Article I, Section 3, Clause 7: "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..."
It's an option, but not automatic.
Actually I read that as the definitive result of conviction: removal from office and disqualification from any position of trust.
Oops, no, you’re right. Being barred from future office is at the discretion of the Senate.
The clause outlines the maximum punishment. IOW, the senate can’t impose prison time or have you hanged or shot...although I would expect some Dem senators to try to do that.