This is just barely likely enough and theoretically well motivated enough to have some credibility, but seems to solve problems that is isn't clear that we had in the first place. I'm skeptical, as are most physics bloggers looking at the announcement. Like Motl, I just don't see where the theoretical motivation for a fifth force comes from unless you have something like composite quarks or leptons out there that need to be held together and sometimes decay in high energy environments.
While cynical, it is also appropriate to note that these are the final data being released from an experiement that is about to lose federal funding and be shut down, so the incentive to keep the experiment going based on temptations to make major new discoveries, by spinning the news with less than conservative intepretations of not very high sigma anomalies with little theoretic justification for being real, is greater than usual. In the biz these are called "fundinos." The final announcement would be due miraculously just as funding for the experiement is about to end in the fall of 2011. Of course, if the boson is real, LHC is going to see it anyway sooner rather than later, so the extra funding would mostly influence which country's experiment gets bragging rights for discovering it, rather than delaying the progress of science for more than two or three years.
The conventional wisdom in the field is that despite the theoretical meaning, a three sigma event really means about a 50-50 chance of being real: "a "3-sigma" signal is an evidence for a new effect, but might be produced by background fluctuations a few times in a thousand. A "5-sigma" effect is instead enough to grant the right of claiming the "observation" of the new effect."
One interpretation calls it a light Z' boson that is leptophobic (posted March 31, revised April 1):
New gauge bosons with Standard Model-like couplings to leptons are constrained by collider searches to be heavier than approximately ~1 TeV. A Z' boson with suppressed couplings to leptons, however, could be much lighter and possess substantial couplings to Standard Model quarks. In this article, we consider a new leptophobic Z' gauge boson as a simple and well motivated extension of the Standard Model, and discuss several of its possible signatures at the Tevatron. We find that three of the recent anomalies reported from the Tevatron - in particular the top-quark forward-backward asymmetry and excesses in the 3b and W + 2 jets final states - could be explained by a new Z' with a mass of approximately 150 GeV, relatively large couplings to quarks, and suppressed couplings to electrons and muons. Moreover, we find that such a particle could also mediate the interactions of dark matter, leading to potentially interesting implications for direct detection experiments.A new boson (an integer spin fundamental particle) would seem to imply a new fundamental force, as all other bosons have fundamental forces associated with them if they have spin one, and this boson isn't acting as we would expect a hypothetical spin zero scalar field Higgs boson to behave, or as we would expect a hypothetical spin two graviton to behave. This force would presumably be a short range force (since the carriier boson is massive), would quite likely not be CP symmetry conserving (for the reasons I've suggested about massive v. non-massive bosons in relation to CP symmetry), and would, by hypothesis, exist primarily between quarks rather than between leptons (i.e. electrons, neurinos and higher flavor cousins of them).
Lubos Motl (whose physics is much more credible than his poiltical and climate change postings) counts noses: Enthusiasts include Lisa Randall and Neal Weiner; more skeptical are Nima Arkani-Hamed and Tommaso Dorigo ("I do not particularly like to play the die-hard sceptic -this is after all a paper I myself reviewed and signed!- but I believe this is nothing but the umpteenth would-be new physics signal, destined to be buried by the analysis of further data, by the crafting of more precise simulations, or by the better understanding of Standard Model sources. Nevertheless, it is quite interesting to see this paper coming out now. Both DZERO, and the LHC experiments ATLAS and CMS, have now a lead to investigate their own data! If they were to see a 3-sigma effect in the same mass range and in the same kind of events, it would be already time to put the champagne in the fridge...."). Woit doubts it too.
While a "splicing dicing artifact" is a likely option, I am not going to claim that it is impossible for a new Z' boson to be this light and have the required properties. If such a new particle exists, however, it will be another stunning example of "Who ordered that?". . . .
The real question is: Why? There's no excessively good reason for the Z' boson to exist and no reason for it to not exist. We just usually prefer to believe in the non-existence unless we have a reason to do otherwise - unless we see a role that such a new particle could play. We don't know of such a role.
Of course, that doesn't mean that the particle can't exist. It surely means that such a new fifth force would remain a fifth wheel for some time. Imagine - people would say that there are five basic forces. One of them holds galaxies together and keeps us on the Earth; the other is responsible for all of chemistry, biology, and material science, not to speak about electromagnetic communication; the third force keeps atomic nuclei together; the fourth force causes some nuclei to beta-decay; and the fifth force adds 100 bizarre events at the Tevatron. ;-)
I am exaggerating and oversimplifying a bit. As Paul Langacker argues, Z' bosons could be good for an extended Higgs sector, which may be desired for various reasons; they could solve the mu problem in supersymmetric model building; mediate SUSY breaking; and add interesting yet dangerous predictions of flavor changing processes and new interactions with dark matter. The string-derived (beyond ordinary GUT) Z' bosons have also been claimed to be essential for light neutrino masses and proton stability.
See generally here.
In other words, they could make lots of details of exotic phenomena predicted by theories that have no empirical support yet work better. We already have a force that interacts with just quarks and the associated bosons (the strong force mediated by gluons). We already have a force that interacts with just charged particles (the electro-magnetic force mediated by photons) - i.e. not neutrinos. We already have a force that interacts with just left parity fermions (the weak force mediated by the W and the Z). As the name implies, the assumption is that this force would be weak force-ish.
Résonaances is also on the beat and skeptical:
It is well known that sigmas come in varieties: there or more significant 3 sigmas, less significant 3 sigmas, and astrophysical 3 sigmas. To my taste the latest CDF claim belongs to the 2nd category. We are dealing with a small hump on top of a huge background, and a small systematic error in its modeling could easily show up as a false peak. Furthermore, D0 does not see anything, they actually have a small deficit near 150 GeV. Last not least, recent experience with papers submitted simultaneously to ArXiv and BBC or New York Times is not encouraging ;-) . . .
What could it be? It is not a Higgs; anything Higgsish with 150 GeV mass would prefer decaying to a pair of W bosons rather than to 2 light jets. The simplest explanation, proposed in this April Fools' paper [linked above] involves a 150 GeV Z' boson.