## Wednesday, January 05, 2011 ... //

### Tevatron: CDF sees 3.4-sigma top quark pair asymmetry

The Wilson Hall rebuilt to celebrate the top quark; note the top-antitop asymmetry: the reflection in the water isn't identical :-)

Jester at Résonaances was rightfully attracted by a new experimental paper by the CDF collaboration at the Fermilab:

Evidence for a Mass Dependent Forward-Backward Asymmetry in Top Quark Pair Production
They see something strange happening with the top quarks and antiquarks; the forward-backward asymmetry has a 3.4-sigma anomaly. Now, this is just a little bit higher than my 3-sigma threshold for quantities I previously didn't care about but it may deserve to be noticed.

The discrepancy used to be 2 standard deviations but with the 5.3 inverse femtobarns of the CDF data, it managed to grew to 3.4 standard deviations. What is the quantity that is misbehaving?

The Tevatron collider smashes protons and antiprotons. Unlike the LHC beams (two proton beams), these two beams are different from one another and we may distinguish them. The usual convention is that the direction of the protons is "forward" while the direction of the antiprotons is "backward".

Now, consider the events in which top quark-antiquark pairs are produced.

A top quark is a quark, not an antiquark, so it might be natural to expect that it will prefer to move in the same direction as the protons - which contain 3 quarks. Similarly, the top antiquark could prefer to move in the opposite direction, in the direction of the antiproton beam.

However, this is not what the theory predicts. In fact, the top quark and the top antiquark have to emerge from a neutral intermediate state - such as a virtual gluon. And once you produce a virtual gluon, the odds for a top quark to move forward are balanced with the odds of its moving backward.

At the leading order, there is no asymmetry between forward-moving top quarks and backward-moving top quarks. Parity is enough to prove it.

At the next-to-leading order (NLO), the theory modifies its tree-level prediction and indeed, the intuitive correlation starts to operate a little bit. How much? Let us look at the energy frontier. More precisely, let us require that the invariant mass of the top quark-antiquark pair (the rest-frame energy of the virtual particle that decayed to the pair) exceeds 450 GeV (slightly).

The theory predicts that in the rest frame of the top-antitop system, the asymmetry should be
A = (#forward-#backward) / (#forward+#backward) = 0.088+-0.013
I hope that in the even higher-order corrections would be relatively small and wouldn't change the smallness of this figure. However, the observed asymmetry is much higher,
A = (#forward-#backward) / (#forward+#backward) = 0.475+-0.114
That's pretty large. Imagine that for 74 top quarks that move forward, only 26 top quarks fly backward. If these were elections, the self-described progressives (who move "forward" even though it usually means back to the Stone Age) would celebrate a shamefully convincing victory.

Note that the difference of the mean values is 0.387. The hypertenuse of the Pythagorean triangles with the 0.013 and 0.114 catheti is 0.115 or so and 0.387/0.115 = 3.36 standard deviations.

If the signal is real, there should be new physics - or, if I am more straightforward, a new massive particle - that influences the decays into the top quark-antiquark pairs. The experimenters promote a paper with a heavy gluon. If I understand well, it means a new massive particle in the s-channel.

However, there could also be new particles in the t-channel (or u-channel) - and new sources of flavor-changing processes that only operate at high energies. At any rate, I guess that if there are new particles that can do such effects near 500 GeV, the LHC could soon find them.

The ultimate explanation may be prosaic but the proposed mechanisms are often exciting: color sextet or triplet scalars, including remnants from grand unification, axigluons, and others (review).

The Minimal Supersymmetric Standard Model has to violate the R-parity in order to produce this asymmetry - and the agreement is still poor after that (see the review above).

On the other hand, the fresh "one-Higgs-doublet" supersymmetric model by Rajaraman et al. could be promising because it produces R-parity-positive fourth-generation squarks that could help to build the asymmetry.

In particular, I can imagine the following Yukawa-like mixing coupling,
NewLowerSquark * DownQuark (a - gamma5) TopQuark,
to be responsible for the new effect. Note that all the fields above are R-parity-positive and the dimension of the operator is four - a Yukawa coupling. The colors may be contracted via the antisymmetric 3-tensor and (any) two of the three fields in the product may be SU(2) doublets.

It is somewhat confusing which particles should be called "squarks" and which "antisquarks" for a mirror generation but I chose the convention that keeps the electric charges uniform for all generations and mirror generations of (s)quarks. The electric charge conservation forced me to add a down quark to the top quark - because the Rajaraman et al. model has no new electrically neutral or charge-4/3 particle - and the scalar added had to be the new lower squark.

To conserve the baryon charge, I have to assign the new lower squark with the baryon charge -2/3. Not sure whether it's consistent with other things. As Arvind has emphasized to me, all the new physics models are heavily constrained by the fact that only the asymmetry seems to be wrong but the total cross section seems OK.

Any new particle will enhance the total cross section - that's true for the new squarks, too. I believe that only if the intermediate particle transforms in the same way under SU(3)_{color} as the gluon - an octet - there is a chance to redistribute the original contribution of the gluon. But new heavy color octets are hard. Of course, it could be a gluon moving in an extra dimension or an excited string similar to a gluon except that such models look awkward - and they're usually inconsistent with the empirical data - with so light new particles.

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