Sum rules and the DGLAP evolution in presence of $U(1)_B$ anomaly

Abstract

The possibility to modify both quarks sum rules and the DGLAP evolution equation are investigated. In presence of anomalous baryon global symmetry, the quark sum rules are no longer the same as usual. In addition, the DGLAP equation is also changed to be self-consistent with modified sum rules. This way of modification turns out to satisfy the Sakharov's baryogenesis requirements. We also assume the existence of the factorization theorem in relevant scale to maintain the naive parton model. Consequently, if this is presumably going to be true, there might be a new powerful constraint for constructing the beyond standard model physics.