The Collider Reach tool gives you a quick (and dirty) estimate of the relation between the mass reaches of different proton-(anti)proton collider setups.

The Collider Reach tool gives an estimate of the system mass (e.g. $m_{Z'}$ or $2m_{\tilde g}$) that can be probed in BSM searches at one collider setup ("collider 2", e.g. LHC 14 TeV with 300 fb${}^{-1}$) given an established system mass reach of some other collider setup ("collider 1", e.g. LHC 8 TeV with 20 fb${}^{-1}$).

The slides of a talk about the tool can be found here: slides.pdf.

The estimate is obtained by determining the system mass at collider-2 for which the number of events is equal to that produced at collider-1, assuming that cross sections scale with the inverse squared system mass and with partonic luminosities. The exact results depend on the relevant partonic scattering channel, as represented by the different lines ($q \equiv \sum_i (q_i + \bar q_i)$), and the band covers the spread of those different partonic channels.

There are quite a few caveats in interpreting the numbers: (1) they assume that signal and background are driven by the same partonic scattering channel; (2) they assume that reconstruction efficiencies, background rejection rates, etc., all stay reasonably constant as the collider setup changes; (3) they assume that the cross-sections are simply proportional to the partonic luminosity at a given scale (divided by the mass-scale squared), ignoring detailed production spectra, higher-order QCD effects, etc. Quite often these assumptions turn out to be reasonable.

The spirit in which we take the numbers is as first guidance on what one might expect. If a more sophisticated analysis appears gives a substantially different picture, then it can be useful to ask why: e.g., has a new background appeared? Have cuts been fully adapted at the new collider setup to take into account possibly different signal and background kinematics? Etc.

The reliability of the results depends on the reliability of the PDFs. By default, PDFs don't always cover the $x$ and $Q$ regions that are needed here. Currently, if $\sqrt{s}$ of either collider setup exceeds the maximum $Q$ supported natively in the PDF, DGLAP NNLO evolution is rerun (including a top threshold) to cover the full range of $Q$ values up to $\max(\sqrt{s_1},\sqrt{s_2})$. For the $x$ range, PDFs are essentially unconstrained below $x=10^{-6}$: in most usages the tool will be using larger $x$ values than that, however at some point we may add a warning if that's not the case.

The Collider Reach project is maintained in spare time. Features that we may add in the future include PDF uncertainties, results when signal and backgrounds are driven by different partonic channels, etc... If you find any issues, please let us know.