The CMS Momentum Scale And Resolution

While the focus of the international conference in high-energy physics in Paris last week has been on the search for new physics and the precise measurement of standard model quantities, I will offer to you today something more technical, but in no way less physics-rich; it was presented in Paris, but with the many parallel sessions it may have well gone unnoticed... What I wish to explain to you is the procedure by means of which the CMS experiments calibrates the scale and resolution of its charged particle momentum measurement.

The dull sound of the topic as stated above should not deceive you: this is a really exciting, interesting technology, which allows the measurement of physical quantities with high precision. Since the M in CMS stands for "muon", we certainly care for the precise measurement of muons -and muons are the particles used for the calibration procedure.

What happens when a charged particle leaves ionization deposits ("hits") in the silicon tracking system is that we can reconstruct its trajectory, forming a track. The track is curved in the plane transverse to the beam, because the S in "CMS" stands for "solenoid", a big cylinder that provides a B= 3.8 Tesla magnetic field within its volume. If you know what the Lorentz force is, you might also remember the formula P = 0.3 B R, expressing the proportionality of the momentum of a charged particle and its curvature in a magnetic field. This demands that within the CMS solenoid a P = 1.14 GeV muon follow a curved trajectory, which resembles a circle of radius R = 1 meter if observed in the "transverse" plane to the beam axis, the one along which the solenoid is symmetrical. By measuring the curvature, we determine the transverse momentum!

Things are always complicated if you want perfection. We of course can measure the position of the silicon hits with extreme accuracy, but alignment and positioning errors may create imperfections in the measurement of the track curvature. We also know the magnetic field with high accuracy, through Hall probes and other means, but imprecisions will affect the momentum measurement. Finally, the amount of material of which the tracking detector is composed affects the trajectory, producing further imprecisions if our map of the material is not perfect.

In the end, all the effects and all the details of the geometry of our detector are encoded in a carefully crafted simulation. With the simulation we can figure out what a 1-GeV track would look like, given our reconstruction and our assumptions about geometry, material, and magnetic field. But we need real data to verify that our model is correct, and to tune it in case it is not!

Real data: we now have it. CMS uses resonance decays to opposite-charge particles for this business: they are easy to identify, have little background, and there are plenty to play with. In particular, we use J/Psi meson decays to muon pairs for some of the checks of the momentum scale and resolution. Other dimuon resonances are also used -there is a large amount of such decays already available in the data so far collected- but here I will only discuss what CMS did with its J/Psi signal.

The dimuon mass spectrum in the vicinity of the nominal J/Psi mass value is shown in the picture below. A large number of signal events is observed. These events can be used to calibrate the momentum scale.



If one looks closely, one observes that the measured mass is very slightly lower than the nominal 3.097 GeV. This is already evidence for a very small underestimation of the momentum scale. To dig further, a simple thing one can do is to divide the J/Psi events depending on the value of the particle's reconstructed momentum or rapidity, measuring the mass in all sub-samples to check if in particular kinematical regions there is a bias. The bias, of course, would arise from the momentum reconstruction of the individual muons; but if one only measures the mass, which is a quantity constructed with the measurement of two muons, surely only an "average" bias can be detected, right ?

Wrong. Each muon from the decay of each J/Psi has a different momentum, travels through different parts of the detector, and is subjected to different reconstruction biases: we can turn these differences to our advantage. What we can do is to assume we know the functional form of these biases, and plug them into a likelihood function.

A further benefit with respect to methods I have seen in the past for the correction of scale biases is that a well-written likelihood function is also capable of extracting the momentum resolution from the same set of data. One just needs to produce a functional form (whose exact shape is suggested by simulation studies) that describes how the resolution on the momentum depends on the track kinematics; then, the likelihood fit will take care of finding the best parameters of the resolution function as well, by comparing the expected lineshape of the resonance with the mass value measured for each particle decay.

The likelihood is very complicated, because it accounts for the dependence of the mass on the muon momenta and the resolutions, and momenta and resolution in turn are functional forms of bias parameters. I know very well the code of this likelihood function, and I can tell you it is not for everybody! So I will abstain for once from finding a suitable analogy, lest I squeeze my brains for the rest of the evening. Let me just say that in the end, the likelihood maximization produces the most likely value of the parameters describing the bias functions, allowing a correction of the bias in the track momentum measurement!

