Next steps

[mvesteri]

Understanding the composition of the NoMuID data and validating the accuracy of the QCD background simulation

• [ ] Can we describe the initial sample in terms of a sum of light-hadron and heavy-hadron simulation?
• [ ] What are the 10% of ID==0 tracks?

Validating/improving our model of the light-hadron background in the mW fit

• [ ] What effect do the 20% of protons have on the modelling of the hadron -> muon pT shape?
• [ ] How well do the 1/P weights approximate simulating the hadron decay?
• [ ] What effect does the trigger have on the "" ""
• [ ] Could we directly use the simulation in the mW fit

Study muon mis-ID in the simulation

Aside this paper reports a measurement of identified charged particle ratios.

[GeorgeCocks-01]

Hi @mvesteri, I'm still struggling with the maths for this misID decay curve.

From the equations L = gamma*c*t = p/m*c*t and f(t) = e^(-t/tau), I got f(L) = e^[(-L*m)/(p*c*tau)]. I then integrated f(L) from L = 0 to 5 and plotted that for different p values, however, the plot looks as follows

I figure that I must have done some of the maths wrong since this graph does make sense for what I'm plotting, with the peak value of the graph equal to the upper integration limit. I'm just not too sure where in the maths I have gone wrong.

I'm also a little confused as to what f actually is, other than it must be somehow related to the decay probability.

Thanks

[GeorgeCocks-01]

@mvesteri @mramospe or if you want me to start on one of the other tasks then let me know

[mvesteri]

Regarding the graph, I'm a bit confused but perhaps you can draw graphs of f(L) for different p values?

Then what you want is the integral from 0 - 5 metres, divided by the total integral.

From the suggested plot of f(L) graphs you should be able to see roughly what that ratio of integrals will look like as a function of p.

[GeorgeCocks-01]

Ah, I didn't realise we had to divide by the total integral. I think this looks much better now. Would I have to times the y-axis scale by 100 to compare with the % mislabeled I had in the mis-ID graph? If so it looks as though it will map rather well onto the data we got.

[mvesteri]

Looks good. Maybe the easiest comparison to do with the data is to check that indeed the kaon mis-ID rate is higher than pions. Just overlay another graph for the kaons (remember the branching fraction as well as the different mass and lifetime)

[GeorgeCocks-01]

Yup, the theoretical mis-ID rate for kaons is larger

[mvesteri]

Great stuff.

I wonder if you could try to "fit" the points from the simulated pions and kaons with a curve with the same functional form as what you plot above? You could probably write the function in such a way that the detector length is directly one of the parameters of the function, so you can basically "measure" the detector length via the fit.

We may also see that the fit isn't great, because it only accounts for the [pion,kaon] decay component. The fact that there are some mis-identified protons means that there is a significant "punch through" component too.

I'm not 100% sure about the functional form of that, but it is probably a logarithmic scaling with momentum.

[GeorgeCocks-01]

Great I'll get on that now then. Just a couple of questions, would it make sense to times f(p) by 100 as that would make it match the range of the data (since the data is as a percent)? And I assume you want one fit for pions and another for kaons, so two values for the length which we can average out?

[mvesteri]

Ah yes sure. It's just a stylistic/aesthetic choice whether to convert to percent but it makes sense to make the same choice for similar/related figures 👍

[mvesteri]

Maybe also start the above plot from say 10 or 20 GeV of momentum. Otherwise the plot is dominated by the large values at low momentum where we don't have any simulation to compare to

[GeorgeCocks-01]

I just realised that I wasn't limiting the PT values of misID to be >20. The graph doesn't look as good now but I think it's because the minimum P value with PT = 20 is higher so you can't see the peaks of the pions or protons.

[mvesteri]

What if you plot over a wider range of momentum, up to say 1 TeV, but use a log x axis?

[GeorgeCocks-01]

I get this, with a log axis. Quite messy for large P but reducing the bin count will do so over the whole plot.

[GeorgeCocks-01]

I managed to get this fit of the data, however the kaon fit gave L = 11.35m, while the pion fit gave L = 25.8m.

[mvesteri]

Interesting:

• the plot with wider [log] x axis quite clearly shows the growing "punch through" component
• Regarding the pion and kaon fits giving different length parameters: this might be because of the punch through component, which is a larger component for the pions than for the kaons (simply because the decay part is bigger for the kaons)

[mvesteri]

Maybe you could see if the graphs could be described by the a composite function that is the sum of a decay part and a punch through part (f(p) ~ log(p), I guess). There are some missing prefactors etc.. for you to fill in...

[GeorgeCocks-01]

@mvesteri should I do that by fitting the data with a function but on the log scale graph? Or will the composite function fit the data on the regular graph?

[GeorgeCocks-01]

I'm also not too sure what the prefactors would be. Having played around with variables a little is it the particle's mass among others?

[mvesteri]

Yes the idea would be to fit over the wider range of momentum with a sum of a decay part and a punch-through part.

By prefactors I just mean things like the f in f*decay_part + (1-f)*punch_through_part. Maybe that is it, but I leave it as an exercise for you to figure out the form of the function 😉

[GeorgeCocks-01]

I tried to fit the prefactor but the graphs and data are quite far off. Can I double-check that the log term should just be added on after the integral of the decay term has been done? Like so: f(p) = integral0-5(decay)/integral0-infinity(decay) + log10(p), with some prefactor terms added

[GeorgeCocks-01]

When you write f*decay_part + (1-f)*punch_through_part, do you mean that I should be adding some other prefactor to the decay part as well? At the moment the only prefactor on the decay part is the branching_frac.

