HERMES results on azimuthal modulations in the spin-independent SIDIS cross section
description
Transcript of HERMES results on azimuthal modulations in the spin-independent SIDIS cross section
HERMES results on azimuthal modulations in the spin-independent SIDIS cross section
Francesca GiordanoDESY, Hamburg
For the collaboration
Madrid, DIS 2009
2
),,(...... zyxFF
LUUTUU FyBFyAxxyQdzdydx
d,,
2
2
23
)()(2
1
TUUF , LUUF ,
Collinear approximation
Unpolarized Semi-Inclusive DIS
2Q
xy
Negative square
four-momentum transfer to the target
Fractional energy of the virtual photon
Bjorken scaling variable
Fractional energy transfer to the
produced hadron
z
3
),,(...... zyxFF
LUUTUU FyBFyAxxyQdzdydx
d,,
2
2
23
)()(2
1
TUUF , LUUF ,
Collinear approximation
Unpolarized Semi-Inclusive DIS
2Q
xy
Negative square
four-momentum transfer to the target
Fractional energy of the virtual photon
Bjorken scaling variable
Fractional energy transfer to the
produced hadron
z Beam polarization Virtual
photon polarizatio
n
FTarget
polarization
4
Unpolarized Semi-Inclusive DIS
),,,(...... hPzyxFF
hhUUhUUh FyBFyC 2coscos 2cos)(cos)( hUUF 2cosh
UUF cos
LUUTUUhh
FyBFyAxxyQdPddzdydx
d,,
2
2
2
2
5
)()(2
1
TUUF , LUUF ,
5h
hh
hhd
dnPzyxn
)5(
)5(cos),,,(cos
Unpolarized Semi-Inclusive DIS
hhUUhUUh FyBFyC 2coscos 2cos)(cos)( hUUF 2cosh
UUF cos
LUUTUUhh
FyBFyAxxyQdPddzdydx
d,,
2
2
2
2
5
)()(2
1
TUUF , LUUF ,
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DF
FF
Leading twist expansion
11, DfF TUU C
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DF
FF
Leading twist expansion
11, DfF TUU CN / q U L T
U
L
T
Distribution Functions (DF)
1h
Tg1
1g Lh1
1hTh1,
Tf1
1f
q/h U
U
T
1D1H
Fragmentation Functions
(FF)
8
DF
FF
Leading twist expansion
11, DfF TUU CN / q U L T
U
L
T
q/h U
U
T
1D1H
Distribution Functions (DF)
Fragmentation Functions
(FF)
1h
Tg1
1g Lh1
1hTh1,
Tf1
1f
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= Boer-Mulders = Boer-Mulders
functionfunctionCHIRAL-ODDCHIRAL-ODD
1h
Leading twist expansion
CHIRAL-CHIRAL-
EVENEVEN!
chiral-odd
DF
chiral-oddFF
11 HhC
N / q U L T
U
L
T
q/h U
U
T
1D1H
Distribution Functions (DF)
Fragmentation Functions
(FF)
1h
Tg1
1g Lh1
1hTh1,
Tf1
1f
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Leading twist azimuthal
modulation
(Implicit sum over quark flavours)
112cos ))((2
HhMM
pkpPkPF
h
TTThThUU
h
C
11 Hh
11(Implicit sum over quark flavours)
...neglecting interaction dependent terms....
...
21111
cos DfxM
kPHhx
M
pP
Q
MF Th
h
ThUU
h
C
112cos ))((2
HhMM
pkpPkPF
h
TTThThUU
h
C
11Df
11 Hh
Leading & next to leading twist
azimuthal modulation
11 Hh
12
...
21111
cos DfxM
kPHhx
M
pP
Q
MF Th
h
ThUU
h
C
Cahn and Boer-Mulders
effects
112cos ))((2
HhMM
pkpPkPF
h
TTThThUU
h
C
11 Hh
11 Hh
CAHN EFFECT
11DfxM
kP Th
11Df
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BOER-MULDERS EFFECT
...
