During a meeting for a particular project I was asked to think about the way to detect a push on a button with a MCU. The detection should consume as little power as possible. At the first glance, I thought the typical circuit with a pull-up or a pull-down :

^{simulate this circuit – Schematic created using CircuitLab}

I don't account for some anti-bounce features here, as that is beyond this question's scope. In either case, when the button is pushed, the total current value that flows depends on the resistor value. To minimize it (the current), I could increase the resistor value but not so much since, if I am right, it also depends on the input pin leakage value. Plus, a large resistor would recover slowly.

My question is the following one : what are the smart ways to detect a button pressed that doesn't consume power (typically for a high power consuming application)? Are there any methods that are barely power-consuming when the button is pressed?