is discussed in sect.V. Then, we summarize what we have found in sect.VI.

Brief review of the nucleon spin decomposition problem    - Where are we now ? -
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As is widely known, there have been two popular decompositions of the nucleon spin. One is the Jaffe-Manohar decomposition [@JM90], and the other is the Ji decomposition [@Ji97PRL],[@Ji97]. Only the intrinsic quark spin part is common in these popular decompositions and the other parts are all different. A disadvantage of the Jaffe-Manohar decomposition is that each term is not separately gauge-invariant except for the quark spin part. On the other hand, each term of the Ji decomposition is separately gauge-invariant. Unfortunately, further gauge-invariant decomposition of $J^g$ into its spin and orbital parts is given up in this widely-known decomposition. Especially annoying fact was that the sum of the gluon spin and OAM in the Jaffe-Manohar decomposition does not coincide with the total angular momentum of gluons in the Ji decomposition. Undoubtedly, this observation is inseparably connected with the fact that the quark OAMs in the two decompositions are also different.

In fact, first pay attention to the difference of the quark OAM parts in the two decompositions. What appears in the 