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![Page 1: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/1.jpg)
Single-spin asymmetry in interference fragmentation on a transversely polarized
hydrogen target at HERMES
Tomohiro KobayashiTokyo Institute of Technology
Semi-Inclusive Reactions (SIR) Workshop 2005 (May 19th)
Contents• Transversity & Semi-inclusive DIS with transversely polarized target• SSA in HERMES (data taking period : 2002~2004)• Conclusion
![Page 2: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/2.jpg)
Motivation
Understand spin structure of the nucleon
Quark transversity is one of the important aspects of relativistic nature of quarks inside the nucleon.
![Page 3: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/3.jpg)
Access to transversity
1 hadron semi-inclusive DIS
]P̂k[~ 11hT)sin( Hh
MIA S
UT
1H : Collins FF (chiral odd)
1h
[...]kz
Ppkp[...] Th
T)2(
T2
T2
ddI
2 hadron semi-inclusive DIS
![Page 4: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/4.jpg)
Access to transversity
2 hadron semi-inclusive DIS
1h
hpA. Bacchetta and M. Radici, Proceedings of DIS’2004 (2004), hep-ph/0407345
: Interference FF (chiral odd)1H
GAgHhA LULR
~~ 11sin
11sin)sin( ~ HhA SR
UT
are not convoluted with .11Hh TT k ,p
![Page 5: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/5.jpg)
Longitudinally polarized deuterium target
UTULUL AAA θsinθcos v.r.t. virtual photon directionw.r.t. beam direction
1111
sin
~ HBhGAgHhA
L
ULR
First measurement of Small asymmetry is observed
XPPkedke )()()()( 21
RULA sin
![Page 6: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/6.jpg)
, s-p wave interference in ππ scattering theory
R. L. Jaffe, Xuemin Jin, and Jian Tan, Phys. Rev. Lett. 80, 1166 (1998)
P. Estabrooks and A. D. Martin, Nucl. Phys. B79, 301 (1974)
)()sin(sinsin),( ',11010
2,1 zHMzH spsp
scatteringnp using analysisshift phase
FF ceInterferen of dependenceM),(cos),(),cos,( 2,
12,
12
1 MzHMzHMzH ppsp
1H
dependenceM
Partial wave expansion
The sign changes at 0 MM
![Page 7: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/7.jpg)
Spectator model for fragmentationRadici et al., hep/ph-0110252
No strong dependence.M
![Page 8: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/8.jpg)
SSA in sin)sin( SRUTA
![Page 9: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/9.jpg)
Event selection
Kinematic cuts : ≥ 1 GeV2
≥ 4 GeV2
≥ 0.023 0.1 < < 0.85 > 2.5 GeV (for DIS lepton) > 1 GeV (for Hadron)
> 2 GeV, whereE
ppyxW
Q
track
track
2
2
p
px
MMM
E2
22
Xeep SIDIS events with at least pion pair( ) appeared were analyzed.
,
To cut exclusive channel.
Data set : 2002~2004
![Page 10: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/10.jpg)
Evaluate
DISDIS
DISDIS
/),,(/),,(/),,(/),,(1),,(NNNNNNNN
SA
SRSR
SRSR
TSRUT
UTA
0.54.75 TSwhere is the average target polarization. ( )TS
,...sin)sin(~ 11 HhSR
What is measured
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)sin(10 SRaa
Fit
with
sin( )
1sin
0.040 0.009
R SUTA a
)(vs.sin SRUTA
009.0040.0006.0000.0
1
0
aa
11sin )sin(~ HhSRAUT
0.51 < < 0.97 GeVM011 Hh
![Page 12: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/12.jpg)
sin)sin(ofdependence SRUTAM
Sign of the asymmetry does not change around
0 MM
sin)sin(10 SRaa
Fit
with 11sin)sin(~ HhA SRUT
1sin)sin( aA SR
UT
binning :0.25, 0.40, 0.55, 0.77, 2.0 [GeV]
M
![Page 13: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/13.jpg)
Conclusion
• Transversity and interference fragmentation function are related to SSA :
• HERMES has been taking data with transversely polarized hydrogen target since 2002.
• SIDIS events with at least two hadrons ( ) were analyzed.
• Asymmetry of order 4% is observed.
• Around , asymmetry becomes large.
• No sign change is observed.
,
11sin)sin( HhA SR
UT
009.0040.0sin
)sin(
SRUTA
0 MM
![Page 14: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/14.jpg)
Outlook
•3.5 M DIS evens in 2002~2004.
•3~3.5 M events is expected in 2005.
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backup
![Page 16: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/16.jpg)
spectrumM
With or without cut]GeV[2.0E
p
px
MMM
E2
22
![Page 17: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/17.jpg)
spectrumz
With or without cut]GeV[2.0E
p
px
MMM
E2
22
![Page 18: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/18.jpg)
double spin asymmetry
Beam polarization don’t affect to the asymmetry
sin)sin(sin)sin( SRSR cba
Fit
for both beam polarization.
11sin)sin(~ HhA SRUT
Beam polarization (%)
0Pfor 012.0040.0 0Pfor 011.0041.0
beam
beam
sin)sin(
bA SRUT
No double spin asymmetry
![Page 19: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/19.jpg)
Angle distribution
Correlation in the distribution due to the HERMES acceptance and spectrometer magnet field.
) ,( SR
Monte Carlo studies show : no face asymmetriesDue to those correlations
]rad[R
]rad[s
) ,( SR
![Page 20: Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.](https://reader036.fdocuments.in/reader036/viewer/2022062909/5a4d1b987f8b9ab0599c4816/html5/thumbnails/20.jpg)
Single spin asymmetryXPPkedke )()()()( 21
SS
Target spin vector
Lepton scatteringplane
Hadron scattering plane
...cossin)( 10 RRR baaf fit with 1sin aA RUL ⇒
RULA sin