DESY - Zeuthen · Gunar Schnell (DESY), HERMES Collaboration LightCone 2002 – Los Alamos, August 6th, 2002 – p.3. hermes Particle Identiﬁcation-20-15-10-5 0 5 0 5 10 15 20 25

hermes

Probing Quark Distributions inSemi-Inclusive Single Spin Asymmetries

Gunar Schnell

DESY - Zeuthen

For the hermes Collaboration

Gunar Schnell (DESY), HERMES Collaboration LightCone 2002 – Los Alamos, August 6th , 2002 – p.1

hermes Polarized Beam at HERA

Longitudinal

HERA B

HERMES

ZEUS H1HERA Electron Ring

TransversePolarimeter

Spin Rotator Spin Rotator

DirectionBeam

Polarisationtransverse

PolarisationPolarimeterLongitudinal

Comparison of rise time curves

0

20

40

60

80

6 6.5 7 7.5 8Time [hours]

Pol

ariz

atio

n [%

]

Transverse Polarimeter

Longitudinal Polarimeter• 27.5 GeV e+/e− beam• Self-polarizing through

Sokolov-Ternov-Effect• Average beam polariza-

tion of about 55%


hermes The HERMES Experiment

1

0

2

-1

-2

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m

LUMINOSITY

CHAMBERSDRIFT

FC 1/2

TARGETCELL

DVC

MC 1-3

HODOSCOPE H0

MONITOR

BC 1/2

BC 3/4 TRD

PROP.CHAMBERS

FIELD CLAMPS

PRESHOWER (H2)

STEEL PLATE CALORIMETER

DRIFT CHAMBERS

TRIGGER HODOSCOPE H1

0 1 2 3 4 5 6 7 8 9 10

RICH

SILICON

270 mrad

270 mrad

MUON HODOSCOPEWIDE ANGLE

FRONTMUONHODO

MAGNET

m

IRON WALL

MUON HODOSCOPES

e+

27.5 GeV

140 mrad

170 mrad

170 mrad

140 mrad

• Internal storage cell: pure gas target

• Forward acceptance spectrometer: 40 mrad ≤ Θ ≤ 220 mrad

• Tracking: 57 tracking planes: δP/P = (0.7 − 1.3)%, δΘ ≤ 0.6 mrad

• PID: Cherenkov (RICH after 1997), TRD, Preshower, Calorimeter


hermes Particle Identification

-20-15

-10-5

05

05

1015

2025

3035

4045

50

0250500750

100012501500175020002250

x 10 2

PID [ Cer, Pre, Cal ] TRD S

igna

l (ke

V)

Excellent e+/e− identification:• Efficiency ≥ 99%

• Hadron contamination ≤ 1%

Until 1997 only used Threshold Cherenkov



-20-15

-10-5

05

05

1015

2025

3035

4045

50

0250500750

100012501500175020002250

x 10 2


igna

l (ke

V)



After 1997 use dual radiatorRing Imaging CHerenkov



-20-15

-10-5

05

05

1015

2025

3035

4045

50

0250500750

100012501500175020002250

x 10 2


igna

l (ke

V)



After 1997 use dual radiatorRing Imaging CHerenkov↪→ very good hadron identification inthe range 2 GeV ≤ Ph ≤ 15 GeV

p (GeV)

ΘC (

rad

)0

0.05

0.1

0.15

0.2

0.25

0 2 4 6 8 10 12 14 16 18 20


hermes HERMES Internal Gas Target

• Storage cell with atomic beam source• Pure target (NO dilution)• Polarized or unpolarized targets possible• Different gas targets available (H, D, He, N, Kr ...)

~~ T<P > 0.90e’

polarimeter3%

against synchrotron radiation(movable) collimators

thin exit window

0.35 Tesla

electron beam

coil

coil

solenoidsource for

polarized gas

dete

ctor

pump

pump

storage cell29 x 9.8 x 400 mm

d = 0.3 mm SS

10 atoms/sec

d < 0.1 mm Aln = 1-3.5 x 10 atoms/cm 214

3

17


hermes Twist-2 Quark Distribution Functions

Functions Survivingon Integration over

Transverse Momenta

� The others are sensitive to intrisic � �� in

the nucleon & in the fragmentation process

Higher TwistFunctions

(no pictures)

Sensitive to parton-parton correlations

Have a twist-2 part ... e.g.

