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V. E. Troitsky

Publications and source records attributed to V. E. Troitsky.

At least 19 recordsLinked to original sources
arXiv2026

Double integral representation in the invariant masses of a composite system and nonperturbative calculation of the asymptotics of light-meson electromagnetic form factors

We obtain nonperturbative asymptotic expansions of the electromagnetic form factors of the pi and rho mesons at large spacelike momentum transfer, Q^2->\infty. The calculation is based on a double integral representation in the invariant masses of the composite system. The model parameters are kept at the values fixed in the authors' earlier description of meson electroweak properties. We show that, in the limit of vanishing constituent-quark mass, with the constituent quarks taken to be pointlike, the asymptotic ratio of the longitudinally polarized rho-meson to pion form factors in the helicity basis is consistent with the prediction of perturbative QCD (pQCD) within the adopted parameter ranges.

hep-ph↗
arXiv2025

A step towards estimation of the neutral-hadron size: the gravitational mass radius of pi0 meson in a relativistic theory of composite particles

We extend our nonperturbative essentially relativistic approach, elaborated previously, to perform an approximate estimation of the size of pi0 meson. We present detailed argumentation for choosing the mass mean square radius (MSR) for this purpose. Its value calculated in our approach, using three model quark-antiquark wave functions in pion, is (0.5-0.53) fm. The neutral-pion electromagnetic form factor is zero in accordance with the charge-conjugation symmetry. We demonstrate ambiguities encountered when using standard definitions of mechanical MSR for the size. We discuss MSRs obtained in various approaches and their comparison with each other and with our results.

hep-ph↗
arXiv2023

Pion gravitational form factors at large momentum transfer in the instant-form relativistic impulse approximation approach

We extend our relativistic theory of gravitational structure of composite hadrons to obtain the pion gravitational form factors at large momentum transfers. The approach was used in the case of intermediate region of the variable in our preceding works arXiv:2010.11640 and arXiv:2201.04991. The calculation is carried out in the framework of a relativistic composite-particle model complemented by the special relativistic form of impulse approximation. It is found that in the limit of massless and pointlike quarks, the obtained asymptotic expansion coincides with the predictions of perturbative QCD for gravitational pion form factors. The principal contribution to the asymptotics, coinciding with the predictions of QCD, is given by the relativistic effect of spin rotation. In particular, the asymptotics of the D form factor is completely determined by this kinematic effect. Several constraints on the allowed form of gravitational form factors of quarks are derived.

hep-ph↗
arXiv2022

Relativistic composite-particle theory of the gravitational form factors of pion: quantitative results

We use a version of the instant-form relativistic quantum mechanics of composite systems to obtain the gravitational form factors of the pion in a common approach to its electroweak and gravitational properties. In the preceding work [arXiv:2010.11640] we formulated the mathematical background, presented the principal scheme of calculation and testified the obtained qualitative results to satisfy the general constraints given by the principles of the theory of hadron structure. In the present work we give the detailed calculation of the gravitational form factors in large range of momentum transfer, their static limits and the slopes at zero value, the mean-square mass and mechanical radii of the pion. Now we take into account the qravitational structure of the constituent quarks. We show that the results are almost insensitive to the type of the model two-quark wave function in a close analogy to the case of the pion electromagnetic form factor. We present a correct calculation of the form factor $D$ and corresponding matrix element of the energy-momentum tensor, going beyond the scope of the modified impulse approximation. Most of the parameters that we use for the calculation had been fixed even earlier in our works on the pion electromagnetic form factors. The only free parameter is the $D$-term of the constituent quark, which we fix by fitting the result for the slope at zero of the normalized to pion $D$-term form factor $D$ of pion, to a choosen experimental value.

hep-ph↗
arXiv2021

K0 and K+ meson electromagnetic form factors: a nonperturbative relativistic quark model versus experimental, perturbative and lattice Quantum-Chromodynamics results

