Both beam energy and luminosity are important for succesful particle accelerator

Question

Both beam energy and luminosity are important for succesful particle accelerator experiments. The LHC's nominal design is for 7 TeV beams and 1E34 cm^-2 sec^-1 luminosity, while the SSC's nominal design was for 20 TeV beams and 1E33 cm^-2 sec^-1 luminosity. The LHC has 10x greater luminosity while the SSC would have had almost 3x greater energy. If the SSC was alive and both machines were operating at nominal levels, which would have the greater advantage for discovery of: i. the Higgs boson, ii. supersymmetry, iii. extra dimensions? I'm asking on the assumption that all three of these exist.

Explanation / Answer

with the energies and luminosities you described (which are not necessarily those that may be quickly achieved by either machine, and the LHC is still not there), the SSC would be a more potent machine to discover all the things you mentioned, especially the physics associated with the very heavy scales - a few TeV (which is surely extra dimensions, if they exist, and maybe even SUSY) - that the LHC may be unable to reach.

The new particles near the upper bound of a collider's energy reach become extremely rare - so the LHC is producing e.g. a top quark many times a second while it used to be produced once a month at a lower energy but comparable luminosity by the Tevatron.

But even if the luminosity of a higher-energy machine is smaller, it may still produce many more particles even if they're lighter because a more energetic collision contains more particles in the final state. So for example, despite the fact that the LHC has only collided 0.3/fb in each detector, it has beaten the Tevatron with its 10/fb in pretty much everything - and in some "disciplines", the LHC advantage has become overwhelming. Of course, examples of the latter include supersymmetry - the exclusion limits by the LHC are far more far-reaching than those by the Tevatron and the Tevatron couldn't even match the current LHC results even if it were running for another decade.

There remain some special features, such as the top-antitop asymmetry, that are harder to be seen on the LHC than on the Tevatron because the latter is a proton-antiproton collider.

Despite the advantage of the SSC, it would be a kind of a brute-force, expensive machine. The LHC is doing many things in a smarter, cheaper, and technologically more advanced way. The names may be confusing. The SSC was "super", like in "superconducting". Of course, the magnets in the LHC are also superconducting and technologically more advanced, in fact, than the SSC plans

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