and this should come out to 180 degrees or pi. In this graph we can see a data peak around the pi area showing that this data probably contains a large amount of cosmic rays. This is proof that all these cuts and filters are good at seperating the possible cosmic rays from the rest of the relevant data that we are actually looking at.

Data with filters and cuts and SumEta and Deltaphi

And here's the Block Histogram with the data cuts and filters to just grab the peaks of the other data. media type="custom" key="11432946" As we see in this histogram it is centered around zero and in the outer edges of the graph. This tells us that the cuts we made have given us mostly the cosmic rays that we were trying to make these cuts for.

More Cosmic Ray Cuts: Grinding it down to the bare bones of the rays

For these cuts it's all about exacting our measurements so we can finally see these cosmic rays in all their glory. From this data we can see that these cosmic rays mostly occur in the 3.140-3.143 range in deltaphi graph. In the sumeta direction it is zero. From these two variables we can see that deltaphi is 180 degrees and that sumeta is zero. This tells us that within the three dimensional range that these events are back to back straight lines, exactly what were looking for when searching for cosmic rays.

Here is the graph for these cuts from the data sets:

Deltaphi's graph

media type="custom" key="11518520" and Sumeta's

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Cosmic Ray Direction: Where are they coming from.

To find out from exactly where or what direction the rays are coming from we need to combine the phi's and the eta to have all of that data under one value so that we can see the back to back relations and see exactly where they are coming in from on the unit circle, or in our case the detector. With these graphs we can see that the phi combined graph has two almost identical peaks and areas surrounding them. We can also see that the highest peaks are at -1.5 and 1.5. also both sets are equal distance from zero. this tells that these are straight lines coming from above around the 90 degree area.

Here is the phi graph:

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From there we go to the eta combined graph where we see again that there are two peaks once again centered around zero. From this info we now know that we need to cut out the negative numbers from phi so that we will be able to see the direction from which the rays are coming down at. Once this is done we can see that the rays are coming in from the are around 90 degrees or mostly straight down. This makes sense since by coming straight down there is less earth to go through in order t reach the detector. That is why most rays come from close to 90 degrees.

Here is the original graph without the cuts to phi in order to find the direction.

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and with the phi cuts in order to see the direction:

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Summary of the Cosmic Ray Detection and Locating:

To start out with we have to summarize exactly what cosmic rays are. They are streams of particles that travel throughout space until they hit solid ground or another object. Sometimes they interfere with our particle data due to the fdact that the detector has a opening above it that let's these rays in. The hole was actually used to lower the detector underground and into the chamber it now resides. Anyways these rays interfere with our data multiple times. Luckily there are many properties that allow these rays to be picked out and the real events to be analyzed wihtout the interference. These traits include the back to back relationship that they have in many of our data values. They also always come from above due to the fact the surrounding ground would have absorbed them by the time they reach the detector. Armed with this data we can make the cuts neccesary to isolate these rays from the rest of the particles.

To get to our final cuts and eventual analysis of the data.which turns out that we were not successful in isolating all of the cosmic rays from the dataset and thus still have their interference in our data. To get to this point we utilized mainly two programs, excel and Many Eyes which allow us to create datasets and then visualize them so that we may make more effective cuts to the dataset. Using these we whittled down on our events until we found those that are coming from above. We then made two new variable sets name Deltaphi and SumEta which allowed us to see if the events we were looking at came from above and whether or not they were coming in back to back or in a straight line. Once that was done we were closer to finding the rays within the dataset.. Through all of this I both used and fought with Excel and Many Eyes both of which had their testy moments. After we founfd the tracts that had back to back relationships we saw that there weres till many cuts to be made. To start out with we slowly hacked off the data that we know weren't cosmic rays until we got to the bare minimum of events that we could shave off until we started cutting away rays. We had to use this method because these particle rays were very siilar to any other particle that we would normally have in the detector so we could not use many of the other more conventional ways to single them out, like Mass or Energy. Once we got to this point we had to observe exatly where these particles were coming from so we observed them in all three dimensions of the detector, x which is the side view, z which is straight down the barrel of the detector, and y which is the top down view. By using these we further cut down on the data till we reached the point where we either had the rays or not. Uploading all of these datasets into Many Eyes the highliting the peaks where we believed the rays to be, we swithced through all the various variables to see if all the dat amtcheed up. Unfortunately, our cuts, pains with technology, and sweat, did not amopunt to success in this case. However we had learned much about the science of particle physics, and I believe that I learned much about it. Even though I'm not the greatest at math all of this is very pratcial math and I was able to use it effectively for the most part. Also it was nice being able to tell people that I was workning on isolating Cosmic Rays from massive particle accelerators

All of the aforementione graphs and excel datasets can be viewed at my Many eyes account, The link is at the top of the wiki page.

