Wearing a belt-Gartle during Davening:^[1]

Wears a belt throughout the day: One who is accustomed to wear a belt throughout the day is required to also wear a belt [called a Gartel] during prayer. One is, however, not required to wear a belt when he recites blessings.

Does not wear a belt throughout the day: One who is not accustomed to wear a belt throughout the day, is not required to wear a belt during Davening so long as his clothing creates a separation between his heart and below the waist. Nonetheless, the above is only for the letter of the law however there is an act of piety to wear a belt for prayer even if he is not accustomed to wearing one throughout the day.[2] If, however, there is no separation between his heart and below his waist, such as one who is wearing a loose robe with no underclothing, then he is required to wear a belt for Davening and the saying of blessings.

Gartel wearing:[3] It is based upon the above law that it is the custom amongst Chassidim to Daven wearing a Gartel around their waist, as although it is not worn throughout the day, and hence not technically required from the letter of the law, it at the very least contains a Midas Chassidus. Most of Jewry however is not accustomed to wear a Gartel for prayer, and various justifications have been written behind their position.

[1] Admur 91:2; Ketzos Hashulchan 12:5; Piskeiy Teshuvos 91:1

[2] M”B 91:5 in name of Magen Giborim; Ketzos Hashulchan ibid;

[3] See Piskeiy Teshuvos 91:1