Distribution Functions Fragmentation Functions=

=

=

f1

h1T

g1L g1T =

f1T =

h1 =

h1T =h1L =

=

=1L

1

G

=H1T

=1TG

D

D1T

1H

=

=

H1L= H1T =

– Typeset by FoilTEX – 1


hermes ... surviving k⊥ integration

1f =q g =1L -q1h = -q

↓ ↓ ↓Unpolarizedquarks andnucleons

q(x): spinaveraged (well

known)

Longitudinallypolarized quarks

and nucleons

∆q(x): helicitydifference (known)

HERMES1995-2000

Transverselypolarized quarks

and nucleons

δq(x): helicity flip(unmeasured)

HERMES 2002. . .


hermes Transversity

• Non-relativistic quarks: ∆q(x) = δq(x)⇒ δq probes relativistic nature of quarks

• obvious bound: |δq(x)| ≤ q(x)

• Soffer bound: |δq(x)| ≤ 12 [q(x) + ∆q(x)]

• Sum Rule: first moment → tensor charge reliablycalculable in lattice QCD (i.e. at Q2 = 2GeV 2):δΣ =

∑

f

∫ 10 dx(δqf − δq̄f ) =0.562 ± 0.088

• transversity distribution CHIRAL ODD

↪→ No Access In Inclusive DIS

X

+ -

+ -


hermes Transversity Phenomenology

• ∃ a number of model calculation(facing a lack of experimental data)

• h1 must satisfy Soffer inequality• in common: h1 behaves more

valence-like

χQSM (A.V. Efremov et al)

0.0 0.2 0.4 0.6 0.8 1.0x

−1.0

0.0

1.0

2.0

hu

1

hd

1

hu_

1

hd_

1

Quark-Diquark (solid), pQCD based model (dashed) (B.Q. Ma et al)


hermes Transversity Measurements

How can one measure transversity?Need another chiral-odd object!

Semi-Inclusive DIS −→ HERMES with transverselypolarized target

σep→ehX =∑

q

fH→q ⊗ σeq→eq ⊗ Dq→h

⇓ ⇓

chiral-odd chiral-oddDF FF


hermes Candidates for Fragmentation

Want to measure polarization of outgoing quarkvarious “polarimeters” proposed in the literaturepossible at HERMES:

1. ep↑ −→ e′π(k⊥)X

2. ep↑ −→ e′Λ↑X

3. ep↑ −→ e′ππX

⇐ Favoured Process ⇒ Signature:Single-Spin Azimuthal Asymmetry

1. Collins,93, Kotzinian,95, Mulders et al,96

2. Baldracchini,82, Jaffe,96

3. Jaffe et al,97


hermes Single Spin Asymmetries

ep↑ −→ e′πX

k ’

yx

k

P

zγθ

T

L

φ

q

SS

Φ = φ + φls Collins angle

φls. . . angle between target spin

vector and scattering plane

study azimuthal distribution of π’s:

AsinΦ ∝∑

N+

i=1sin Φi−

∑

N−

i=1sin Φi

1

2(N++N−)

with transversely polarized target:

Asin ΦT ∝

∑

q e2qδq(x)H⊥,q

1 (z)∑

q e2qq(x)Dq

1(z)

H⊥

1(z) Collins fragmentation function

(T-odd, chiral odd)


hermes Single Spin Asymmetries at HERMES

HERMES 1996/97: longitudinal polarized proton target

transverse component ST

of target spin (w.r.t. virtual photon):

ST ∝ sin Θγ '2Mx

Q

√

1 − y ∼ 0.15

⇒ glimpse on transversity?!

Longitudinal target SSA:

AUL(φ) =1

〈P 〉·N+(φ) − N−(φ)

N+(φ) + N−(φ)

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 π-π

A(φ

)

φ

π0P1 + P2 sin(φ)

P1 = -0.001 ± 0.005P2 = 0.019 ± 0.007

0 π-π

A(φ

)

φ

π+

P1 = 0.004 ± 0.003P2 = 0.020 ± 0.004

0 π-π

A(φ

)

φ

π-

P1 = 0.003 ± 0.004P2 = -0.001 ± 0.005

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


hermes HERMES Results on Deuteron Target

• HERMES 1998-2000:

longitudinal polarized

deuteron target

• High statistics:

∼8 Million DIS

• Very good hadron

identification due to RICH

• First measurement of Kaon

SSA

-0.04

-0.02

0

0.02

0.04

-3.14 -1.57 0 1.57 3.14

-0.04

-0.02

0

0.02

0.04

-3.14 -1.57 0 1.57 3.14

-0.04

-0.02

0

0.02

0.04

-3.14 -1.57 0 1.57 3.14

-0.04

-0.02

0

0.02

0.04

-3.14 -1.57 0 1.57 3.14

-0.02

0

0.02

0.04

e d→

→ e π+ XP1 * sin φP1 * sin φ + P2 * sin 2φ

P1 = 0.012 ± 0.002P2 = 0.004 ± 0.002

AU

L(φ

)

-0.02

0

0.02

0.04

e d→

→ e π0 X

P1 = 0.021 ± 0.005P2 = 0.009 ± 0.005

AU

L(φ

)

-0.02

0

0.02

0.04

e d→

→ e π- X

P1 = 0.006 ± 0.003P2 = 0.001 ± 0.003

AU

L(φ

)

-0.02

0

0.02

0.04

-0.04

e d→

→ e K+ X

P1 = 0.013 ± 0.006P2 = -0.005 ± 0.006

AU

L(φ

)

-π -π/2 0 π/2 πφ (rad)

PRELIMINARY


hermes Attempt of Interpretation

• observe non-vanishing 〈sin φ〉-moments• 〈sin 2φ〉-moment small (consistent with zero)