Particle Physics, although it may seem like a daunting, extremely complex and highminded sicentific undertaking, I found it to be very interesting and very reasonable branch of science. And this is coming from a person for whom math is not exactly his strongest suit. One of the biggest reasons I was able to enjoy and understand Particle Physics was because of the fact that if you study up on what is needed to know to gain some knowledge many of the projects and ideas can be reasoned through with common sense, and time of course. I'm not saying that this project was a cake walk, it most certainly was not, but rather I'm saying that if you use your innate common sense, and actually work towards the answers you will arrive at the correct solution, in time of course. The second thing that really attracted me and intrested me in this field of science is the fact that there are so many new exciting things going, just during the time I was working on this project two major shockwaves went through the field of science. The first occured when scientist in Europe supposedly discovered faster than light neutrinos, although that one is being heavily scrutinized as if it is true it turns conventional physic right on its head. The second, the closing in on discovery of the Higgs has been going on for a while, but recently there were some major strides into finding the God Particle which grants mass unto all that pass through its field. media type="custom" key="11976147" Above a theoretical Higgs Boson, I don't know if it's scientifically accurate or not.

To really understand what exactly my project is and what it entails, you first need to learn what Cosmic Rays are. Cosmic rays are streams of particles traveling throughout Space and they do this for a very long time. Although these Cosmic Rays sound like the things that gave the Fantastic Four their powers, they aren't, because if they were then we would all be superheroes (and villains). This is because these Cosmic Rays are everywhere, you've probabbly encountered thousands upon thousands of them already since you've woken up this morning. To illustrate this point, in Quarknet we have a small Cosmic Ray Detector that counts how many of these streams of particles have passed through it, one day at four thirty in the afternoon it had counted over seven thousand Cosmic Rays. This detector was inside to where it's more difficult for these rays to get inside. And if you are wondering just how complicated it is to measure these rays, it reall is pretty simple, at least to my limited technical understanding of the machine. It works by sending a charge through the scintilator tiles on the top and bottom whenever a ray passes through both tiles. That charge then goes to a simple microchip that counts and displays the number of rays that went through it. It's also a very small machine unlike many of Particle Physics tools of the trade. Here is a picture. media type="custom" key="11976253" Although it may look futuristic it really is easy to understand.

Speaking of Particle Physic's tools of the trade you need to know about our biggest and most important ones, the accelerators and the detectors, namely the CMS in my personal experience. The CMS is massive, the accelerators track is 17 miles long which for reference is like running more a little more than two thirds of a marathon, which are 26 miles long. The detector is also very impressive it weighs as much as 30 jumbo jets, which comes out of neccesity as in order to be as accurate as it is bigger is better, due to the amount of iron needed to offset the immense magnetic forces going on during an experiment. A simple explanation of the CMS's parts follows, the tracker picks up anything that has a charge and shows it's direction, the electronic calorimeter picks up negatively charged particles and photons (light), the hadronic calorimeter picks up quarks and positively charged particles, and the muon chambers pick up, you guessed it muons. By using the information from these we can piece together what is happening during an event. The amount of work that went into making all of this is truly impressive, many countries have contributed to the CMS project and the work it took to make it is immense. They even had to make a tunnel and put it underground to block out interference from weather, and other things, namely Cosmic Rays. However to put the CMS into the tunnel they had to have an opning which is how the Cosmic Rays get into the data and interfere with the data. Since that opening allows them in and the Rays are all over the place that causes a problem. media type="custom" key="11976375" CMS site wiht the 17 mile track media type="custom" key="11976381" CMS itself look at the guy on the ground for size reference. Now when we look at the tens of thousands of events and all the many variable we use it is impossible to extract just the Cosmic Rays from the data by looking at it. That's why Microsoft Excel and a website called Many Eyes have been my two best friends. By using Many Eyes I can visualize the cuts that I am making to be able to actually see what I am doing by manipulating the numbers and variables within Excel. For our purposes in this Cosmic Ray project only a few variables really mattered to me in Excel, eta and phi along with variations on those two. Although it is hard to explain in words Eta is like a variable measuring position in a area that looks like a yo-yo on it's side while phi is just a circle. The variations are SumEta which is Eta1+ Eta2 and DeltaPhi which is Phi1-Phi2. Using all of these variable in Excel lets me find out what exactly to cut on, and where to cut, along with the Many Eyes visualizations. Although I would go through all the math and minute details of everything I did, I believe that would just be ardous and lengthier than need be. To go through and summarize the proccess I'll explain it as simply and accurately as possible. By using the aforementioned variables SumEta and DeltaPhi we found all the particles that had a straight line relation, as in they are in a single line, and that they were coming from above. Both of those things are properties of Cosmic Rays. Next with that information we whittled down the eta and phi data by putting filters on where we know that there will be Cosmic Rays. Then we to Many Eyes and using the Histogram feature we went in and found the peaks of data where the Cosmic Rays were and then cut down and filtered regular events out. And although we were not able to isolate all of the Rays I believe that we did in the end get most of them. Even though we failed I think it was a challenging, and really a great look into the process of Science, which in this case involved manyy technological difficulties and arguments with the computer. To really show the proccess though I think you need to see the pictures of the graphs that came out of me making the cuts into the dataset of the events. Here are the most key graphs.

