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Register a new userAnalytic properties of different unitarization schemes
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The analytic properties of the eikonal and U-matrix unitarization schemes are examined. It is shown that the basic properties of these schemes are identical. Both can fill the full circle of unitarity, and both can lead to standard and non-standard asymptotic relations for the ratio of the elastic cross section to the total cross section. The relation between the phases of the unitarized amplitudes in each scheme is examined, and it is shown that demanding equivalence of the two schemes leads to a bound on the phase in the U-matrix scheme.
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The analytic properties of the elastic hadron scattering amplitude are examined in the impact parameter representation at high energies. Different unitarization procedures and the corresponding non-linear equations are presented. Several unitarisation schemes are presented. They lead to almost identical results at the LHC.
We consider two well-known classes of unitarization of Born amplitudes of hadron elastic scattering. The standard class, which saturates at the black disk limit includes the standard eikonal representation, while the other class, which goes beyond the black-disk limit to reach the full unitarity circle, includes the U matrix. It is shown that the basic properties of these schemes are independent of the functional form used for the unitarisation, and that U matrix and eikonal schemes can be extended to have similar properties. A common form of unitarisation is proposed interpolating between both classes. The correspondence with different nonlinear equations are also briefly examined.
Different forms of non-linear equations which mimic parton saturation in the non-perturbative regime are examined. These equations lead to corresponding unitarization schemes in the impact parameter representation of the hadron scattering amplitude. It is shown how specific properties of the non-linear equations reflect different features of the diffraction processes.
We comment on the paper On application of the time-energy uncertainty relation to Mossbauer neutrino experiments (see arXiv: 0803.1424) in which our paper Time-energy uncertainty relations for neutrino oscillation and Mossbauer neutrino experiment (see arXiv: 0803.0527) has been criticized. We argue that this critique is a result of misinterpretation: The authors of (arXiv: 0803.1424) do not take into account (or do not accept) the fact that at present there exist different schemes of neutrino oscillations which can not be distinguished in usual neutrino oscillation experiments. We stress that a recently proposed Mossbauer neutrino experiment provides the unique possibility to discriminate basically different approaches to oscillations of flavor neutrinos.
With the progress of increasingly precise measurements on the neutrino mixing angles, phenomenological relations such as quark-lepton complementarity (QLC) among mixing angles of quarks and leptons and self-complementarity (SC) among lepton mixing angles have been observed. Using the latest global fit results of the quark and lepton mixing angles in the standard Chau-Keung scheme, we calculate the mixing angles and CP-violating phases in the other eight different schemes. We check the dependence of these mixing angles on the CP-violating phases in different phase schemes. The dependence of QLC and SC relations on the CP phase in the other eight schemes is recognized and then analyzed, suggesting that measurements on CP-violating phases of the lepton sector are crucial to the explicit forms of QLC and SC in different schemes.
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