Embedded Files
Dilaton Project
Goals:
Develop a lower limit on the mass of the dilaton.
How to:
Dilaton has an identical decay pattern to the higgs
If we were to analyze LHC data as if we were looking for a Higgs at a lower mass we could potentially see a Dilaton
All we have to do is scale the couplings a little bit.
The cuts should be almost equivalent to the Higgs cuts.
Literature
https://en.wikipedia.org/wiki/Goldstone_boson
http://arxiv.org/pdf/1111.2580v2.pdf
2/14/2016
Since the Dilaton looks exactly like the Higgs in the Gamma Gamma decay channel we thought it would be best to learn how to do the H->yy analysis first
Jacob and I looked on the CERN twiki for a tutorial on how to do a Higgs to gamma gamma analysis. The link to that page is this:
https://twiki.cern.ch/twiki/bin/view/CMS/SWGuideCMSDataAnalysisSchool2014HggExercise
In the tutorial it says that you have to use these commands to initialize your environment
mkdir ~/cmsdas2014hgg cd ~/cmsdas2014hgg cmsrel CMSSW_6_1_2 cd CMSSW_6_1_2/src/ cmsenv
However, on tier 3 there is no CMSSW_6_1_2 release do we decided to implement CMSSW_6_2_12 which seemed like it would be closest to the CMSSW_6_1_2 release.
We used the command
scram list CMSSW
This command shows a list of all available versions of CMSSW on the cluster.
After that part of the tutorial we were told to find the Root files for the Higgs exercise at the following link
/afs/cern.ch/work/b/bendavid/cmspublic/CMSDas2014HGGLongExerciseUpdated/
However, clicking this link does nothing an only leads to a 404 error. We then checked in the CMSSW_6_2_12 directory and could not find an afs directory.
We looked in all of the cluster directories and could not find it.
Then I looked for the cms github repository. With quick google search you can find it the link to the page is this:
https://github.com/cms-sw/cmssw
We used the command
git clone https://github.com/cms-sw/cmssw
This copied all of the cmssw files into our directory.
There was a directory called Higgs Analysis that we looked into an we found another directory called HiggsToGammaGamma
We looked in this directories and found the directories called src,test and interface.
In these directories we found files called PhotonFix
After trying to exectute the PhotonFix.cc file just to see what it did we received an error telling us that we didn't have permission
To get permission to execute files use this command
chmod u+x <File name>
This gives the user permission to execute a file.
After doing this and trying to execute the file again, we recieved the error
//.. Permission denied.
Badly placed ()'s.
I dont know if this an issue with the code or not. It brought our work to a standstill for the day. Numerous apporaches to fix this did not work.
TODO:
Find out how to acces afs file
Maybe not use the entire cmssw library from github. I think that doing cmsrel already clones cmssw for you.
2/26/16
Update: We are no longer doing any further research into the Dilaton. Now we will be doing Monte Carlo simulations.
A good tool for performing Monte Carlo simulations is MadGraph.
In order to install MadGraph you need to go to the website:
After you are on this website, click the link to register for a password. This is the only way you can actually download the MadGraph software.
Note: The form for getting a password is buggy. Be PATIENT with the form and until they email you after filling it out. That way you wont receive 10 different passwords.
Madgraph should have sent you log in information by now so you can log into the downloads page
Download the latest version of MadGraph and upload it to your desired folder.
Enter this command to unzip the file into the current directory.
[davis@hepcms-in1 MadGraph]$ tar -zxvf MG5_aMC_v2.3.3.tar.gz
After you have unpacked the file enter the directory MG5_aMC_v2_3_3
NOTE:before proceeding make sure that you use cmsenv
To run MadGraph use the command
./bin/mg5_aMC
This should open the interface for MadGraph. Use this command to start the tutorial.
MG5_aMC>tutorial
If you follow the tutorial you will input the command
MG5_aMC>generate p p > t t~
This will cause MadGraph to generate proton proton to top anti top quark events.
