The terrorist attacks of September 11, 2001 affected productivity in the United States in the short term but have not done so in the long term.
In the short term, there were real impacts on American productivity. The major reason for this was the changes in various procedures that were meant to improve security. For a number of days after the attack, there was no commercial air traffic. This alone would have reduced productivity in the short term. There were other disruptions to supply chains as transportation procedures were changed.
However, these changes did not affect the long-term productivity of the United States. Once the new procedures were in place, businesses adjusted to them and productivity returned to normal. If there had been more stringent measures taken (like more inspections of cargo arriving in the US) productivity might have gone down in the long term but such measures have not been taken.
The one way in which productivity may have been affected is more theoretical and difficult to measure. It is possible that immigrants who could have come and made America more productive have either been barred from coming or have been scared away by the barriers erected for new immigrants because of the attacks. However, it is not possible to measure this possible effect.