probing the transverse spin structure of the proton and ... · proton and tmds at hermes rhic &...
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Probing the transverse spin structure of the proton and TMDs at HERMES
RHIC & AGS Annual Users´ Meeting 2009
Charlotte Van Hulse, University of Ghent on behalf of the HERMES collaboration
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Overview
● single-spin asymmetries in DIS off transversely polarized protons:
one-hadron production
hadron-pair production● non-collinear spin-independent cross-section
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HERMES: HERA MEASUREMENT of SPIN
Beamlongitudinally pol. e+ & e-
E= 27.6 GeV
● lepton-hadron PID: high efficiency (~98%) & low contamination (<2%) ● hadron PID: RICH 2-15 GeV
data taking from 1995 untilJune, 30 2007
Gaseous internal targettransversely pol. H (~75%)unpol. H,D,Ne,Kr,..longitudinally pol. H,D,He (~85%)
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HERMES: HERA MEASUREMENT of SPIN
Beamlongitudinally pol. e+ & e-
E= 27.6 GeV
● lepton-hadron PID: high efficiency (~98%) & low contamination (<2%) ● hadron PID: RICH 2-15 GeV
data taking from 1995 untilJune, 30 2007
Gaseous internal targettransversely pol. H (~75%)unpol. H,D,Ne,Kr,..longitudinally pol. H,D,He (~85%)
aerogel: n=1.03
C4F
10: n=1.0014
RICH:Cerenkov angle versus momentum
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Distribution functions Fragmentation functions
chiral odd: involve helicity flip of quark
T-odd : appear in pairs in spin-independent x-section & double-spin asymmetries single in single-spin asymmetries
Transverse momentum dependent distributions (TMDs)
leading twist
Sivers
transversity
Boer-Mulders Collins
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Single-spin asymmetries
ep ehX
» sin(ÁR? + ÁS)X
q
e2qhq1TH
];q1
+sin(Á ¡ ÁS)X
q
e2qI[~kT :Ph?Mh
f?;q1T Dq1]
» sin(Á+ ÁS)X
q
e2qI[~pT :Ph?Mh
hq1T H?;q1 ]
in semi-inclusive deep-inelastic scattering on transversely polarized target
ep eh1h
2X
¾UT =1
2(¾U" ¡ ¾U#)
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Single-spin asymmetry: one-hadron production
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● results from 2002-2005 data● positive for+
● large & negative for -
● isospin symmetry fulfilled
H?;fav1 ¼ ¡H?;unfav1
Collins amplitudes for pions
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● results from 2002-2005 data● positive for+
● large & negative for -
● isospin symmetry fulfilled● extraction by Anselmino et al. (Phys. Rev. D75: 054032, 2007) based on data from BELLE, COMPASS & HERMES
H?;fav1 ¼ ¡H?;unfav1
Collins amplitudes for pions
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Sivers amplitudes for pions
● results from 2002-2005 data● positive for+
non-zero orbital angular momentum!
● consistent with 0 for - ● isospin symmetry fulfilled
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Sivers amplitudes for kaons
● results from 2002-2005 data● K+ larger than +
non-trivial role of sea-quarks● K-, like -, consistent with zero
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Sivers distribution for valence quarks
● Sivers distribution for d-valence >> u-valence or● Sivers distribution for u-valence is large & <0 (more likely)
A¼+¡¼¡
UT =1
hjST ji(¾¼
+
U" ¡ ¾¼¡U" )¡ (¾¼
+
U# ¡ ¾¼¡
U# )
(¾¼+
U" ¡ ¾¼¡U" ) + (¾
¼+U# ¡ ¾¼
¡U# )
hsin(Á¡ ÁS)i¼+¡¼¡
UT ¼ ¡4f?;uv1T ¡ f?;dv1T
4fuv1 ¡ fdv1
suppressed exclusive 0 contribution
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Single-spin asymmetry: hadron-pair production
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Single-spin asymmetry:+- production
● independent method to probe transversity: transverse spin of fragmenting quark transferred to relative orbital angular momentum of hadron pair
● integration over hadron momenta direct product but
● more complex cross section (9 variables)● less statistics
~Ph = ~P1 + ~P2
~RT = ~R¡ ( ~R:Ph)Ph
H];q1 : T-odd and chiral-odd
dihadron fragmentation function
¾UT » sin(ÁR? + ÁS)X
q
e2qhq1H
];q1
~R =1
2(~P1 ¡ ~P2)
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Extraction of +- asymmetry
● Legendre expansion (M
<1.5 GeV):
H]1 = H];sp
1 +H];pp1 cos µ
D1 = D1 +Dsp1 cos µ +Dpp
1
1
4(3 cos2 µ ¡ 1)
AUT » sin(ÁR? + ÁS) sin µ
Pq e
2qhq1T (x)H
];q1 (z;M¼¼; cos µ)P
q e2qfq1 (x)D
q1(z;M¼¼; cos µ)
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Extraction of +- asymmetry● Legendre expansion (M
<1.5 GeV):
● symmetrization around = /2
H]1 = H];sp
1 +H];pp1 cos µ
D1 = D1 +Dsp1 cos µ +Dpp
1
1
4(3 cos2 µ ¡ 1)
H];pp1 cos µ Dsp
1 cos µand
a ´ Asin(ÁR?+ÁS) sin µU?
