Theorists vs multi-muons

There has not been much talking recently about the CDF multi-muon anomaly. Unlike the PAMELA/ATIC cosmic-ray anomaly, the CDF one did not trigger a lot of theoretical activity. There is more than one reason for this shroud of silence. On one hand, even though it is possible to write an ad-hoc particle models that describe various characteristics of the multi-muon signal, it seems hopeless to fit that in a bigger picture. On the other hand, multiple members of the CDF collaboration refer to the multi-muon publication as "that crap" (when being polite), while those who signed it admit the fact with certain embarrassment. Besides, the main author of the analysis is, hmm, a controversial figure, which does not help either (to understand the context, see Tommaso's account of the superjets saga).

Nevertheless, there is always a possibility that the multi-muon anomaly signals genuine new physics rather than mice in the detector, and few theorists try their luck. Today there was a paper on arXiv that sheds some light on the possible production mechanism of the mysterious ghost particles. As explained earlier, the multi-muon signal can be a result of a pair of "ghost" scalar particles with the mass around 15 GeV cascade-decaying into four tau leptons each. But the question how these ghosts particles are produced in the first place was not addressed in the original publications. It turns out that a vialable possibility is to couple the ghost field $\phi$ to the Standard Model quarks q via higher-dimensional operators. The non-renormalizable dimension-5 operator:
$\frac{1}{\Lambda} (\bar q q) \phi^2$
provides a pretty good fit to the invariant mass distribution of the ghost muons, see the plot.
Dimension-six operators involving the ghost fields coupled to quarks or gluons are disfavored.

One can think of this dimension-5 operator as an effective interaction left after integrating out a heavier particle with renormalizable interactions (in analogy to the Fermi theory of weak interactions after integrating out the W boson). For example, what would do here is a heavy doublet field $H_q$ (but not the Higgs!) interacting with the quarks via $Q u H_q$ and with the ghost pair via $H \phi^2$. But there is a tension here. The cross-section for the ghost pair production is required to be very large for the particle physics standard: 200 picobarns or so. To match that, the scale $\Lambda$ suppressing the dimension-5 operator has to be as low as 200 GeV. In consequence, the integrated-out particle cannot be too heavy and there is a danger that it violates some of the known experimental bounds. In particular, it could generate other higher-dimension effective operators, like the four-quark operator $(q q)^2/\Lambda^2$ that would affect dijet distributions at the Tevatron. Surprisingly, unlike four-lepton operators that were extremely well constrained by LEP, there is no strong bounds in the literature on four-quark effective operators (except for the bound on $(Q \gamma_\mu Q)^2/2\Lambda^2$ which is $\Lambda > 700$ GeV, but that's not directly applicable here). Improving the bounds on four-quark operators could clarify the situation and, in fact, would be extremely interesting for many other applications.