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Tommaso Dorigo: luminosity class is tough!

The discussions with people whose knowledge about physics follows the weaker part of the physics blogosphere but whose self-confidence would suggest that they are Newittons - hybrids of Newton and Witten - often reaches comical proportions.

That was the case of a recent debate with Tommaso Dorigo about luminosity, too. As we mentioned, Tommaso wanted Matt Strassler to admit that experimenters like Dorigo were infallible.

But in the middle of bizarre sociological Dorigo's prayers to the new deity, there was one cute technical comment. For no good reason, Tommaso decided that Matt Strassler's interpretation of the CDF estimate of the cross section for the ghost events - namely 75 pb (picobarns) on page 3 of Matt's paper - is incorrect by a factor of three or so. I suspect that Dorigo just invented this absurd "correction" for the sake of it, in order to undermine Matt's authority a little bit, believing that no one would notice that his "correction" is wrong.

Matt obtained the cross section of the "new", ghost events in the following simple way:

153,895 / (2100/pb) = 73.28 pb
Tommaso Dorigo proposes a different calculation,
153,895 / (742/pb) = 207.4 pb
although he is never quite able to complete this division and announce his - ludicrously high - result. Given the fact that e.g. Giromini et al. predict the cross section to be 50 pb or 35 pb on page 4 for various masses of the Higgs, in a paper that claims to match the data, Dorigo could perhaps find a reason to figure out that 207.4 pb could be too high. But he seems to have no idea about the difference between 75 pb and 200 pb.

Dorigo offers no technical arguments to support his bizarre figures. Instead, he mysteriously tells us that he has talked to the "main author of the CDF study". Well, maybe he should subtly inform her that she is dumb as a door knob, too, if she exists. ;-) On the other hand, Matt includes a very detailed and crystal clear explanation of the way how the cross section - and especially the number of events - was calculated.

Fine: so 742/pb or 2,100/pb?

Of course, the total integrated luminosity, 2,100/pb (two thousand and one hundred inverse picobarns) must be used as the denominator, as Matt Strassler explains in detail, and my task will be to explain this simple fact so that even people like Tommaso Dorigo will understand. It may be a bit like Brian Greene in the TV show, trying to explain Einstein's equations to his dog ;-), but let me try, anyway.

The luminosity is a quantity that determines how many times the initial state of two-particle collisions has been repeated in an experiment. It is expressed as the "number of colliding particle pairs per unit area and per unit time". The more particles you collide each second, the more collisions you will get. The more accurately you focus the beams, the smaller the area becomes and the higher chance of collisions you get. That explains various proportionality laws.

All the areas are usually expressed in barns: one barn is exactly 10^{-28} squared meters, roughly the cross section of a proton. The typical cross sections of new, interesting processes in particle physics are much smaller, e.g. several picobarns: one picobarn is 10^{-40} squared meters.

If you integrate the luminosity over time, you obtain the so-called "integrated luminosity". It is expressed as the "number of colliding particle pairs per unit area". The integrated luminosity has units of inverse area: note that the inverse seconds have disappeared. This quantity is a coefficient that you should multiply by a cross section "sigma" of a given process to predict the dimensionless number of actual events.

The Tevatron, the accelerator at Fermilab, has been colliding protons against antiprotons. So the "total integrated luminosity" refers to the flux of colliding proton-antiproton pairs.

Analogously, the cross sections that should be multiplied by this "total integrated luminosity" to get the number of events are cross sections calculated from proton-antiproton pairs as the initial states. Protons and antiprotons are pretty complicated beasts and the theoretical calculations with proton-antiproton initial states require a lot of dirty QCD technology - like the parton distribution functions. But that's what you have to do if you want to predict how many times the colliding protons and antiprotons produce e.g. a top-quark.

Now, there's no doubt that the total integrated luminosity (of proton-antiproton beams) used to suggest the "lepton jets" in the recent CDF paper is 2,100/pb: see e.g. the second sentence of the abstract. If you want to keep things simple, the right denominator has always been 2,100/pb and there is nothing to talk about. But still, you may ask: why the hell Tommaso Dorigo is talking about 742/pb? Isn't he supposed to know at least some basic things here?

Silicon vertex tracking

So let me explain what the number 742/pb means and why it's wrong to use it as the denominator in the calculation of the "ghost events" cross section. I have spent literally hours, trying to explain it to Tommaso. And I have mostly given up, much like Brian Greene did with his dog. It is probably not possible. But I am almost sure you will get it.

