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Three – Jet energy resolution for novices June 20, 2006

Posted by dorigo in personal, science.

A few days ago I discussed here the meaning of jet energy scale and jet energy resolution… See the relevant post in https://dorigo.wordpress.com/2006/06/16/jet-energy-scale-for-total-beginners/ if you must.

Today, I would like to discuss with some detail why I have been spending lots of my time on the issue of improving the resolution of CDF measurements of the energy of b-quark jets.

Actually, if a little auto-biography is allowed here, let me make a diversion for a moment, to say I have been working at improving the measurement of hadronic-decaying resonances for the whole of my career as a physicist:

– Sought a signal for top decays into six jets, 1992-1995. Found a signal, published "First observation of the all-hadronic decay of ttbar pairs", 1997.

– Sought a signal for Z decays to b-quark pairs, 1996-1998. Found a signal, got PhD thesis, 1999. Not published – moved to more pressing issues with CMX construction

– Sought a signal for associated production of Upsilon mesons and W/Z bosons (including the jet decay of the bosons). Found no signal, demonstrated that the jet decay was the one yielding highest sensitivity. Published "Search for associated production of Upsilon and Vector boson",  2002.

– Took on problem of improving the resolution of H->bb decay in the Higgs Sensitivity Working Group. Devised algorithm that achieves 10% resolution on mass of resonance.

– Sought a signal of Z->bb decays in Run II data. Found a signal, blessed it. Signal now being used to extract a measurement of the b-jet energy scale. Expect determination for late summer 2006.

– Managed Jet Energy and Resolution Working Group in CDF, September 2004- September 2005. Devised b-specific jet energy corrections with Hyperball algorithm. Corrections now under testing on Z->bb signal.

Ok. Now that the picture of why I care for the jet energy measurement is clear, if you got this deep in the post you deserve some insight on Why the hell am I so interested in improving the b-jet energy resolution.

The answer lies in the figure above. It shows three sets of curves in a plot where the x axis is the unknown mass of the Higgs boson, and the y axis is the total integrated luminosity CDF and D0 wish they will collect during Run II. The two curves for each color show predictions of 1998 (the thick ones) and 2003 (the thin ones). The purple curves indicate what luminosity y is needed to exclude the existence of a Higgs boson with a mass lower than x. The green curves indicate the luminosity y' needed for a first indication of the existence of the Higgs boson at the mass x; and the blue ones indicate the luminosity y'' needed to claim discovery, again if the mass is x. 

The plot is the result of a lot of work by several people in CDF and D0 during 1998-1999, and again by a smaller committee in 2003. The 2003 results basically ended up confirming the previous ones (the thinner bands show more precise determination of luminosity thresholds, but no systematic uncertainties were considered to derive them – basically for lack of time), and are credible since they are based not on an extrapolation of the predicted behavior of the detectors, but on real data actually collected by CDF and D0 until spring 2003.

Ok, so how about b-jet resolution ? Well. In order to push those curves down to the low luminosity values you see in the plot – low enough that the Tevatron still hopes to discover the Higgs boson, there being a chance that before 2009 the Tevatron will deliver 8 fb-1 to each experiment (check what mass corresponds to 8 fb-1 in the green band above) – CDF and D0 needed to demonstrate that the resolution for a resonance decaying to a pair of b-quark jets was of the order of 10%.

Which leads us to my own plot – my contribution to the HSWG in 2003. With the hyperball algorithm, together with two other steps of jet corrections, we did get to a 10% mass resolution, as can be seen in the bottom right quadrant.

In the plot, the red points show the mass reconstructed from a set of simulated Higgs boson decays (for a Higgs mass of 120 GeV), and the other histograms describe the various backgrounds that one has to cope with when trying to identify the Higgs boson in the production process ppbar -> WH -> l u bb , that is when a proton-antiproton collision at the Tevatron yields a W boson and a Higgs, and the former decays to a lepton-neutrino (lu) pair, while the Higgs decays to two b-quarks (which hadronize into two b-jets).

Amusingly, soon after producing the plot above, CDF issued a first analysis of their W+jets data in the search for a Higgs boson, and sported a 17% mass resolution… But that was before any optimization! In fact, that less-than-satisfactory result was what spurred the creation of the Jet Energy and Resolution Working Group, which collected people working in four different smaller working groups in CDF.

By the end of the summer, CDF will have something to say about their predictions for a 10% resolution: it will be a by-product of the determination of the jet energy scale, by analyzing the Z->bb signal. Stay tuned!


1. Avantika - June 4, 2008

Can you please explain why everything is quoted in terms of luminosity and not in terms of number of events or cross-section?

2. dorigo - June 4, 2008

Hi Avantika,

the number of events collected by an experiment depends on many subtleties connected to the experimental setup, the trigger conditions, the data acquisition bandwidth. Also, even if one experiment were able to collect ALL the produced inelastic interactions, the number of events N alone would say little, because one would then need to know the inelastic cross section at the experiment’s energy to compute the cross section of a rare phenomenon yielding a smaller number M of events: s(rare) = M/N s(inelastic). Please note, the inelastic cross section s(inelastic) is not known with great accuracy!

