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magnetic combinations of unpolarized gluon GPDs 

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and for the following combinations of polarized gluon GPDs: 

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One may come to the same conclusion employing the general method for determining the invariant amplitudes of a binary scattering process suggested in [34, 35] (see also [25]). Using this method it is also straightforward to check that the electric combination H g ( E ) and pseudoscalar combination ˜ H g ( PS ) are to be expanded in the Legendre polynomials of cos θ$_{t}$ P$_{l}$ (cos θ$_{t}$ ) while the magnetic combination H g ( M ) and ˜ H g are to be expanded in the derivatives of the Legendre polynomials P ′ $_{l}$(cos θ$_{t}$ ). Note that to the leading order of 1 / Q expansion the t -channel scattering angle 3 is expressed through the kinematical variables as 

For the electric combination of gluon GPDs H g ( E ) J PC = 0 $^{++}$, 2 $^{++}$, ... intermedi- ate meson states ( e.g. f$_{0}$ , f$_{2}$ ) contribute, while for the magnetic combination H g ( M ) the contributions of J PC = 2 $^{++}$, 4 $^{++}$, ... intermediate meson states are relevant. For ˜ H g J PC = 1 $^{++}$, 3 $^{++}$, ... intermediate meson states contribute and, finally, for ˜ H g ( PS ) J PC = 0 − $^{+}$, 2 − $^{+}$, ... meson states contribute. 

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Taking into account all these considerations one can write down the following partial wave expansion for electric and magnetic combinations of unpolarized gluon GPDs in the nucleon $^{4}$: 

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