Single-spinasymmetries with 2 hadron fragmentation: The ... · 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85...
Transcript of Single-spinasymmetries with 2 hadron fragmentation: The ... · 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85...
Single-spin asymmetrieswith 2 hadron fragmentation:
The Measurement
Paul Bastiaan van der Nat (NIKHEF)On behalf of the HERMES collaboration
Layout:Introduction
Results
Interpretation
Transversity workshop - Trento – p.1/16
The holy grail
� � � � � �Characteristics of
��� :
leading twist -> on equal footing with��� and � �
chiral-odd -> can NOT be probed in inclusive DIS
Solution: couple
� to chiral-odd fragmentation function
Two options: 1 or 2 particle semi-inclusive DIS
Transversity workshop - Trento – p.2/16
Single Spin Asymmetry
��� � ��� � ����longitudinally polarized deuterium target
���� ���� � ��� ���! � "# ���� � �$ " #&%' ( ) " * ���� � � $ " *% ' (" # ���� � � $ " #+%' ( � " * ���� � � $ " *+%' (
Transversity workshop - Trento – p.3/16
Asymmetries -Theory
A. Bacchetta, M. Radici, PRD 69, 0740XX (2004)
� ,� - . �0/ �21 354 ���� � � �76 � � 8 9� � : �0/ �21 354 ��76 � ; �=< < < �
� ,�� - : �0/ �21 354 ���� � � ; � � 8 9� � � � >@? 9 �
A$B � C target spin defined w.r.t. virtual photon
Transversity workshop - Trento – p.4/16
Asymmetries - Experiment
��� D � ,�� ) 1 354 EGF � ,� target spin define d w.r.t. beam
target spin w.r.t. virtual photon
HJI KHIHML H@N
OQP
R1 3 4 EGF S � R � TVU W � ) / S D XZY X [\
��� - : �0/ �21 354 ���� � � ; � � 8 9� � � � > ? 9 � � . , �/ �1 3 4 ���� � �; � 8 9�
if
8 9� ]� X
:
� C 2 hadron fragmentation can probe transversity!
Transversity workshop - Trento – p.5/16
Interference FF
R2^_ 1 E Sa` X � C 8 9�b c c� drops out!
8 9� �0d!e ^_ 1 Ee �f f �� 8 9�b g c� �0d!e � f f � � ^_ 1 E 8 9�b c c� �0d e � f f �
CM
h i
h j kmln
m(GeV)
sinδ
0sin
δ 1sin
(δ0-
δ 1)
-0.4
-0.2
0
0.2
0.4
0.6
0.5 0.6 0.7 0.8 0.9 1
Jaffe et al. [hep-ph/9709322]:
8 9�b g c� �0d e � f f �� 1 3 4 oqp 1 354 o � 1 354 � oqp ) o � � 8 9�b g c r� �0d �
s�t (
s�u ) v S(P)-wave phase shifts
� w � �f f � 8 9�b g c r� �d �
x y z|{} might depend stongly on
~=� �
Transversity workshop - Trento – p.6/16
The HERMES Experiment
1
0
2
-1
-2
� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �
� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �
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
RICH270 mrad
270 mrad
MUON HODOSCOPEWIDE ANGLE
FRONTMUONHODO
MAGNET
m
IRON WALL
e+
27.5 GeV
140 mrad
170 mrad
170 mrad
140 mrad
MUON HODOSCOPES
SILICON
Forward acceptance spectrometer: 40 mrad
� O � � ��
mrad
Tracking: 57 tracking planes:
s� � � x � ��� ��� �� � ��
,
s O � ��� �
mrad
Transversity workshop - Trento – p.7/16
Analysis method
Fitting method:
z|{} �� ��� � � � � �� �� � � fit withx y � � �0� � � x � t � � u � ¢¡ � � £ u ¤¥ � � � � � �
z ¦ §©¨ ª{}Weighting method:
z ¦ §©¨ ª{} � « ¬¯®u � ¢¡ � � « °¯®u � ¡ � u± � � �� � � �Used fitting method for released resultsx y less sensitive to detector acceptance
Transversity workshop - Trento – p.8/16
Results
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
AU
L
sin
φ R⊥
Mππ [GeV]
ρ0
sys. unc. = 0.007x > 0.023 <x> = 0.074
<z> = 0.48
ed→
→ e' h+h- XHERMES PRELIMINARY
sin
φ R⊥
first measurement everof
� ² ³µ´ ¶a· ¸��small asymmetries
Transversity workshop - Trento – p.9/16
¹-dependence
Attempt to study º and d -dependence:� ² ³µ´ ¶»· ¸�� ¼ � � º � 8 9�b g c� �d e f f � � � Y Y Y �-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
AU
Lsi
nφ R
⊥
ρ0
sys. unc. = 0.0070.023 < x < 0.046
<x> = 0.036<z> = 0.45 0.046 < x < 0.076
<x> = 0.059<z> = 0.49 x > 0.076
<x> = 0.13<z> = 0.50
ed→
→ e' h+h- X HERMES PRELIMINARY
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
ρ0
sys. unc. = 0.0070.023 < x < 0.046
<x> = 0.036<z> = 0.45 0.046 < x < 0.076
<x> = 0.059<z> = 0.49 x > 0.076
