The reaction of carboxylic acid $\ce{RCOOH}$ with $\ce{PCl5}$/ $\ce{SOCl2}$ / $\ce{PCl3}$ yields an acyl chloride $\ce{RCOCl}$. With $\ce{PCl5}$ and $\ce{SOCl2}$ the reaction is quite simple utilizing one mole reactants and yielding products.
But in case of $\ce{PCl3}$ the balanced reaction is as follows: $$\ce{3RCOOH + PCl3 -> 3RCOCl + H3PO3}$$
First I thought the reaction would proceed with $\ce{PCl2−}$ attacking the oxygen from which the oxygen-hydrogen bond cleavage happened but then I realized that it would form product $\ce{POCl}$ which is not a real compound I suppose so I am stuck how would the reaction proceed.
So what is the mechanism for this reaction?