Strange Quarks in the Nucleon
Strange Quark Parton Distributions from K± Production in DIS on the Deuteron
H. E. Jackson
Argonne National Laboratory
for
The HERMES Collaboration
arXiv:0803.2993
H. E. Jackson DIS 2008 2
What do we know about S(x) and ΔS(x)?
Charm production in scattering is current source of information on . Extraction of pdfs is uncertain because of heavy quark mass effects in final state .
Usual Assumption is at some low factorization scale
Recent inclusive polarized DIS (e,e’) experiments with the deuteron give for the helicity distribution
S(x) = s(x)+ ¹s(x)
s(x)=¹s(x)=r(¹u(x)+¹d(x))=2 r¼0:5
See Lai et al., JHEP0704, 89 (2007)
HERMES, PRD75, 012007(2007)
º;(¹º)
¢S = ¡ 0:085§ 0:013(theo) § 0:008(exp)
H. E. Jackson DIS 2008 3
Status of ΔS(x)(cont’d)
But recent results from semi-inclusive DIS at HERMES using flavor tagging of hadron spin asymmetries Ah
1(x,Q2) suggest
ΔS(x)≈0
PRD71,(2005)012003
H. E. Jackson DIS 2008 4
Extraction of strange pdfs with isoscalar targets
Strange quarks carry no isospin → s(x)proton=s(x)neutron
In deuteron fragmentation in DIS can be described with fragmentation functions with no isospin dependence.
Require only isospin symmetry between the proton and neutron, and charge-conjugation invariance in fragmentation.
In LO the scattering cross sections can be written in terms of two pdfs, eg.
WhereS(x)´ s(x)+¹s(x)
d2ND I S (x)dxdQ2 =KU(x;Q2)[5Q(x)+2S(x)]
Q(x) ´ u(x)+ ¹u(x)+d(x)+ ¹d(x)
H. E. Jackson DIS 2008 5
Isoscalar targets(cont’d)
Similarly, for semi-inclusive charged kaon production
where
Neglecting 2S(x) compared to 5Q(x) gives
Providing access to if can be determined from the multiplicity.
S(x)RDKS (z)dz
RDKQ (z)dz
d2N K (x)dx dQ2 =KU(x;Q2)[Q(x)
RDKQ (z)dz+S(x)
RDKS (z)dz]
DKQ (z) ´ 4DKu (z)+D
Kd (z) andD
KS (z) ´ 2D
Ks (z)
S(x)RDKS (z)dz ' Q(x)
h5 d2N K (x)dNDI S(x) ¡
RDKQ (z)dz
i
H. E. Jackson DIS 2008 6
x=Q2/2m =E-E’
Q2=-q2=4EE’sin2( /2) zh=Ehadron/
K±
Flavor tagging with Semi-inclusive DIS
Observation of a coincident hadron in DIS probes flavor in detail because of the correlation between the flavor structure of the exiting hadron and that of struck quark.
In the measurement reported here K± production on a deuteron target has been used to probe the strange sea.
H. E. Jackson DIS 2008 7
K± multiplicities in d(e,e’)K±,x
Born multiplicities in 4π
S(x) from CTEQ6L with
as free parameters (dotted) does not fit data
In LO the charged kaon multiplicity is
RDKQ (z)dz &
RDKS (z)dz
dNK § (x)dND I S =
Q(x)RDKQ (z)dz+S(x)
RDKS (z)dz
5Q(x)+2S(x)
H. E. Jackson DIS 2008 8
Fitting dNK(x)/dNDIS(x)
!RDKQ (z)dz5
x>0:2 dNK (x)dND I S =
Q(x)RDKQ (z)dz+S(x)
RDKS (z)dz
5Q(x)+2S(x)
Using this value and CTEQ6L values of Q(x) we have extracted in LO the product S(x)
R0:80:2 D
KS (z)dz
ÃR0:80:2DKQ (z)dz=0:398§ 0:010
H. E. Jackson DIS 2008 9
Fitting dNK(x)/dNDIS(x)
!RDKQ (z)dz5
x>0:2 dNK (x)dND I S =
Q(x)RDKQ (z)dz+S(x)
RDKS (z)dz
5Q(x)+2S(x)
Using this value and CTEQ6L values of Q(x) we have extracted in LO the product S(x)
R0:80:2 D
KS (z)dz
ÃR0:80:2DKQ (z)dz=0:398§ 0:010
H. E. Jackson DIS 2008 10
S(x) at Q20=2.5 GeV2
xS(x) obtained by evolution of data to 2.5 GeV2 by taking
Shape incompatable with CTEQ6L and with average of isoscalar nonstrange sea.