Maybe it is best to show a couple of figures. The first one below shows the average mass of the J/Psi meson as a function of the pseudorapidity of the muons from its decay. The hatched red line shows the true value of the J/Psi mass; but more meaningful are the crosses, which show what should be measured with a perfect detector, given the fitting procedure (which, I am bound to specify, assumes that the lineshape follows a Crystal Ball form). The crosses are our "target": if we measure a mass in agreement with them, given our fitting procedure to extract the mass, our momentum scale is perfect.



In blue you can see that the mass, before corrections, is biased low, especially at high rapidity. Instead, after the likelihood maximization and the correction procedure, we obtain the purple crosses. The agreement with the black crosses is still not perfect, and the statistics is too poor to detect further small deviations, but the demonstration of the validity of the procedure is clear!

And then, the resolution. This is also a function of rapidity in CMS, due to the way the detector is built and the decay geometry. The figure below shows what resolution we expected to measure as a function of rapidity, from simulated J/Psi decays (in black), given the measurement method.



In red the figure also shows what the true resolution is, from simulated muons that are then compared to reconstructed ones. In blue, the band shows what instead CMS measured. The agreement between data and simulation is encouraging, and the result demonstrates the validity of the method. This functional form and its parameters are extracted from the way the reconstructed masses of J/Psi decays distribute around the nominal mass, accounting for the fact that muons in those events have different rapidity: the likelihood knows all the details, and produces a very complete answer to our question.

I think the method is very powerful and I cannot wait to see it applied to all resonances together, with more data -the different dimuon resonances have different kinematics and produce muons of widely varied momenta, allowing a very complete picture of the calibration and resolution of the CMS detector!

A Spectroscopist's Delight!

While everybody is busy discussing the latest Tevatron results on the Higgs boson searches -is that the light-mass excess the internet was abuzz, is it consistent with a signal as we expected it, how long will it take to confirm it is not a fluke, etcetera, etcetera, etcetera- I think I have a different plot with which to enthuse you.

If you do not like the figure below, courtesy CMS Collaboration 2010, you are kindly requested to leave this blog and spend your time reading something else than fundamental physics. I do not know what will ever make you believe particle physics is beautiful, if not what is shown here.



The figure shows, using a logarithmic scale on both axes, the reconstructed mass of pairs of muon candidates of opposite charge, collected by CMS in its first 280 inverse nanobarns of 7-TeV proton-proton collisions collected until a week ago. Nothing fancy has been done to prettify this graph: these are honest-to-god muon pairs, as Nature (the bitch, not the magazine) has produced them in the core of CMS. True, the interecession of a detector and a reconstruction software were needed to go from ionization clouds to event counts; but this is the absolute minimum of manipulation you can ever expect from particle signals.

Now, what should enthuse you about the graph is the following. The distribution reveals, clearer than a million words could describe, the structure of all the most important bound states decaying by electroweak interactions into pairs of muons which we can produce in hadron collisions. We immediately spot the Z boson on the far right, and the towering peak of J/Psi mesons; but we also see Upsilon mesons, and at lower energy, we detect the ligher resonance decays of rhos, omegas, and phi mesons. What a spectroscopist's delight! This figure is tremendously informative! If we sent it to outer space, without labels or units, no intelligent race could ever mistake its meaning!

You also notice that these jewels stand atop a background of unidentified muon pairs. Muons can be produced singly by the weak decay of kaons and pions, for instance, or even more massive states like bottom and charm. Occasionally, pairs of muons of opposite charge can emerge that do not have the same parent: the frequent production of these uncorrelated pairs creates the significant backgrounds you see in the picture. Note, however, how these backgrounds die out for large dimuon masses: the Z boson is basically background-free, a fact I have noted in my previous posting here.