Luminosity allows different experiments, using different apparata and triggering choices, to compare their effective data sizes. For any given process of cross section s, one has N=sL .

However, if you were to insist arguing that in the end the two choices would be roughly equivalent, I would have to concur.


3. Newto this - May 25, 2009

I am totally new in this subject and may be it will be strange that I am asking these questions. But I just do not know.
Could you explain bit in details, how to evaluate jet energy scale and jet energy resolution if I have only a calorimeter and nothing else? I have simulated data. With reconstructed jets and witj generator level jets. Difference of Et of these two gives me around 10GeV after two jet association in eta phi space. Here I am bit confused. Is this jet energy scale determination?


4. dorigo - May 26, 2009


The jet energy scale is a factor which relates the true energy to the measured one. So it is a ratio, not a difference.

With just a calorimeter you still have ways to calibrate your measurement. Let us take the case of a calorimeter which has not withstood any test-beam run, which does not have a tracker suitable for measuring single tracks before they interact, etcetera. Let us take the case of an experiment looking for cosmic rays, which does not even have the luxury of selecting two-jet events like collider experiments do (the two jets balance in the transverse plane and that gives you some handle).

In such a case, you do what you were suggesting: You compare generator-level jets with reconstructed ones. You do this as a function of jet energy, because the effects that the jet measurement is subjected to will depend on that variable (for instance, the single particle response usually grows with particle energy, and the energy of single tracks in a jet grows, albeit only logarithmically, with jet energy).
You can also do it as a function of other variables which describe local effects in your detector, like angles and point of impact.

Once you have a distribution of the ratio E_rec/E_gen as a function of E_gen (say), you can try to parametrize the ratio and assume that as a correction to the absolute energy scale. Of course, you will be totally dependent on how well your MC models the detector and the physical processes; but hopefully, you will be able to study the MC shortcomings in other ways, thus getting to the point of assigning some meaningful systematic uncertainty…

Hope that helps,

PS please note that this blog has moved elsewhere.

5. Newto this - May 27, 2009

Thanks for your answer.

Exactly, it will depend on my model. For now calorimeter exists only in simulation. Why it is not possible to have ratio vs the jet measured energy instead of particle level jet energy? In my understanding E_rec/E_gen vs E_rec is more convenient. I had in mind also constructing this kind of variable

(E_rec + )/E_gen,

where will be mean of difference got from Gaussian fit to the difference distribution

6. dorigo - May 28, 2009

I think it depends what you want to do with the distribution. If you are going to estimate a systematic uncertainty, then it is better to have the generated parton energy on the x axis, because you will be able to estimate a spread as a function of the thing you want to measure; if you are going to correct a measured energy for the deviation you observe, instead, maybe plotting the bias as a function of the reconstructed energy is the right thing to do, but then be careful with how the original data populates the profile histogram.

To be clear, imagine a very steeply falling distribution of generated energy is used to fill that profile histogram. If you plot Erec-Egen as a function of Erec, you will get for any Erec you will be likely to get a positive bias (i.e. always Erec-Egen>0), because the chance that that bin receives a contribution from larger Egen (which is highly depleted with respect to smaller Egen) is overpowered by whatever genuine bias you have in the reconstruction.


7. Newto this - June 2, 2009

Thanks for answer. Sorry that I am bothering you so frequently. But I am just interesting in this subject. I came with some stuff which I need to understand. I constructed the distribution Emeas/Egen vs Emeas and it has clear exponential dependence. Fit with the function like this 1-a*exp(-b*Emeas) is good. Now I think that b can be expressed like 1/Escale, which is some scale. And Escale determined from there. Of course this can be used then to correct Emeas to get flat ratio. Please do not be angry if I am writing stupidity

8. dorigo - June 2, 2009

Hi Newto,

I think you are confused by trying to find some value of energy that magically solves the problem, as in your example, where b indeed must take on 1/GeV values. Instead, an energy scale is just a multiplicative factor that must be applied to “scale” the measured energy to the true value. So, in your example, if Emeas/Egen = 1-a*exp(-b*Emeas), then the answer is just that the energy scale is 1/(1-a*exp(-b*Emeas)), period.

That is: if you want to “correct” Emeas, then take Emeas and multiply it by 1/(1-aexp(-bEmeas)) and you get your best estimate of Egen. You have an energy-dependent absolute jet energy scale, which is a very common situation. Nothing to worry about.

Does that make sense to you ?

9. Newto this - June 2, 2009

Hi. Indeed it does make a sense. After just correcting I have nice flat distribution. Thanks so much.

10. Newto this - June 2, 2009

I was advised to make fit this function by my college. So energy dependent, energy dependent.

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