References - Bogoliubov Laboratory of Theoretical Physics - JINR

LL
D
1
0.5
0
-0.5
-1
-1.5
NOMAD
HERMES
E665
COMPASS
Λ
-0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8
xF
LL
D
1.5
1
0.5
0
-0.5
NOMAD
E665
COMPASS
Λ
-0.2 0 0.2 0.4 0.6 0.8
xF
(a) (b)
Figure 2: The DLL dependence on xF for the Λ (a) and ¯ Λ (b) in comparison with the
world data [2–5].
It should be noted that the ¯ Λ spin transfer dependence on xF was measured for the first
time.
Different values of Λ and ¯ Λ spin transfer could be explained qualitatively by the
following arguments. In the parton model the spin transfer from a polarized lepton
scattered off an unpolarized target to the hyperon is given by the equation [6]:
�
D Λ(¯ Λ)
LL (x, z) =
(z)
�
q e2q q(x)DΛ(¯ , (1)
Λ)
q (z)
q e2q q(x)ΔDΛ(¯ Λ)
q
where eq is the quark charge, q(x) is the parton distribution functions, D Λ(¯ Λ)
q (z) and
ΔD Λ(¯ Λ)
q (z) are the fragmentation functions of unpolarized and polarized quarks respectively.
Since the spin of Λ( ¯ Λ) is carried mainly by the strange quarks, then ΔD Λ(¯ Λ)
q (z) ∼ 0
for u, d, ū and ¯ d quarks. Eq. 1 then results in:
D Λ LL(x, z) ≈ 1 s(x)ΔD
9
Λ s (z)
�
q e2q q(x)DΛ q (z),
D ¯ Λ LL (x, z) ≈ 1
9
¯s(x)ΔD ¯ Λ ¯s (z)
(2)
�
q e2q q(x)D ¯ . (3)
Λ
q (z)
At first sight the difference between (2) and (3) could arise only if s(x) �= ¯s(x). But
actually, even if s(x) =¯s(x), equations (2) and (3) could have different denominators,
which are accordingly proportional to the production cross-section of Λ and ¯ Λ-hyperons.
The production cross-section for the Λ is almost two times bigger than for the ¯ Λat
COMPASS energy range. This leads to a decrease of the magnitude of the Λ-hyperon
polarization in comparison with that of ¯ Λ.
A comparison of the COMPASS data with theoretical predictions [7] is shown in
Fig. 1b. The calculations confirm the high sensitivity of D ¯ Λ LL to the strange quark distributions
in the nucleon. Independently of the specific hyperon model, the spin transfer
to ¯ Λ vanishes if we turn off the contribution from the strange quarks (dotted line for BJ
spin model [11] and dash-dotted line for SU(6) spin model).
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