The helicity structure of the diffractive electroproduction of rho mesons, e + p -> e + rho + Y, is studied in a previously unexplored region of large four-momentum transfer squared at the proton vertex, t: 0 < t' < 3 GeV^2, where t' = |t| - |t|_min. The data used are collected with the H1 detector at HERA in the kinematic domain 2.5 < Q^2 < 60 GeV^2, 40 < W < 120 GeV. No t dependence of the r^04_00 spin density matrix element is found. A significant t dependent helicity non-conservation from the virtual photon to the rho meson is observed for the spin density matrix element combinations r^5_00+2r^5_11 and r^1_00+2r^1_11. These t dependences are consistently described by a perturbative QCD model based on the exchange of two gluons.
Measurements of the combinations of spin density matrices as a function of TP = |T| - |Tmin|, where |Tmin| is the minimal values of |T| kinematically required for the vector meson and the system X to aquire their effective mass through longitudinal momentum transfer.
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