Karn's Sylex

Other things may still cause players to pay life, such as a resolving spell or ability.

Players may always pay 0 life, even if an effect says they can’t pay life.

If a spell or an activated ability that isn’t a mana ability has a cost that requires a player to pay life, that spell or ability can’t be cast or activated.

An activated mana ability is one that produces mana as it resolves, not one that costs mana to activate.

Activated abilities contain a colon. They’re generally written “[Cost]: [Effect].” Some keyword abilities are activated abilities (such as cycling) and will have colons in their reminder text.