High energy photon colliders (γγ,γe) are based on e-e-linear colliders where high energy photons are produced using Compton scattering of laser light on high energy electrons just before the interaction point. This paper is a part of the Technical Design Report of the linear collider TESLA.1Physics program, possible parameters and some technical aspects of the photon collider at TESLA are discussed.

The physical meaning of the decomposition of the Rosenbluth formula into two terms containing only squares of Sachs form factors has been established. A new method has been proposed for their independent measurement in the e p → e p elastic process when the initial proton at rest is fully polarized along the direction of motion of the final proton.

In this work we discuss questions related to the interpretation of unexpected results of measurements of the proton form factors ratio GE/GM in the high-precision double polarization experiments done in JLab in the region of 0.5 ≤ Q 2 ≤ 8.5 GeV 2 . For this purpose, in the case of the hard scattering mechanism we calculated (in the leading approximation) the matrix elements of the proton current J ±δ,δ p for the full set of spin combinations corresponding to the number of the spin-flipped quarks, which contribute to the proton transition without spin-flip (J δ,δ p ) and with the spin-flip (J −δ,δ p ). This set is: (0,1), (0,3), (2,1), (2,3), where the first number in parentheses is the number of the spin-flipped quarks, which contribute to the J δ,δ p , and the second one is the number of the spinflipped quarks which contribute to the J −δ,δ p . For the sets of (0,1) and (2,3), we found that the ratio GE/GM ∼ 1, and the form factors GE and GM behave for the set of (0,1) as GE, GM ∼ 1/Q 6 , and for the set of (2,3) as GE, GM ∼ 1/Q 4 . At the same time the set of (0,1) is realized for τ ≪ 1, and the set (2,3) for τ ≫ 1 (τ = Q 2 /4m 2 ). This allows us to suppose that: 1) at the lower boundary of the experimental measurements of the ratio GE/GM not dipole dependence appears but the law of GE, GM ∼ 1/Q 6 ; 2) the conditions for the observation of the dipole dependence in the experiments has not yet been achieved; 3) since for quarks J δ,δ q ∼ 1 and J −δ,δ q ∼ √ τ , then the dipole dependence is realized when τ ≫ 1 in the case when the quark transitions with spin-flip are dominate; 4) the law of the linear decrease of GE/GM at τ < 1 is due to additional contributions to the J δ,δ p by spin-flip transitions of two quarks and an additional contribution to J −δ,δ p by spin-flip transitions of three quarks, in this case their relative contributions are small.

The backward Compton scattering is a basic process at future higher energy photon colliders. To obtain a high probability of e→ γ conversion the density of laser photons in the conversion region should be so high that simultaneous interaction of one electron with several laser photons is possible (nonlinear Compton effect). In this paper a detailed consideration of energy spectra, helicities of final photons and electrons in nonlinear backward Compton scattering of circularly polarized laser photons is given. Distributions of γγ luminosities with total helicities 0 and 2 are investigated. Very high intensity of laser wave leads to broadening of the energy (luminosity) spectra and shift to lower energies (invariant masses). Beside complicated exact formulae, approximate formulae for energy spectrum and polarization of backscattered photons are given for relatively small nonlinear parameter ξ 2 (first order correction). All this is necessary for optimization of the conversion region at photon colliders and study of physics processes where a sharp edge of the luminosity spectrum and monochromaticity of collisions are important.

The ratio of the squares of the electric and magnetic proton form factors is shown to be proportional to the ratio of the cross sections for the elastic scattering of an unpolarized electron on a partially polarized proton with and without proton spin flip. The initial proton at rest should be polarized along the direction of the motion of the final proton. Similar results are valid for both radiative ep scattering and the photoproduction of pairs on a proton in the Bethe-Heitler kinematics. When the initial proton is fully polarized in the direction of the motion of the final proton, the cross section for the ep → ep process, as well as for the ep → epγ and γp → eēp processes, without (with) proton spin flip is expressed only in terms of the square of the electric (magnetic) proton form factor. Such an experiment on the measurement of the cross sections without and with proton spin flip would make it possible to acquire new independent data on the behavior of G 2 E (Q 2 ) and G 2 M (Q 2 ), which are necessary for resolving the contradictions appearing after the experiment of the JLab collaboration on the measurement of the proton form factors with the method of polarization transfer from the initial electron to the final proton.