arXiv subjects

María Gómez-Rocha

Publications and source records attributed to María Gómez-Rocha.

27 records · Page 2Linked to original sources

arXiv2016

From asymptotic freedom toward heavy quarkonia within the renormalization group procedure for effective particles

The renormalization group procedure for effective particles (RGPEP), developed as a nonperturbative tool for constructing bound states in quantum field theories, is applied to QCD. The approach stems from the similarity renormalization group and introduces the concept of effective particles. It has been shown that the RGPEP passes the test of exhibiting asymptotic freedom. We present the running of the Hamiltonian coupling with the renormalization-group scale and summarize the basic elements needed in the formulation of the bound-state problem.

hep-ph↗

arXiv2016

Asymptotic freedom in the Hamiltonian approach to binding of color

We derive asymptotic freedom and the $SU(3)$ Yang-Mills $β$-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.

hep-ph↗

arXiv2016

Asymptocic Freedom of Gluons in Hamiltonian Dynamics

We derive asymptotic freedom of gluons in terms of the renormalized $SU(3)$ Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles (RGPEP) to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of $g$ up to third order. The resulting three-gluon vertex is a function of the scale parameter $s$ that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian $β$-function coincides with the one obtained in an earlier calculation using a different generator.

hep-ph↗

arXiv2013

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 Poincaré 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 Poincaré group are applied is presented. The angular momentum decomposition of chiral multiplets is given in the instant and in the front forms.

hep-ph↗

arXiv2012

Angular momentum decomposition of chiral multiplets in front form

In this article we derive the unitary transformation that relates the $q\bar q$ chiral basis $\{R; I J^{PC} \}$ to the $\{I; ^{2S+1}L_J\}$-basis in a front-form framework. From the most general expression for the Clebsch-Gordan coefficients of the Poincaré group one can see that the chiral limit brings the angular momentum coupling into a simple form that permits the relation in terms of SU(2) Clebsch-Gordan coefficients. We demonstrate that such a transformation is identical to the one was obtained for canonical spin in the instant form.

hep-th↗

arXiv2012

Electroweak hadron structure within a point-form approach

We present a relativistic point-form approach for the calculation of electroweak form factors of few-body bound states. As an example, the transition form factors for the semileptonic weak decay $B\to D^*e\bar ν_e$ are discussed and it is sketched how they can be extracted unambiguously from the invariant transition amplitude that describes the process. It is shown how these form factors go over into one universal function, the Isgur-Wise function in the heavy-quark limit, $m_Q\to \infty$, and comparison with the available experimental data is made.

hep-ph↗

arXiv2012

Electroweak hadron structure in point-form dynamics -- heavy-light systems

We present a general formalism that uses the point form of relativistic Hamiltonian dynamics to describe the electroweak structure of heavy-light mesons within constituent quark models. We study the heavy quark limit (i.e. $m_Q\to \infty$) and check that the predictions of heavy quark symmetry are satisfied. A simple analytic expressions is given for the Isgur-Wise function. In addition, cluster properties and the relation of our approach to front form calculations are discussed.

hep-ph↗

arXiv2012

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 Poincaré invariant way by making use of the point-form of relativistic quantum mechanics. The electromagnetic and weak meson currents are extracted from the 1-$γ$ 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.

hep-ph↗

arXiv2011

Form Factors of Few-Body Systems: Point Form Versus Front Form

We present a relativistic point-form approach for the calculation of electroweak form factors of few-body bound states that leads to results which resemble those obtained within the covariant light-front formalism of Carbonell et al. Our starting points are the physical processes in which such form factors are measured, i.e. electron scattering off the bound state, or the semileptonic weak decay of the bound state. These processes are treated by means of a coupled-channel framework for a Bakamjian-Thomas type mass operator. A current with the correct covariance properties is then derived from the pertinent leading-order electroweak scattering or decay amplitude. As it turns out, the electromagnetic current is affected by unphysical contributions which can be traced back to wrong cluster properties inherent in the Bakamjian-Thomas construction. These spurious contributions, however, can be separated uniquely, as in the covariant light-front approach. In this way we end up with form factors which agree with those obtained from the covariant light-front approach. As an example we will present results for electroweak form factors of heavy-light systems and discuss the heavy-quark limit which leads to the famous Isgur-Wise function.

hep-ph↗