It has been previously shown that a particular nonperturbative constituent-quark model of hadrons describes experimental measurements of electromagnetic form factors of light charged mesons through a small number of common phenomenological parameters, matching at the same time the Quantum-Chromodynamics (QCD) asymptotics for the pi-meson form factor at large momentum transfer. Here we start with the determination of the K0 electromagnetic form factor in this approach. Precise measurement of the K0 charge radius makes it possible to constrain model parameters with high accuracy. Then, with all parameters fixed, we revisit the K+ form factor and find that it matches experimental measurements in the infrared, lattice results at moderate momentum transfer and the perturbative QCD asymptotics in the ultraviolet. In this way we obtain a narrow constraint on the K+ charge radius, = 0.403 +0.007 -0.006 fm^2, and extend the successful infrared-ultraviolet connection from pi to K mesons.

hep-ph↗
arXiv2021

The K-meson form factor and charge radius: linking low-energy data to future high-energy Jefferson Laboratory results

Starting from a successful model of the pi-meson electromagnetic form factor, we calculate the similar form factor, f_K(Q^2), of the charged K meson for a wide range of the momentum transfer squared, Q^2. The only remaining free parameter is to be determined from the measurements of the K-meson charge radius, r_K. We fit this single parameter to the published data of the NA-7 experiment which measured f_K(Q^2) at Q^2->0 and determine our preferred range of r_K, which happens to be close to recent lattice results. Still, the accuracy in the determination of r_K is poor. However, future measurements of the K-meson electromagnetic form factor at Q^2<~5.5 GeV^2, scheduled in Jefferson Laboratory for 2017, will test our approach and will reduce the uncertainty in r_K significantly.

hep-ph↗
arXiv2021

Pion gravitational form factors in a relativistic theory of composite particles

We extend our relativistic theory of electroweak properties of composite systems to describe simultaneously the gravitational form factors of hadrons. The approach is based on a version of the instant-form relativistic quantum mechanics and makes use of the modified impulse approximation. We exploit the general method of the relativistic invariant parametrizaton of local operators to write the energy-momentum tensor of a particle with an arbitrary spin. We use the obtained results to calculate the gravitational form factors of the pion assuming point-like constituent quarks. All but one parameters of our first-principle model were fixed previously in works on electromagnetic form factors. The only free parameter, $D_{q}$, is a characteristic of the gravitational form factor of a constituent quark. The derived form factors of the pion satisfy the constraints given by the general principles of the quantum field theory of hadron structure. The calculated gravitational form factors and gravitational mean-square radius are in a reasonable agreement with known results.

hep-ph↗
arXiv2018

Quadrupole moments of spin-1 systems: the rho meson, the S-wave deuteron and some general constraints

We costruct the relativistic operator of the quadrupole moment of two-particle composite spin one systems with zero orbital moment of the relative motion and derive explicit analytical expression for the quadrupole moment using the approach to relativistic composite systems based on our version of the instant-form relativistic quantum mechanics (RQM). We calculate the quadrupole moments of the rho meson and of the S-wave deuteron without any free parameters, using our unified pi&rho model (Phys. Rev.D 93, 036007 (2016); 97, 033007 (2018)) and our previous results on deuteron. Our calculation gives Q_rho=-0.158+-0.04 GeV^-2 and Q_d=-1.4*10^-4 GeV^-2. Having in our disposition the rather general form of the quadrupole-moment operator we for the first time formulate the problem of the upper and lower bounds for possible values of the quadrupole moment of a two-particle system with indicated quantum numbers for a large range of constituent masses, and partially solve it.

hep-ph↗
arXiv2018

Magnetic moment of the rho meson in instant-form relativistic quantum mechanics

We derive an explicit analytical expression for the magnetic dipole moment of the rho meson, mu_rho, in a relativistic constituent-quark model. We adopt our relativistic approach to composite systems, modified instant-form (mIF) Relativistic Quantum Mechanics (RQM), that we used particularly to construct a unified pi&rho model (Phys. Rev. D93, 036007 (2016) = arXiv:1602.00907) describing electroweak properties of light mesons. This model provides a parameter-free calculation to give mu_rho=(2.16+-0.03) [e/2M_rho] which is in accordance with the conventional experimental data. The magnetic, quadrupole and charge form factors also are derived and presented. We consider the small uncertainty of our value of magnetic moment as one of undoubted advantages of the method. A comparison is made with recent lattice QCD results and previous calculations using a variety of methods.

