## Which way did it go? The differential cross section for top-antitop production is measured. The observed forward-backward asymmetry is described by an expansion in Legendre polynomials. The polynomials from a1 to a7 are measured.

For several years, CDF and DZero physicists have been studying a puzzle in the production of top quarks at the Tevatron: The outgoing top quarks prefer to travel in the same direction as the incoming protons (forward) and the top antiquarks prefer to go in the opposite direction (backward). The Standard Model predicts a small amount of such “forward-backward asymmetry,” but the observed asymmetry is much larger and raises the question of whether the Standard Model calculation is deficient or something else is going on.

In a new study, instead of just counting tops that go forward and backward, CDF looks in detail at the angle between the top quark and the proton direction. The shape of this angular distribution is a prediction of the Standard Model, and the comparison to the data can potentially illuminate whether the asymmetry is just more of the Standard Model effect or something else.

In order to quantify the shape, CDF breaks it down into a sum of standard shapes called Legendre functions. These functions measure the amount of “wiggle” in a curve: the first function is flat, the second is a line, the third has one oscillation, the next has two oscillations and so forth. The amount of each that goes into a given shape is the Legendre coefficient. CDF finds that the distribution of the top quark angle agrees with the Standard Model prediction except for the coefficient of the first Legendre function, which describes a linear correction to the angular distribution. This one coefficient is responsible for the anomalously asymmetric production of top quarks.

Using the full CDF run II data set, the first coefficient a1 is measured to be 0.40 ± 0.12, while the Standard Model prediction is 0.15 +0.07/-0.03. This sharpens the search for an explanation of the asymmetry. Some nonstandard theories involving a new heavy partner of the gluon (axigluon) would include such a linear term. Alternatively, any missing ingredient in the Standard Model calculations would need to have this form. There is unfortunately too much uncertainty in the Tevatron measurement to point one way or another, but when applied to the much larger top quark samples at the LHC, this powerful new technique can perhaps provide further clues to the mystery of the top quark asymmetry.

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edited by Andy Beretvas These CDF physicists contributed to this data analysis. Top row from left: Dan Amidei, Ryan Edgar, Dave Mietlicki and Tom Schwarz, all from the University of Michigan. Bottom row from left: Jon Wilson and Tom Wright, both from the University of Michigan, and Joey Huston from Michigan State University.