Attribute asymmetry to Collins fragmentation andtransversity:

Asin φ

U L∼ SL〈sin φ〉

U L− ST 〈sin φ〉

U T

Longitudinally polarized in experiment L/T polarized in theory

(along beam direction) (along virtual gamma direction)

〈sin φ〉UL ∼ 1Q

∑

q e2q(h

qL(x)H

⊥(1),q1 (z) − 1

zh⊥(1),q1L (x)H̃(z))

〈sin φ〉UT ∼∑

q e2qxh

q1(x)H

⊥(1),q1 (z) but ST ∼ 1

Qlike twist-3

〈sin 2φ〉UL ∼∑

q e2qxh

⊥(1),q1L (x)H

⊥(1),q1 (z)





AsinφUL ∼ SL〈sin φ〉UL − ST 〈sin φ〉UT


∑

q e2q(h

qL(x)H

⊥(1),q1 (z) − 1

zh⊥(1),q1L (x)H̃(z))


q e2qxh

q1(x)H

⊥(1),q1 (z) but ST ∼ 1

Qlike twist-3


q e2qxh

⊥(1),q1L (x)H

⊥(1),q1 (z)







∑

q e2q(h

qL(x)H

⊥(1),q1 (z) − 1

zh⊥(1),q1L (x)H̃(z))


q e2qxh

q1(x)H

⊥(1),q1 (z) but ST ∼ 1

Qlike twist-3


q e2qxh

⊥(1),q1L (x)H

⊥(1),q1 (z)







∑

q e2q(h

qL(x)H

⊥(1),q1 (z) − 1

zh⊥(1),q1L (x)H̃(z))


q e2qxh

q1(x)H

⊥(1),q1 (z) but ST ∼ 1

Qlike twist-3


q e2qxh

⊥(1),q1L (x)H

⊥(1),q1 (z)


hermes What about Twist-3?

distribution functions are related:

hL(x) =mq

M

h1(x)

x−

2

xh⊥(1)1L (x) + h̃L(x)

Lorentz covariance ⇒ hL(x) = h1(x) − ddxh

⊥(1)1L (x)

↪→ hL(x) = h̃L(x) + 2x

∫ 1

x

dy

y2[h1(y) − h̃L(y)]

set h̃L = 0 ⇒ hL(x) = −2

xh⊥(1)1L (x)

= 2x

∫ 1

x

dy

y2h1(y)

“Reduced Twist-3”


hermes Attempt of Interpretation II

Attribute asymmetry to Sivers effect:

• Final state interactions (Brodsky et al.)

• Sivers function (Sivers, Mulders et al)

〈sin φ〉UL ∼ f⊥(1)1T D1

longitudinally polarized target ⇒ Sivers effect indistinguishable from

Collins effect

Transversely polarized target

Sivers Collins〈sin(φl

h − φls)〉 moment 〈sin(φl

h + φls)〉 moment


hermes Let’s assume Collins

0.2 0.4 0.6

-0.05

0

0.05

0.1 0.2

z

AU

L

sin

φ

π0

π+

π-

x P⊥ (GeV)

0.25 0.5 0.75 1

Original predictions by Collins (here: proton target):

• Larger for π+, π0 than for π− (u-quark dominance in case of proton target)

• Peak around x = 0.3 (valence quark dominance)

• Grow with p⊥ and peak around 1 GeV (H⊥

1

D1∝ McMh

M2c +p2

⊥

with Mc '1 GeV)


hermes Model Predictions for Deuteron• deuteron target• h1 from χQSM, quark-diquark

and pQCD model• assume reduced twist-3• H⊥

1 : Collins Ansatz or fit toDELPHI data

• sin 2φ using χQSM model

-0.02

0

0.02

0.04

0.06

0 0.1 0.2 0.3

x

AU

L

sin

2φ

e d→

→ e π X

π+

π-

π0

PRELIMINARY

-0.02

0

0.02

0.04

0.06

0 0.1 0.2 0.3

-0.02

0

0.02

0.04

0.06

0 0.1 0.2 0.3

-0.02

0

0.02

0.04

0.06

0 0.1 0.2 0.3

AU

L

sin

φ

e d→

→ e π+ X

χQSM

QdQ

pQCD

AU

L

sin

φ

e d→

→ e π0 X

χQSM

QdQ

pQCD

x

AU

L

sin

φ

e d→

→ e π- X

χQSM

QdQ

pQCD PRELIMINARY


hermes Outlook

New Target Magnet for HERMES

• Transverse target (B = 0.295T )

• High uniformity along beam direction:

∆B ≤ 4.5 · 10−5T

• Transversely polarized hydrogen

• Target polarization above 80%

• 〈sin φ〉UT becomes dominant• Sivers and Collins distinguishable

↪→ h1 and H⊥1 as well as f⊥

1T accessible


Documents

DESY - Zeuthen · Gunar Schnell (DESY), HERMES Collaboration LightCone 2002 – Los Alamos, August 6th, 2002 – p.3. hermes Particle Identiﬁcation-20-15-10-5 0 5 0 5 10 15 20 25