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where u ( p ) an d u ( p $^{′}$) are nucleon Dirac spinors. In the meson-domina nce approximation it can be written as 

The nucleon m ass is given by Eq. (42). 

The quark c ontributions to the GPD’s of the nucleon have been deter mined on the lattice [72, 73] for masses as small as twice t he physical pion mass. The decomposition corresponding t o the energy-momentum tensor reads 

where σ µν = i $_{2}$[ γ $^{µ}$, γ$^{ν}$] (the Bjorken-Drell notation), the scalar functions are moments of the GPD’s, the momen- tum transfer is denoted as Δ = p ′ − p , and the average nucleon momentum is P = ( p ′ + p ) / 2. Taking the trace and applying the Gordon identity, 2 M$_{N}$ ¯ u ( p $^{′}$) γ $^{µ}$u ( p ) = ¯ u ( p $^{′}$)( iσ $^{µρ}$Δ$_{ρ}$ + 2 P $^{µ}$) u ( p ), as well as the Dirac equation, (/ p − M$_{N}$ ) u ( p ) = 0 and ¯ u ( p $^{′}$)( / p ′ − M$_{N}$ ) = 0, we obtain the following expression for the spin-0 gravitational form factor of the nucleon: 

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Due to the multiplicative character of the QCD evolution for the conserved energy-momentum tensor operator, one has 

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The combination (77) can be directly constructed from the results of the LHPC Collaboration [73], where the data points for the A$_{20}$ , B$_{20}$ , and C$_{20}$ form factors are provided for six values the pion mass: m$_{π}$ = 757, 681, 595, 495, 356, and 352 MeV. The values of the corre- sponding nucleon masses are M$_{N}$ = 1565, 1489, 1379, 1292, 1216, and 1158 MeV. We add the statistical errors in quadrature. The result for the two lowest pion masses is shown in Fig. 5. We note that while the A$_{20}$ ( t ) function is determined to a better than 10% accuracy, the large errors in Θ q N originate from the less accurate B$_{20}$ ( t ) and 

