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Δ + = − 2 ξP $^{+}$; ˜ F αβ ≡ 1 $_{2}$ϵ $^{αβγδ}$F$_{γδ}$ is the dual gluon field strength. Throughout this paper we adopt the light-cone gauge A + = 0, so that the gauge link does not appear in the operators in definitions (2), (3). 

The definition (2) differs from other definitions encountered in the literature (see [4]). For 0 ≤ x ≤ 1: 

<img src='content_image/329247.jpg'>

The same relations hold for E g and ˜ E g respectively. 

As the gluon itself is its own antiparticle gluon GPDs H $^{g}$( x, ξ, t ), E $^{g}$( x, ξ, t ) defined in (2) are even functions of x : 

<img src='content_image/329246.jpg'>

Gluon GPDs ˜ H $^{g}$( x, ξ, t ), ˜ E $^{g}$( x, ξ, t ) defined in (3) are odd functions of x : 

<img src='content_image/329245.jpg'>

Let us stress that in what follows we consider the gluon GPDs in nucleon (2), (3) on the interval 0 ≤ x ≤ 1. g g 

In the froward limit gluon GPDs H and ˜ H reduce to usual forward gluon distributions in the nucleon g ( x ) and Δ g ( x ), while GPD E g and ˜ E g are reduced to unknown gluon distributions, which we denote as e $^{g}$( x ) and Δ e $^{g}$( x ): 

<img src='content_image/329244.jpg'>

Note that the forward gluon distributions g ( x ), Δ g ( x ) and e $^{g}$( x ), Δ e $^{g}$( x ) are continued to the negative value of their argument according to: 

<img src='content_image/329243.jpg'>

