No abstract

We report a measurement of the process γγ * → π 0 with a 759 fb −1 data sample recorded with the Belle detector at the KEKB asymmetric-energy e + e − collider. The pion transition form factor, F (Q 2 ), is measured for the kinematical region 4 GeVGeV 2 , where −Q 2 is the invariant mass squared of a virtual photon. The measured values of Q 2 |F (Q 2 )| agree well with the previous measurements below Q 2 ≃ 9 GeV 2 but do not exhibit the rapid growth in the higher Q 2 region seen in another recent measurement, which exceeds the asymptotic QCD expectation by as much as 50%.

We study the Nonlinear (Polynomial, N -fold,...) Supersymmetry algebra in one-dimensional QM. Its structure is determined by the type of conjugation operation (Hermitian conjugation or transposition) and described with the help of the Super-Hamiltonian projection on the zero-mode subspace of a supercharge. We show that the SUSY algebra with transposition symmetry is always polynomial in the Super-Hamiltonian if supercharges represent differential operators of finite order. The appearance of the extended SUSY with several (complex or real) supercharges is analyzed in details and it is established that no more than two independent supercharges may generate a Nonlinear superalgebra which can be appropriately specified as N = 2 SUSY. In this case we find a non-trivial hidden symmetry operator and rephrase it as a non-linear function of the Super-Hamiltonian on the physical state space.The full N = 2 Non-linear SUSY algebra includes "central charges" both polynomial and non-polynomial (due to a symmetry operator) in the Super-Hamiltonian.