Parton degrees of freedom in PDFs from the hadronic tensor and large momentum effective theory

We point out a problem of the phenomenological definition of the valence partons as the difference between the partons and antipartons in the context of the next-to-next-leading-order evolution equations. After demonstrating that the classification of the parton degrees of freedom (PDF) of the parton distribution functions (PDFs) are the same in the QCD path-integral formulations of the hadronic tensor and the quasi-PDF with large momentum effective theory (LaMET), we resolve the problem by showing that the proper definition of the valence partons should be in terms of those in the connected insertions only. We also prove that the strange partons appear as the disconnected sea in the nucleon.