Transition from a relativistic constituent-quark model to the quantum-chromodynamical asymptotics: a quantitative description of the pion electromagnetic form factor at intermediate values of the momentum transfer

We adopt a non-perturbative relativistic constituent-quark model for the pi-meson electromagnetic form factor, which have successfully predicted experimental results, and supplement it with the effective momentum-dependent quark mass to study quantitatively the transition to the perturbative QCD asymptotics. The required asymptotical behaviour (including both the Q^{-2} fall-off and the correct coefficient) settles down automatically when the quark mass is switched off; however, the present experimental data on the form factor suggest that this cannot happen at the values of the momentum transfer below ~10 GeV^2. The effective constituent-quark mass below this scale acquires substantial non-perturbative contributions.Comment: 7 pages, RevTex 4.1, 5 figures. V2: a reference added, minor textual changes, version accepted by Phys. Rev.

Constraining scenarios of the soft/hard transition for the pion electromagnetic form factor with expected data of 12-GeV Jefferson Lab experiments and of the Electron-Ion Collider

It has been shown previously [PRD 88 (2013) 093005, arXiv:1310.1770] that a non-perturbative relativistic constituent-quark model for the pi-meson electromagnetic form factor allows for a quantitative description of the soft/hard transition, resulting in the correct Quantum-Chromodynamical asymptotics, including normalization, from the low-energy data without further parameter tuning. This happens universally whenever the constituent-quark mass is switched off. The energy range where the transition happens is therefore determined by the quark-mass running at intermediate energies and is not tightly constrained theoretically. Here we consider possible ways to pin down this energy range with coming experimental data. We demonstrate that expected experimental uncertainties of the 12-GeV Jefferson-Lab data are larger than the span of predictions of the model, so these data might be used for testing the model but not for determination of the soft/hard transition scale. Contrary, the projected Electron-Ion Collider will be capable of pinning down the scale.Comment: V2: 11 pages, 3 figures (presentation improved; results unchanged; matches the PRD accepted version

Hilbert C*-modules from group actions: beyond the finite orbits case

Continuous actions of topological groups on compact Hausdorff spaces $X$ are investigated which induce almost periodic functions in the corresponding commutative C*-algebra. The unique invariant mean on the group resulting from averaging allows to derive a C*-valued inner product and a Hilbert C*-module which serve as an environment to describe characteristics of the group action. For uniformly continuous, Lyapunov stable actions the derived invariant mean $M(\phi_x)$ is continuous on $X$ for any element $\phi \in C(X)$, and the induced C*-valued inner product corresponds to a conditional expectation from $C(X)$ onto the fixed point algebra of the action defined by averaging on orbits. In the case of selfduality of the Hilbert C*-module all orbits are shown to have the same cardinality. Stable actions on compact metric spaces give rise to C*-reflexive Hilbert C*-modules. The same is true if the cardinality of finite orbits is uniformly bounded and the number of closures of infinite orbits is finite. A number of examples illustrate typical situations appearing beyond the classified cases.Comment: 18 page

Instant-Form Approach to Two-Body Systems

We present a relativistic treatment of the problem of soft electromagnetic structure by the modified instant form of relativistic Hamiltonian dynamics. Our approach uses relativistic parametrization and so picks out the relativistic invariant quantities on each stage of the calculation. The electromagnetic current matrix element satisfies the current conservation law automatically. We use relativistic modified impulse approximation. It is constructed in relativistic invariant way. For composite systems (including the spin 1 case) the approach guarantees the uniqueness of the solution and it does not use such concepts as "good" and "bad" current components. The approach describes correctly the spin Wigner rotation and so gives the correct (QCD) asymptotic.Comment: 9 pages, latex, no figures Talk presented by V.T. at the Workshop on Relativisic Approaches to Few-Body Systems, Groningen, July 21, 199

A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras

A C*-algebra $A$ is C*-reflexive if any countably generated Hilbert C*-module $M$ over $A$ is C*-reflexive, i.e. the second dual module $M''$ coincides with $M$. We show that a commutative C*-algebra $A$ is C*-reflexive if and only if for any sequence $I_k$ of disjoint non-zero C*-subalgebras, the canonical inclusion $\oplus_k I_k\subset A$ doesn't extend to an inclusion of $\prod_k I_k$.Comment: 9 page

