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RELATIVISTIC CORRECTION TO THE FIRST MOMENT OF THE
SPIN-DEPENDENT STRUCTURE FUNCTION OF THE DEUTERON
Γ d 1 (Q2 ) IN THE LIGHT-CONE FORMALISM
F.F. Pavlov †
St.Petersburg State Polytechnical University
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
† E-mail: pavlovfedor@mail.ru, f.pavlov@tuexph.stu.neva.ru
Abstract
Thisarticlecalls attention totheestimation oftherelativistic correction tothemean
proton helicity in the deuteron by way of application of available modern realistic
deuteron wave functions. A receipt has been proposed for the consistent calculation
of relativistic nuclear correction to the first moment of the spin-dependent structure
function of the deuteron. Relativistic correction induced change in the Bjorken sum
rule has been discussed.
If the transverse momentum of a quark is negligible compared to its longitudinal
momentum in the deep inelastic scattering of leptons on protons at high energies, the
4-momentum of the quark can be represented in the form x N p µ , where x N = Q 2 /2pq
(0 < x N < 1) is the Bjorken dimensionless scaling variable for the nucleon, p µ is the 4-
momentum of the nucleon, q µ is the 4-momentum transferred by the virtual photon, and
Q 2 = −q 2 . Furthermore, if the 4-momentum of the quark is represented in the form x d P µ ,
where x d = Q 2 /2Pq and P µ is the 4-momentum of the deuteron, then p µ = (x d /x N )P µ ,
p + = (1/ √ 2)(p 0 +p 3 ) = (x d /x N )P + = zP + , z = x d /x N [1].
The spin structure function of the nucleon g N 1 (x N ,Q 2 ) can be represented in the form
of the half-sum of the spin structure functions of the proton and neutron:
g N 1 (x N ,Q 2 ) = 1 2
[
g
p
1(x N ,Q 2 )+g n 1(x N ,Q 2 ) ] . (11)
The first moment of the spin structure function of the deuteron is
Γ d 1(Q 2 ) =
∫ 1
0
g d 1(x d ,Q 2 )dx d . (12)
Expression for the first moment of the spin structure function of the deuteron can be
separated into the nonrelativistic part and relativistic correction ∆ rel as [1]
(
Γ d 1 (Q2 ) =< ν p > Γ N 1 (Q2 ) = 1− 3 )
2 w D Γ N 1 (Q2 )+∆ rel Γ N 1 (Q2 ), (13)
where first moment of the spin structure function of the nucleon
Γ N 1 (Q2 ) =
∫ 1
0
g N 1 (x N,Q 2 )dx N , (14)
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