<x> = 0.13<z> = 0.50
ed→
→ e' h+h- X HERMES PRELIMINARY
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
Mππ [GeV]
ρ0
sys. unc. = 0.0070.023 < x < 0.046
<x> = 0.036<z> = 0.45 0.046 < x < 0.076
<x> = 0.059<z> = 0.49 x > 0.076
<x> = 0.13<z> = 0.50
ed→
→ e' h+h- X HERMES PRELIMINARY
no strong º-dependence observed
statistics doesn’t allow finer binningTransversity workshop - Trento – p.10/16
½-dependence
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
AU
Lsi
nφ R
⊥
ρ0
sys. unc. = 0.0070 < z < 0.52
<x> = 0.070<z> = 0.38 0.52 < z < 1
<x> = 0.081<z> = 0.64
ed→
→ e' h+h- X HERMES PRELIMINARY
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
Mππ [GeV]
ρ0
sys. unc. = 0.0070 < z < 0.52
<x> = 0.070<z> = 0.38 0.52 < z < 1
<x> = 0.081<z> = 0.64
ed→
→ e' h+h- X HERMES PRELIMINARY
d � ¾ f f¿
no strong d -dependence observed
no more than two bins possible
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3 3.5Mππ [GeV]
z
Transversity workshop - Trento – p.11/16
comparison to model prediction
Model by Jaffe et al.:
predicts mass dependence
NO statements on size/signof the asymmetry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1Mhh [GeV]
sin
δ 0sin
δ psi
n(δ
0-δ p
)
Fit data with: À Á Âà à ÄÆÅ ÇÈ É Á Â Ã Ã ÄµÊ Ç Â
by extracting ÇÈ & Ç Â a qualitative comparisoncan be made to the model prediction
Transversity workshop - Trento – p.12/16
comparison to model prediction
ÇÈ Ë ÌZÍ Ì Î Ì Ï ÌÍ ÌÐÑ
Ç Â ËÓÒ ÌÍ Ì ÌÔ Ï ÌÍ Ì Ì Î
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
AU
L
sin
φ R⊥
Mππ [GeV]
ρ0
sys. unc. = 0.007x > 0.023 <x> = 0.074
<z> = 0.48
ed→
→ e' h+h- XHERMES PRELIMINARY
sin
φ R⊥
hint of a sign change atthe Õ Ö mass
À Á Âà à ÄÆÅ ÇÈ É Á Â Ã Ã ÄµÊ Ç Â
Transversity workshop - Trento – p.13/16
×-dependence
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
AU
Lsi
nφ R
⊥
ρ0
sys. unc. = 0.0070.023 < x < 0.046
<x> = 0.036<z> = 0.45 0.046 < x < 0.076
<x> = 0.059<z> = 0.49 x > 0.076
<x> = 0.13<z> = 0.50
ed→
→ e' h+h- X HERMES PRELIMINARY
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
ρ0
sys. unc. = 0.0070.023 < x < 0.046
<x> = 0.036<z> = 0.45 0.046 < x < 0.076
<x> = 0.059<z> = 0.49 x > 0.076
<x> = 0.13<z> = 0.50
ed→
→ e' h+h- X HERMES PRELIMINARY
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
Mππ [GeV]
ρ0
sys. unc. = 0.0070.023 < x < 0.046
<x> = 0.036<z> = 0.45 0.046 < x < 0.076
<x> = 0.059<z> = 0.49 x > 0.076
<x> = 0.13<z> = 0.50
ed→
→ e' h+h- X HERMES PRELIMINARY
higher Ø: hint of sign change atÕ Ö according to Jaffe’s modelÇÈ Á Ø Ä0Ù Ú È Á Ø Ä ?-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14xbj
c1
Transversity workshop - Trento – p.14/16
Û-dependence
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
AU
Lsi
nφ R
⊥
ρ0
sys. unc. = 0.0070 < z < 0.52
<x> = 0.070<z> = 0.38 0.52 < z < 1
<x> = 0.081<z> = 0.64
ed→
→ e' h+h- X HERMES PRELIMINARY
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
Mππ [GeV]
ρ0
sys. unc. = 0.0070 < z < 0.52
<x> = 0.070<z> = 0.38 0.52 < z < 1
<x> = 0.081<z> = 0.64
ed→
→ e' h+h- X HERMES PRELIMINARY
sign change at Õ Ö according toJaffe’s model for low d
ÇÈ Á0d Ä Ù Ü Ý�Þ ß cÈ Á0d e Ã Ã Ä ?-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.2 0.3 0.4 0.5 0.6 0.7 0.8z
c1
x > 0.023x > 0.046
Transversity workshop - Trento – p.15/16
Conclusions & Outlook
Conclusions:
Presented first measurement of
à á â©ã äæå çèé
Asymmetries of order ê ë ì
, but also consistent with zeroí=î î -dependence consistent with model by Jaffe et al.
Comparison with model prediction hints at ï and ð dependenceñ ò sensitive to
ó�ô õ ï ö÷ øúù ûüô õ ðý í=î î ö
?
Outlook to
à á â ã äå çèþ :
comparable uncertainty:
L polarized target ÿ ê8M DIS eventsT polarized target ÿ ê4M DIS events?
� à � � � �� ÿ � àdominated by statistical uncertainty
much larger transverse target polarization ÿ ê1/0.045 ñ ë ë
times bigger!
Transversity workshop - Trento – p.16/16