21111
cos DfxM
kPHhx
M
pP
Q
MF Th
h
ThUU
h
C
112cos ))((2
HhMM
pkpPkPF
h
TTThThUU
h
C
11DfxM
kP Th
11 HhxM
pP
h
Th
11 Hh 11Df
11
))((2Hh
MM
pkpPkP
h
TTThTh
11 Hh
CAHN EFFECT
Cahn and Boer-Mulders
effects
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HERa MEasurement of SpinHERA storage ring @ DESY
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HERa MEasurement of Spin
Lepton (Electron/Positron) HERA beam (27.6 GeV)
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HERMES spectrometer
Resolution: p/p ~ 1-2% <~0.6 mrad
Electron-hadron separation efficiency ~ 98-99%
Hadron identification with dual-radiator RICH
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HERMES spectrometer
Resolution: p/p ~ 1-2% <~0.6 mrad
Electron-hadron separation efficiency ~ 98-99%
Hadron identification with dual-radiator RICH
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HERMES spectrometer
Resolution: p/p ~ 1-2% <~0.6 mrad
Electron-hadron separation efficiency ~ 98-99%
Hadron identification with dual-radiator RICH
Aerogel n=1.03
C4F10 n=1.0014
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dwLwBwAwn hhEXP 2cos)(cos)(1)(0
),,,( hPzyxw
hB 2cos2
hA cos2
Experimental extraction
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Experimental extraction
),,,( hPzyxw
hh wBwA 2cos)(cos)( ),(),( hhacc wwRAD
dwL 1)(0 wnEXP
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unfolding procedure
Experimental extraction
),,,( hPzyxw
hh wBwA 2cos)(cos)( ),(),( hhacc wwRAD
dwL 1)(0 wnEXP
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Multidimensional ( )unfolding procedure
w
),,,( hPzyxw
Experimental extraction
hh wBwA 2cos)(cos)( ),(),( hhacc wwRAD
dwL 1)(0 wnEXP
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BORNEXP
nn S Bgn
The unfolding procedure
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BORNEXP
nn S Bgn
Probability that an event generated with kinematics wis measured with kinematics w’
(w)
(w’)
The unfolding procedure
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The unfolding procedure
Accounts for acceptance, radiative and smearing
effects
depends only on instrumental and radiative effects
BORNEXP
nn S Bgn
Probability that an event generated with kinematics wis measured with kinematics w’
(w)
(w’)
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Includes the events smeared into the
acceptance
Accounts for acceptance, radiative and smearing
effects
depends only on instrumental and radiative effects
The unfolding procedure
BORNEXP
nn S Bgn
Probability that an event generated with kinematics wis measured with kinematics w’
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The unfolding procedure
BORNEXP
nn S Bgn
EXPBORN
nn 1S Bgn
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Monte Carlo + Cahn model
Measured inside acceptance
Generated in 4
Why a multi-dimensional analysis?
hh wBwA 2cos)(cos)( ),(),( hhacc wwRAD
dwL 1)(0 wn CahnMC
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Why a multi-dimensional analysis?
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Why a multi-dimensional analysis?
4D binned in
),,,( hPzyx
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BINNING
400 kinematical bins x 12 -bins
Variable Bin limits #
x 0.023 0.042 0.078 0.145 0.27 1 5
y 0.3 0.45 0.6 0.7 0.85 4
z 0.2 0.3 0.45 0.6 0.75 1 5
Ph . 0.05 0.2 0.35 0.5 0.75 4
The multi-dimensional analysis
x bin=2x bin=3
hP
x bin=1
x bin=5
h
First y bin
x bin=4
z
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The multi-dimensional analysis
hcos
unfolding+fi
t
x bin=2x bin=3
hP
x bin=1
x bin=5
h
First y bin
x bin=4
z
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)(
cos)()(cos
4
4
bi
bibi
xx
xxxx
bx
projecti
on
The multi-dimensional analysis
hcos
x bin=2x bin=3
hP
x bin=1
x bin=5
h
First y bin
x bin=4
z
34
hcos
)(
cos)()(cos
475.0
05.0
275.0
2.0
85.0
3.0
475.0
05.0
275.0
2.0
85.0
3.0
bi
bibi
xxh
xxxxh
b
dPdzdy
dPdzdyx
)(
cos)()(cos
4
4
bi
bibi
xx
xxxx
bx
The multi-dimensional analysisx bin=2
x bin=3
hP
x bin=1
x bin=5
h
First y bin
x bin=4
z
Results
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Hydrogen data
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uu HH ,1
,1
Hydrogen data
uH ,1
uH ,1
M. Anselmino et al., Phys. Rev. D75:054032, 2007
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Hydrogen data
112cos ))((2
HhMM
pkpPkPF
h
TTThThUU
h
C
11 Hh
uu HH ,1
,1
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Hydrogen data
...
