the total gluon angular momentum into its spin and orbital parts. Another noteworthy feature of this decomposition is that it reduces to the gauge-variant decomposition of Jaffe and Manohar in a particular gauge, $\bm{A}_{pure} = 0, \,\bm{A} = \bm{A}_{phys}$ [@JM90].

Chen et al.’s papers [@Chen08],[@Chen09] arose much controversy on the feasibility as well as the observability of the complete decomposition of the nucleon spin [@Tiwari08] -[@Chen12]. We believe that we have arrived at one satisfactory solution to the problem, through a series of papers [@Wakamatsu10],[@Wakamatsu11A],[@Wakamatsu11B]. In the 1st paper [@Wakamatsu10], we have shown that the way of gauge-invariant decomposition of nucleon spin is not necessarily unique, and proposed another gauge-invariant decomposition. The characteristic features of this decomposition is as follows. First, the quark part of this decomposition is common with the Ji decomposition, including both of spin and OAM parts. Second, the quark and gluon spin parts are common with the Chen decomposition. A crucial difference with the Chen decomposition appears in the orbital parts. The sum of the quark and gluon OAMs in both decompositions is just the same, but each term is different. The difference of the gluon OAM in the two decompositions, which is equal to the 