[mvesteri]

The f is basically a "fraction of decay part".

[GeorgeCocks-01]

I'm still quite confused as to what f should be. I've tried different combinations of the variables we've been using but none of them seem to give good fits.

[mvesteri]

Maybe just think of the function like A*decay_functional_form(momentum) + B*punch_through_functional_form(momentum), where A and B are just arbitrary normalisation parameters that you float in the fit?

[mvesteri]

The two function components also have their own free parameters in addition

[GeorgeCocks-01]

The fit isn't great, especially for the pions. I used the lengths from the old fit since if I include it as a fit parameter here I get very small and negative lengths.

Below are the A and B fit params I got.

Kaon fit params: [0.21348514 0.35433869]
Pion fit params: [-0.58957287  0.35099777]

[mvesteri]

Hi @GeorgeCocks-01, sorry for the slow response. Did you manage to figure out how to get a better fit to the data? I will be in the department tomorrow so we could discuss in person

[GeorgeCocks-01]

Hi @mvesteri, no worries. I didn't manage to get much further than what I sent, and Miguel gave me other tasks throughout the week which I've been working on. I'm not sure what the problem could be unless I used the wrong functional type to fit the data. I used the same integral as before, and then simply added B*log10(p) to the end.

[GeorgeCocks-01]

I've had more of a look through my code but I'm not sure why it isn't fitting well. I tried fitting the length as well for this compound function and while the fit is better, the lengths are 0.35m for both.

[mvesteri]

I think the logarithmic term needs to be a bit more flexible. Maybe leave the base floating, like log(p)/log(C) where C is another floating parameter in the curve fit?

[GeorgeCocks-01]

The fit still gives the same result graphically, and gave lengths of 0.015 and 1m. I also tried using log(cp). This gave a much better kaon fit but a worse pion fit which I can't seem to fix. The lengths f or this fit are -178 and 1 for kaons and pions respectively.

[GeorgeCocks-01]

I also should mention that I'm still using the same A and B parameters as earlier, so I think it makes sense that the 1/log(c) term wouldn't make much difference as it could be absorbed into the B term since it is a constant.

[mvesteri]

OK. Can you write down the precise functional form that you put in the curve fit? (raw python code is probably fine for me to understand)

[GeorgeCocks-01]

This is my current code (100*prefac1*mass*bfrac*integrate.quad(f, 0, length, args = (p, mass, tau))[0])/(p*c*tau) + prefac2*np.log10(p)/np.log10(prefac3).

where f returns np.exp(-(L*mass)/(p*c*tau))

I used 1/(p*c*tau) since it should give the same value as integrating the function f from 0 to infinity.

[GeorgeCocks-01]

I should probably also note that the 100* is because we were using percent for the data, however, I could probably remove it and it would just increase the fit params by a factor of 100.

[GeorgeCocks-01]

@mvesteri is my functional form ok or have I made a mistake?

[GeorgeCocks-01]

@mvesteri did you manage to figure out what was wrong with my code?

[mvesteri]

Suggest to extend the set of plots like this one with

• track eta
• pT
• Hcal ET
• Ecal ET
• phi
• log10(IPCHI2)
• log10(isolation)

[mvesteri]

For the trigger efficiency, plot the fraction of hadron candidates with mu_L0Global_TOS==true. Suggest to do this as a function of pT, eta,... , as separate 1D plots.

[mvesteri]

Try to read files from /storage/epp2/phshgg/Public/DVTuples__v24g/

[GeorgeCocks-01]

Here's that first Log(IPCHI2) graph, you can see the addition from the other particles you drew on the whiteboard in the real W data.

I'll get to work on the other graphs now.

[GeorgeCocks-01]

Here are the other graphs. The EcanET has that huge peak which makes it hard to see the rest of the data, not too sure why that is or if I should do anything to counteract it.

I'll move onto the trigger efficiency for now though.

[GeorgeCocks-01]

Here are the graphs of trigger efficiency for all the same variables as the above graphs. Just wanted to double check, this was meant to be done with the QCD simulation data right?

[mvesteri]

👍 on the recent graphs. Some comments/suggestions:

• On the distributions for the different particle species/categories: some of the trends for the category-zero seem to support the hypothesis that these are slightly mis-reconstructed tracks. The isolation tends to be higher, which would cause more confusion in the tracking. The pT distribution is a bit "harder", consistent with a worse resolution. etc...
• For the trigger efficiencies I suggest to draw points with error bars

[GeorgeCocks-01]

Here are the trigger efficiencies as errorbar plots. I used the same errors as for misID: sqrt(frac*(1-frac)/withouttrigger), with frac = withtrigger/withouttrigger.

[GeorgeCocks-01]

@mvesteri if those graphs are good then is there another task I can move onto?

[mvesteri]

Can you try again with this?

git clone ssh://git@gitlab.cern.ch:7999/LHCb-QEE/WmassMeasurement.git WmassMeasurement
cd WmassMeasurement
git submodule init
git submodule update
./run --cmake -- -G Ninja
./run --install -- ninja

[GeorgeCocks-01]

Still the same access denied. I haven't set the CERN account up fully yet since it said I needed to wait 24hr to get my password. That was at 4pm yesterday.

[mvesteri]

Ah, OK.

In that case, a different problem to think about: do you think the detector would measure a different momentum for pions and kaons that have decayed to muons? Think about the kinematics of the decay, and the way that LHCb basically measures a deflection between two straight-line trajectories, due to the dipole

[mvesteri]

(This detail is currently ignored in our model)