Speaker
Description
In view of the growing need of theoretical tools that can be used in QCD to understand the dynamics of gluons in hadrons, the renormalization group procedure for effective particles (RGPEP) has been applied to several problems in QCD in order to study its utility. The method, based on the Glazek-Wilson similarity renormalization group for Hamiltonians, uses the concept of effective particles, which differ from the point-like canonical ones by having a finite size $s$. The size plays the role of renormalization group parameter. However, instead of integrating out high-energy degrees of freedom, our RGPEP procedure is based on a transformation of the front-form QCD Hamiltonian from its canonical form with counterterms to the renormalized, scale-dependent operator that acts in the Fock space of effective quanta of quark and gluon fields, keeping all degrees of freedom intact but accounting for them in a transformed form. The notion of effective size allows one to select the relevant energy scale in a particular problem.
In this talk, I present the general concepts of the method and show recent results for quarkonia and triply-heavy baryons, as they are the simplest possible systems one can consider in theory and compare with data. I display numerical estimates for meson and baryon masses, which match predictions given by lattice QCD and quark models. Furthermore, I present a new application of the method to hadron-hadron interactions, considering the pipi scattering problem as an example and showing how the RGPEP can be used to select the relevant energy scale in the physical process.
As it turns out from the study of heavy-quark bound states, the second-order solutions to the RGPEP equation yield a Coulomb potential in the effective quark-(anti)quark component, which appears to be corrected by a harmonic oscillator term. An effective confining effect appears as a result of assuming that the non-Abelian and non-perturbative dynamics generate an effective gluon mass. The framework accounts for gluonic degrees of freedom explicitly, and therefore it is very convenient for the study of hybrids.
References:
[1] M. Gómez-Rocha, S.D. Glazek, Asymptotic freedom in the front-form Hamiltonian for quantum chromodynamics of gluons
Phys.Rev. D92 (2015) no.6, 065005.
[2] S.D. Głazek, M. Gómez-Rocha, J. More, K. Serafin, Renormalized quark–antiquark Hamiltonian induced by a gluon mass ansatz in heavy-flavor QCD
Published in Phys.Lett. B773 (2017) 172-178.
[3] K. Serafin, M. Gómez-Rocha, J. More, S.D. Głazek,
Approximate Hamiltonian for baryons in heavy-flavor QCD
Eur.Phys.J. C78 (2018) no.11, 964.
[4] M. Gómez-Rocha, E. Ruiz Arriola, Wilsonian approach to pipi scattering
In preparation.
| Graduate Student | No |
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