Probing the transverse spin structure of the proton and ... · proton and TMDs at HERMES RHIC & AGS Annual Users´ Meeting 2009 Charlotte Van Hulse, University of Ghent ... Transverse

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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● 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


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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° =2Mx

Q; F = F (x;Q; z; ~Ph?)

d¾

dxdydzdP 2h?dÁh=

®2

xyQ2(1 +

°2



cos 2ÁhUU g


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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° =2Mx

Q; F = F (x;Q; z; ~Ph?)

d¾

dxdydzdP 2h?dÁh=

®2

xyQ2(1 +

°2



cos 2ÁhUU g


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 is challenging!azimuthal modulations also possible due to ● detector geometrical acceptance● higher-order QED effects


dÁh¾UU (!; Áh)



! = (x; y; z; P 2h?)

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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


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


dÁh¾UU (!; Áh)



! = (x; y; z; P 2h?)

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fully differential analysis neededunfolding procedure with 400 x 12 bins *

unfolding

bin i

bin i


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?)


dÁh¾UU (!; 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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Probing the transverse spin structure of the proton and ... · proton and TMDs at HERMES RHIC & AGS Annual Users´ Meeting 2009 Charlotte Van Hulse, University of Ghent ... Transverse

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