Abstract :
The heterotic superstring theory of Gross et al. contains two axions, found by Witten – the model-independent axion, whose decay constant is fA≈2.18gs2×1016 GeV, where gs2 is the strong-interaction coupling parameter, and the second axion, deriving from the Green–Schwarz anomaly-cancelling term BF̂4, for which fB≡λfA. The parameter λ is not precisely known, but also relates the masses of the gravitino and gaugino by supersymmetry as m3/2≈λmg̃. After diagonalization, the decay constant of the QCD axion, which couples only to the observable-sector gauge field Fij assuming gaugino condensation in the hidden sector, is fa=12(1+λ2)1/2fA. In the absence of fine tuning of the initial conditions, the constraint on fa found by Lazarides et al. by requiring the energy density today in coherent axion oscillations ρa not to exceed the critical density ρ0 implies that λ≲1, while the nucleosynthesis constraint and the lightness of the Higgs doublet require that m3/2≳10 TeV and mḡ≲1 TeV, respectively, so that λ≳10. Combination of these arguments selects the value 1≲λ≲10, in which case the mass of the axion mini-star is 1.5×10−2M⊙≲Ma≲0.3M⊙, in agreement with the microlensing observations towards the galactic centre and the Large and Small Magellanic Clouds. The difference from the weak-coupling, four-point value λ∼105 is explained either by the effect of higher-point contributions, or by strong coupling of the string theory – or if the hidden-sector gauginos do not condense, so that fa≈fA irrespective of the value of λ.
