Inclusive W and Z cross sections
The inclusive W and Z production cross sections are benchmarks for any hadron collider. Excellent measurements were published by CDF and D0, but the superior detector capabilities of CMS and ATLAS allows for even better measurements. Fiducial cross sections are relatively free from theoretical uncertainties and can be used to constrain the parton distribution functions (PDFs), which are of central importance for nearly all measurements done at a hadron collider. In fact, ATLAS published an interesting constraint on the strange-quark density on the basis of inclusive cross section measurements. I’ll return to this result in a future post.
The first results were published back in 2010 and then updated in 2011 and 2012, based on 7 TeV data. Since W and Z bosons are produced copiously at the LHC, very small statistical uncertainties can be achieved with a rather small amount of integrated luminosity. (We have tens of millions of Z bosons detected in leptonic decay channels, for example, far more than the LEP experiments recorded. And we have roughly ten times the number of W bosons.) Remarkably, experimental systematic uncertainties are reduced to the 1% – 1.5% level, which is amazing considering the need to control lepton efficiencies and background estimates. (I am setting aside the luminosity uncertainty, which was about 3% – 4% for the early data.) The measurements done with only 35 pb-1 are nearly as precise as the theoretical predictions, whose errors are dominated by the PDF uncertainties. We knew, back in 2011, that a new era of electroweak physics had begun.
Experimenters know the power of ratios. We can often remove a systematic uncertainty by normalizing a measured quantity judiciously. For example, PDFs are a major source of uncertainty. These uncertainties are highly correlated, however, in the production of W and Z bosons. So we can extract the ratio (W rate)/(Z rate) with a relatively small error. Even better, we can plot the W cross section against the Z cross section, as ATLAS have done:
The elongated ellipses show that variations of the PDFs affect the W and Z cross sections is nearly the same way. The theoretical predictions are consistent with the data, and tend to lie all together. (The outlier, JR09, is no longer a favored PDF set.)
It is even more interesting to plot the W+ cross section against the W– cross section, because the asymmetry between W+ and W– production relates to the preponderance of up-quarks over down-quarks (don’t forget we are colliding two protons). Since the various PDF sets describe the d/u-ratio differently, there is a larger spread in theoretical predictions:
During the 8 TeV running in 2012, the instantaneous luminosity was much higher than in 2010, leading to high pile-up (overlapping interactions) which complicate the analysis. The LHC collaborations took a small amount of data (18 pb-1) in a low pile-up configuration in order to measure the W and Z cross sections at 8 TeV, and CMS have reported preliminary results. They produced ellipses plots similar to what ATLAS published:
You might notice that the CMS ellipse appear larger than the ATLAS ones. This is because the ATLAS results are based on fiducial cross sections – i.e., cross sections for particle produced within the detector acceptance. One has to apply an acceptance correction to convert a fiducial cross section to a total cross section. This acceptance correction is easily obtained from Monte Carlos simulations, but it comes with a systematic uncertainty coming mainly from the PDFs. (If a PDF favors a harder u-quark momentum distribution, then the vector bosons will have a slightly larger momentum component along the beam, and the leptons from the vector boson decay will be missed down the beam pipe more often. Such things matter at the percent level.) Since modern theoretical tools can calculate fiducial cross sections accurately, it is not necessary to apply an acceptance correction in order to compare to theory. Clearly it is wise to make the comparison at the level of fiducial cross sections, though total cross sections are also useful in other contexts. The CMS result is preliminary.
Back when I was electroweak physics co-convener in CMS, I produced a plot summarizing hadron collider measurements of W and Z production. My younger colleagues have updated that plot to include the new 8 TeV measurements:
This plot nicely summarizes the history of these measurements, and suggests that W and Z production processes are well understood.
As I learned a the WNL workshop, the collaborations are learning how to measure these cross section in the high pile-up data. We may see even more precise values, soon.
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