Speaker
Description
Computational access to the logarithmically scale-dependent Hamiltonian eigenstate picture of hadrons in the space of virtual quark and gluon states, within the canonical front form of QCD, is impeded by small-x divergences that are stronger than logarithmic. We propose introducing a gluon mass parameter and an auxiliary color-octet scalar field to overcome this barrier, using the renormalization group procedure for effective particles (RGPEP) [1]. At the end of the effective Hamiltonian computation, the gluon mass parameter is taken to zero and the auxiliary field decouples from the dynamics, as required in gauge theory. The same method also leads to the cancellation of quadratic ultraviolet transverse divergences in self-interactions. We explain how this approach works in virtual quark and gluon scattering amplitudes, as well as in Hamiltonian eigenvalue problems for bound states, with the discussion focusing on the case of heavy quarkonia [2]. Previously [3], it was suggested that QCD vacuum effects, such as those appearing in QCD sum rules [4] and those due to instantons [5], can manifest themselves in the effective dynamics through front-form counterterms to small-x singularities. We use our approach to advance the hypothesis that the corresponding effective interaction terms can instead emerge in finite renormalization-group evolution as the scale parameter is lowered toward Lambda_QCD in the RGPEP scheme.
[1] S. D. Glazek, https://doi.org/10.1140/epjs/s11734-026-02127-y
[2] K. Serafin et al., Phys.Rev.D 109, 016017 (2024)
[3] K. G. Wilson et al., Phys.Rev.D 49, 6720 (1994)
[4] M. Shifman, A. Vainshtein, I. Zakharov, Nucl.Phys.B 147, 385 (1979)
[5] E. Shuryak, I. Zahed, https://arxiv.org/abs/2601.15085