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Stanisław D. Głazek

Publications and source records attributed to Stanisław D. Głazek.

15 recordsLinked to original sources
arXiv2026

Gluon mass and small-x dynamics in hadrons

Precise derivation of the logarithmically scale-dependent Hamiltonian eigenstate picture for hadrons in the space of virtual quark and gluon states of the canonical front form of QCD requires addressing first the problem of divergences stronger than logarithmic, and especially the small-x divergences in the dynamics of gluons. We propose to facilitate the regularization and cancellation of these divergences using a gluon mass parameter and an auxiliary color-octet scalar field corresponding to the longitudinally polarized gluons. The auxiliary field decouples from the hadronic constituent dynamics when the mass parameter tends to zero, as required in the gauge theory. The same method applies in the cancellation of the quadratic ultraviolet transverse divergences in the self-interactions. After explaining how the method works in computations of the scattering amplitudes, we describe its application to the bound-state eigenvalue problems. We focus on the results it leads to already in the second-order weak-coupling expansion for effective Hamiltonians of heavy quarks. They include the concept of confinement in an effective theory with the gluon mass parameter sent to zero and a heuristic scenario concerning extension of the Hamiltonian approach to the dynamics of light quarks.

hep-th↗
arXiv2021

Elementary example of exact effective-Hamiltonian computation

We present an exact computation of effective Hamiltonians for an elementary model obtained from the Yukawa theory by going to the limit of bare fermions being infinitely heavy and bare bosons being at rest with respect to the fermions that emit or absorb them. The coupling constant can be arbitrarily large. The Hamiltonians are computed by solving the differential equation of the renormalization group procedure for effective particles (RGPEP). Physical fermions, defined in the model as eigenstates of the effective Hamiltonians, are obtained in the form of an effective fermion dressed with a coherent state of effective bosons. The model computation illustrates the method that can be used in perturbative computations of effective Hamiltonians for realistic theories. It shows the mechanism by which the perturbative expansion and Tamm-Dancoff approximation increase in accuracy along the RGPEP evolution.

hep-th↗
arXiv2018

Approximate Hamiltonian for baryons in heavy-flavor QCD

Aiming at relativistic description of gluons in hadrons, the renormalization group procedure for effective particles (RGPEP) is applied to baryons in QCD of heavy quarks. The baryon eigenvalue problem is posed using the Fock-space Hamiltonian operator obtained by solving the RGPEP equations up to second order in powers of the coupling constant. The eigenstate components that contain three quarks and two or more gluons are heuristically removed at the price of inserting a gluon-mass term in the component with one gluon. The resulting problem is reduced to the equivalent one for the component of three quarks and no gluons. Each of the three quark-quark interaction terms thus obtained consists of a spin-dependent Coulomb term and a spin-independent harmonic oscillator term. Quark masses are chosen to fit the lightest spin-one quarkonia masses most accurately. The resulting estimates for bbb and ccc states match estimates obtained in lattice QCD and in quark models. Masses of ccb and bbc states are also estimated. The corresponding wave functions are invariant with respect to boosts. In the ccb states, charm quarks tend to form diquarks. The accuracy of our approximate Hamiltonian can be estimated through comparison by including components with two gluons within the same method.

hep-ph↗
arXiv2018

The Ridge Effect, Azimuthal Correlations, and other Novel Features of Gluonic String Collisions in High Energy Photon-Mediated Reactions

One of the remarkable features of high-multiplicity hadronic events in proton-proton collisions at the LHC is the fact that the produced particles appear as two "ridges", opposite in azimuthal angle $ϕ$, with approximately flat rapidity distributions. This phenomena can be identified with the inelastic collision of gluonic flux tubes associated with the QCD interactions responsible for quark confinement in hadrons. In this paper we analyze the ridge phenomena when the collision involves a flux tube connecting the quark and antiquark of a high energy real or virtual photon. We discuss gluonic tube string collisions in the context of two examples: electron-proton scattering at a future electron-ion collider or the peripheral scattering of protons accessible at the LHC. A striking prediction of our analysis is that the azimuthal angle of the produced ridges will be correlated with the scattering plane of the electron or proton producing the virtual photon. In the case of $ep \to eX$, the final state $X$ is expected to exhibit maximal multiplicity when the elliptic flow in $X$ is aligned with the electron scattering plane. In the $pp \to ppX$ example, the multiplicity and elliptic flow in $X$ are estimated to exhibit correlated oscillations as functions of the azimuthal angle $Φ$ between the proton scattering planes. In the minimum-bias event samples, the amplitude of oscillations is expected to be on the order of 2 to 4 percent of the mean values. In the events with highest multiplicity, the oscillations can be three times larger than in the minimum-bias event samples.

hep-ph↗
arXiv2017

Renormalization group procedure for potential $-g/r^2$

Schrödinger equation with potential $-g/r^2$ exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at $r=0$. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of $g$.

