U(1)A symmetry in two-doublet models, U bosons or light pseudoscalars, and ψ and Υ decays

ψ and Υ decays may be used to search for light neutral spin-1 or spin-0 bosons associated with a broken extraU(1) symmetry, local or global, acting axially on quarks and leptons, as may be present in supersymmetric theories with a λ H1H2 S superpotential. A light spin-1 gauge boson U may be produced very much as the corresponding Goldstone boson (or light pseudoscalar) a associated with the global U(1) breaking, i.e. as a mixing of doublet and singlet components, with pseudoscalar couplings fP = 2mq,l mU fA to quarks and leptons. Υ decays into γ+ invisible neutral constrain, for invisible decays of the new boson, an axial coupling to b to fbA < 4 10 −7 mU (MeV), corresponding to a pseudoscalar coupling fbP < 4 10, 5 times smaller than the standard Higgs coupling. This implies, from universality properties, feA < 4 10mU (MeV), or feP < 4 10. The extra U(1) should then be broken at a scale larger than electroweak with the pseudoscalar a for > 96% singlet and < 4% doublet at most, for tanβ > 1. 1. U(1) symmetries in two-doublet models Particle physics theories involving two Englert-Brout-Higgs doublets, now denoted as (h◦1, h − 1 ) and (h + 2 , h ◦ 2), allow for a possible U(1) symmetry acting as h1 → e h1 , h2 → e h2 , constraining both their interaction potential and Yukawa couplings to fermions [1] 1. This occurs naturally within supersymmetric extensions of the standard model, which require two doublet superfields H1 and H2 responsible for the electroweak breaking and the generation of quark and lepton masses [2, 3]. Such a transformation may also be used as a possible way to rotate away CP -violating effects in QCD [4]. This U(1) symmetry, broken through < h ◦ i > = vi/ √ 2 with tanβ = v2/v1 , would lead, after the Goldstone combination Im (cosβ h ◦ 1 − sinβ h ◦ 2 ) gets eliminated by the Z , to a quasi-massless “axion” field A = √ 2 Im ( sinβ h ◦ 1 + cosβ h ◦ 2 ) , (1) if it were not broken explicitly as in [2] 2. This explicit breaking through f(S) superpotential terms provides a mass, proportional to the λ parameter of the λH1H2 S superpotential coupling with the singlet S introduced in [2], for the 1The allowed quartic interactions in V (h1, h2) are (h † 1 h1), (h † 2 h2), (h † 1 h1)(h † 2 h2) and |h1h2| or equivalently |h†1h2| = (h † 1 h1)(h † 2 h2)− |h1h2|. Within supersymmetry they appear as electroweak gauge interactions, with V quartic= [(g+g)/8] (h†1h1−h † 2 h2) +(g/2) |h†1h2| [2]. 2We used i φ” = h1, i φ = h c 2 (described by left-handed and right-handed doublet superfields respectively), with φ” → eiα φ”, φ →