You have studied the gas-phase oxidation of HBr by
O2: 4HBr(g)+O2(g)⟶2H2O(g)+2Br2(g)
You find the reaction to be first order with respect to HBr and first order with respect to O2.
You propose the following mechanism:
HBr(g)+O2(g)⟶HOOBr(g)
HOOBr(g)+HBr(g)⟶2HOBr(g)
HOBr(g)+HBr(g)⟶H2O(g)+Br2(g)
If you are unable to detect HOBr or HOOBr among the products, does this disprove your mechanism?