quant-ph↗
arXiv2017

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.

hep-ph↗
arXiv2017

Elementary example of energy and momentum of an extended physical system in special relativity

An instructive paradox concerning classical description of energy and momentum of extended physical systems in special relativity theory is explained using an elementary example of two point-like massive bodies rotating on a circle in their center-of-mass frame of reference, connected by an arbitrarily light and infinitesimally thin string. Namely, from the point of view of the inertial observers who move with respect to the rotating system, the sums of energies and momenta of the two bodies oscillate, instead of being constant in time. This result is understood in terms of the mechanism that binds the bodies: the string contributes to the system total energy and momentum no matter how light it is. Its contribution eliminates the unphysical oscillations from the system total four-momentum. Generality of the relativistic approach, applied here to the rotor example, suggests that in every extended physical system its binding mechanism contributes to its total energy and momentum.

physics.class-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↗
arXiv2015

Asymptotic freedom of gluons in the Fock space

Asymptotic freedom of gluons is described in terms of a family of scale-dependent renormalized Hamiltonian operators acting in the Fock space. The Hamiltonians are obtained by applying the renormalization group procedure for effective particles to quantum Yang-Mills theory.

hep-th↗
arXiv2014

Effective confining potentials for QCD

We observe that the linear potential used as a leading approximation for describing color confinement in the instant form of dynamics corresponds to a quadratic confining potential in the front form of dynamics. In particular, the instant-form potentials obtained from lattice gauge theory and string models of hadrons agree with the potentials determined from models using front-form dynamics and light-front holography, not only in their shape, but also in their numerical strength.

hep-ph↗
arXiv2013

Model of the AdS/QFT duality

It is observed and illustrated in a greatly simplified example that the idea of AdS/QFT duality can be considered a special case of the Ehrenfest's correspondence principle between classical and quantum mechanics in the context of relativistic dynamics of fields and renormalization group procedure for effective particles.

hep-ph↗
arXiv2013

Neutrino oscillations in the front form of Hamiltonian dynamics

Since future, precise theory of neutrino oscillations should include the understanding of the neutrino mass generation and a precise, relativistic description of hadrons, and observing that such a future theory may require Dirac's FF of Hamiltonian dynamics, we provide a preliminary FF description of neutrino oscillations using the Feynman--Gell-Mann-Levy version of an effective theory in which leptons interact directly with whole nucleons and pions, instead of with quarks via intermediate bosons. The interactions are treated in the lowest-order perturbative expansion in the coupling constants in the effective theory, including a perturbative solution of the coupled constraint equations. Despite missing quarks and their binding mechanism, the effective Hamiltonian description is sufficiently precise for showing that the standard oscillation formula results from the interference of amplitudes with different neutrinos in virtual intermediate states. This holds provided that the inherent experimental uncertainties of preparing beams of incoming and measuring rates of production of outgoing particles are large enough for all of the different neutrino intermediate states to contribute as alternative virtual paths through which the long-baseline scattering process can manifest itself. The result that an approximate, effective FF theory reproduces the standard oscillation formula at the level of transition rates for currently considered long-baseline experiments--even though the space-time development of scattering is traced differently and the relevant interaction Hamiltonians are constructed differently than in the commonly used IF of dynamics--has two implications. It shows that the common interpretation of experimental results is not the only one, and it opens the possibility of considering more precise theories taking advantage of the features of the FF that are not available in the IF.

hep-ph↗
arXiv2007

This manuscript (hep-th/9906140v1) is incomplete

This manuscript (hep-th/9906140v1) is incomplete. Please read instead S. D. Głazek, T. Masłowski, Renormalized Poincaré algebra for effective particles in quantum field theory, Phys.Rev. D65 (2002) 065011, (hep-th/0110185).

hep-th↗
arXiv2001

Renormalized Poincaré algebra for effective particles in quantum field theory

Using an expansion in powers of an infinitesimally small coupling constant $g$, all generators of the Poincaré group in local scalar quantum field theory with interaction term $g ϕ^3$ are expressed in terms of annihilation and creation operators $a_λ$ and $a^\dagger_λ$ that result from a boost-invariant renormalization group procedure for effective particles. The group parameter $λ$ is equal to the momentum-space width of form factors that appear in vertices of the effective-particle Hamiltonians, $H_λ$. It is verified for terms order 1, $g$, and $g^2$, that the calculated generators satisfy required commutation relations for arbitrary values of $λ$. One-particle eigenstates of $H_λ$ are shown to properly transform under all Poincaré transformations. The transformations are obtained by exponentiating the calculated algebra. From a phenomenological point of view, this study is a prerequisite to construction of observables such as spin and angular momentum of hadrons in quantum chromodynamics.

hep-th↗