# Advantage of using higher luminosity accelerator

If two accelerators operate at the same energy but different luminosity, is the only advantage of accelerator with a higher luminosity that there will be more events in a given amount of time, thus it can operate for a shorter amount of time to observe same number of events?

Or is there some fundamental advantage in which some processes can only be studied by the accelerator with higher luminosity?

In most cases we are looking for a small signal on a large background and the usual signal-to-noise rules apply. If we do $N$ observations we expect the signal strength to be proportional to $N$ while the noise is proportional to $\sqrt{N}$. So the signal to noise ratio is proportional to $\sqrt{N}$. The higher the luminosity the greater the value of $N$ so the better the signal to noise ratio.
• Yes, I think we are saying the same thing: if you multiply the lumi for a cross section and for a time you get the number of events $N$, which is also generically called statistics. Sep 16, 2015 at 6:40