It is pointed out that a global U(1) symmetry, that has been introduced in order to preserve the parity and time-reversal invariance of strong interactions despite the effects of instantons, would lead to a neutral pseudoscalar boson, the "axion, " with mass roughly of order 100 keV to 1 MeV. Experimental implications are discussed. One of the attractive features of quantum chromodynamics' (QCD) is that it offers an explanation of why C, P, T, and all qua, rk flavors a,re conserved by strong

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... eractions, and by order-& effects of weak interactions. ' However, the discovery of quantum effects' associated with the "instanton" solution of QCD has raised a puzzle with regard to P and T conservation. Because of Adler-Bell-Jackiw anomalies, the chiral transformation which is needed in QCD to bring the quark-mass matrix to a real, diagonal, y,free form will in general change the phase angle 8 associated' with instanton effects, leaving 8 = 8+argdetm invariant. [Here m is the coefficient of 2(1+y,) in a decomposition of the quarkmass matrix into 2(1+y,). ] The condition for P a,nd T conserva, tion is that 0 =0 when the quark fields are defined so that m is real, or more generally, that 8 =0. But 8 is a free parameter, and in QCD there is no reason why it should take the value -argdet~. Furthermore, even if we simply demanded that the strong interactions in isolation conserve P and T, so that 0 =0, there would still be a danger that the weak interactions would introduce Pand T -nonconserving pha. ses of order 10 '0'. in m, leading to an unacceptable neutron electric dipole moment, of order 10 " e. cm. An attractive resolution of this problem has been proposed by Peccei and Quinn. ' They note that the quark-. mass matrix is a function m(( y) } of the vacuum expectation values of a set of weakly coupled scalar fields p&. Although 8 is arbitrary, (cp) is not; it is determined by the minimization of a potential V(y) which depends on 8. Peccei and Quinn assume that the Lagrangian has a global U(1) chiral symmetry [which I will call U(1)pg], under which detm (p) changes by a phase. The phase of detm(y) at the minimum of V(y) is then undetermined in any finite order of perturbation theory, and is fixed only by instanton effects which break the U(1)pg symmetry. However, the potential will then depend on 8, but not separately on 8 and argdetm, so tha, t it is not a, miracle if the phase of detm(p) at the minimum of V(p) happens to have the Pand T-conserving value -8. Peccei and Quinn' show in a number of examples that this is just what happens. Now, the U(1)pg symmetry of the La,grangian is intrinsically broken by instantons, and so at first sight one might not expect that it would have any further physical consequences. Certainly it does not lead to the strongly interacting isoscalar pseudoscalar meson below 4 Brn", ' that was the bugbear of the old U(1) problem. However, the scalar fields p do not know about instantons, except through a semiweak (~Gp' ') coupling to qua, rks. Hence the spontaneous breakdown of the chiral U(1)pg symmetry associated with the appearance of nonzero vacuum expectation values (y) leads' to a very light pseudoscalar pseudo-Goldstone boson, ' the "axion, " with m, ' proportional to the Fermi coupling GF. For insight in to the properties of the axion, it is useful to examine how they appear in the simplest realistic model that admits a U(1)pg symmetry. We assume an SU(2) U(1) gauge group, with quarks in N/2 left-handed doublets and N right-handed singlets, and just two scalar doublets jy&', p&'j, carrying U(1)pg quantum numbers such that p, (y,) couples right-banded quarks of charge -r (+~) to left-handed quarks. By writing the Yukawa interaction in terms of quark fields of definite mass, we easily see that the interaction of neutral scalar fields with quarks is'