Nevertheless, it's fun to play the following game of imagination: what kind of new physics could show up in the early LHC without having been already discovered at the Tevatron? For that, two general conditions have to be satisfied:
- There has to be a resonance coupled to the light quarks (so that it can be produced at the LHC with a large enough cross section) whose mass is just above the Tevatron reach, say 700-1000 GeV (so that the cross section at the Tevatron, but not at the LHC, is kinematically suppressed).
- The resonance has to decay to electrons or muons with a sizable branching fraction (so that the decay products can be seen in relatively clean and background-free channels).
The possible couplings of Z' to quarks and leptons can be theoretically constrained: imposing anomaly cancellation, flavor independence, and the absence of exotic fermions at the TeV scale implies that the charges of the new U(1) acts on the standard model fermions as a linear combination of the familiar hypercharge and the B-L global symmetry. Thus, one can describe the parameter space of these Z' models by just three parameters: two couplings gY and gB-L and the Z' mass. This simple parametrization allows us to quickly scan through all possibilities. An example slice of the parameter space for the Z' mass 700 GeV is shown on the picture to the right. The region allowed by the Tevatron searches is painted blue, while the region allowed by electroweak precision tests is pink (the coupling of Z' to the electrons induces effective four-fermion operators that have been constrained by the LEP-II experiment). As you can see, these two constraints imply that both couplings have to be smallish, of order 0.2 at the most, which is even less than the hypercharge coupling g' in the standard model. That in turn implies that the production cross section at the LHC will be suppressed. Indeed, the region where the discovery at the LHC with 7 TeV and 100 inverse picobarns is impossible, marked as yellow, almost fully overlaps with the allowed parameter space. Only a tiny region (red arrow) is left for that particular mass, but even that pathetic scrap is likely to be wiped once the Tevatron updates their Z' analyses.
The above example illustrates how difficult is to cook up a model suitable for an early discovery at the LHC. A part of the reason why Z' is not a good candidate is that it is produced by quark-antiquark collisions. That is a frequent occurrence in the proton-antiproton collider like the Tevatron, whereas at the LHC, who is a proton-proton collider, one has to pay the PDF price of finding an antiquark in the proton. An interesting way out that goes under the name of diquark resonance was proposed in another recent paper. If the new resonance carries the quantum numbers of two quarks (rather than quark-antiquark pair) then the LHC would have a tremendous advantage over the Tevatron, as the resonance could be produced in quark-quark collisions that are more frequent at the LHC. Because of that, a large number of diquark events may be produced at the LHC in spite of the Tevatron constraints. The remaining piece of model building is to ensure that the diquark resonance decays to leptons often enough.
Diquarks are not present in the most popular extensions of the standard model and therefore they might appear to be artificial constructs. However, they can be found in somewhat more exotic models like for example the MSSM with a broken R-parity. That model allows for couplings like $u^c d^c \tilde b^c$, where $u^c,d^c$ are right-handed up and down quarks, while $\tilde b^c$ is the scalar partner of the right-handed bottom quark called the (right) sbottom. Obviously, this coupling violates R-symmetry because it contains only one superparticle (in the standard MSSM, supersymmetric particles couple always in pairs). The sbottom could then be produced by collisions of up and down quarks, both of which are easy to find in protons.
Decays of the sbottom are very model dependent: the parameter space of supersymmetric theories is as good as infinite and can accommodate numerous possibilities. Typically, the sbottom will undergo a complex cascade decay that may or may not involve leptons. For example, if the lightest supersymmetric particle is the scalar partner of the electron, then the sbottom can decay into a bottom quark + a neutralino who decays into an electron + a selectron who finally decays into an electron and 3 quarks:
$\tilde b^c -> b \chi^1 -> b e \tilde e -> b e e j j j$
As a result, the LHC would observe two hard electrons plus a number of jets in the final state, something that should not be missed.
To wrap up, the first year at the LHC will likely end up being an "engineering run", where the standard model will be "discovered" to the important end of calibrating the detectors. However, if the new physics is exotic enough, and the stars are lucky enough, then there might be some real excitement store.