hep-ph↗
arXiv2017

Relativistic constituent model in sector of light mesons

We present a brief survey of some results on electroweak properties of composite systems that are obtained in the frameworks of our version of the instant form of relativistic quantum mechanics (RQM). Our approach describes well the $π$- and the $ρ$- mesons in wide range of momentum transfers $Q^{2}$. At large $Q^{2}$ the obtained pion form factor asymptotics coincides with that of QCD predictions. The method permits to perform analytic continuation of pion form factor to complex plane of momentum transfers that is in accordance with predictions of quantum field theory.

hep-ph↗
arXiv2016

The radius of the rho meson determined from its decay constant

We present a unified model describing electroweak properties of the pi and rho mesons. Using a general method of relativistic parametrization of matrix elements of local operators, adjusted for the nondiagonal in total angular momentum case, we calculate the rho-meson lepton-decay constant f_rho using the same parameters of free constituent quarks that have ensured exclusively good results for the pi meson previously. The only free parameter, characterizing quark interactions, which include additional spin-spin contribution and hence differ from the $π$-meson case, is fixed by matching the decay constant to its experimental value. The mean square charge radius is calculated, =(0.56+-0.04) fm^2. This result verifies, for the rho-meson case, the conjecture of equality between electromagnetic and strong radii of hadrons tested previously for proton, pi and K mesons.

hep-ph↗
arXiv2015

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.

hep-ph↗
arXiv2013

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.

hep-ph↗
arXiv2009

Nonperturbative relativistic approach to pion form factor: predictions for future JLab experiments

Some predictions concerning possible results of the future JLab experiments on the pion form factor F_pi(Q^2) are made. The calculations exploit the method proposed previously by the authors and based on the instant-form Poincare invariant approach to pion considered as a quark-antiquark system. Long ago, this model has predicted with surprising accuracy the values of F_pi(Q^2) measured later in JLab experiment. The results are almost independent from the form of wave function. The pion mean square radius and the decay constant f_pi also agree with experimental values. The model gives power-like asymptotic behavior of F_pi(Q^2) at high momentum transfer in agreement with QCD predictions.

nucl-th↗
arXiv2008

Asymptotics of the deuteron form factors in the nucleon model and JLab experiments

Using the instant form dynamics of Poincaré invariant quantum mechanics and the modified relativistic impulse approximation proposed previously we calculate asymptotics of electromagnetic form factors for the deuteron considered as two--nucleon system. We show that today experiment on the elastic $ed$-scattering has reached asymptotic regime. The possible range of momentum transfer when the quark degrees of freedom could be seen in future JLab experiments is estimated. The explicit relation between the behavior of deuteron wave function at $r=0$ and the form factors asymptotics is obtained. The conditions on wave functions to give the asymptotics predicted by QCD and quark counting rules are formulated.

nucl-th↗
arXiv2007

Asymptotic estimation of some multiple integrals and the electromagnetic deuteron form factors at high momentum transfer

A theorem about asymptotic estimation of multiple integral of a special type is proved for the case when the integrand peaks at the integration domain bound, but not at a point of extremum. Using this theorem the asymptotic expansion of the electromagnetic deuteron form factors at high momentum transfers is obtained in the framework of two-nucleon model in both nonrelativistic and relativistic impulse approximations. It is found that relativistic effects slow down the decrease of deuteron form factors and result in agreement between the relativistic asymptotics and experimental data at high momentum transfers.

nucl-th↗
arXiv2006

Deuteron tensor polarization component T_20(Q^2) as a crucial test for deuteron wave functions

The deuteron tensor polarization component T_20(Q^2) is calculated by relativistic Hamiltonian dynamics approach. It is shown that in the range of momentum transfers available in to-day experiments, relativistic effects, meson exchange currents and the choice of nucleon electromagnetic form factors almost do not influence the value of T_20(Q^2). At the same time, this value depends strongly on the actual form of the deuteron wave function, that is on the model of NN-interaction in deuteron. So the existing data for T_20(Q^2) provide a crucial test for deuteron wave functions.

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