MadGraph by default will begin looking for minimal orders that give the process and will generate diagrams for each process. The output looks like this.
INFO: Checking for minimal orders which gives processes.
INFO: Please specify coupling orders to bypass this step.
INFO: Trying coupling order WEIGHTED=2
INFO: Trying process: g g > t t~ WEIGHTED=2 @1
INFO: Process has 3 diagrams
INFO: Trying process: u u~ > t t~ WEIGHTED=2 @1
INFO: Process has 1 diagrams
INFO: Trying process: u c~ > t t~ WEIGHTED=2 @1
INFO: Trying process: c u~ > t t~ WEIGHTED=2 @1
INFO: Trying process: c c~ > t t~ WEIGHTED=2 @1
INFO: Process has 1 diagrams
INFO: Trying process: d d~ > t t~ WEIGHTED=2 @1
INFO: Process has 1 diagrams
INFO: Trying process: d s~ > t t~ WEIGHTED=2 @1
INFO: Trying process: s d~ > t t~ WEIGHTED=2 @1
INFO: Trying process: s s~ > t t~ WEIGHTED=2 @1
INFO: Process has 1 diagrams
INFO: Process u~ u > t t~ added to mirror process u u~ > t t~
INFO: Process c~ c > t t~ added to mirror process c c~ > t t~
INFO: Process d~ d > t t~ added to mirror process d d~ > t t~
INFO: Process s~ s > t t~ added to mirror process s s~ > t t~
5 processes with 7 diagrams generated in 0.158 s
Total: 5 processes with 7 diagrams
At this point you can add processes using the command
MG5_aMC>add process p p > W+ j, W+ > l+ vl @2
You can replace the process with what ever you want it to be. In this case the command adds a decay chain process, with the W+ boson decaying leptonically.
You can also use the command
MG5_aMC>display processes to display all the processes.
Example output:
Process: g g > t t~ WEIGHTED=2 @1
Process: u u~ > t t~ WEIGHTED=2 @1
Process: c c~ > t t~ WEIGHTED=2 @1
Process: d d~ > t t~ WEIGHTED=2 @1
Process: s s~ > t t~ WEIGHTED=2 @1
MG5_aMC>display particles to display all of the particles in your current model
Example output:
w+/w- ve/ve~ vm/vm~ vt/vt~ u/u~ c/c~ t/t~ d/d~ s/s~ b/b~ e-/e+ mu-/mu+ ta-/ta+
a z g h
MG5_aMC>display multiparticles to display all the multiparticles present
Example output:
all = g u c d s u~ c~ d~ s~ a ve vm vt e- mu- ve~ vm~ vt~ e+ mu+ t b t~ b~ z w+ h w- ta- ta+
l- = e- mu-
j = g u c d s u~ c~ d~ s~
vl = ve vm vt
l+ = e+ mu+
p = g u c d s u~ c~ d~ s~
vl~ = ve~ vm~ vt~
Proceding with the tutorial use the command
MG5_aMC>output MY_FIRST_MG5_RUN
This will set up a new directory called MY_FIRST_MG5_RUN
The tutorial then asks you to use the command
MG5_aMC>launch MY_FIRST_MG5_RUN
DO NOT DO THIS. MadGraph defaults to using all cores on the server which is good if you want everyone else on the cluster to hate you.
Instead type the command exit and go back to the main MadGraph directory.
You should see a directory called MY_FIRST_MG5_RUN.
cd into this directory and then cd into the Cards directory.
open the me5_configuration.txt file in emacs.
Uncomment run_mode
run_mode=1
Uncomment cluster_type and cluster_queue
cluster_type = condor
cluster_queue = None
Doing this will make MadGraph submit the job to Condor, which is way better for the server.
To simulate your process use the command
./bin/generate_events
Madgraph will start generating events and will also open up a firefox browser and display this( I ran this code twice so there are two results)
This shows the cross section of the events as predicted my MadGraph.
You can navigate this interactive webpage to view information about the events you generated.
