single-spin asymmetries in two hadron production of polarized deep inelastic scattering at hermes...
TRANSCRIPT
Single-spin asymmetries in two hadron production of polarized deep
inelastic scattering at HERMES
Tomohiro KobayashiTokyo Institute of Technology
for the HERMES collaboration
Second Joint Meeting of the Nuclear Physics Divisions of APS and JPS, Hawaii (Sep. 22nd, 2005 Session JE-9)
Contents• The HERMES experiment• Quark distribution functions• Single-spin asymmetry in 2-hadron semi-inclusive DIS• Conclusion and outlook
HERMES experiment at DESY
positron (electron) beam
27.6 [GeV]
current ~ 30[mA]
Xepe
Transversely polarized hydrogen target (2002~2005)
polarization ~ 75[%]
HERA Target magnet
HERMES Spectrometer
• acceptance : 40 mrad ≦ 220 mrad≦• Tracking resolution : P/P = (0.7-1.3)% 、 = 0.6 mrad• PID : Hodoscope 、 Calorimeter 、 TRD and RICH Lepton ID efficiency > 97%, Hadron contamination < 1% Hadron ID(K, P) at 2‐15 GeV/c
e+ beam
27.6GeV
8m
Internal gas targetH(pol) 、 D ( pol )、He 、 Ne 、 Kr 、 Xe
unknownchiral odd
Quark distribution functions
Quark momentum distribution:
Quark Helicity:
Quark Transversity:
At leading twist
)()(2
1)(
)()(
xqxqxq
xqxq
• quark’s relativistic nature
• positivity bound :
Soffer bound :
)()( xqxq
)(xq
)(xq
)(xq:)(xq
quark spin
proton spin
Access to transversity
chiral odd Need another chiral odd objects.
Transversity couples to …• Collins fragmentation function (FF)• 2-hadron interference FF• Polarized Lambda FF• Spin-1 FF :
:)(xq
Inclusive DIS Semi-inclusive DIS
Not accessible accessible
)(xq
Single-spin asymmetry of 2-hadron production
Azimuthal single-spin asymmetries
hpXPPkepke )()()()( 21
)()(sin)sin(~ 1 zHxqSR
Transversity Interference FF (chiral odd)
describes interference between different production channels of pion pairs
)(1 zH
),,( SRUTA
(data taken in 2002…2004)
can be extracted using measured by e+ e- collider, BELLE
)( xq )(1 zH
DISDIS
DISDIS
NNNN
NNNN
S SRSR
SRSR
T /),,(/),,(
/),,(/),,(1
beam spin target spin
: s-p wave interference in 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,( 2,1
2,1
21 MzHMzHMzH ppsp
1H
dependenceM
Partial wave expansion
Sign of the phase shift changes at
0 MM
might depend strongly on MUTA
Spectator model for fragmentation
M. Radici et al., hep/ph-0110252
No strong dependence.M
),(cos),(),cos,( 2,1
2,1
21 MzHMzHMzH ppsp
Partial wave expansion
Single-spin asymmetry in 2-hadron production
Single-spin asymmetries
First observation of transverse asymmetries in interference process
1sin)sin(~ qHA SRUT
(no binning)
)sin(10 SRaa
Fit
with
SystStat1 003.0009.0040.0 a
009.0040.0
006.0000.0
1
0
a
a
1sin)sin(~ qHSR
AUT
01 Hq
Single-spin asymmetry in 2-hadron production
Single-spin asymmetries
Amplitude of the asymmetry modulation
Positive asymmetry is observed around 0 MM
sin)sin(10 SRaa
Asymmetry is fitted with
1sin)sin( aA SR
UT
Single-spin asymmetry in 2-hadron production
If we look at dependence,M M( : invariant mass of pion pair)
Spectator model for fragmentation
Marco Radici at Como, 7 - 10 Sept 2005
),(cos),(),cos,( 2,1
2,1
21 MzHMzHMzH ppsp
Partial wave expansion
Conclusion
ConclusionConclusion• Single-spin asymmetry in production is measured with transversely polarized hydrogen target at HERMES.
• This is the first observation of transverse target spin asymmetry in interference process.
• modulation of is observed at 4 sigma level.
• Positive asymmetry is observed for measured invariant mass range. ( =0.25 - 2.0 [GeV/c2])
,
,
)sin( SR UTA
01 Hq
SystStat 003.0009.0040.0sin
)sin(
SRUTA
M
Outlook
OutlookOutlook• 4~5 M more DIS events are expected in 2005, compared to 3.5 M DIS events in 2002~2004.
backup
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
p
p
y
x
W
Q
track
track
2
2
p
px
M
MME
2
22
Xeep SIDIS events with at least pion pair( ) appeared were analyzed.
,
To cut exclusive channel.
Data set : 2002~2004
Evaluate
DISDIS
DISDIS
/),,(/),,(
/),,(/),,(1),,(
NNNN
NNNN
SA
SRSR
SRSR
TSRUT
UTA
0.54.75 TSwhere is the average target polarization. ( )TS
,...sin)sin(~ 11 HhSR
What is measured
sin)sin(ofdependence SRUTAM
Positive asymmetry is observed around 0 MM
sin)sin(10 SRaa
Asymmetry is fitted with
1sin)sin( aA SR
UT
binning :0.25, 0.40, 0.55, 0.77, 2.0 [GeV]
M
Single-spin asymmetry in 2-hadron production
M : invariant mass of pion pair
spectrumM
With or without cut]GeV[2.0E
p
px
M
MME
2
22
spectrumz
With or without cut]GeV[2.0E
p
px
M
MME
2
22
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
Polarized cross section for 2 hadron SIDIS
GAgHhA LULR
~11
sin
GCfeHA RLU
~11
sin
2 hadron semi-inclusive DIS
Single spin asymmetries
11)sin( HhA SR
UT
)~
(sin 112 aaqqaaqq
LRq
qUL GAgHhed
aaqqaaqqR
qqLU GCfHeed 1112 ~sin
(...)sin)sin( 112
Saaqq
SRq
qUT BHhed
Polarized cross section for 2 hadron SIDIS
2 hadron semi-inclusive DIS
Gfz
eHM
M
Q
RyWed
DxfM
MH
M
RH
zh
Q
MyV
HhM
RyB
Sed
Ggz
HhM
M
Q
RyVSed
hHM
MD
z
f
Q
RyVDfyAed
h
xRe
qqLU
Th
o
h
hS
hSR
qqUT
Lh
xLR
qqUL
h
xR
qqUU
~1sinsin)(
sin~1
sin)(
sin)sin()(
~1sin)(sin
~sincos)()(
112
1)1(
12
2
21
11
2
112
11
112
yyyWyyyV
yyB
yyyA
12122
12
12
)()()(
)(
)(
In Wandzura-Wilzcek approx.,function with tilde vanish.