The Qweak experiment has measured the parity-violating asymmetry in polarized e-p elastic scattering at Q^2 = 0.025(GeV/c)^2, employing 145 microamps of 89% longitudinally polarized electrons on a 34.4cm long liquid hydrogen target at Jefferson Lab. The results of the experiments commissioning run are reported here, constituting approximately 4% of the data collected in the experiment. From these initial results the measured asymmetry is Aep = -279 +- 35 (statistics) +- 31 (systematics) ppb, which is the smallest and most precise asymmetry ever measured in polarized e-p scattering. The small Q^2 of this experiment has made possible the first determination of the weak charge of the proton, QpW, by incorporating earlier parity-violating electron scattering (PVES) data at higher Q^2 to constrain hadronic corrections. The value of QpW obtained in this way is QpW(PVES) = 0.064 +- 0.012, in good agreement with the Standard Model prediction of QpW(SM) = 0.0710 +- 0.0007. When this result is further combined with the Cs atomic parity violation (APV) measurement, significant constraints on the weak charges of the up and down quarks can also be extracted. That PVES+APV analysis reveals the neutrons weak charge to be QnW(PVES+APV) = -0.975 +- 0.010.
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