What choices for central banks if Phillips curve effects have disappeared?

Let us consider the extreme hypothesis, not very far from reality, where Phillips curve effects have disappeared: the link between the unemployment rate (output gap) and core inflation no longer exists, demand stimulation policies, including monetary policy, no longer have an effect on inflation. So what can central banks then do? Claim that Phillips curve effects are still present, and conduct a persistently highly expansionary monetary policy, saying that it will eventually lift inflation; Consider another monetary policy objective: yield curve control (in countries where inflation is very low), nominal GDP growth (which amounts to a real growth target if inflation is low and stable), steady liquidity growth (due to the risk of high variability in interest rates), control of asset prices (equities, real estate, which makes sense in a low inflation environment normally leading to very low interest rates, but may give rise to moral hazard).