Документ взят из кэша поисковой машины. Адрес оригинального документа : http://qfthep.sinp.msu.ru/talks2015/1435258212_Krutov_Polezhaev_Troitsky1_2015.pdf Дата изменения: Thu Jun 25 21:50:12 2015 Дата индексирования: Sat Apr 9 23:34:55 2016 Кодировка:

The XXII International Workshop High Energy Physics and Quantum Field Theory June 24­ July 1, 2015 Samara, Russia

Radiative decays V P * in the instant form of relativistic quantum mechanics

Krutov .F., Polezhaev R.G., (Samara State University) Troitsky V.E., (SINP, Moscow State University)
St.


Problems description of bound state
1. Quantum chromodynamics (QCD) gives a reliable description of the so-called "hard" processes (at large momentum transfers). In this regard, it is necessary to 1,2 consider different options for composite quark models.

,3

2. The construction of matrix element of the current 1 according to the conditions of covariance and conservation.
1

,2,3

A.V. Anisovich, V.V. Anisovich, L.G. Dakhno, M.A. Matveev, V.A. Nikonov, A.V. Sarantsev. Phys.Atom.Nucl. Vol. 73, 2010, 462-477. Shan Cheng, Zhen-Jun Xiano. Phys.Rev. D. 90, 2014, 076001.

2 3

Jianghao Yu, Bo-Wen Xiano, Bo-Qian Ma. J.Phys. G. 34, 2007, 1845-1860.


Relativistic quantum mechanics

4

· The construction of the electromagnetic current operator with the

conditions of current conservation and Lorentz ­ covariance.
· Good description of the meson electroweak properties of meson

and deuteron in the frame of instant form of dynamics.
Q2 · Asymptotic of the electromagnetic form factors at

coinciding with predictions QCD and quark counting rules. · The impulse approximation does not violate the conditions of covariates and current conservation .
4

A.F. Krutov, V.E. Troitsky. Physics of Particles and Nuclei. Vol. 40, 2009, 136


The construction basis in the frame of instant form of relativistic quantum mechanics
In one-particle basis:

(1)

In two-particle basis:

(2)


The description of the processes with spindiagonal matrix element

(3)
modified impulse approximation

Free electromagnetic form factor with (J=J'= L=L'= S=S' =0)

(4)


The invariant parameterization of the e.m. current for the two particles system (non-diagonal case)
Breit system

(5)

(6)


The invariant parameterization of the e.m. current for the two particles system (non-diagonal case)
the transition to the canonical basis
5

(7)

(8)

5

A.R. Edmonds. Geneva, 1955


Free non-diagonal form factors
In one-particle basis:

(9)

(10) (11)

(12)


Form factor of the free system

(13)

Form factor of the composite system
(14)


The variational method
(15)

(16)

Harmonic oscillation wave function

(17)

(18)


Transition form factors measured in experiment

(19)

(20) (20.1)

(21)


Solid line ­ our model Green and blue dashed line- LFQM 7 Dotted line ­ VMD model
3.0 2.5
3

6,7

GeV Q4 F Q
2

2.0 1.5 1.0 0.5 0.0 1 2 3 Q
2

4 GeV
2

5

6

7

8

6 7

F. Cardarelli, I.L. Grach, I.M. Narodetskii, G.Salme, S. Simula. Phys.Lett. B 359, 1995, 1; J. Yu, Bo-Wen Xiao, Bo-Qiang Ma, J. Phys. G 34, 2007, 1845.


0.10 0.08

GeV Q4 F Q
2

3

0.06 0.04 0.02 0.00 0.0 0.1 0.2 Q
8
2

0.3 GeV
2

0.4

0.5

experiment

8

W.N. Yao (Particle Data Group). J.Phys.G: Nucl.Part. Phys, Vol. 35, 2006, 1


Conclusions
Matrix element of the electromagnetic current was constructed for the non-diagonal case in the instant form of RQM in the impulse approximation.
The electromagnetic current satisfies the conservation law and Lorentz-covariance conditions.

Analytic expression was obtained for the transition form factors in the radiative decay rho meson. Numerical calculation of the transition form factor shows good agreement with other approaches at small momentum transfers (is the matching principle).