What is the interaction between Feds fund rates and interest rates paid to holders of US debt?

If the Fed lowers rates to try to prevent or forestall a recession, does this affect the 'attractiveness' of US debt to investors such as China? Is there a limit to how much rates can be cut without making US Treasuries unattractive to their potential customers?

What is the interaction between Feds fund rates and interest rates paid to holders of US debt?
I dont think there is a 'limit' as to rate cuts which could make US Treasuries unattractive. After 9/11 the Fed Funds was at its lowest on June 25th 2003 at 1%. At which time there was no rush by holders to liquidate their Bond holdings, the yield on a 10 year T bond was 3.85% (july 2003). By the way another US Debt instrument is the US Dollar Bank Notes (Cash USDollars) on which the government pays ZERO interest. On December 2005 the US Treasury estimated that 450 BILLION USDollar Bank notes were held (owned) abroad. Maybe you can check the latest amounts.