The ground state hyperfine splitting in positronium, $Delta _{mathrm{HFS}}$, is sensitive to high order corrections of QED. A new calculation up to $O(alpha ^3)$ has revealed a $3.9 sigma$ discrepancy between the QED prediction and the experimental results. This discrepancy might either be due to systematic problems in the previous experiments or to contributions beyond the Standard Model. We propose an experiment to measure $Delta_{mathrm{HFS}}$ employing new methods designed to remedy the systematic errors which may have affected the previous experiments. Our experiment will provide an independent check of the discrepancy. The measurement is in progress and a preliminary result of $Delta_{mathrm{HFS}} = 203.399 pm 0.029 mathrm{GHz} (143 mathrm{ppm})$ has been obtained. A measurement with a precision of O(1) ppm is expected within a few years.
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