The orbital period of the binary pulsar PSR 1913+16 has been observed to decrease at the rate of 2.40 \times 10 ^ { -12 } s/s which agrees with the prediction of the quadropole formula for gravitational radiation to within one percent .
The decrease in orbital period may also occur by radiation of other massless particles like scalars and pseudoscalar Nambu-Goldstone bosons .
Assuming that this energy loss is less than one percent of the gravitational radiation , we can establish bounds on couplings of these particles to nucleons .
For a scalar nucleon coupling of the form g _ { s } ~ { } \phi~ { } \bar { \psi } ~ { } \psi we find that g _ { s } < 3 \times 10 ^ { -19 } .
From the radiation loss of massless Goldstone bosons we establish the upper bound \theta / f < 7.5 \times 10 ^ { -16 } GeV ^ { -1 } on the QCD vacuum angle \theta and the scale f at which the baryon number symmetry can be broken spontaneously .