  We present a Rabi-type measurement of two ground-state hydrogen hyperfine
transitions performed in two opposite external magnetic field directions. This
puts first constraints at the level of 2.3 10^-21 GeV on a set of coefficients
of the Standard Model Extension, which were not measured by previous
experiments. Moreover, we introduce a novel method, applicable to antihydrogen
hyperfine spectroscopy in a beam, that determines the zero-field hyperfine
transition frequency from the two transitions measured at the same magnetic
field. Our value, nu_0 = 1.420 405 751 63(63) GHz, is in agreement with
literature at a relative precision of 0.44 ppb. This is the highest precision
achieved on hydrogen in a beam, improving over previous results by a factor of
6.
