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Some weeks ago, there was lots of talk about this CDF paper:

Evidence for a Mass Dependent Forward-Backward Asymmetry in Top Quark Pair Production

where they measured a much higher asymmetry than the one predicted in the SM. In trying to understand the paper, I had some question which I thought would fit in a discussion here.

Experimental question

When all $t\bar{t}$ events are considered, the asymmetry is merely $1.4\, \sigma$ above the SM prediction. Well, no one would be excited with such small mismatch. However, in the paper above, they separate the data in 2 bins of $t\bar{t}$ mass, above and below $450\, GeV$ and claim a $3.6\, \sigma$ difference for the high mass bin. Oh! 3.6 is way more exciting (most of the people said).

But my question is: where did this $450\, GeV$ come from? In the paper they claim:

We find that the significance of the asymmetry at high mass is maximized when the bin division is at $M_{t\bar{t}} = 450 GeV/c^2$

Can this be justified statistically? I mean, can you simply ignore the rest of your data and focus on the subset which gives the largest statistical evidence?

Notice that I'm not necessarily questioning the CDF paper, which is well written, I'm just asking whether people should have been so excited about the significance of this "evidence".

Theoretical question

I was trying to understand where this asymmetry comes from. There is this paper:

Renormalization-Group Improved Predictions for Top-Quark Pair Production at Hadron Colliders

which discusses, among many other things, the reason for the asymmetry. They say:

These [the $t\bar{t}$ asymmetry] arise if, in the interference of one-loop and tree-level diagrams, the top-quark fermionic line and the light-quark fermionic line are connected by three gluons.

Is that so obvious? I really don't understand the reasoning. Would someone care to explain why this is the reason in more details?

They even have a Feynman diagram which, they claim, depicts the asymmetry (I thought it would be useful to have it here in case someone wants to refer to it while answering).

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The ttbar-asymmetry tag was even worse though. Honestly, how many questions do you think there are/will be about it? –  Noldorin Jan 25 '11 at 15:36
    
Ok, I agree with that. But people who search for "symmetry" are not looking for this type of discussion. I like the way it is now. –  Rafael Jan 25 '11 at 15:51
    
Yeah, 'symmetry' was really vague, in hindsight. Let's leave it how it is I say. :) –  Noldorin Jan 25 '11 at 17:34
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2 Answers

yes, the threshold was chosen at 450 GeV because this turned out to maximize the deviation as the number of standard deviations, given the data they have acquired. If the effect is real, then 450 GeV is the actual boundary where the "new physics" responsible for this effect begins to occur.

Consequently, the choice of the boundary at 450 GeV is cherry-picking or a legitimate measurement depending on the question whether the effect is real or not. Only in the future, when this question is settled, people will know. But of course, experimenters are always trying to look for real - i.e. most promising - deviations from the theory. That's the reason why they're doing the experiments.

And of course, the fact that they had to make a choice somewhat diminishes the p-value - the strength - of their experimental evidence. Imagine that they could choose the boundary anywhere in an interval whose length is 500 GeV, and they had to choose it with the precision 20 GeV to get an effect that is at least 3.5 sigma (I don't claim that the numbers 500 GeV and 20 GeV are exact - you should substitute the right ones instead).

That means that they had about 25 places to cherry-pick from. The 3.6-sigma evidence is equivalent to the probability of noise being approximately "1 in 2,000", but because the cherry-picking of the threshold increases the probability of a "fake 3.6-sigma signal" by the factor of 25, as argued at the beginning of the inerval, the 1-in-2,000 really decreases to 1-in-2,000/25 = 1-in-80.

If the cherry-picking is reflected in the p-value, then, given my numbers, the signal decreases to something like 2.5 sigma.

Theoretical question

No, the statement is not obvious. This is why the paper contains not only the sentences you quoted but also additional sentences. If you continued to read the paper, the following page would answer your question. The formulae (120) and (121) exactly tell you the color-dependent coefficients of the main and crossed terms and quantify the difference.

If the tree-level diagrams produce no asymmetry, it's clear that one has to go to non-tree diagrams i.e. loop diagrams (plus nonperturbative effects). Among the non-tree diagrams, one loop diagrams are the most important ones, usually, followed by the two-loop diagrams. Whenever internal loops appear in the diagrams, one wants to take them to be heavy fermions with the right numbers because the corresponding Yukawa couplings are maximized.

The loop diagrams lead to more complex mathematical expressions, so it's not surprising that the main amplitude and the crossed ones are no longer equal. To get the probability of a specific process with specific initial and final states - which is what is being calculated here - one first has to calculate the probability amplitude. The probability amplitude is the sum over all Feynman diagrams (or histories) with the same initial and final states; they may constructively and destructively interfere. And because the loop diagram is asymmetric with respect to the exchange of the top quark and its antiparticle, the interference will lead to an asymmetric result, too.

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I am pondering what role the triangle diagram plays here. There appear to be anomaly cancellations involved with this $t$$\bar t$ asymmetry.

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