Three-Quark Light-Cone Amplitudes of The Proton And Quark-Orbital-Motion Dependent Observables

We study the three-quark light-cone amplitudes of the proton including quarks’ transverse momenta. We classify these amplitudes using a newly-developed method in which light-cone wave functions are constructed from a class of light-cone matrix elements. We derive the constraints on the amplitudes from parity and time-reversal symmetries. We use the amplitudes to calculate the physical observables which vanish when the quark orbital angular momentum is absent. These include transverse-momentum dependent parton distributions $\mathrm{\Delta }{q}_T(x,k_{\perp })$, $q_T(x,k_{\perp })$, $\delta q(x, k_\perp)$,and$\delta q_L(x,k_\perp)$,twist-threepartondistributions$g_T(x)$and$h_L(x)$,helicity-flipgeneralizedpartondistributions$E(x, \xi=0, Q^2)$anditsassociates,andthePauliformfactor$F_2(Q^2)$.