Hadron tomography by generalized distribution amplitudes in the pion-pair production process \({γ}^{*}γ→{π}^{0}{π}^{0}\) and gravitational form factors for pion

I introduce a gauge invariant decomposition of the nucleon spin into quark helicity, quark orbital, and gluon contributions. The total quark (and hence the quark orbital) contribution is shown to be measurable through virtual Compton scattering in a special kinematic region where single quark scattering dominates. This deeply-virtual Compton scattering (DVCS) has much potential to unravel the quark and gluon structure of the nucleon.