Spin transfer to Λ and $$\bar \Lambda$$ hyperons in deep inelastic scattering at HERMES
3
ISSN 10637796, Physics of Particles and Nuclei, 2014, Vol. 45, No. 1, pp. 129–131. © Pleiades Publishing, Ltd., 2014. 129 1 It is commonly agreed that the Λ spin is preferen tially carried by the strange quark while the contribu tion from the light quarks, even the sign of this contri bution, is still debatable. In the naïve constituent quark model the first moments of the polarized quark distributions are: = 0 and = 1, i.e. the Λ hyperon spin is entirely carried by the squark, while the light quarks are not polarized. A similar con clusion follows from the latticeQCD calculations [1]: = = –0.02 ± 0.04 and = 0.68 ± 0.04. Alternatively, it was shown in [2] that the hyperfine interaction responsible for Δ – N and Σ 0 – Λ mass splitting results in significantly positive polarized non strange quark distributions. Experimental information on the hyperon spin structure can be obtained by measuring the spin trans fer to the hyperon produced in the process of polarized quark fragmentation. Here we present the preliminary HERMES results on the spin transfer to the Λ and hyperons in DIS which surpass substantially the data in [3, 4] in statistical precision. Unlike previous publi cations, the spin transfer is treated as a vector in the Λ rest frame. In the quarkparton model, the process of frag mentation of a polarized struck quark to the polarized Λ (or ) hyperon can be quantified in terms of the partial (for a given flavour f) spin transfer (z) = (z)/ (z), where (z) and (z) is spin dependent (polarized) and spin independent (unpo larized) fragmentation function, respectively, z = E Λ /ν is the fractional energy carried by the emitted 1 The article is published in the original. Δ q u Λ Δ q u Λ = Δ q s Λ Δ q s Λ Δ q d Λ Δ q s Λ Λ Λ D f Λ Δ F f Λ F f Λ Δ F f Λ F f Λ Λ hyperon, ν is the photon, and E Λ is the Λ hyperon energy. If the target is unpolarized, the observed Λ polarization reads: (1) Here, D Λ (x, z, Q 2 ) is the total spin transfer, P b is the beam polarization, D(y) = [1 – (1 – y) 2 ]/[1 + (1 – y) 2 ] represents the spin transfer from the incident positron to the struck quark (or the depolarization factor of the virtual photon), y = ν/E beam is the fractional energy carried by the photon. The Bjorken scaling variable x in the target rest frame is given by x = Q 2 /2M p ν, where M p is the proton mass, and Q 2 is the negative of the fourmomentumtransfer squared. The value P b D(y) stands for the polarization of the struck quark, (x, z, Q 2 ) represents the purity (fractional probability) for a quark (antiquark) of flavour f to fragment to the Λ hyperon. It appears intuitive to relate the spin transfer to the hyperon spin structure, which might constitute a use ful starting point for qualitative understanding of the spin transfer to a hyperon in DIS. Due to valence quark dominance ( + ≈ 1), the measurement of D Λ may provide a measure of the nonstrange quark polarization in the Λ hyperon. The experiment and event selection were described in detail in [4]. The spin transfer can be defined in the Λ rest frame as a vector with longitudinal and trans verse components both belonging to the production plane formed by the virtual photon momentum and P Λ xyzQ 2 , ,, ( ) D Λ xzQ 2 ,, ( ) P b Dy () = = ω f Λ xzQ 2 ,, ( ) D f Λ zQ 2 , ( ) f ∑ ⎝ ⎠ ⎛ ⎞ P b Dy () . ω f Λ ω u Λ ω d Λ pγ Spin Transfer to Λ and Hyperons in Deep Inelastic Scattering at HERMES 1 S. L. Belostotski for the HERMES Collaboration Petersburg Nuclear Physics Institute,188300 Gatchina, St. Petersburg email: [email protected] Abstract—Preliminary results on the spin transfer to the Λ and hyperons measured by the HERMES Collaboration are presented. Longitudinal spin transfer directed along the virtualphoton momentum in the Λ rest frame is found to be = 0.19 ± 0.04 stat ± 0.02 syst , the transverse component being compatible with zero. For both longitudinal and transverse components are compatible with zero within statistical errors of ±0.1. DOI: 10.1134/S1063779614010146 Λ Λ D LL Λ Λ
Transcript of Spin transfer to Λ and $$\bar \Lambda$$ hyperons in deep inelastic scattering at HERMES
ISSN 1063�7796, Physics of Particles and Nuclei, 2014, Vol. 45, No. 1, pp. 129–131. © Pleiades Publishing, Ltd., 2014.
129
1 It is commonly agreed that the Λ spin is preferen�tially carried by the strange quark while the contribu�tion from the light quarks, even the sign of this contri�bution, is still debatable. In the naïve constituentquark model the first moments of the polarized quark
distributions are: = 0 and = 1, i.e.the Λ hyperon spin is entirely carried by the s�quark,while the light quarks are not polarized. A similar con�clusion follows from the lattice�QCD calculations [1]:
= = –0.02 ± 0.04 and = 0.68 ± 0.04.Alternatively, it was shown in [2] that the hyperfineinteraction responsible for Δ – N and Σ0 – Λ masssplitting results in significantly positive polarized non�strange quark distributions.
