PDF《AXIONS》

135 MeV and fπ ≈

92 MeV is the pion decay constant. In more detail one ?nds mA = z1/2

1 + z fπmπ fA = 0.60 meV fA/1010 GeV , (3) where z = mu/md is the up/down quark-mass ratio. For this numerical estimate we used a canonical value of z = 0.56 [7], but it could vary in the range z = 0.3C0.6 [8]. In the original axion model, fA ? vweak [1,2]. Tree-level ?avor conservation ?xes the axion mass and its couplings in July 16,

2008 10:42 C 3C terms of a single parameter tan β, the ratio of the vacuum expectation values of the two Higgs ?elds that appear as a minimal ingredient. This standard axion is excluded after extensive experimental searches [9]. A reported observation of a narrow-peak structure in positron spectra from heavy ion collisions [10] suggested an axion-like particle of mass 1.8 MeV that decays into e+e?, but extensive searches for the A0(1.8 MeV) ended negative. Variant axion models were proposed which keep fA ? vweak while dropping the constraint of tree-level ?avor conservation [11], but these models are also excluded [12]. Axions with fA vweak evade all existing experimental limits. Two classes of models are often discussed in the liter- ature. In hadronic axion models, one introduces new heavy quarks carrying the U(1)PQ charge, leaving the usual quarks and leptons without any tree-level axion couplings. The proto- type is the KSVZ model [13], which has the additional property that the heavy quarks are electrically neutral. Another model class simply requires a minimum of two Higgs doublets with the usual quarks and leptons carrying PQ charges, the prototype being the DFSZ model [14]. All of these models contain at least one electroweak singlet scalar boson, which acquires a vac- uum expectation value and thereby breaks the PQ symmetry. The KSVZ and DFSZ models are frequently used as generic examples, but other models exist where both heavy quarks and Higgs doublets carry PQ charges. In one recent example, the PQ charges of all ?elds were derived within a superstring model [15]. I.2 Model-dependent axion couplings: Although the gene- ric axion interactions scale approximately with fπ/fA from the corresponding π0 couplings, there are non-negligible model- dependent factors and uncertainties. The axion'

s two-photon interaction plays a key role for many searches, LAγγ = GAγγ

4 F?ν ? F?ν φA = ?GAγγE ・ B φA . (4) Here, F is the electromagnetic ?eld-strength tensor, ? F its dual, and E and B the electric and magnetic ?elds, respectively. The July 16,

2008 10:42 C 4C coupling constant is GAγγ = α 2πfA E N ?

2 3

4 + z

1 + z = α 2π E N ?

2 3

4 + z

1 + z

1 + z z1/2 mA mπfπ , (5) where E and N, respectively, are the electromagnetic and color anomalies of the axial current associated with the axion. In grand uni?ed models, and notably in the DFSZ case [14], we have E/N = 8/3, whereas E/N =

0 for KSVZ [13] if the electric charge of the new heavy quark is taken to vanish. However, in general, E/N is not known so that for ?xed fA, a broad range of GAγγ values is possible [16]. Axions or axion-like particles with a two-photon vertex decay with a rate ΓA→γγ = G2 Aγγm3 A

64 π = α2

256 π3 E N ?

2 3

4 + z

1 + z

2 (1 + z)2 z m5 A m2 πf2 π = 1.1 * 10?24 s?1 mA eV

5 , (6) where the ?rst expression is for general pseudoscalars, the second for axions, and the third assumes z = 0.56 and E/N = 0. Axions decay faster than the age of the universe if mA >

?

20 eV. The interaction with fermions f has a derivative structure so that it is invariant under a constant shift φA → φA + φ0 as behooves a NG boson, LAff = Cf 2fA ? Ψf γ? γ5Ψf ??φA or ? i Cf mf fA ? Ψf γ5Ψf φA . (7) Here, Ψf is the fermion ?eld, mf its mass, and Cf a model- dependent numerical coe?cient. The dimensionless combina- tion gAff ≡ Cf mf /fA plays the role of a Yukawa coupling and αAff ≡ g2 Aff /4π of a ?ne-structure constant. The pseu- doscalar form is usually equivalent to the derivative structure, but one has to be careful in processes where two NG bosons are attached to one fermion line, for example in the context of axion emission by nucleon bremsstrahlung [17]. July 16,