21111
cos DfxM
kPHhx
M
pP
Q
MF Th
h
ThUU
h
C
11Df11 Hh
uu HH ,1
,1
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cos2h interpretation
L. P. Gamberg and G. R. Goldstein,
Phys. Rev. D77:094016, 2008
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cos2h interpretation
Boer-Mulders
All contribution
sCahn (twist
4)
V. Barone et al. Phys.Rev.
D78:045022, 2008
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cos2h interpretation
B. Zhang et al.,Phys. Rev.
D78:034035, 2008
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cosh interpretation
M. Anselmino et al., Phys. Rev.
D71:074006, 2005Eur. Phys. J. A31:373,
2007
44
cosh interpretation
...
21111
cos DfxM
kPHhx
M
pP
Q
MF Th
h
ThUU
h
C
11Df11 Hh
45
h+
du hh ,1,1
Hydrogen vs. Deuterium data
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h-
du hh ,1,1
Hydrogen vs. Deuterium data
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Summary The existence of an intrinsic quark transverse motion gives origin to an azimuthal asymmetry in the hadron production direction:
Cahn effect: an (higher twist) azimuthal modulation related to the existence of intrinsic quark motion;Boer-Mulders effect: a leading twist asymmetry originated from the correlation between the quark transverse motion and transverse spin (a kind of spin-orbit effect).
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Summary
Monte Carlo studies show that: A fully differential unfolding procedure is essential to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section.
The existence of an intrinsic quark transverse motion gives origin to an azimuthal asymmetry in the hadron production direction:
Cahn effect: an (higher twist) azimuthal modulation related to the existence of intrinsic quark motion;Boer-Mulders effect: a leading twist asymmetry originated from the correlation between the quark transverse motion and transverse spin (a kind of spin-orbit effect).
49
Flavour dependent experimental results: Negative <cosh> moments are extracted for positive
and negative hadrons, with a larger absolute value for the positive ones The results for the <cos2h> moments are negative
for the positive hadrons and positive for the negative hadrons
- Evidence of a non-zero Boer-Mulders function
Summary
Monte Carlo studies show that: A fully differential unfolding procedure is essential to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section.
The existence of an intrinsic quark transverse motion gives origin to an azimuthal asymmetry in the hadron production direction:
Cahn effect: an (higher twist) azimuthal modulation related to the existence of intrinsic quark motion;Boer-Mulders effect: a leading twist asymmetry originated from the correlation between the quark transverse motion and transverse spin (a kind of spin-orbit effect).
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The existence of an intrinsic quark transverse motion gives origin to an azimuthal asymmetry in the hadron production direction:
Cahn effect: an (higher twist) azimuthal modulation related to the existence of quark intrinsic motion;Boer-Mulders effect: a leading twist asymmetry originated by the correlation between the quark transverse motion and spin (a kind of spin-orbit effect).
Summary
Monte Carlo studies show that: A fully differential unfolding procedure is able to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section.
THANK
THANK
YOU!YOU!
Flavour dependent experimental results: Negative <cosh> moments are extracted for positive
and negative hadrons, with a larger absolute value for the positive ones The results for the <cos2h> moments are negative
for the positive hadrons and positive for the negative hadrons
- Evidence of a non-zero Boer-Mulders function
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Compass results
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Experimental status: hcos
EMC
E665
ZEUS
c)
Negative results in all the existing measurements
No distinction between hadron type or charge
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h2cos
EMC
ZEUS collaborationXhHe
0.12.0 z
222 /7220180 cGeVQ 01.001.0 x 8.02.0 y
ZEUS
Drell-Yan
Experimental status:
Positive results in all the existing measurements
No distinction between hadron type or charge (in SIDIS experiments)
Indication of small Boer-Mulders function for the sea quark (from Drell-Yan experiments)