The gemarah brings Pasuk regarding Begdai Cahuna, the Avnet ( belt / gartel ) , and the Megvaout ( hat ).
Can we learn the concept of wearing a gartel for davening from the Cohanim, a long time tradition. Since jews always wore gartels for davening , to separate the heart and Ervah, before the advent of belts and waistbands.
To the best of my knowledge, the source for wearing a belt for Davening is Tosfos Shabbos 10a DH Teruchusa
M. Kornfeld