If you cd into the Cards directory you will see .dat files.
Some have _default in the name. If you want MadGraph to use these files you must rename them without the _default
You can open these cards in emacs to tweak different parameters of each.
3/4/16
We now have a new project to work on. We are working with Christopher, one of Chacko's grad students.
We are still looking at the Dilaton particle. In order to do this we will first need to recreate the bounds at which
the Dilaton has been ruled out. Then we can change the energy of the collider and show where the bounds on a
Dilaton will be for a new particle collider.
3/7/16
Our goal is to reproduce the graph of the (m,f) plane which is the graph of the Dilaton Mass vs the scale of symmetry breaking.
One possible channel to look for the Dilaton in is the g g> X > y y which is a dilaton created through gluon fusion. When a Dilaton is made
through gluon fusion MadGraph cannot handle the loops that are made in these processes.
The loops result in a very messy integral that MadGraph cannot solve. The good thing is that someone has already dealt with these loops in the case of the Higgs Boson. The MadGraph model that handles these loops is called heft. heft stands for Higgs Effective Field Theory. In this model the Higgs Boson couples directly to gluons and photons without a heavy quark loop. To do this the mass of the top quark in the loop is taken to be infinity. When you do this the effective verticies can be derived from this equation
and the gluom to higgs coupling constant is given by
So using this approximation you can approximate loops as a vertex. There are some potential issues that come with using this model. According to the paper http://arxiv.org/pdf/0706.2334.pdf for the top loop approximation to hold, the Higgs mass should be smaller than twice the top mass, also all other kinematic variables, such as the transverse momentum of the Higgs boson, should be smaller than twice the top quark mass. This could be an issue if we try to scale the change the higgs mass in this model and pretend that it acts as a dilaton. Regardless of this I'm going to load up some simulations of Higgs decays in MadGraph to see heft works.
In order to import the heft model into MadGraph you must enter these commands
./bin/mg5_aMC
MG5_aMC>import model heft
After doing this you can generate any Higgs event that you would like in this case I will generate g g > H > a a which generates Higgs event from gluon fusion that then decay into two gamma rays. To do this use the commands
MG5_aMC>generate g g > h > a a
MG5_aMC>output "filename"
You can then go into the directiry you named with the output "filename" to generate events
Make sure you edit the me5_configuration.txt file to run on one core then do
./bin/generate_events
After doing this you will find that the cross section for this event is 0.01859 +- 3.576e-05 pb
This is the feynman diagram of the event.
The plots for the pt of the daughter photons look like this. If you were to add them up you should see a mass peak at 125 GeV
3/9/2016
I'm following the tutorial on the Higgs cuts using the heft model.
You have to install Delphes in order to do the analysis. To install Delphes type this command in your MadGraph folder.
wget http://cp3.irmp.ucl.ac.be/downloads/Delphes-3.2.0.tar.gz
tar -xf Delphes-3.2.0.tar.gz cd Delphes-3.2.0/ make
This installs Delphes in your MadGraph folder. Before you run anything cd into input and open mg5_configuration.
edit the line that by default says
# delphes_path = ./Delphes
to
delphes_path = ./Delphes-3.2.0
To simulate Higgs decay to two gamma with the background you must open up MG5_aMC
Type the commands
generate p p > h, h > a a
add process p p > a a / h
This will make higgs to gamma gamma events as well as the background of any event that also has two gammas as its product.
I went into the run_card.dat and set the events to 100000.
Then do ./bin/generate_events
At the prompt that asks what programs you want to run type
1 then enter
2 then enter
3 then enter
0 then enter
This turns on pythia pgs and delphes.
Now get ready to wait! This process takes a while.
When you finish this process you can see wonderful graphs like these!
These graphs are the delphes plots for the two photons that are created in a di photon event.
Delphes is a detector simulator that smears values to look like what you would see in an actual particle detector.
3/16/2016
These graphs are not complete however. It would be helpful to show the combined invariant mass of each photon pair
3/17/2016
I will now combine the invariant masses of the two electrons created.
