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Sharing the momentum among quarks

Posted November 14, 2014
This plot shows the probabilities of finding up and down quarks with different fractions of a proton’s momentum. The vertical axis is arbitrary and different for the two curves.

This plot shows the probabilities of finding up and down quarks with different fractions of a proton’s momentum. The vertical axis is arbitrary and different for the two curves.

The parts inside of a proton are called, in a not terribly imaginative terminology, partons. The partons that we tend to think of first and foremost are quarks — two up quarks and a down quark in each proton — but there are other kinds of partons as well.

Each parton in a moving proton carries some momentum, which is a fraction of the total momentum of the proton. Because the partons interact with each other constantly, the momentum of a parton keeps changing. So at any particular time, there is some probability that the down quark is carrying, say, half the momentum of the proton, and later it might be a quarter of the total momentum. The fraction is called x. When the down quark is carrying half the momentum of the proton, it has an x of 0.5. These probabilities are key ingredients in calculating what happens in a hadron collider and can only be deduced from experiment.

The figure shows plots of the probabilities of finding up or down quarks at particular values of x. The vertical scale is a little arbitrary, but that won’t matter for us. Notice how the curve for down quarks, in blue, peaks at the left, at low values of x. That means that at any instant, the down quark tends to have a relatively small fraction of the proton’s momentum. The up quark curve, in red, has a ledge, a sort of bump in the generally downward slope atx around 0.2 or so. That means that the chances of an up quark having more momentum than a down quark are really pretty good.

When a proton with a higher-momentum up quark hits an antiproton with a lower-momentum down antiquark, then these two partons can form a W+ boson, and that W+ boson is headed in the direction of the higher momentum. In a collision of an up antiquark and a down quark, aW boson can be created that tends to travel in the antiproton direction. Things get a little more complicated when a W+boson decays to a positron or a Wdecays to electrons, but the positron and electron directions still carry information about the x-values of the colliding quarks.

So the curves in the figure can be measured — or measured better — by looking at events in the Tevatron where a W+ or W is produced and decays into a positron or electron and measuring the difference, or asymmetry, in the final electron and positron directions.

DZero has measured the asymmetry in electron and positron directions relative to the direction of the proton’s motion when it collides with antiprotons in the Tevatron. The result is the most precise measurement of this asymmetry to date and provides important information about the momentum of the partons of protons. That information is critical in predicting what happens in all sorts of collisions involving protons, such as those at neutrino and LHC experiments.

Source: FNAL, written by Leo Bellantoni

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