Most of the proton-antiproton collisions are boring. They produce a few jets - streams of strongly interacting particles arising from gluons or light quarks or antiquarks. They must also be correctly described by QCD, and they arguably are, but every sane person believes QCD, anyway. What is interesting and "uncertain" are some events in which heavy particles are almost universally produced in the collisions.

Now, what are the heavy particles that the Tevatron routinely produces? The top quark is the heaviest quark but it is too heavy: the Tevatron doesn't produce too many. The generic heavy particles produced by such colliders include the other heavy quarks, bottom and, to a lesser extent, charm. They are referred to as the "heavy flavors".

Can you select the events in which the bottom quarks were created? Yes, you can and you should. A few years ago, they built the silicon vertex tracker (SVT).

It is a small specialized "computer" that takes the data from the silicon vertex detector (SVXII) and the central outer tracker (COT). The gadget quickly reconstructs the tracks and if it finds sufficiently unambiguous evidence that the bottom quarks appeared in the collision area, right after the collision, it tells the system that the event was interesting - at least for the people who study B-physics (of bottom quarks), e.g. in the context of CP-violation (that requires three generations, including the third one with the bottom quark).

Now, only a subset of the events are picked by the strict SVT criteria: the jets in these events are said to be "b-tagged". The precise percentage depends on how strict criteria the SVT adopts: it is partly a matter of conventions. In reality, about 24.4% of the events that excite the dimuon triggers also pass the strict SVT filter: this percentage is referred to as the "efficiency" of the (heavy flavor) QCD events. The silicon vertex tracker may also choose the events "loosely"; in that case, the efficiency jumps to 88% or so. However, if you assume that there is no new physics, pretty much all events in which the dimuon trigger "clicks" should be caused by heavy flavors - essentially by the bottom-antibottom initial states.

In these most special 24.4% events, bottom-antibottom pairs "almost certainly" appear at the very beginning. So at the very beginning, it looks like you just collided bottom-antibottom pairs instead of proton-antiproton pairs. If you now interpret the Tevatron as a machine where you effectively collide bottom-antibottom pairs, it has a smaller luminosity because only a small portion of the proton-antiproton collisions included protons and antiprotons that were "ready to make heavy flavor collisions". Even though the remaining 75.6% dimuon events probably also contained bottom quarks, you discard the collisions as inconclusive.

You may define the corresponding fraction of all the events and normalize it in the same way as you would do with bottom-antibottom collisions. Assuming that the bottom quarks are there whenever the SVT says "Yes", the integrated luminosity of this subset is just 742/pb, not 2,100/pb. The collisions up to this day that have passed the intermediate, loose SVX filter, give you the integrated luminosity of 1,426/pb or so.

So is it OK for someone to write 742/pb in the denominator when he calculates the cross section of the "lepton jets" ghost events? The answer is, of course, No. It's because these "new" events are actually argued not to include bottom quarks as the initial states. For example, Giromino et al. claim that the Higgs is produced and subsequently decays to various h1, h2, and/or h3 pairs (and 16 tau's at the very end). Nima and Neal use various supersymmetric particles instead. So you can't normalize the initial states with the assumption that the bottom quarks are there in the initial states because they are not there.

If the "ghost events" show any new physics or new particles, they are of a very different type than the events okayed by the SVT tracker: let me emphasize that the "ghost events" are okayed by the dimuon triggers only, not by the SVT tracker.

The tight SVT efficiency is 24.4% for the heavy flavor QCD processes but it is close to 0.0% for the ghost events! In that case, it is a childish mistake to clump these two different sets together because the initial states are very different. There are no bottom-antibottom pairs in the initial states of these "ghost events" so you can't simplify the calculation by assuming that they have bottom-antibottom initial states. Instead, you must return to the collisions of protons and antiprotons, unconstrained by any SVX filters, to use the luminosity of proton-antiproton pairs, and to calculate the corresponding cross sections from proton-antiproton initial states.

The relevant integrated luminosity is 2,100/pb and because it is pretty high, the calculated cross sections will be deservedly low. Let me summarize the integrated luminosities:
  • 2,100/pb: all, SVX-unfiltered events; a small part (743,006) were dimuon events; the number 153,895 or so ghost events among them was reconstructed
  • 1,426/pb: the loosely SVX-filtered events; a small part (590,970) were dimuon events; the number 72,553 or so of ghost events among them was reconstructed
  • 742/pb: the tightly SVX-filtered events; a small part (143,743) were dimuon events; none of them (0) was a ghost event but the detailed composition of the QCD events is known and important

There's one more simple, graphical way to see that the 153,895 events were (and had to be) chosen from the broader 2100/pb sample and not from the 742/pb sample and that the interpretation of the numbers in this list above is correct.

