Proton-proton elastic scattering has been measured by the TOTEM experiment at CERN Large Hadron Collider at {\}s = 7 TeV in dedicated runs with the Pot detectors placed as close as seven times the transverse beam size(sbeam) from the outgoing beams. After careful study of the accelerator optics the detector alignment, |t|, the square of four-momentum transferred in the scattering process, has been determined with an uncertainty of d t =0.1GeV p|t|. In this letter, first results of the differential cross section presented covering a |t|-range from 0.36 to 2.5GeV2. The differential-section in the range 0.36 < |t| < 0.47 GeV2 is described by an with a slope parameter B = (23.6{\±}0.5stat {\±}0.4syst)GeV-2, by a significant diffractive minimum at |t| =(0.53{\±}0.01stat{\±}0.01syst)GeV2. For |t|-values larger than ~ 1.5GeV2, the-section exhibits a power law behaviour with an exponent of -7.8_\±}0.3stat{\±}0.1syst. When compared to predictions based on the different models, the data show a strong discriminative power despite the small-range covered.
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