Abstract
We present a theoretical study of the γγ⁎→π+π−,π0π0 processes from the threshold through the f2(1270) region in the ππ invariant mass. We adopt the Omnès representation in order to account for rescattering effects in both s- and d-partial waves. For the description of the f0(980) resonance, we implement a coupled-channel unitarity. The constructed amplitudes serve as an essential framework to interpret the current experimental two-photon fusion program at BESIII. They also provide an important input for the dispersive analyses of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment.
Highlights
The two-photon fusion reaction is a prime example where using S-matrix constraints, such as analyticity and unitarity one can make predictions, which serve as direct input into the Standard Model calculation of the hadronic light-by-light (HLbL) scattering contribution to the muon’s anomalous magnetic moment aμ
The aim of this work is to extend the dispersive approach to the coupled-channel case by including KKintermediate states and to include for the first time the d-wave contribution, which allows for a full dispersive formalism through the prominent f2(1270) tensor meson region. This will allow for a validation of such approach by forthcoming BESIII data for the γγ∗ → ππ reaction, which is a prerequisite for a data-driven approach in quantifying the uncertainty of the HLbL contribution to aμ
Hμν = i d4 x e−i q1·x π(p1)π(p2)|T ( jμem(x) jνem(0))|0, where the lepton momentum k2 is detected, whereas the second lepton momentum k1 goes undetected. This corresponds with the kinematical situation where the photon with momentum q2 has a finite virtuality q22 = −Q22 ≡ Q2, while the first photon with momentum q1 is quasi-real, hadron tensor Hμν satisfies gauge i.e. q21 = −Q21 invariance, i.e
Summary
The two-photon fusion reaction is a prime example where using S-matrix constraints, such as analyticity and unitarity one can make predictions, which serve as direct input into the Standard Model calculation of the hadronic light-by-light (HLbL) scattering contribution to the muon’s anomalous magnetic moment aμ. The aim of this work is to extend the dispersive approach to the coupled-channel case by including KKintermediate states and to include for the first time the d-wave contribution, which allows for a full dispersive formalism through the prominent f2(1270) tensor meson region. This will allow for a validation of such approach by forthcoming BESIII data for the γγ∗ → ππ reaction, which is a prerequisite for a data-driven approach in quantifying the uncertainty of the HLbL contribution to aμ
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