Exact results in QED
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xact Results in QED1 A. B. Arbuzova, V. V. Byteva, E. A. Kuraeva, E. TomasiGustafssonb, and Yu. M. Bystritskiya a
Joint Institute for Nuclear Research b IPN, Orsay, France
Abstract—This review is devoted to exact calculations of cross sections of QED processes in relativistic approach. We consider the case when the velocity of final heavy particles are not particularly close to the speed of light. Especially the cases of muon radiative pair creation is considered. In frames of QED with pion formfactor we estimate the pion radiative pair creation. All leading terms are included in the frames of struc ture function approach. The annihilation of electronpositron to the hadronic final state with one additional tagged photon is considered. The radiative corrections are calculated and the numerical estimation is made. Target spin asymmetry and charge asymmetry are investigated for eµ scattering processes. Initial state radia tion (returning to resonance) mechanism is investigated including radiative corrections to initial and final states. Possible method of experimental extraction of the ratio of electric and magnetic formfactors of proton is suggested for different processes in lepton proton scattering. Some useful algebraic relations and integrals are presented. DOI: 10.1134/S1063779611010023 1
CONTENTS
1. Introduction 2. Exact results for 2 3 type processes 2.1. The cross sections of the charged muon and pion pairs production at electronpositron annihilation near the threshold 2.1.1. Final state radiation (FSR) in muon pair production 2.1.2. Initial state radiation (ISR) in muon pair production 2.1.3. Two charged pion production in electronpositron annihilation 2.1.4. Final state radiation in pion pair production 2.1.5. Initial state radiation in pion pair production 2.1.6. Estimation of accuracy 2.2. Radiative muon pair production in high energy electronpositron annihilation and crossed channel processes 2.2.1. Born crosssection and RC 2.2.2. Calculations of boxtype RC 2.2.3. Vertextype FD 2.2.4. Masterformula 2.3. Target normal spin asymmetry and charge asymmetry for eμ elastic scattering and the crossed processes μ+ + μ–(γ) 2.3.1. Process e+ + e– TPE amplitude 2.3.2. Scattering channel
2.3.3. Soft photon emission in scattering channel. Charge asymmetry 2.3.4. Soft photon emission in annihilation channel. Charge asymmetry 2.3.5. Crossing Symmetry 2.3.6. Derivation of the additional structure: annihilation channel 2.3.7. One spin asymmetry caused by proton polarization 2.4. Compton tensor with heavy photon in the case of longitudinally polarized fermion 2.5. Double logarithmical corrections to beam asymmetry in polarized electronproton scattering 2.5.1. Calculation in Double Logarithm approximation 2.6. Possible method to measure the ratio of proton form factors in processes with proton spin transmission 2.6.1. Matrix elements of the proton current in the diagonal spin basis 2.6.2. Generalization of the diagonal spin basis to the case of partially polarized protons 2.6.3. Kinematics of the Elastic P
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