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### Not all things are created equally… At the end of my last post, I left you all with the above plot (from this ATLAS conference note) without any real explanations. It’s actually quite a nice result, so I thought I might go through it in a little more detail today. So what does the plot show? Reading the axes, it shows the lepton charge asymmetry as a function of lepton pseudorapidity of leptonic W events.

What does this actually mean? To answer this, let’s go back to what a W boson is. On the right here, it’s a cute little plush toy, which you can buy from Particle Zoo. In real life, it’s massive charged elementary particle. This means there is a positive W boson, and a negative W boson, $$W^+$$ and $$W^-$$ respectively. When a W boson decays into a charged lepton and corresponding neutrino, due to charge conservation, the charge of the lepton must match the charge of the W boson. So the above plot of lepton charge asymmetry is actually a plot of W charge asymmetry, which can be interpreted as a W production asymmetry, $$A_W = \frac{\sigma_{W^+} – \sigma_{W^-}}{\sigma_{W^+} + \sigma_{W^-}}$$. So why is there a W production asymmetry? Let’s look at how a W boson is produced in a proton-proton collision. On the left here, we have a Feynman diagram of this process, where you can see that to make a positive W boson, you need a certain combination of quark and antiquark, most often an up quark and an antidown quark. To make a negative W boson, you need the opposite combination, a down quark and an antiup quark. The production asymmetry occurs because, as illustrated in the diagram on the right, the proton contain two valence up quarks and one valence down quark in a sea of quark-antiquark paris and gluons. So in a proton-proton collision, there is a higher probability of a up and an antidown quark interacting than an antiup quark and a down quark, and hence more positive W bosons are produced compared to negative W bosons.

So that’s why there’s a W production asymmetry, but why does it depend on pseudorapidity? And what is pseudorapidity anyway? Well, pseudorapidity is a measure of the angle at which the W boson was produced, which depends on the momentum of the two quarks from which the W boson was produced. The quarks and gluons within a proton carry a fraction, $$x$$, of the total proton momentum, which is described by a parton density function $$f(x)$$. The plot on the left shows the proton parton distribution functions for various types of quarks and anitiquarks, as well as gluons, for a particular proton collision energy scale $$Q$$.

So the momentum of the quarks which produce the W boson varies from collision to collision, depending on their parton density functions, which causes the W production asymmetry, caused by the quark content of the proton, to vary with pseudorapidity. Which is what the plot shows!

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