Theoretical analysis of the γγ→π0η process

Abstract

We present a theoretical study of the γγ → πη process from the threshold up to 1.4 GeV in the πη invariant mass. For the s-wave a0(980) resonance state we adopt a dispersive formalism using a coupled-channel Omnès representation, while the d-wave a2(1320) state is described as a Breit-Wigner resonance. An analytic continuation to the a0(980) pole position allows us to extract its two-photon decay width as Γa 0 →γγ = 0.27(4) keV.

The hadronic light-by-light contribution to the muon’s anomalous magnetic moment

“…The a 2 (1320) resonance was taken into account explicitly within the assumption that it is predominantly produced by the helicity-2 state (similar to f 2 (1270) in [199]). Together with the proposed dispersive method for a 0 (980) this yielded a parameter-free description of the γγ → π 0 η cross section [162], which was in the reasonable agreement with the data from the Belle Collaboration [132]. Then the uncertainty coming from the hadronic final state interactions were narrowed down using this data.…”

“…For the double virtual process γ * γ * → ππ, in addition to σ T T and σ T L , Figure 33: Total and differential cross sections for γγ → π 0 η (| cos θ| ≤ 0.9) and γγ * → π 0 η (| cos θ| ≤ 1.0) with Q 2 = 0.5 GeV 2 taken from [162,189]. The data are taken from [132,139].…”

Dispersive analysis of the γγ⁎ → ππ process

“…with ∆ ≡ p 1 − p 2 , and where the numbering is chosen such that in the real photon case only L µν 1,2 contribute. The latter coincide with the tensor structures used in [13,18]. The invariant amplitudes F i depend on the Mandelstam variables s = (q 1 + q 2 ) 2 , t = (p 1 − q 1 ) 2 and u = (p 1 − q 2 ) 2 which satisfy the relation s + t + u = 2 m 2 π − Q 2 .…”

Dispersive analysis of the γ*γ*→ππ process

“…The location of s j is determined by the condition that the imaginary part of the logarithm in (21) changes sign and therefore requires a proper choice of the Riemann sheet which we want to avoid. The merit of (22) is such that it works for both anomaly and non-anomaly cases, so one can use it for any space-like Q i including the "transition" line when…”