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Exact and approximate solutions for the electron nonsinglet structure function in QED

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Zeitschrift für Physik C Particles and Fields

Abstract

Two exact, valid up to infinite perturbative order, numerical solutions of the Lipatov equation for the nonsinglet electron structure function in the QED are presented. One of them is of the Monte Carlo type and another is based on the numerical inversion of the Mellin transform. They agree numerically to a very high precision (better than 0.05%). Within the leading logarithmic approximation, the exact solution is compared with the perturbative second and third order exponentiated solutions. It is shown that the perturbative second order solution inspired by the Yennie-Frautschi-Suura (exclusive) exponentiation is much closer to the exact solution than the other ones. New compact analytical formula for the third order exponentiated solution is given. It is shown to be in perfect numerical agreement with the infinite order solution of the Monte Carlo and Mellin type.

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Author notes

  1. S. Jadach

    Present address: CERN, CH-1211, Geneva, Switzerland

Authors and Affiliations

  1. Institute of Physics, Jagellonian University, ul. Reymonta 4, PL-30-059, Kraków, Poland

    M. Skrzypek & S. Jadach

Authors
  1. M. Skrzypek
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  2. S. Jadach
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Additional information

Work partly supported by Polish Government grants CPBP 01.03,01.09 and RRI.14.1. This is a revised version of TPJU-3/89

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Skrzypek, M., Jadach, S. Exact and approximate solutions for the electron nonsinglet structure function in QED. Z. Phys. C - Particles and Fields 49, 577–584 (1991). https://doi.org/10.1007/BF01483573

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  • DOI: https://doi.org/10.1007/BF01483573

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