Asymptotic freedom in the Hamiltonian approach to binding of color

We derive asymptotic freedom and the $SU(3)$ Yang-Mills $\beta$-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size $s$ is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian $H_s$, which is a matrix written in a basis that depend on the scale (or size) parameter $s$. The effective Hamiltonians $H_s$ and the (regularized) canonical Hamiltonian $H_{0}$ are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.Comment: Presented at XII Quark Confinement and the Hadron Spectrum, Thessaloniki (Greece) August 29th - September 3rd 2016. 8pages, 4 figure

Electroweak hadron structure within a relativistic point-form approach

In this thesis a general relativistic framework for the calculation of the electroweak structure of mesons of arbitrary constituent-quark masses is presented. The physical processes in which the structure is measured, i.e. electron-meson scattering and semileptonic weak decays, are treated in a Poincar\'e invariant way by making use of the point-form of relativistic quantum mechanics. The electromagnetic and weak meson currents are extracted from the 1-photon or 1-W-exchange amplitudes that result from a Bakamjian-Thomas type mass operator for the respective systems. The covariant decomposition of these currents provides the electromagnetic and weak (transition) form factors. The formalism is first applied to the study of heavy-light systems. Problems with cluster separability, which are inherent in the Bakamjian-Thomas construction, are discussed and it is shown how to keep them under control. It is proved that the heavy-quark limit of the electroweak form factors leads to one universal function, the Isgur-Wise function, confirming that the requirements of heavy-quark symmetry are satisfied. These results are discussed and compared with analogous calculations in the front form of dynamics. The formalism is further applied to the study of bound states whose binding is caused by dynamical particle exchange. The problem of how to take into account retardation effects in the particle-exchange potential is formulated and it is shown how they affect the binding energy and wave-function solution for a dynamical model of the deuteron. At the end of this work an example where the Clebsch-Gordan coefficients of the Poincar\'e group are applied is presented. The angular momentum decomposition of chiral multiplets is given in the instant and in the front forms.Comment: PhD Thesis, University of Graz (January 2013). 145 pages, 43 figures, 11 table

Renormalized quark-antiquark Hamiltonian induced by a gluon mass ansatz in heavy-flavor QCD

In response to the growing need for theoretical tools that can be used in QCD to describe and understand the dynamics of gluons in hadrons in the Minkowski space-time, the renormalization group procedure for effective particles (RGPEP) is shown in the simplest available context of heavy quarkonia to exhibit a welcome degree of universality in the first approximation it yields once one assumes that beyond perturbation theory gluons obtain effective mass. Namely, in the second-order terms, the Coulomb potential with Breit-Fermi spin couplings in the effective quark-antiquark component of a heavy quarkonium, is corrected in one-flavor QCD by a spin-independent harmonic oscillator term that does not depend on the assumed effective gluon mass or the choice of the RGPEP generator. The new generator we use here is much simpler than the ones used before and has the advantage of being suitable for studies of the effective gluon dynamics at higher orders than the second and beyond the perturbative expansion.Comment: 8 pages, 2 figures, journal versio

Renormalization group and scattering-equivalent Hamiltonians on a coarse momentum grid

Work supported by the Spanish MINECO and European FEDER funds (FIS2017-85053-C2-1-P) , Junta de Andalucia (grant FQM-225) and Juan de la Cierva-Incorporacion Programme, grant agreement No. IJCI-2017-31531.We consider the 7r7r-scattering problem in the context of the Kadyshevsky equation. In this scheme, we introduce a momentum grid and provide an isospectral definition of the phase shift based on the spectral shift of a Chebyshev angle. We address the problem of the unnatural high momentum tails present in the fitted interactions which reaches energies far beyond the maximal center-of-mass energy of root s = 1.4 GeV. It turns out that these tails can be integrated out by using a block-diagonal generator of the SRG.Spanish Government FIS2017-85053-C2-1-PEuropean Commission FIS2017-85053-C2-1-PJunta de Andalucia FQM-225Juan de la Cierva-Incorporacion Programme IJCI-2017-3153

Electroweak form factors of heavy-light mesons -- a relativistic point-form approach

We present a general relativistic framework for the calculation of the electroweak structure of heavy-light mesons within constituent-quark models. To this aim the physical processes in which the structure is measured, i.e. electron-meson scattering and semileptonic weak decays, are treated in a Poincar\'e invariant way by making use of the point-form of relativistic quantum mechanics. The electromagnetic and weak meson currents are extracted from the 1-$\gamma$ and 1-$W$-exchange amplitudes that result from a Bakamjian-Thomas type mass operator for the respective systems. The covariant decomposition of these currents provides the electromagnetic and weak (transition) form factors. Problems with cluster separability, which are inherent in the Bakamjian-Thomas construction, are discussed and it is shown how to keep them under control. It is proved that the heavy-quark limit of the electroweak form factors leads to one universal function, the Isgur-Wise function, confirming that the requirements of heavy-quark symmetry are satisfied. A simple analytical expression is given for the Isgur-Wise function and its agreement with a corresponding front-form calculation is verified numerically. Electromagnetic form factors for $B^-$ and $D^+$ and weak $B\rightarrow D^{(\ast)}$-decay form factors are calculated with a simple harmonic-oscilllator wave function and heavy-quark symmetry breaking due to finite masses of the heavy quarks is discussed.Comment: 20 pages, 14 figure