Exactly-solvable model of the linear singular oscillator in the relativistic configurational space is considered. We have found wavefunctions and energy spectrum for the model under study. It is shown that they have correct non-relativistic limits.
In this article, we investigate the contribution of the higher-twist Feynman diagrams to the large-p T inclusive pion production cross section in proton-proton collisions and present the general formulae for the higher-twist differential cross sections in the case of the running coupling and frozen coupling approaches. The structure of infrared renormalon singularities of the higher twist subprocess cross section and the resummed expression (the Borel sum) for it are found. We compared the resummed higher-twist cross sections with the ones obtained in the framework of the frozen coupling approach and leading-twist cross section. We obtain, that ratio R = (Σ HT π + ) res /(Σ HT π + ) 0 , for all values of the transverse momentum p T of the pion identically equivalent to ratio r=(∆ HT π ) res /(∆ HT π ) 0 .It is shown that the resummed result depends on the choice of the meson wave functions used in calculation. Phenomenological effects of the obtained results are discussed.
An exactly solvable problem for the finite-difference Schrödinger equation in the relativistic configurational space is considered. The appropriate finite-difference generalization of the factorization method is developed. The theory of new special functions ‘‘the relativistic Hermite polynomials,’’ in which the solutions are expressed, is constructed.
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