This graph is the values of SumEta plotted against those of DeltaPhi. throught this we see that the data is centered around and peaks at 3.14 or pi. Which in radians meusure is 180 degrees or a straight line. This is the graph that showed us the data that matches that property of Cosmic Rays. To capture that data and give it a little leeway,because we know that Cosmic Rays Can come in at slight angles also we made the cuts around that area

This graph came in after we made those cuts, and then combined the eta values into on big column and the same with the phis. From this we see the two peaks that almost mirror each other exactly. From this we once again see that theses events are striaght lines because of the back to back on the 0 line. We can also see that they are coming from mostly the 90 degree area which tells us that these are probably Cosmic Rays. From there we moved on to see if the peaks matched up with the other data that we knew to be Cosmic Rays and unfortunately they did not match up that well, meaning we were not able to isolate all of the Rays. However I believe that it was a great proccess and I definitely have a better understanding what exactly is happening within all of these events. As I said earlier if you work at understanding Particle Physics you will learn it.

CMS and the Master Class, W/Z

For these past few weeks we have been working on differentiating between W events and Z events. The W events are events that consist of a neutrino paired with either a muon or an electron. The neutrino is neutrally charged and causes the detector to project a yellow missing energy arrow which gives the W away. A W with an electron is a W- and one with a muon is a W+. On the other hand a Z is a neutrally charged boson. It consists of either a pair of oppositely charged muons or electrons, which balance out into a neutral charge. There should be no or very little missing energy in a Z event. Another indicator of a Z is the mass which sits in and around 90. Using this information and the CMS event display it is possible to discern these particles from each other. To this end I have done the 300s and am working on the 500s on the masterclass events.Some pictures follow

A Z event as you can see from the two muon chamber hits

A W event. You can see the missing energy arrow and the electron track.

Differentiating between an electron and a muon (without looking at the event display)

Although this idea is a little rocky, It might just work. I believe that by using excel and many eyes along with some logical thinking it would be possible to do this. As we know muons shoot through the detector just leaving tracks, while electrons die in the tracker to be able to measure there energy. This means that muons travel through the detector much, much farther than any electron would. My idea is as follows. Using phi, and some kind of variable that can measure how far along an events is upon the phi we would be able to see just how far a muon or electron goes in the detector. Now that I think about it, if we use the unit circle and place it on the detectors Z axis so that they line up, we can use the numbers that we already have and plot out all the different events, and make them vectors. That would let us differentiate between the muons and the electrons. My math on this might be a little rocky, but I believe the basic idea, if applied rightly should work.

A Seminar with the Nobel Prize Winners.

For this class I attended a seminar at Notre Dame University with the winners of the Nobel Prize in Physics. They had won for their research into the the Universe using super novae, and distances. They discovered that the Universe is made up of mostly Dark Energy. 74 percent in fact. They had also discovered that he Universe is accelerating, it is still expanding. From what I understand they sent particles of light, or traced them from the super novae, and what they found out is that instead of slowing down as they traveled through space, they actually sped up. From this they deduced that the Universe was expanding, and that it is actually speeding up in this expansion.

More W and Z events

From the research and talking we have done in class i now know much more about these events and the differentiation between them. One of the things that i learned first is that this data is not very comparative with nature. The Z boson is much more rare than the W, so that means that there were some cuts and filtering done within the Masterclass to make it more accessible. Even with this we still get some stranger events such as ones that contain both an electron and a muon. These as i found out could be Taus that have developed in the chamber, thus making both the electron and the muon appear. We have done some work into making data cuts and filters to just be able to look at W events and Z events separately in Many Eyes. This was done by setting filters on each type than copying and pasting them onto another spreadsheet which was then uploaded into Many Eyes. The results from my Excel wizardry are as follows. media type="custom" key="12881032" The Invariant Mass of the Z bosons. This captures all of the Zs in our data that we currently have. Will update once every event is consolidated

media type="custom" key="12881058" The Invariant Mass of the W+ events media type="custom" key="12881078" The Invariant Mass of the W- events

Some Particle Physics News

CERN has consolidated data with the European Governments, Scientific Communities, and many other data companies to have a massive cloud computing storage system. This collaboration is necessary due to the amount of data that needs to be stored before it can be processed. Once this program has started up only the scientific and governmental agencies will be able to use it. After an undisclosed amount of time however, this system will become available to the wider public and could become a multinational data storage system for Europe.