To do this you want to edit the plot_card.dat file in the Cards directory.
Insert the line
a 0 #Class number 3
under the class creation section.
This will make class number 3's symbol a. It will also make class 3 represent photons.
"0" is the code for photons
In between "BeginPlotDefs" and "End PlotDefs" insert the line
mij 3 2
This will make madgraph graph the highest pt class 3 objects (photons) for each event.
You can also edit the plotting method by going to the section of the plot card that starts with
"Begin PlotRange" and "End PlotRange"
I changed pt to read
pt 5 0 200 # bin size, min value, max value
5 GeV is the bin size, 0 is the min value and 200 is the max value.
The mass plot of the photons combined looks like this.
As you can see there is no easily identifiable mass peak. This is what you would see in a particle detector.
Some cuts would need to be done in order to isolate the Higgs from these events.
3/21/16
Twiki for Branching Ratios
https://twiki.cern.ch/twiki/bin/view/LHCPhysics/CERNYellowReportPageBR
3/23/16
I will try to graph some of these functions using arbitray units in Mathematica
You can download and install Mathematica for free from terpware.
I graphed some functions with this code.
Remove [ft]
Remove[F12]
Remove[Rg]
Remove[Bg]
Remove[taut]
Remove[tauW]
Remove[taub]
Remove[tauc]
Remove[tau\[Tau]]
Mt = 172;
MW = 80.4;
Mb = 4.2;
Mc = 1.4;
M\[Tau] = 1.777;
\[Sigma]ppH = 17.62;
\[Sigma]ggH = 1.529*10;
\[Sigma]VBFH = 1.24;
v = 246;
taut[Mx_] = 4*(Mt^2/(Mx)^2);
tauW[Mx_] = 4*(MW^2/(Mx)^2);
taub[Mx_] = 4*(Mb^2/(Mx)^2);
tauc[Mx_] = 4*(Mc^2/(Mx)^2);
tau\[Tau][Mx_] = 4*(M\[Tau]^2/(Mx)^2);
Bg[Mx_] = 7;
ft[taui_] =
Piecewise[{{(ArcSin[Sqrt[1/taui]])^2,
taui >= 1}, {(-1/
4)*(Log[(1 + Sqrt[1 - taui])/(1 - Sqrt[1 - taui])] -
I*\[Pi])^2, taui < 1}}];
F12[tau12_] = -2*tau12*(1 + (1 - tau12)*ft[tau12]);
Rg[Mx_] = (Abs[-Bg[
Mx] + (1/2)*(F12[taut[Mx]] + F12[tauW[Mx]] + F12[taub[Mx]] +
F12[tauc[Mx]] + F12[tau\[Tau][Mx]])])^2/(Abs[(1/
2)*(F12[taut[Mx]] + F12[tauW[Mx]] + F12[taub[Mx]] +
F12[tauc[Mx]] + F12[tau\[Tau][Mx]])])^2;
Plot[Rg[Mx]/100, {Mx, 20, 1000}]
\[Sigma]ppX[f_,
Mx_] = ((v^2/
f^2)*(Rg[
Mx]*\[Sigma]ggH + \[Sigma]VBFH)/(\[Sigma]ggH + \
\[Sigma]VBFH))*\[Sigma]ppH
Plot3D[\[Sigma]ppX[f, Mx], {f, 500, 3000}, {Mx, 20, 1000},
ColorFunction -> "BrightBands"]
The first graph is a function of Rg in terms of Mx
The second graph is a function of sigma(pp->X) in terms of f and Mx
3/25/2016
So The F1/2 equation means that you loop over all 1/2 spin particles which means all quarks.
That was the issue we were running into so here are the correct graphs.
The graphs from the paper are
Ours are
Which matches the graphs from the paper perfectly.
This is our correct graph of the cross section of production of the Dilaton
This is our graph of Rgamma
It is exactly like the graph of Rgamma that is shown in the paper that we cited earlier.
