Abstract
Amplitudes of the form gamma ^*(q^2)rightarrow gamma P_1P_2 appear as sub-processes in the computation of the muon g-2. We test a proposed theoretical modelling against very precise experimental measurements by the KLOE collaboration at q^2=m^2_phi . Starting from an exact, parameter-free dispersive representation for the S-wave satisfying QCD asymptotic constraints and Low’s soft photon theorem we derive, in an effective theory spirit, a two-channel Omnès integral representation which involves two subtraction parameters. The discontinuities along the left-hand cuts which, for timelike virtualities, extend both on the real axis and into the complex plane are saturated by the contributions from the light vector mesons. In the case of P_1P_2=pi eta , we show that a very good fit of the KLOE data can be achieved with two real parameters, using a T-matrix previously determined from gamma gamma scattering data. This indicates a good compatibility between the two data sets and confirms the validity of the T-matrix. The resulting amplitude is also found to be compatible with the chiral soft pion theorem. Applications to the I=1 scalar form factors and to the a_0(980) resonance complex pole are presented.
Highlights
We develop here a similar approach, in the case of one virtual photon, which can be applied in an energy region of the P1 P2 system slightly larger than 1 GeV
We focus on the case where P1 P2 = π 0η, (K K )I =1 and will test the method against the very precise measurements performed by the KLOE collaboration close to the φ(1020) meson peak [6]
A very similar phase shift pattern was found to emerge in the mesonmeson scattering model developed in Ref. [21] which was applied to γ γ → π η scattering in Ref. [22] and found to describe reasonably well the data by the Belle collaboration [23]
Summary
We first recall that amplitudes involving two real or virtual photons and two pseudo-scalar mesons γ ∗(q2) → γ ∗(q1)P1( p1)P2( p2) can be derived from a correlation function involving two electromagnetic currents. We consider here the situation where one photon is real and the other is virtual, q12 = 0, q22 ≡ q2 = 0. In this case, the tensors T4μν, T5μν are not physically relevant. This amplitude can be expanded in terms of the independent tensors as.
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