The U.S Tevatron atom smasher has confirmed the results of the LHC's tentative Higg's discovery. The differences between these two machines, and the fact that they are both seeing the same things is very encouraging. This was just yesterday and the scientific community seemed very excited about this, once again taking another step towards the Higgs

Google Fusion Pros and Cons Pros Fusion Allows us to edit and filter the data within the spread sheet itself. It als has a very user freindly interface, and the zoomable linegraph is a very helpful tool also. Cons Fusion only shows a random selection of the events. Not the whole picture. The graphing options are not expansive While the idea behind being able to edit within the spreadsheet is awesome and time saving, it didn't work for us. Summary It is a very nice idea, and is easy to use, but for our purposes it is not very effective due to the fact it only shows a sampling of the data.

The Higgs the data keeps on coming in The LHC, Tevatron, and CMS have all come up with encouraging conclusions on their research. Although not enough to claim discovery, these conclusions are very supportive of the Higgs theory. Another boost comes from the relative differences between these machines, and gives us a good outlook on the eventual discovery of the illusive Boson. An exciting time indeed.

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Here using the w to e mu data set I decided to test drive the new visualization and graphing, platform we recently acquired. It has no name quite yet though. Anyways I used the vaulue of E 1 and compared it to the E 1 of the Z to 2mu dataset. Here we see a peak around the 7.5 area. This actually ended up being a very comparison to make due to the complete difference between the data sets I chose. Here is the second set.

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I did end up really liking this visualization program that we used though. It is very barebones just a slider or two. However, the ability to use those sliders to manipulate and narrow down on the variables is a very useful function. It is almost as good as Many Eyes.

Simple Particle Physics

I have been having trouble remembering the basics of the particles, namely the particles themselves. So I have decided to list them out here, because I thought it would be a lot more convenient that staring at the building blocks poster in the lab.

Leptons- light particles, weightless hadrons as in hadronic colliders (LHC)- made up of 3 particles Charm is an up and is heavy j/psi is charm and anti charm upsilon- B bar and B an anti B Pi-ons up and down found at the same time otherwise known as protons mesons are made of quarks of two different types of quarks



These are the two datasets that we are now working with. We will break the data down into observable numbers, analyze, and generally use a lot of spreadsheet programs on them.



This is the data histogram using bin sizes of tens, it is not accurate enough for our purposes. We will have to go much smaller to be precise.



Same data with histogram bins of 5. You can see much more detail within the data, and it provides much more information on the data and events. Still a little to broad, we need to go a little smaller



This is a histogram using bins of 2, and it is perfect. It shows us good detail without being overloaded with very small fluctuations within the data. It gives both a more precise look, but conserves the general view.

These were all created using some Excel wizardry courtesy of a certain Mr. Antonelli, Graphical Analysis, and some common sense with basic electron and Muon knowledge.



This is an experiment using the graphical analysis' fit tool. We used the Gaussian option to find the peak frequency, the median, and other variables that come along with a Gaussian curve. The testing came in trying to decide just how much data to include in each Gaussian fit. The top left is just the large peak taken into account, the top right is a slightly expanded version of the previous, and the bottom right is the entire data set.

Here is a Histogram with the J/psi and upsilon areas highlighted and fitted with a Gaussian Curve. You can't see the values on this picture, but the J/psi is lying on the 3.135 range and the upsilon is sitting on the 9.5-9.6 range. The Gaussian is telling us how many events are in that bin at that area and the average mass of those events within the selction. Calculating the Mass with E=MC^2 To find the mass of the Z, which decays into two oppositely charged particles, we must take it's energy and it's momnetum in space. To accomplish this I needed to take E1 and E2 and add them together. That takes care of the energy variable in the equation. To get the momnetum we need to take the particles movement in any direction, the x, the y, and the z. So we take (E1+E2)-((Px1+Px2)^2+(Py1+Py2)^2+(Pz1+Pz2)^2)^1/2 to get the mass. I ran this through Excel and the mass ended up matching up perfectly to the given mass. So I declare success on this matter, and equation. This is the Calculated Mass right next to the Given Mass on the Excel Spreadsheet.



Now moving on I need to calculate the Mass for the Z particle, this however is much harder than it sounds de to the missing energy. Because the W decays into a neutrino and either an electron or muon, there is always missing energy with the neutrino, and the fact that the detector's beamline has no detection equipment. To calculate mass we need the Energy, which we have, and the momentum in space, which we don't have. We do have the x, and y momentum, but not the z. This lead us to calculating the Transverse Mass which is the Mass without the Z variable. With the transverse mass for both the Z and the W particles we can find a ratio that fits both of them. We can then apply that ratio to find the W's mass.