Cross sections of muon and charged pion pair production in electron-positron annihilation near the threshold

Abstract

The processes of muons (tau) and charged pions pairs production at electronpositron annihilation with O(α) radiative corrections are considered. The calculation results are presented assuming the energies of final particles (cms implied) to be not far significantly from threshold production. The invariant mass distributions for the muon (tau) and pion pairs are obtained both for the initial and final state radiation.Some analytical calculations are illustrated numerically. The pions were assumed to be point-like objects and scalar QED was applied for calculation. The QED radiative corrections related to the final state radiation, additional to the well known Coulomb factor, are treated near threshold region exactly.

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“…is the kaon velocity and C FS ¼ 1 þ α π η K ðsÞ is the final-state correction for radiative effects [42][43][44]. The calculated form factors are listed in Table I. From pQCD, the form factor of a spin zero meson is predicted to be F K ¼ 16πα s ðsÞf 2 K =s [45], where α s ðsÞ is the strong coupling constant and f K is the decay constant of the charged kaon.…”

Precise determination of the low-energy hadronic contribution to the muong−2from analyticity and unitarity: An improved analysis

“…where ǫ = 1.9×10 −3 . Finally, η π (t) is the FSR correction, calculated in scalar QED [48,49]. We are interested in the contribution to (1) of the energies below 0.63 GeV.…”

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“…is the finalstate correction [27][28][29]. At the φ mass, the 4.2% deviation from unity of C FS is completely dominated by the Coulomb interaction between K + and K − .…”