We develop the minimal model of a new leading order parameterization of GPDs introduced by Shuvaev and Polyakov. The model for GPDs H and E is formulated in terms of the forward quark distributions, the Gegenbauer moments of the D-term and the forward limit of the GPD E. The model is designed primarely for small and medium-size values of x_B, x_B leq 0.2. We examined two different models of the t-dependence of the GPDs: The factorized exponential model and the non-factorized Regge-motivated model. Using our model, we successfully described the DVCS cross section measured by H1 and ZEUS, the moments of the beam-spin A_{LU}^{sin phi}, beam-charge A_{C}^{cos phi} and transversely-polarized target A_{UT}^{sin phi cos phi} DVCS asymmetries measured by HERMES and A_{LU}^{sin phi} measured by CLAS. The data on A_{C}^{cos phi} prefers the Regge-motivated model of the t-dependence of the GPDs. The data on A_{UT}^{sin phi cos phi} indicates that the u and d quarks carry only a small fraction of the proton total angular momentum.
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