Particle physics bounds from the Hulse-Taylor binary.

The orbital period of the binary pulsar PSR 1937+16 has been observed to decrease at the rate of 2:40 10 12 s/s which agrees with the prediction of the quadropole formula for gravitational radiation to within one percent. Assuming that the energy carried away by radiation of other massless particles like scalars and pseudoscalar Nambu-Goldstone bosons is less than one percent of the gravitational radiation we can establish bounds on couplings of these particles to nucleons. We nd that the scalar mediated fth force is weaker than the gravitational force between two nucleons by a factor of < 10 . This bound is about ve orders of magnitude more stringent than the bounds obtained from terrestial fth force experiments. From the radiation loss of massless Goldstone bosons we establish the upper bound =f < 10 22 GeV 1 on the QCD vacuum angle and the scale f at which a global symmetry can be broken spontaneously. Typeset using REVTEX [email protected] [email protected] 1 The Hulse-Taylor (H-T) binary consisting of the pulsar PSR 1937+16 orbiting around an unseen companion star provides rm evidence for the existence of gravitational waves [1]. The observed loss of orbital period agrees with the prediction from the quadropole formula of gravitation radiation [2] to within one percent. In this letter we compute the orbital energy loss due to radiation of other massless particles like scalars and pseudoscalar Nambu-Goldstone bosons. Massless scalars which couple to nucleons arise in scalar-tensor theories of gravity [3], as dilatons in theories with spontaneously broken conformal symmetry [4] and in string theories [5]. Assuming a generic scalar-nucleon coupling Ls = gs s we nd that the radiation of s particles from the H-T binary is less than 1% of the gravitational radiation loss if gs < 10 . This gives an upper bound s = g 2 s=Gm 2 n < 10 10 on the ratio of a long range scalar mediated fth force to the gravitational force between two nucleons. This bound is about six orders of magnitude more stringent than the best bounds obtained from terrestrial fth force search experiments [6,7]. In theories with a spontaneously broken global symmetry like the baryon number or the lepton number we have massless Nambu-Goldstone bosons (NGB) which have a generic coupling Lp = (m=f) p i 5 where m is the fermion mass and f is the scale of the global symmetry breaking [8]. The pseudoscalar eld of a macroscopic source adds up coherently only if the spins of the constituents are polarised. It was observed by Chang, Mohapatra and Nussinov [9] and Barbieri et al [10] that the CP violating operator G ~ G in the QCD sector induces a coupling L = ( =f)(mumd=(mu +md)) p between the NGB p and nucleons. This coupling give rise to a 1=r type long range force and the NGB eld of the constituent nucleons a macroscopic test body add up coherently even when these are randomly aligned. From the constraints on the energy carried away by the radiation of NGBs from the H-T binary we obtain the upper bound ( =f) < 10 23 GeV . This improves by ve orders of magnitude the value obtained from the separately established bounds < 10 9 (from the measurement of the neutron electric dipole moment [11,12]) and f > 10 GeV (from the cooling rate of helium stars [13]). Finally we compute the energy loss by the radiation of neutrino pairs from the con2 stituent neutrons of the H-T binary. We nd that for the neutral current coupling L = (1= p 2)GFn(x) , the energy radiated by neutrino pair emission is suppressed by the phase factor and is negligibly smaller than the gravitational radiation. Therefore if experimentally one observes a discrepancy between the observed period loss of the binary orbit and the prediction from gravitational radiation formula, it would be a signal of new kind of massless particle radiation and an unequivocal signal of new physics beyond the standard model. Gravitational radiation : We use the Feynman rules of linearised quantum gravity [14{17] to compute the gravitational radiation from the Hulse-Taylor binary system. Assuming a universal graviton-matter coupling LI = p 8 G h T we nd that the energy loss by gravitational brehmstrahlung at tree level agrees with the Peter-Mathew expression [2] for classical gravitational wave radiation from binary system. The e ective Lagrangian for the graviton matter interaction is L = 1 4 ~h 2~h + ~ h T (1) where the graviton eld h is a perturbation of the metric g = + h to the rst order in = p 8 G. We have made the harmonic gauge choice, @ h = (1=2)@ h and de ned ~ h = h 12 h The universal coupling of ~ h with matter at the tree level is a re ection of the equivalence principle of classical gravity. The rate of graviton emission is given by