fit
»P
q e2qh1T (x)H
];sp1 (z;M¼¼):P
q e2qf1(x)D1(z;M¼¼)
a
1 + b4(3 cos2 µ ¡ 1) sin(ÁR? + ÁS) sin µ
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Final HERMES results
● first evidence for non-zero T-odd and chiral-odd dihadron fragmentation function!
A. Airapetian et al., JHEP 0806:017,2008
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Comparison with model
A. Bacchetta, M. Radici, Phys. Rev. D74:114007,2006
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Spin-independent semi-inclusive deep-inelastic cross section
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Non-collinear cross section
° =2Mx
Q; F = F (x;Q; z; ~Ph?)
d¾
dxdydzdP 2h?dÁh=
®2
xyQ2(1 +
°2
2x)fA(y)FUU;T +B(y)FUU;L
+C(y) cosÁhFcosÁhUU +B(y) cos 2ÁhF
cos 2ÁhUU g
Spin-independent semi-inclusive DIS cross section
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Non-collinear cross section
° =2Mx
Q; F = F (x;Q; z; ~Ph?)
d¾
dxdydzdP 2h?dÁh=
®2
xyQ2(1 +
°2
2x)fA(y)FUU;T +B(y)FUU;L
+C(y) cosÁhFcosÁhUU +B(y) cos 2ÁhF
cos 2ÁhUU g
Spin-independent semi-inclusive DIS cross section
leading twist
F cos 2ÁhUU = I[¡2(Ph?:~kT )(Ph?:~pT )¡ ~kT :~pT
MhMh?1 H
?1 ]
Boer-Mulders DF Collins FF
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Non-collinear cross section
° =2Mx
Q; F = F (x;Q; z; ~Ph?)
d¾
dxdydzdP 2h?dÁh=
®2
xyQ2(1 +
°2
2x)fA(y)FUU;T +B(y)FUU;L
+C(y) cosÁhFcosÁhUU +B(y) cos 2ÁhF
cos 2ÁhUU g
Spin-independent semi-inclusive DIS cross section
sub-leading twist
F cosÁhUU =2M
QI[¡ Ph?:~kT
Mf1D1 ¡
Ph?:~pTMh
k2TM2
h?1 H?1 + :::]
Cahn effect quark-gluon-quark correlations
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and
Cahn effect
M. Anselmino et al., Phys. Rev. D71:074006, 2005
R. N. Cahn, Phys. Lett. B78:269, 1978 Phys. Rev. D40: 3107, 1989
after integration over azimuthal dependence remains, reflected in cosÁh
d¾
dxdQ2dzdP 2h?»X
q
Zd2kTf
q1 (x; kT )
d¾lq!lq
dQ2Dq1(z; p?)::::
2¼®2
x2s2s2 + u2
Q4» ~l:~kT » cos'
~Ph? ' z~kT + ~pT
kT
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Extraction of the cosine moments
hcos(nÁh)i th:=RdÁh cos(nÁh)¾UU (!; Áh)R
dÁh¾UU (!; Áh)
hcos(nÁh)i exp:=RdÁh cos(nÁh)²acc(!; Áh)²rad(!; Áh)¾UU (!; Áh)R
dÁh²acc(!; Áh)²rad(!; Áh)¾UU (!; Áh)
! = (x; y; z; P 2h?)
