Article I, Section 3, Clause 7 of the Constitution states:
"Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law."
Note the entry "...disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States...".
Does this mean that the Senate, rather then removing Trump from office, could instead simply deny him the right to run for office again, including in 2020? This might give some Republicans a way to have their cake and eat it too. They left Trump in office, but put a limit on his ability to continue to harm the nation by making him a one-term president.
http://www.heritage.org/constitution/#!/articles/1/essays/18/punishment-for-impeachment

OCU