Underlying Event – a definitive study by CDF
This weekend I read a superb paper by the CDF Collaboration (arXiv:1003.3146):
Studying the Underlying Event in Drell-Yan and High Transverse Momentum Jet Production at the Tevatron
This paper is written so very clearly that a very thorny and confusing phenomenon can be grasped with little effort. Even better, new results are presented which elucidate the underlying event in ways that help a lot to understand what is going on.
First, what is the “underlying event” and why do we care about it? The UE is all that you see in a hadron collider event which is not coming from the primary hard scattering process. So, aside from a q-qbar pair annihilating to give you a pair of leptons for example, there are tracks and calorimeter energy coming from the non-scattering fragments of the two beam particles, potentially from other partons in the same beam particles which interact along with the “primary” ones, and other beam particles which happen to interact. All three pieces are hard to calculate because these processes are soft and so non-perturbative interactions play a dominant role. We must use models (HERWIG or PHOJET or PYTHIA, with several “tunes” of model parameters) to simulate these events. Since the UE has several components, adjusting these models to mimic the data is challenging.
The need to tune and test these models is urgent now, since they tend to give wildly different predictions for the UE at the LHC. Why? The three main components of the UE (beam remnant, multiple parton interaction or MPI, and pile-up of different beam-beam interactions) do not vary the same way with c.m. energy, so a match at 1.96 TeV does not guarantee a match at 7 TeV.
Let’s build up the picture as follows. Consider a typical hard 2→2 scatter, producing two jets which are back-to-back in the transverse plane. Inevitably, one of them will have a higher transverse energy, ET, than the other. The higher-ET jet is the “tag” for the event, and we’ll put it at 12 o’clock. The other jet, called the “away” jet, would normally be at 6 o’clock. The authors call the 12 o’clock direction the “toward” side, which matches better with the word “away.”
In an e+e- collider, that would be the end of the story, for two-jet events. In a hadron collider, however, the “transverse” regions at 3 o’clock and 9 o’clock are interesting because they will not be empty – the UE contributes there as well as anywhere else. The CDF analysis method consists of examining the transverse regions, characterizing the level of activity by the particle density and by the mean pT there.
An important innovation is to substitute a Z-boson for the tag jet. The Z boson is color-neutral, so the particle density in the toward region should be low, similar to the transverse regions (after excluding the two leptons from the Z decay). Thus the intense particle flow from the tag jet does not obscure the UE in the toward region.
The authors compare to a selection of models. PYTHIA is the work-horse of event generators, and the UE model in PYTHIA has been tuned multiple times. The interesting cases are called “A” (good for di-jet events), “AW” (good for Z+jet) and “ATLAS” (meant to be accurate at the LHC). In addition, there is HERWIG augmented by an MPI model – this is expected to be less accurate that PYTHIA and it is.
The first interesting results are shown below:
The horizontal axis is a measure of the “hardness” of the primary interaction – the pT of the jet [top plot] or Z-boson [bottom plot]. In both cases, the particle density opposite the tag object (jet or Z) increases rapidly with pT – see the blue dots . This is clear – the recoil jet in the away side must balance this pT. In contrast, the particle density in the transverse region (green dots) does not care about pT, which is also intuitive – this is the UE. Notice the dramatic contrast in particle density for the toward (or tag) area: it matches the recoil jet when the tag is a jet, and it matches the transverse density when the tag is a pair of leptons. This is very pretty, and very well reproduced by PYTHIA.
There is plenty of evidence that HERWIG does not reproduce the data as well as a tuned version of PYTHIA. Here is one particularly clear example:
This plot shows the particle density in the transverse regions, for Z-boson events, as a function of the pT of the Z-boson. Clearly, HERWIG (“HW”) is too low while PYTHIA (“pyAW”) gets it right. The main cause for the difference is the lack of MPI in HERWIG. So the difference between the two curves can be seen as a measure of MPI (multiple-parton interactions). It is not negligible, and should increase rapidly with c.m. energy.
if the pT of the Z boson is large, then there is a lot of energy available for gluon radiation in the initial state. If there are more than one ISR jet, the particle density in the transverse region will rise – basically, the second and third jets will tend to leak into the transverse region and will not be confined to the away region. The toward region, however, where the Z-boson went, will still be clear of ISR jets. Here is a comparison of the particle density in the transverse and toward regions, illustrating this effect:
The authors differentiate the two transverse regions (at 3 o’clock and 9 o’clock) according to their energies – TransMIN is the lesser of the two, and should be more sensitive to the UE; TransMAX will have the contamination of any extra ISR. This is an excellent place to check models (HERWIG vs PYTHIA) and tunes of models. Here is the plot of the charged particle density as a function of the pT of the Z-boson, in the TransMIN region:
PYTHIA matches the data very well, both with tune “AW” and tune “DW”. The ATLAS tune of PYTHIA is also reasonably good. A more detailed look (available in the paper), however, indicates that the ATLAS tune produces somewhat too many particles which are, however, too soft. HERWIG alone (“HW”) is too low, as already noted. Trying to fix HERWIG by adding in a model for MPI called JIMMY (“JIM” curve) does not work – it is too high. Perhaps a tune of the combination HERWIG+JIMMY would yield better results.
The point of showing so many models at Tevatron energies is to prepare for an extrapolation to LHC energies (14 TeV). Here is a comparison of two successful PYTHIA tunes as well as HERWIG:
The two tunes (DW and DWT) show a large increase in the particle density, but the increase is significantly different and could be easily verified with the first LHC data. CDF data taken at 630 GeV favor the DW tune over the DWT tune. HERWIG, which lacks MPI, shows a much smaller increase. Thus, much of the increase comes from MPI (in which there are two parton-parton scatters from the same beam particles).
The final study in this excellent paper involves soft collisions logged through a minimum-bias trigger. Such collisions are related to the UE, but are not the same as the UE. Despite this fact, collider physicists use min-bias events as a model of the UE. Thus it is important to study min-bias models to unravel what is truly happening in the UE and how well or how poorly it is represented by min-bias events.
The main observable is the increase of the average transverse momentum, <pT>, with the number of charged particles, Nch. The soft and hard components of min-bias events play varying roles as a function of Nch. This also gives a handle in the MPI. A comparison of the models to CDF min-bias data shows that PYTHIA with tune AW gets it right, while the ATLAS tune is too low. (Again, too many particles with too low momentum.)
One can also compare this observable for min-bias events and Z-boson events with a low pT (so that there is little ISR). The behavior is very similar even though the theoretical framework is, at first glance, very different.
The PYTHIA tunes match the data in both cases, indicating the MPI plays an important role in both cases.
This blog post gives only a cursory treatment of this fine paper. The analysis is done in a very careful way – there are many interesting technical details which I did not even mention. Also, details of the various PYTHIA tunes are spelled out. Of course, there are many plots and discussion which I cannot reproduce here.
All students of collider physics should read this paper. The very murky issues in understanding the underlying event are clearly explained, and there are new results which elucidate the role of multiple-parton interactions.
I wrote already about double-parton scattering some months ago, and I’ll bet that this phenomenon crops up again and again, since its role increases rapidly with c.m. energy.
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