As these pages testify, CMS and ATLAS have presented scores of interesting physics results at ICHEP this week. None of those were groundbreaking ones; a few were significant advances, though, and many others were just meant to demonstrate that the experiments are ready for big challenges, such as discovering new physics, the Higgs, measuring the top mass better than the Tevatron, etcetera. The presented results took about a hundred man-years to produce, and I have a lot of respect for them -not to mention the fact that I did my little bit to contribute. But it is my humble opinion that the graph shown above could well be the one to single out and attach on the bulletin board of all the universities and institutes participating in the LHC experiments!

The present and future of the LHC

Today's been a hectic day: between Sarkozy's speech, the press conference, and the lack of wireless internet in the auditorium where the plenary talks are being held, there's been little time to blog. So any time I've been able to grab during coffee breaks has been spent uploading blog entries to my usual haunt, symmetry breaking. There you can read about the 10-year plan for LHC running and whether or not it might affect some Tevatron scientists' hopes to run their accelerator for a further three years. Plus my take on the new measurements reported by the LHC experiments at ICHEP, such as the W cross section measurements at 7 TeV, and the limits ATLAS and CMS have placed on some exotic physics. (Keep in mind that symmetry is for a more general audience; my fellow ICHEP bloggers have covered those results in much more detail here.)

How do you know ICHEP's just around the corner?

Two ways you know that ICHEP is imminent:

1. The blogosphere, Twitterverse and science media are abuzz with rumors regarding possible new results;
2. The families of particle physicists worldwide bemoan the temporary disappearance of their loved ones.
   

Here at CERN, activity among scientists involved with the LHC experiment has reached fever pitch. Students, postdocs and senior physicists alike are consuming even more coffee than usual, as they work to put the final touches on data analyses, results, posters and PowerPoint presentations.

With the size of today's particle physics collaborations - peaking at more than 3,000 people each for the ATLAS and CMS collaborations - getting a result approved for presentation at a major conference like ICHEP is no simple task. With so many people involved, the collaborations put in place rules and procedures governing approval processes for results and publications, with the goal of ensuring that all results have passed rigorous review and that every collaboration member has the opportunity to review and comment on every result. For the LHC experiments, the rules that have been painstakingly assembled over a decade or more have been getting their first real workout this summer, first for the PLHC conference in Hamburg, and now for ICHEP.

To give you an idea of the work behind each plot presented in an LHC talk at ICHEP, here's a quick overview of the steps involved (symmetry Magazine has a more in-depth look at this data-to-discovery process).

A small group of a few to a few dozen physicists spends weeks, months, or years analyzing data and preparing a result. Depending on the nature of the result, it may or may not be combined with result(s) from other group(s) within the same collaboration. It's then unveiled to the entire collaboration for review, and after a certain period where any collaboration member can comment (remember: 3,000 people!), receives final approval for presentation in public. Or not, in which case the process starts all over again.

And that's all just the first step. Once the result is approved, be it in the form of a plot, chart or paper for publication, then the work begins for the people who have been selected to present it and other results in public at a conference like ICHEP. They select from the approved results, prepare their poster or PowerPoint, go through a similar approval process, and practice in front of their colleagues in the collaboration.

And in cases like the current Higgs limits from the Tevatron, results could be combined from two different experiments, which doubles the complexity of the entire process. It's no wonder that, around the time of major conferences, sleep is a rare commodity.

(But even with ICHEP just around the corner, I bet some of those same hard-working scientists will take a few hours off to attend CERN's annual music extravaganza, the Hardronic Festival.)

I'll end with a quick introduction, since I'm the new girl on the blog - I'm a nuclear physicist turned science communicator, working for Fermilab Office of Communication but based at CERN for the past three years. I spend most of my time telling the story of the LHC project and U.S. scientists' involvement to journalists and the public, and the rest of my time trying to keep up with developments in the larger world of particle physics. So I can't wait to see and hear what's presented at ICHEP, and to write about it here and at the other blog I contribute to, symmetry breaking.

What should we expect from LHC?

June is coming, summer conferences are approaching, LHC physicists are feverishly working to produce results to show.