3/26/16
I changed the graphs to be on the same axis and match the paper better.
The code for these graphs is this.
Me = .0000511;
M\[Mu] = .1057;
M\[Tau] = 1.777;
MW = 80.4;
Mu = 0.0023;
Md = 0.0048;
Ms = 0.095;
Mc = 1.4;
Mt = 172;
Mb = 4.2;
\[Sigma]ppH = 17.62;
\[Sigma]ggH = 1.529*10;
\[Sigma]VBFH = 1.24;
v = 246;
Bem[Mx_] = -11/3;
Bg[Mx_] = 7;
taue[Mx_] = 4*(Me^2)/(Mx^2);
tau\[Mu][Mx_] = 4*(M\[Mu]^2)/(Mx^2);
tau\[Tau][Mx_] = 4*(M\[Tau]^2)/(Mx^2);
tauW[Mx_] = 4*(MW^2)/(Mx^2);
tauu[Mx_] = 4*(Mu^2/(Mx)^2);
taud[Mx_] = 4*(Md^2/(Mx)^2);
taus[Mx_] = 4*(Ms^2/(Mx)^2);
tauc[Mx_] = 4*(Mc^2/(Mx)^2);
taut[Mx_] = 4*(Mt^2/(Mx)^2);
taub[Mx_] = 4*(Mb^2/(Mx)^2);
ft[taui_] =
Piecewise[{{(ArcSin[Sqrt[1/taui]])^2,
taui >= 1}, {(-1/
4)*(Log[(1 + Sqrt[1 - taui])/(1 - Sqrt[1 - taui])] -
I*\[Pi])^2, taui < 1}}];
F1[tau1_] = 2 + 3*tau1 + (3*tau1)*(2 - tau1)*ft[tau1];
F12[tau12_] = -2*tau12*(1 + (1 - tau12)*ft[tau12]);
SumLoopCorrectionR\[Gamma][Mx_] =
F12[taue[Mx]] + F12[tau\[Mu][Mx]] + F12[tau\[Tau][Mx]] +
F1[tauW[Mx]] + 3*(2/3)^2*F12[tauu[Mx]] +
3*(-1/3)^2*F12[taud[Mx]] + 3*(2/3)^2*F12[tauc[Mx]] +
3*(-1/3)^2*F12[taus[Mx]] + 3*(2/3)^2*F12[taut[Mx]] +
3*(-1/3)^2*F12[taub[Mx]];
SumLoopCorrectionRg[Mx_] =
F12[tauu[Mx]] + F12[taud[Mx]] + F12[taus[Mx]] + F12[tauc[Mx]] +
F12[taut[Mx]] + F12[taub[Mx]];
Rg[Mx_] = (Abs[-Bg[Mx] + (1/2)*SumLoopCorrectionRg[Mx]])^2/(Abs[(1/2)*
SumLoopCorrectionRg[Mx]])^2;
R\[Gamma][
Mx_] = (Abs[-Bem[Mx] + SumLoopCorrectionR\[Gamma][Mx]])^2/(Abs[
SumLoopCorrectionR\[Gamma][Mx]])^2;
\[Sigma]ppX[f_,
Mx_] = ((v^2/
f^2)*(Rg[
Mx]*\[Sigma]ggH + \[Sigma]VBFH)/(\[Sigma]ggH + \
\[Sigma]VBFH))*\[Sigma]ppH;
Plot[{R\[Gamma][Mx], Rg[Mx]/100}, {Mx, 20, 200},
PlotRange -> {{20, 200}, {0, 3}}, PlotLegends -> "Expressions",
Frame -> True, AxesOrigin -> {20, 0}]
Plot[Rg[Mx]/100, {Mx, 200, 1000},
PlotRange -> {{200, 1000}, {.4, 1.6}}, PlotLegends -> "Expressions",
Frame -> True, AxesOrigin -> {20, 0}]
Plot3D[\[Sigma]ppX[f, Mx], {f, 500, 3000}, {Mx, 0, 1000},
ColorFunction -> "TemperatureMap"]
3/27/16
Here are some relevant equations to finding branching ratios of the Dilaton.
