Inclusive γ ∗ γ interactions to hadronic final states where one scattered electron or positron is detected in the electromagnetic calorimeters have been studied in the LEP 1 data taken by ALEPH from 1991 to 1995. The event sample has been used to measure the hadronic structure function of the photon F 2 γ in three bins with 〈 Q 2 〉 of 9.9, 20.7 and 284 GeV 2 .
The measured values of dsig/dx from the ECAL data in the Q**2 bin 35 to 3000 GeV**2 with a mean of 284 +- 49 GeV**2.
The measured values of dsig/dx from the LCAL data in the Q**2 bin 13 to 44 GeV**2 with a mean of 20.67 +- 016 GeV**2.
The measured values of dsig/dx from the LCAL data in the Q**2 bin 6 to 13 GeV**2 with a mean of 9.93 +- 0.04 GeV**2.
The structure of both quasi-real and highly virtual photons is investigated using the reaction e+e- -> e+e-mu+mu-, proceeding via the exchange of two photons. The results are based on the complete OPAL dataset taken at e+e- centre-of-mass energies close to the mass of the Z boson. The QED structure function F_2^gamma and the differential cross-section dsigdx for quasi-real photons are obtained as functions of the fractional momentum x from the muon momentum which is carried by the struck muon in the quasi-real photon for values of Q**2 ranging from 1.5 to 400 GeV**2. The differential cross-section dsigdx for highly virtual photons is measured for 1.5< Q**2 < 30 GeV**2 and 1.5< P**2 < 20 GeV**2, where Q**2 and P**2 are the negative values of the four-momentum squared of the two photons such that Q**2 > P**2. Based on azimuthal correlations the QED structure functions F_A^gamma and F_B^gamma for quasi-real photons are determined for an average Q**2 of 5.4 GeV**2.
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