# Nuclear Theory/RIKEN Seminar

## "Asymptotic freedom of gluons in the Fock space"

#### Presented by Stanislaw Glazek, University of Warsaw

Friday, September 4, 2015, 2:00 pm — Small Seminar Room, Bldg. 510

Asymptotic freedom of gluons is defined in terms of scale-dependent renormalized QCD Hamiltonian operators that act in the Fock space. These operators are calculable in a new way [1,2], by solving a double-commutator differential equation [3], where the derivative is with respect to a scale parameter defined within the renormalization group procedure for effective particles (RGPEP). The RGPEP equation and its solutions are invariant with respect to boosts and may serve as a tool in attempts to dynamically explain the parton and constituent models of hadrons in QCD. The third-order QCD solution of the RGPEP equation to be discussed [2], provides an explicit example of how asymptotic freedom of gluons is exhibited in the scale-dependence of Hamiltonians as operators in the Fock space. This example also prepares ground for the fourth-order calculations of effective strong interactions using the same RGPEP equation [3], to facilitate Hamiltonian studies of many strong-interaction processes, e.g., those that involve heavy quarkonia in relativistic motion. Applications to other sectors of the Standard Model than the strong interactions await development, while only preliminary results are currently available in the domain of precise calculations in QED[4]. [1] Dynamics of effective gluons, S. D. Glazek, Phys. Rev. D63, 116006, 29p (2001). [2] Asymptotic freedom in the front-form Hamiltonian for gluons, M. Gomez-Rocha, S. D. Glazek, arXiv:1505.06688 [hep-ph], to appear in Phys. Rev. D. [3] Perturbative formulae for relativistic interactions of effective particles, S. D. Glazek, Acta Phys. Pol. B43, 1843, 20p (2012). [4] Calculation of size for bound-state constituent

Hosted by: Soeren Schlichting

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