Saturday, March 10, 2012

Tevatron insists on top-antitop forward-backward asymmetry

Fourteen months ago, we talked about remarkable claims by the Tevatron's CDF collaboration that the top quarks born in their now-defunct accelerator were excessively biased, preferring to move in the direction of the proton beam, while the antitops prefer to move in the direction of the antiproton beam of the proton-antiproton collider.

According to the Symmetry Breaking Magazine that forwarded some insights from the Moriond conference, the CDF folks are still confident that this particular anomaly is there. It hasn't disappeared when the amount of collisions used in the analysis was doubled.

Recall that the asymmetries are usually expressed by the following (or similar) ratio which is a priori between \(-1\) and \(+1\): \[

A_{FB} = \frac{N_\text{forward}-N_\text{backward}}{N_\text{forward}+N_\text{backward}}

\] where the terms in the numerators as well as the denominator count the number of collisions in which a top quark was produced and moved mostly in the forward direction of the proton beam (or the backward direction). In other equations, \[

N_\text{forward} = N_\text{events}(\theta \gt 0), \quad N_\text{backward} = N_\text{events}(\theta\lt 0 )

\] If the top quarks didn't care about the difference between a proton and an antiproton, we would have \(A_{FB}=0\). However, they obviously do care. But according to the Standard Model, they don't care much: \[

A_{FB} = 0.088\pm 0.013

\] at the next-to-leading order (NLO) calculations. The current CDF figure, after the data were doubled, is \[

A_{FB} = 0.296 \pm 0.067

\] if I understand the Symmetry Breaking Magazine article well. They surely don't mean this many percent, do they? The significance of the anomaly hasn't changed dramatically. At this moment, I would estimate it as three sigma: \[

\frac{0.296-0.088}{\sqrt{0.067^2+0.013^2}} \sim 3.06

\] This discrepancy probably gets higher in the CDF case if we focus on high-energy top quarks. D0 seems to confirm the anomaly although it shows no preference for high-energy top quarks. The two experiments are compatible with one another (within the error margins) and the combined statistical significance of the deviation may be well above four sigma at this point.

D0 has refuted some other claims by the CDF, especially the insanely huge CPT violation that the CDF claimed to be hiding in the top-antitop mass difference of order 3 GeV (and the strange \(Wjj\) events similar to a \(Z'\) boson near \(145\GeV\)). But this particular asymmetry seems to be a consensus of the American scientists. The statement that this particular anomaly exists is of course much more plausible than the huge CPT violation and perhaps other things. D0 hasn't doubled their datasets yet. We will see where the update goes later in 2012.

If you want to be updated about models that try to explain this asymmetry, assuming that it is due to new physics, see this paper that is 4 days old:
Confronting Top AFB with Parity Violation Constraints
Moira I. Gresham, Ian-Woo Kim, Sean Tulin, Kathryn M. Zurek divide the models to \(s\)-channel models that require rather exotic colored particles such as new sextets of the QCD gauge group; and \(t\)-channel models that allow the initial quarks to change their flavor so that \(u,d\) quarks in the initial proton may get transformed to a final \(t\) quark with a similar momentum. I personally find the \(t\)-channel models to be more likely.

It seems hard to use the stop squark to produce this effect directly (to say the least, no one is writing papers about this obvious possibility) but the effects reponsible for this asymmetry could still have something to do with the (LHC rumored) stop squark. For example, the new states could perhaps be the flavor-changing gauge bosons or Higgses from "natural supersymmetry" or something like that.

OK, let me say something that may be stupid and phenomenologists may see the stupidity immediately. I don't understand why such papers don't contain the 1-loop box diagram with a loop of gluinos (horizontal lines) and stop squark (vertical lines), with the \(u,d\) quarks and \(\bar u,\bar d\) antiquarks attached at the bottom and the top quarks and antiquarks attached at the top. All the vertices seem to be nonzero to me because the stop squark mass eigenstate is a mixture of the superpartners of the stop and sup quarks, isn't it? Or is this mixing known to be too tiny because of the absence of some other flavor-changing processes?

I can even get rid of these flavor-changing problem: the horizontal line at the bottom may be a sup line while the top one may be a stop line. And I even found this diagram on page 8 here (arXiv). The paper seems to conclude that the superpartner loops may only raise \(A_{FB}\) by \(0.03\) or so, too little.

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