The physics of intersecting thick to thin branes

We model four-dimensional junctions made out of intersections of co-dimension one brane living in higher-dimensional spacetimes through domain walls. We take a new look at the problem of localizing fermion states on brane junctions as a result of intersecting one thick brane to others sufficiently thin. All the branes intersect orthogonally to form a four-dimensional junction embedded in a higher-dimensional bulk. We discuss the effects of the Yukawa coupling and the proton decay on the restriction of the parameters that control the junction stability and the brane thickness which also define the bulk cosmological constant.