We also need to account for Vector Boson Fusion in our Mad Graph Model
The Feynman diagram of this process is this
This process occurs when two quarks exchange either a z or W boson which fuse into a Higgs which then decays as a Higgs would.
These equations were used to make the graphs.
3/30/2016
All of my graphs are wrong. Branching ratios based on the Higgs Decay width are more complex than multiplying by a simple constant.
Assuming things are simple in particle physics theory is a rookie mistake.
This can be dealt with in the model however
The best paper of all time can be found here.
http://arxiv.org/pdf/hep-ph/0503172v2.pdf
This has almost all the information you could ever want about the Higgs.
4/6/2016
I haven't updated my log book in a while so I'm just going to dump a bunch of graphs and equations that I've used.
This function describes the decay width of the Higgs Boson in terms of it's Mass.
Gmu is the Fermi coupling constant
alpha is the fine structure constant ( we use 1/128 at the energies used in the equation)
MH is the mass of the Higgs
Nc is the number of colors
Qf is the charge of particle.
The graph looks like this.
This width can be used to find the Dilaton -> gamma gamma width by multiplying it by Rgamma and v^2/f^2
This function looks like this when you graph it
This function shows the Decay Width of the Higgs into two gluons as a function of mass
This function when graphed looks like this
This width can be used to find the Dilaton ->width by multiplying it by Rgamma and v^2/f^2
Which looks like this
I tried to graph the ratio of the cross sections of production of the higgs and the dilaton, which we can get from these equations. However my contour plot's are not matching the plots from the papers. I still need to review this math to see where I am going wrong. There also seems to be random splotches of nothing on my graphs. This could be what is contributing to the terrible contour plot. I will try to fix this and update as I see fit.
Note: In Mathematica you can make your equations prettier by using these shortcuts
ctrl 2 = sqrt sign
ctrl / = fraction bar
ctr ^ = exponent
a blank space = *
This makes it a lot easier to troubleshoot your equations and code.
4/6/2016
You can get rid of inconsistenies in your graphs by Setting exclusions to None.
4/10/2016
The contours of crossection of (Dilaton to Sm Higgs) that we have calculated are not the same as in the paper.
This is a major issue because we need this ratio to do everything else in the project.
Here are my contours and here are the papers contours. (Dotted lines)
As you can see the shapes aren't even close. I emailed the authors of the paper for clarification and will report back as soon
as possible.
A very helpful application for chrome is called the plot digitizer.
In theory I could use plot digitizer to interpolate functions that are published in other papers.
This way I could use a general form to get any equation i want without modelling it.
4/18/2016
I have finally found the source code for HDecay. It is a fortran code produces the branching ratios and the width of the higgs at various masses
The source code can be found at this website http://tiger.web.psi.ch/hdecay/
The website is really weird because this scientist decided to place advertisements and pop-ups on his website.
Ignore this and download the manual and the tar.gz file for the Hdecay.
Add the files to the cluster and put it into the folder of your choice
Use the command tar -xf hdecay.tar.gz to unzip the code
Type cmsenv
Then type the command make to compile all of the source code.
./run will run Hedecay
Hdecay runs super fast on the cluster because it was written to run on 1997 hardware.
To unzip the manual use the command gunzip
To look at the manual use gv which stands for ghostview
This is an example of what your output files look like for a Higgs Mass of 125 GeV
4/23/2016
So we now have a working Higgs decay function, however I am still having issues on recreating the plots from the paper.
Here are what the working Higgs plots look like.
4/28/2016
In order to make really good looking papers you can use Latex.
It is a coding language for creating papers.
A good way to use Latex is through a package called MikTex
A good way to use Miktex is through TeXstudio.
Here is a manual for how to do Latex
http://texdoc.net/texmf-dist/doc/latex/latex2e-help-texinfo/latex2e.pdf
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