Open the CDF paper on page 16. The set of all dimuon events - 743,006 - is divided to the 589,111 QCD events and our 153,895 ghost events. In the second column of this Table II, you see that only 143,743 events passed the tight SVX filter, neither of which was a ghost event.

Now, if you switch to page 12 and look at Table I, you may add the entries to get 143,000+ and to see that exactly these tight SVX-positive events correspond to the (smaller) integrated luminosity of 742/pb, as the caption of Table I says. For another "written proof" that the 742/pb luminosity corresponds to tightly SVX-filtered collisions, and not all (unfiltered) collisions as Tommaso seems to think, see page 11/52 of Giromini's talk.

In other words, among the 742/pb events (those that passed the tight SVX filter), none of them was a ghost event. You must go to the larger set of all 2100/pb events - unconstrained by any SVX filters - to "see" any ghost events, and their actual number still remains questionable, as Matt argues.

Incidentally, if you only picked the loosely SVX-filtered events, you would get exactly 590,970 events (Table II), roughly 518,417 of which would be heavy flavor QCD events. The remaining 72,553 or so ghost events that passed the loose SVX filter would give you an estimated 72,553 / (1426/pb) = 51 pb cross section for the ghost events, less than 75 pb in the unconstrained ensemble: 1,426/pb is the estimated luminosity after the loose SVX filter. Once again, among the tightly SVX constrained events, your calculated cross section for the ghost events would be 0 pb because the tight SVX constraint doesn't allow the muons to get too far.

If you analyze how various numbers above were determined, you will find out that the number of all dimuon QCD events, 589,111, was actually not directly measured but calculated from the measured number of 143,743 tightly SVX-filtered events, by dividing the latter number by the 24.4% efficiency (by 0.244) that was determined otherwise.

Analogously, the approximately 153,895 ghost events are calculated as the difference of all exactly 743,006 events (which were actually seen) minus all the approximately 589,111 QCD events (whose number was calculated from the efficiency and from the number of tightly SVX-filtered events). However, both of these calculated numbers, 589,111 and 153,895, are subsets of the set of 743,006 events that correspond to the SVX-unconstrained sample whose integrated luminosity is 2100/pb. The sizes of the subsets of all the 743,006 events are calculated from the detailed knowledge of the tightly SVX-filtered events (by a method that Matt has explained, too) but these calculated events are not SVX-filtered themselves: only 143,743 (exactly) events were tightly SVX-filtered.

This key difference between "events actually belonging to an ensemble E742" and "events belonging to a larger ensemble E2100 whose number is not directly measured but rather calculated by looking at a smaller ensemble E742" is another point that has probably confused Tommaso Dorigo profoundly and hopelessly. At any rate, there were dozens of other ways for him to see that his conclusion was wrong. He wasn't able to realize either of them.

The moral of the story

So, a recommendation for Tommaso Dorigo: don't ever try to ignore comments of people like Matt Strassler and their understanding of physics and your papers. Thank me. You're welcome. ;-)

And yes, I think that you should be kind of mildly punished for deliberately directing the anonymous hostile people who read your blog against me in his "appetizer". It's not my fault that you have demonstrated your incompetence. You began these silly attacks of yours and you politely asked me to explain you how Matt calculated those 75 pb which you couldn't possibly get. So I did so. Is that a crime? But you collaborated on it!

Everyone who knows me knows that I love tigers and other animals to live in peace in the dens as well as the holes that you prefer, Tommaso. ;-)


Other members of CDF have sent me the information that indicates that they really meant that the cross section of the new events was above 200 pb i.e. 153,895 ghost events all came from 742/pb. Because the main discussion with Tommaso was about the proposition that they meant, not about the real cross section and not about the natural interpretation of the paper, I gave Tommaso the apology he wanted.

Such a statement of CDF about unexplained events is 3 times more unusual than the already-unusual previous statement and I feel that the paper was written in a confusing way deliberately so that the full craziness of the main statement remains fuzzy not only for the theorists who read about 1/2 of the paper but even for some CDF members.

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