The "heft" model
In order to have the necessary Higgs-gluon-gluon and Higgs-photon-photon
effective couplings, we will need to import the "heft" (Higgs
Effective Field Theory) model.
First, it is
useful to copy the default version of this model to a version of your own.
Then you can modify your own version without affecting anybody else's.
To do so:
a 0 #Class number 3
Here, "a" is the symbol, and "0" is the code, for photon. Now, delete all of the lines between "Begin PlotDefs" and "End PlotDefs". In their place, put just three lines that read:
pt 1 1
pt 3 2
mij 3 2
This tells Madgraph that we want to plot the following things:
Before saving, also edit the lines between "Begin PlotRange" and "End PlotRange" to make the histogram bin size and the range for the plots appropriate. Change the "pt" and "mij" entries to read:
pt 5 0 200 # bin size, min value, max value
mij 2 0 200
Now you can save and exit the file, and type
When you inspect the Delphes plots they should look something like the following. First, the number of jets in each event looks like this:
Recall that we only had photons in the final state of the process we generated. However, Pythia added "extra" jets from the initial state in the parton shower and hadronization, as occurs in the real world.
The number of photons in each event looks like this:
In most events, we see two photons. However, there is a significant probability to not detect one or both of the photons. There are also a few "extra" photons that are generated by Pythia.
Next, look at the transverse momentum (pT) distributions of the leading and sub-leading photons:
Note that these peak at slightly less than half of the mass of the Higgs boson, because they share its energy. Most of the photons have pT > 35 GeV. This will later help us cut down on background. Finally, look at the invariant mass histogram for the signal events:
This has a nice peak centered at MH = 125 GeV, as it should. There are a
few events at 50 GeV or lower; these occur when there is an "extra" photon
that gets erroneously paired with one of the photons from the Higgs.
We can see that the mass resolution, according to Delphes, is a few GeV.
This corresponds at least roughly to the real-world mass resolution from
ATLAS and CMS.
The diphoton background
Now we have to worry about the background. To look at the background alone, do:
Now do the same modifications of the plot_card.dat, and start the run, exactly as above. This time the plots should look something like the following.
The pT distributions of the leading and sub-leading photons are:
Note that quite unlike the signal, these are very sharply peaked at small pT. At the generator level, there was a cut in the run_card.dat file which prevented the photon pT from being too small, otherwise it would keep blowing up at very small pT. (The reason for the generator level cut is to prevent this.)
Similarly, the invariant mass resolution of the background is peaked at small mass:
The Higgs diphoton signal and background together
Next, let us combine the Higgs diphoton signal and the diphoton background
in a single run. To do so, we type:
35 = pta ! minimum pt for the photons
We also don't want Madevent to waste time producing events with small diphoton invariant mass, because those won't be anywhere near the Higgs peak anyway. So change line 168 to read:
90 = mmaa ! min invariant mass of gamma gamma pair
Next, edit the plot_card.dat:
mij 3 2
Also, change the PlotRange on line 144 to read:
mij 2 100 200
so that the histogram bins will be 2 GeV wide, and run from 100 GeV to 200 GeV. (Remember that we already cut events with invariant mass less than 90 GeV, so it is not meaningful to look at plots with invariant mass less than about 100 GeV, taking into account the photon energy resolution.)
Here are the plots that result, for 13 TeV LHC with Delphes:
and for 8 TeV LHC with Delphes:
Sadly, it takes some imagination to claim that one sees the Higgs peak near 125 GeV in these plots.
If you look at the Results and Events database, you will see that Madgraph calculated the cross-section for the generated events as 5.44 pb = 5440 fb for the 13 TeV LHC, and 3.64 pb = 3640 fb for the 8 TeV LHC. Therefore, the integrated luminosity corresponding to the events that were generated is:
(100000 events)/(5440 fb) = 18.4 fb-1 for the 13 TeV LHC
(100000 events)/(3640 fb) = 27.5 fb-1 for the 8 TeV LHC
The 13 TeV LHC hasn't happened yet.
The 8 TeV LHC actually collected about 20 fb-1, so our simulated event
sample corresponds, naively, to more events than were actually collected.
However, Madgraph's estimate of the production cross-section is not
extremely accurate. Also,
the ATLAS and CMS collaborations did a more
treatment of both the signal and background, chose their cuts more
carefully, and did a
analysis, combining also
with the H > ZZ > 4 leptons signal.
Modifying the Higgs effective couplings
To see the Higgs diphoton peak more clearly, we can "cheat" by increasing
coupling to two photons, or by increasing the Higgs coupling to two
gluons. The names for these couplings are, respectively, GC_1 and GC_13,
and they are defined in the file:
Increasing one or both of these Higgs couplings can be used to simulate what would occur if one used a more accurate treatment of the production cross-section. It will give us an enhanced peak.
So, let's edit this file and just double the Higgs-photon-photon coupling compared to the Madgraph heft value. To do this, change line 13 of the file from
value = '-(AH*complex(0,1))',
value = '-2.0*(AH*complex(0,1))',
This increases the signal amplitude by a factor of 2, and therefore increases the signal cross-section by a factor of 4.
Now, redoing everything as before, being sure to quit Madgraph and restart it and import the model heft_$USER again. This should give plots that look like the ones below.
13 TeV LHC with Delphes:
8 TeV LHC with Delphes:
This time the peaks are visible to the naked eye, thanks to our "cheat" of
multiplying the signal cross-section by 4.
Doing your own detector cut-based analysis
In this class, we've relied on Madgraph's own plots. That's what
you should use for the homework. However, for more
sophisticated analyses at the research frontier, you probably want to
impose your own cuts at the
detector-level. There are several ways to do this: