A convenient full-text HTML copy of the federal Constitution is online here.
Word search = standing arm
yields no hits. Thus standing army, standing armies, variants like that are absent from the Constitution. Standing armies were known when the document was authored; but no standing army was chosen to be any part of things.
"Militia" instead is used in the main text, and in the Second Amendment. Do the word search yourself. How it is.
The authors of the Constitution and the voters in the States which approved it wanted a militia organization, not standing armies.
So originalists, why do we have a giant standing army, when, under originalist doctrine, it's unconstitutional?
Dig up Scalia and ask him. His voice was strongest on that mischief.
How about, ask Rand Paul the question?