Experimental information on the hyperon spinstructure can be obtained by measuring the spin trans�fer to the hyperon produced in the process of polarizedquark fragmentation. Here we present the preliminary
HERMES results on the spin transfer to the Λ and hyperons in DIS which surpass substantially the datain [3, 4] in statistical precision. Unlike previous publi�cations, the spin transfer is treated as a vector in the Λrest frame.
In the quark�parton model, the process of frag�mentation of a polarized struck quark to the polarized
Λ (or ) hyperon can be quantified in terms of the
partial (for a given flavour f) spin transfer (z) =
(z)/ (z), where (z) and (z) is spindependent (polarized) and spin independent (unpo�larized) fragmentation function, respectively, z = EΛ/νis the fractional energy carried by the emitted
1 The article is published in the original.
ΔquΛ Δqu
Λ= ΔqsΛ
ΔqsΛ Δqd
Λ ΔqsΛ
Λ
Λ
DfΛ
ΔFfΛ Ff
Λ ΔFfΛ Ff
Λ
Λ hyperon, ν is the photon, and EΛ is the Λ hyperonenergy. If the target is unpolarized, the observedΛ polarization reads:
(1)
Here, DΛ(x, z, Q2) is the total spin transfer, Pb is thebeam polarization, D(y) = [1 – (1 – y)2]/[1 + (1 – y)2]represents the spin transfer from the incident positronto the struck quark (or the depolarization factor of thevirtual photon), y = ν/Ebeam is the fractional energycarried by the photon. The Bjorken scaling variable xin the target rest frame is given by x = Q2/2Mpν, whereMp is the proton mass, and Q2 is the negative of thefour�momentum�transfer squared. The value PbD(y)
stands for the polarization of the struck quark, (x,
z, Q2) represents the purity (fractional probability) fora quark (antiquark) of flavour f to fragment to theΛ hyperon.
It appears intuitive to relate the spin transfer to thehyperon spin structure, which might constitute a use�ful starting point for qualitative understanding of thespin transfer to a hyperon in DIS. Due to valence�
quark dominance ( + ≈ 1), the measurement of
DΛ may provide a measure of the non�strange quarkpolarization in the Λ hyperon.
The experiment and event selection were describedin detail in [4]. The spin transfer can be defined in theΛ rest frame as a vector with longitudinal and trans�verse components both belonging to the production
plane formed by the virtual photon momentum and
PΛ x y z Q2, , ,( ) DΛ x z Q2, ,( )PbD y( )=
= ωfΛ x z Q2, ,( )Df
Λ z Q2,( )f∑⎝ ⎠⎛ ⎞PbD y( ).
ωfΛ
ωuΛ ωd
Λ
pγ
Spin Transfer to Λ and Hyperons in Deep Inelastic Scattering at HERMES1
S. L. Belostotski for the HERMES CollaborationPetersburg Nuclear Physics Institute,188300 Gatchina, St. Petersburg
e�mail: [email protected]
Abstract—Preliminary results on the spin transfer to the Λ and hyperons measured by the HERMESCollaboration are presented. Longitudinal spin transfer directed along the virtual�photon momentum in
the Λ rest frame is found to be = 0.19 ± 0.04stat ± 0.02syst, the transverse component being compatible
with zero. For both longitudinal and transverse components are compatible with zero within statisticalerrors of ±0.1.
DOI: 10.1134/S1063779614010146
Λ
Λ
DLLΛ
Λ
130
PHYSICS OF PARTICLES AND NUCLEI Vol. 45 No. 1 2014
BELOSTOTSKI
the Λ momentum . As the virtual photons are dom�inantly transverse (spin is assumed to direct along the
vector), the Λ polarization component perpendic�ular to the Λ production plane must be equal to zerobecause of parity conservation. The coordinate systemis defined as follows: the Z�axis is taken along the vir�
tual�photon momentum boosted to the Λ restframe, the Y�axis is perpendicular to the productionplane, and the definition of the X�axis follows the con�vention of a right�handed coordinate system. Anextracted spin transfer component is defined as DLi
where subscript L indicates the direction of the virtualphoton spin and i = X, Y, Z.