Relativistic Effects in Two-Body Systems: pi- and K-mesons and Deuteron

The electromagnetic form factors of $\pi$ and $K$ mesons and deuteron are calculated in modified impulse approximation using instant form of relativistic Hamiltonian dynamics. The different model wave functions are used. Meson wave function parameters are fixed by fitting the mean square radius of meson. The internal quark structure is taken into account through electromagnetic quark form factor and quark anomalous magnetic moments. Results of our calculations of electroweak structure of pion and kaon and electromagnetic deuteron properties agree well with the available experimental data. The meson form factors asymptotics at large momentum transfer is the same as in perturbative QCD. Some predictions about CEBAF experiments are given.Comment: 11 pages, latex, 7 .ps figures. Poster presented by V.T. at the 15th International Conference on Few-Body Problems in Physics, Groningen, July 22-26, 199

Comment on New Results for the Charged Pion Electromagnetic Form Factor

In the paper nucl-ex/0010009 by The Jefferson Lab F_pi Collaboration the new results for the charged pion electromagnetic form factor are presented. The approach given in our paper hep-ph/9811318, "On a possible estimation of the constituent--quark parameters from Jefferson Lab experiments on the pion form factor" makes it possible to estimate the mass of constituent quark from such kind of experiment. Now this estimation gives M=0.21 GeV.Comment: 2 page

Electroweak properties of light mesons in relativistic hamiltonian dynamics

The calculation of lepton decay constants and electromagnetic form factors of pion and kaon is performed in the framework of relativistic hamiltonian dynamics. The different model wave function is used. Wave function parameters are fixed from fit of mean square radius of meson. The internal quark structure is taken into account by electromagnetic quark form factor and quark anomalous magnetic moment. The pion and kaon form factors depend only weakly on model wave function. Strong dependence of these values on quark anomalous magnetic moment is obtained in the transfer momentum region of CEBAF experiments.Comment: 6 pages, LATEX, 1 postscript figure. Talk at XIII International Seminar on High Energy Physics Problems, 2-7 September, 1996, Dubna, Russi

Relativistic Instant--Form Approach to the Structure of Two-Body Composite Systems. II. Nonzero Spin

The relativistic approach to electroweak properties of two-particle composite systems developed in previous work is generalized here to the case of nonzero spin. This approach is based on the use of the instant form of relativistic Hamiltonian dynamics. The generalization makes use of a special mathematical technique for the parametrization of matrix elements of electroweak current operators in terms of form factors. In this technique the parametrization is a realization of theWigner--Eckart theorem on the Poincar\'e group and form factors are reduced matrix elements. As in the case of zero spin the electroweak current matrix element satisfies the relativistic covariance conditions and in the case of electromagnetic current it also automatically satisfies the conservation law. Physical approximations such as, for example, the relativistic impulse approximation, are formulated in terms of reduced matrix elements. The electromagnetic structure of $\rho$ meson is calculated as an example of realization of the technique proposed.Comment: 20 pages, 4 figures, 1 table. This is the second part of the paper published in Phys.Rev.C 65, 045501 (2002

IceCube astrophysical neutrinos without a spectral cutoff and (10^15-10^17) eV cosmic gamma radiation

We present a range of unbroken power-law fits to the astrophysical-neutrino spectrum consistent with the most recent published IceCube data at the 68\% confidence level. Assuming that the neutrinos originate in decays of pi mesons, we estimate accompanying gamma-ray fluxes for various distributions of sources, taking propagation effects into account. We then briefly discuss existing experimental results constraining PeV to EeV diffuse gamma-ray flux and their systematic uncertainties. Several scenarios are marginally consistent both with the KASKADE and CASA-MIA upper limits at (10^15-10^16) eV and with the EAS-MSU tentative detection at ~10^17 eV, given large systematic errors of the measurements. Future searches for the diffuse gamma-ray background at sub-PeV to sub-EeV energies just below present upper limits will give a crucial diagnostic tool for distinguishing between the Galactic and extragalactic models of the origin of the IceCube events.Comment: 11 pages, 3 figures, revtex. V.2: references added and correcte