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

Static electromagnetic moments of the meson in the instant form of relativistic quantum mechanics
Krutov .F., Polezhaev R.G., (Samara State University) Troitsky V.E., (SINP, Moscow State University)
St.


Experimental information
K.A. Olive (ParticleData Group). Chin.Phys. C. 38, 2014, 090001.

The problems to construct matrix element of current, according to the conditions of covariant and conservation

1. E.P. Briernat, W. Schweiger. Phys. Rev. C. 89, 2014, 055205.

2. J.P.B.C.de Melo, A.N. da Silva, C.S. Melo, T. Frederico. ArXiv:1504.07175v1, 2015, 4. 3. G.H.S. Yabusaki, I. Ahmed, M.Ali Paracha, J.P.B.C.de Melo, Bruno EL-Bennich. Phys. Rev. D, 2015, 8.


The description of the processes with spindiagonal matrix element

(1)

t Q

2


Electromagnetic form factors of the rho-meson

(1.1)

Free electric formfactor

Free quadrupole formfactor
Free magnetic formfactor


Wave functions
(2.1)
(2.2)
Model wave functions

(2.3)

(2.4)

(2.5)


The parameters of constituent quarks
Sachs form factor
1

2

quark magnetic moments

1

A.F. Krutov and V.E. Troitsky, Teor. Mat. Fiz. 1998, 116- 215. S.B Gerasimov. Phys. Lett. B 357 1995, 666­670.

2


The parameters of constituent quarks
3

(3)

4

(4)

3 4

R.G. Arnold, C.E. Carlson, and F. Gross, Phys. Rev. C 21, 1980, 1426. F. Cardarelli, I.L. Grach, I.M. Narodetskii, E. Pace, G. Salmґe, and S. Simula, Phys. Rev. D 53, 1996, 6682.


Relativistic static moment of rho-meson

(5)


Without spin rotation
(6)


The decay constant of rho-meson
5

(7)

Using non-digional parametrization for matrix element (7) , get (8)

(8)

for wave function (2.3)
5

V.V. Andreev. Physics of Particles and Nuclei. V. 8, 2011, 596


Conclusions
Matrix element of the electromagnetic current was constructed for the 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 relativistic static moment and decay constant of rho meson. Numerical calculation of the decay constant shows good agreement with experiment.