In the next few months there will be three main conferences where physics results from the LHC experiments will be presented: the nearest one is Physics At LHC, that will take place at Desy in Germany the second week of June; the second one is, erm... you know... ICHEP; the third one is the Hadron Collider Physics Symposium in Toronto, at the end of August. The kind of results one might expect to be presented at each of these conferences is rather different. The LHC is in fact steadily delivering proton-proton collisions at 7 TeV: the farther in time the conference, the more integrated luminosity the experiments will be able to use for their analyzes.

Could we try to guess what is likely to be shown at ICHEP by ATLAS and CMS? Well, it's definitively not an easy prediction: even assuming a perfect efficiency of the two experiments in collecting the data and analyzing it, the LHC beam conditions are improving every day, and the exploitable integrated luminosity at - let's say - mid July can largely vary.

Let's then try first a different exercise: which results are more likely to be seen at a conference as a function of the integrated luminosity collected at 7 TeV, from the small amount we already know as been secured by the experiments to the 1 fb^-1 promised by the machine for the end of the 2010-2011 running? Warning: what follows is a very approximate list, I might have missed important signals here and there, and my judgment is certainly biased by my ATLAS experience. Here's what we'll get (or what we already got):

1. 10-100 μb^-1: millions of charged pions to happily redo the charged multiplicity analysis published with the 900 GeV data collected in 2009; a few tens of $J/\psi \to \mu \mu$, a few jets here and there. Any resonance that can be spot using the tracker system (like K's and $\Lambda$'s) has been been seen at this point; signal from $\pi^0$ and $\eta$ decaying in photons pairs is found and well isolated.
2. 100-1000 μb^-1: any hint of a $J/\psi \to \mu \mu$ peak should now be clearly visible;
3. 1-10 nb^-1: more jets. And of course more jets-related measurements.
4. 10-100 nb^-1: a few tens of W begins to appears in the data. The lucky ones might have seen a few Z bosons. A first observation of prompt inclusive electrons should be at reach at this point.
5. 100-1000 nb^-1: more and more jets. The first inclusive muon measurements should be feasible. Signal from prompt photons should have been isolated.
6. 1-10 pb^-1: at this point ATLAS and CMS should have secured enough W and Z to dare to attempt a first cross-section measurement. They might be able to pretend to have seen the top quark.
7. 10-100 pb^-1: first B-physics related measurements. Something could already be said about some exotic scenarios, and some SUSY points.
8. 100-1000 pb^-1: at this point, one could even optimistically hope in some timid news about the Higgs boson (exclusion), at least where the sensitivity is higher.

Where do we stand today? ATLAS and CMS are today around point 4. (more around the 10 nb^-1 lower end, anyway), and that kind of results will most likely be shown at Physics At LHC together with a lot of performance studies. The question is then: how much more luminosity will the machine be able to deliver before ICHEP? Since this post is already long enough, I will postpone my educated guesses to the next ones. Stay tuned.

And CMS, in the meantime...

The blogosphere is abuzz with the recent news of a startling new result by DZERO -see the previous post by Jester on this issue by scrolling down- but in the meantime at CERN experimenters are quietly working at their first meaningful physics results, with proton-proton collisions at the highest energies so far achieved.

This morning, after months of work, finally a paper by the CMS collaboration sees the light. Or should I say the pre-light, since the paper has been sent to the Cornell Arxiv, and to Physical Review Letters, but it is so far only a pre-print: the PRL reviewers will need to approve it for publication. Given the excruciatingly long and painful internal review process that the paper has withstood within CMS, by about 5000 eyes (or 2500 pairs if you prefer), I would say there is not a chance that the paper does not pass the standards of PRL now. But maybe it is better to be cautious, so - pre-light!

The paper reports on a measurement of Bose-Einstein correlations between pairs of charged pions recorded by CMS in its early runs at 0.9 and 2.36 TeV of center-of-mass energy. Nothing too exciting, but indeed a nice clean new measurement from data which allows little else at this stage, due to the small luminosity collected by the LHC this far.

I was personally involved in the analysis of the data for this result, so I quite well know how painful it was to produce the paper. But it has left today, so it is time to cheer up. In the meantime, CMS is working at dozens of other publications, which are expected in time for ICHEP. Paris will be brimming with new LHC results, I am sure. Another reason to look forward to it, besides the ephemeral albeit exciting news from the DZERO detector!