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and
< ν p >= 1− 3 2 w D +∆ rel , (15)
w D is the probability of the D state in the deuteron.
The experimental values of the first moments of the spin structure functions of the
protonΓ p 1 andneutronΓn 1 atQ2 = 5GeV 2 obtainedbytheE155collaborationbyanalyzing
all available data are as follows [3]:
The experimental value for Γ d 1 is
Γ p 1 = 0,118±0,004(stat.)±0,007(sist.), (16)
Γ n 1 = −0,058±0,005(stat.)±0,008(sist.). (17)
Γ d 1
= 0,028±0,004(stat.)±0,005(sist.). (18)
The Bjorken and Ellis-Jaffe sum rules are theoretical relations of the first moments for
the proton and neutron to the fundamental weak coupling constants. The test of the
Bjorken sum rule for Q 2 = 5GeV 2 with the experimental data [3] give Γ p 1−Γ n 1 = 0,176±
0,003(stat.)±0,007(sist.). The first moment ofthe spin structure function ofthe neutron
extracted from the measured first moments of the spin structure functions of the deuteron
Γ D 1 | exp and proton Γ p 1| exp including the relativistic correction is represented in the form
Γ n 1 (Q2 ) = 2Γd 1 (Q2 )| exp
< ν p > −Γp 1 (Q2 )| exp . (19)
At Q 2 = 5GeV 2 , Γ n 1 (Q2 ) = −0.05621. The Bjorken sum at Q 2 = 5GeV 2 gives Γ p 1 −Γ n 1 =
0.17421. There are several different parameterizations for the spin structure function
of the nucleon g N 1 (x,Q 2 ) . In this work, the parameterization of parton distributions
LSS2006 [4] is used. The results were obtained with the Bonn wave function of the
deuteron (w D =0,0425) [5].
References
[1] F.F.Pavlov, Zh. Eksp. Teor. Fiz. 141, 1084(2012)[Sov. Phys. JETP 114, 946(2012)];
arXiv:hep-ph/1206.0676v2.
[2] P.L. Anthony, R.G. Arnold, T. Averett et al., arXiv:hep-ph/0007248v1.
[3] P.L. Anthony et al., Phys. Lett. B 493, 19 (2000).
[4] E. Leader, A.V. Sidorov, and D.B. Stamenov, Phys. Rev. D 75, 074027 (2007).
[5] R. Machleidt, K. Holinde, Ch. Elster, Phys. Rep. 149, 1 (1987).
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