R0:80:2 D
KS (z)dz= 1:27§ 0:13
D. de Florian, et al., PRD75, 114010 (2007)
H. E. Jackson DIS 2008 11
Extraction of ΔQ(x) and ΔS(x)
Ak;d(x)dN D I S (x)dx dQ2 =KLL (x;Q2)[5¢Q(x)+2¢S(x)]
AK §
k;d (x)d2N K (x)dxdQ2 =KLL (x;Q2)£
[¢Q(x)RDKQ (z)dz+¢S(x)
RDKS (z)dz]
Double-spin asymmetries for deuteron target
H. E. Jackson DIS 2008 12
Helicity distributions at Q20=2:5GeV2
.02<xBj<0.6
q8=Q-2S
a8´ q8=s01 q8(x)dx
=0.586§ 0.031 from hyperon decay and SU(3) symmetry
H. E. Jackson DIS 2008 13
Summary and conclusions
Shape of S(x) is much softer than that of the light isoscalar sea.
SU(3) symmetry appears to be violated by strange quark pdfs.
Earlier conclusions from HERMES SIDIS of an unpolarized sea are confirmed.
Results for S(x) provide new information on the origins of the proton sea.
If s01 S(x)dx 0 (as indicated in inclusive experiments)
some non-trival features of S(x,Q2) at low x must emerge from experiment.
H. E. Jackson DIS 2008 14
Additional figures
H. E. Jackson DIS 2008 15
A1,d(x) vs A1,dK§(x)
H. E. Jackson DIS 2008 16
• The value of the strange axial form factor at Q2=0 is equal to the integral of the strange quark helicity distribution at high Q2
• GSa(Q2) has been extracted from combined analysis of PV
measurements in elastic ep scattering (HAPPex and G0) and elastic p scattering (BNL E734)
•
Stephen Pate, et al., hep-ex/0512032v2
Other measurements
The axial current 5 is not only the underlying basis of the axial form
factor, but is also at the heart of the asymmetric part of the virtual Compton
amplitude at work in polarized deep- inelastic scattering. QCD relates the
polarized quark distribution functions q(x,Q2) (q = u, d, or s) with the
corresponding quark contribution to the axial form factor GAq (Q2).
For example :
s GAs (Q2 0) s(x,Q2 )dx
0
1
Thus, the value of the strange axial form factor at Q2 0 is equal to the
integral of the polarized strange quark distribution measured at high Q2.
0 Q2 (GeV2) 1.0
H. E. Jackson DIS 2008 17
• The DIS result that s is zero appears to contradict this result.
• The discrepency could be resolved by the onset of large values of s(x, Q2) at very low values of xbj , x ≈ 10-2 - 10-3.
• Alternatively, a “x=0” contribution to the singlet axial charge coming from a non-perturbative gluon topological contribution has been proposed by Steve Bass, (RMP 77,(2005) 1257.)
• If the axial form factor results can be extrapolated to zero they suggest that indeed s < 0 .
• Similarly, if SU(3) symmetry is preserved in hyperon decay, there must also be missing strength in q8(x) in the low x region.
The low energy issue
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