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Extraction of the cosine moments
extraction is challenging!azimuthal modulations also possible due to ● detector geometrical acceptance● higher-order QED effects
hcos(nÁh)i th:=RdÁh cos(nÁh)¾UU (!; Áh)R
dÁh¾UU (!; Áh)
hcos(nÁh)i exp:=RdÁh cos(nÁh)²acc(!; Áh)²rad(!; Áh)¾UU (!; Áh)R
dÁh²acc(!; Áh)²rad(!; Áh)¾UU (!; Áh)
! = (x; y; z; P 2h?)
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Extraction of the cosine moments
fully differential analysis neededunfolding procedure with 400 x 12 bins *
(*)see F. Giordano, R. LambProceedings of SPIN 2008,Oct. 6-11 2008, Charlottesville, VA, USA hep-ex 0901.2438
extraction is challenging!azimuthal modulations also possible due to ● detector geometrical acceptance● higher-order QED effects
40.750.50.350.20.05PhT
510.750.60.450.30.2z
40.850.70.60.450.3y
510.270.1450.0780.0420.023x
#Bin limitsVariable
BINNING400 kinematic bins x 12 φ -bins
hcos(nÁh)i th:=RdÁh cos(nÁh)¾UU (!; Áh)R
dÁh¾UU (!; Áh)
hcos(nÁh)i exp:=RdÁh cos(nÁh)²acc(!; Áh)²rad(!; Áh)¾UU (!; Áh)R
dÁh²acc(!; Áh)²rad(!; Áh)¾UU (!; Áh)
! = (x; y; z; P 2h?)
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Extraction of the cosine moments
fully differential analysis neededunfolding procedure with 400 x 12 bins *
unfolding
bin i
bin i
extraction is challenging!azimuthal modulations also possible due to ● detector geometrical acceptance● higher-order QED effects
40.750.50.350.20.05PhT
510.750.60.450.30.2z
40.850.70.60.450.3y
510.270.1450.0780.0420.023x
#Bin limitsVariable
BINNING400 kinematic bins x 12 φ -bins
hcos(nÁh)i ¼
(*)see F. Giordano, R. LambProceedings of SPIN 2008,Oct. 6-11 2008, Charlottesville, VA, USA hep-ex 0901.2438
! = (x; y; z; P 2h?)
hcos(nÁh)i th:=RdÁh cos(nÁh)¾UU (!; Áh)R
dÁh¾UU (!; Áh)
hcos(nÁh)i exp:=RdÁh cos(nÁh)²acc(!; Áh)²rad(!; Áh)¾UU (!; Áh)R
dÁh²acc(!; Áh)²rad(!; Áh)¾UU (!; Áh)
RdÁh cos(nÁh)¾UU (!; Áh)R
dÁh¾UU (!; Áh)
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Results for <cos 2h>
● H-D comparison: h?;u1 ¼ h?;d1
● evidence for transversely polarized quarks in unpolarized nucleon
Boer-Mulders
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Results for <cos h>
● H & D: similar ● predictions for Cahn effect: similar for h+ and h−
also other effects have to be taken into account
Cahn+Boer-Mulders+...
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Comparison with model calculations: <cos 2h>
L.P. Gamberg et al. Phys. Rev. D77: 094016, 2008
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Comparison with model calculations:<cos 2h>
V. Barone et al., Phys. Rev. D78:045022, 2008
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Comparison with model calculations: <cos h>
M. Anselmino et al., Phys. Rev. D71:074006, 2005M. Anselmino et al., Eur. Phys. J. A31:373, 2007
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Summary● significant Collins amplitudes for charged pions
access to transversity with knowledge of Collins FF
● significant Sivers amplitudes for + and K+ (role of sea quarks)
non-zero orbital angular momentum
● single-spin asymmetries for hadron-pair production:
first evidence for
naive-T-odd and chiral-odd dihadron fragmentation function
● spin-independent non-collinear cross section:
evidence for non-zero Boer-Mulders distribution function
correlation quark orbital angular momentum and its spin
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Backup
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Collins amplitudes for kaons● results from 2002-2005 data● no Kaon amplitudes significantly ≠ from zero.
● K+ consistent with +
(u-quark dominance)● K- opposite to -
K- is pure sea object
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