During the data�taking period, the beam polariza�tion was reversed on a month basis such that for theselected data sample the condition of helicity�bal�anced beam [Pb] = 0 may be fulfilled. Here, [Pb] is theluminosity�weighted beam polarization. The extrac�tion of the DLi components is essentially facilitated forthe helicity�balanced data sample because no MonteCarlo simulation of the spectrometer acceptancefunction is required in this case [4]. The preliminary
results for the spin�transfer components for Λ and integrated over the whole data sample, are:
pΛ
pγ
pγ
Λ,
DLXΛ
–0.016 0.042star 0.02syst,±±=
DLXΛ
–0.14 0.11star 0.02syst,±±=
DLYΛ 0.004 0.037star 0.02syst,±±=
DLYΛ 0.05 0.10star 0.02syst,±±=
DLZΛ
0.186 0.040star 0.02syst,±±=
DLZΛ 0.05 0.10star 0.02syst.±±=
For both Λ and hyperons, the DLY component isfound compatible with zero as it must be. For Λhyperons, the quantization axis is directed practicallyalong the virtual�photon momentum (along theZ�axis), the transverse component being correspond�
ingly small (compatible with zero). For the statis�tical accuracy is not sufficient to come to a definiteconclusion.
In Fig. 1, dependencies of , L' = Z on DISkinematic variables are presented. The false asymme�tries estimated with the KS data sample are found to benegligibly small and compatible with zero.
In Fig. 2 the preliminary HERMES results arepresented together with a compilation of world data.For Λ hyperons, the obtained results on the longitu�dinal spin transfer are in good agreement with theNOMAD [5] and recent COMPASS [6] experimentsat moderate values of the Feynman scaling variablexF, but the HERMES and COMPASS results are
incompatible at xF larger than 0.4. For hyperons,all DLi components are compatible with zero withinstatistical uncertainties of ±0.1. Open circles inFig. 2 (middle panel) are the HERMES data with
Z = Z '�axis chosen along the momentum of the hyperon in the laboratory frame. The two sets ofpoints are very close and compatible with zero whilethe COMPASS measurements show a sharp increasewith xF. To conclude, the longitudinal component ofthe spin transfer to the Λ hyperon is found to be
= 0.19 ± 0.04stat ± 0.02syst. It is directed alongthe virtual�photon momentum in the Λ rest framewhile two other (transverse) components are com�patible with zero. A positive and statistically signifi�
cant value of can be interpreted in favor of a
Λ
Λ,
DLZΛ
Λ
Λ
DLLΛ
DLLΛ
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.60.40.20 0.6
DLL 'Λ
HERMES preliminary 1996–2007
e + N → e' + Λ + X
xF
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.60.160.080.04 0.20
DLL 'Λ
HERMES preliminary 1996–2007
e + N → e' + Λ + X
x
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.60.40.30.2 0.6
DLL 'Λ
HERMES preliminary 1996–2007
e + N → e' + Λ + X
z0.12 0.5 0.7
Fig. 1. Dependencies of the longitudinal spin transfer to the Λ hyperon on DIS kinematic variables.
PHYSICS OF PARTICLES AND NUCLEI Vol. 45 No. 1 2014
SPIN TRANSFER TO Λ AND HYPERONS IN DEEP INELASTIC SCATTERINGΛ 131
noticeably positive contribution of the light u andd quarks to the Λ spin, in contradiction to the SU(6)prediction based on a value of ΔΣ = 0.33 well�estab�lished for the proton. A possibility of sizeable SU(6)symmetry breaking in the quark distributions of theΛ hyperon and positive non�strange quark polariza�tion in Λ were, e.g., discussed in [2, 7]. Note that fordefinitive interpretation of polarization transfer thecontributions from decays of heavier hyperons topolarized Λ must be taken into account.
REFERENCES
1. M. Gockeler et al., Phys. Lett. B 545, 112 (2002).
2. C. Boros, J. T. Londergan, and A. W. Thomas, Phys.Rev. D 61, 014007 (2000).
3. A. Airapetian et al., Phys. Rev. D 64, 112005 (2001).
4. A. Airapetian et al., Phys. Rev. D 74, 072004 (2006).
5. P. Astier et al., Nucl. Phys. B 588, 3 (2000).
6. M. Alekseev et al., Eur. Phys. J. C 64, 171 (2009).
7. B.�Q. Ma, J.�J. Yang, and I. Schmidt, Phys. Lett. B477, 107 (2000).
0.5
0
–1.0
–1.5
0.4–0.4–0.8
Longitudinal DLzΛ
HERMES (L' = Z) Preliminary
xF0
–0.5
COMPASS (L' = Z)
NOMAD (L' = Z)E665 (L' = Z ')
0.5
0
0.4–0.2–0.4
Longitudinal DLL 'Λ
HERMES (L' = Z) Preliminary
xF0
–0.5
COMPASS (L' = Z)
NOMAD (L' = Z)E665 (L' = Z ')1.0
1.5
0.2 0.6
HERMES (L' = Z ') Preliminary
0.5
0
0.4–0.2–0.4
HERMES (L' = X) Preliminary
xF0
–0.5
NOMAD (L' = X)
1.0
1.5
0.2 0.6
Transverse DLL 'Λ
Fig. 2. World data on the longitudinal and transverse spin transfer to the hyperon and the longitudinal spin transfer to Λ. Taken
in bracket Z or Z ' indicates that the coordinate system is chosen with the Z or Z '�axis along the photon momentum or Λ( )hyperon momentum, respectively.
Λ
Λ
