F Giordano: spin-dependent effects in spin-averaged DIS

SPIN EFFECTS IN
UNPOLARIZED SIDIS
ati
10
Azimuthal cosine modulations
DIS unpolarized cross section
rdano
b
Francesca Giordano
SPIN 2012, Dubna, Russia
1

Francesca Giordano
Collinear case
target
polarization
beam
polarization virtual photon
polarization
d3
⇤
dxdydz =
2
xyQ2 1 + ⇥2
2x {A(y)FUU,T + B(y)FUU,L}
SEMI-INCLUSIVE DIS
2

Francesca Giordano
target
polarization
beam
polarization
SEMI-INCLUSIVE DIS
2

Francesca Giordano
target
polarization
beam
polarization
SEMI-INCLUSIVE DIS
Negative squared
4-momentum transfer to the target
Fractional energy of the virtual photon
Parton fractional momentum
Fractional energy transfer to the
produced hadron
2

TRANSVERSE MOMENTUM
DEPENDENT FUNCTIONS
DF
σ
FF
3

TRANSVERSE MOMENTUM
DEPENDENT FUNCTIONS
DF
σ
FF
distribution functions
PDF probabilistic interpretation
f q
1 (x)
gq
1 (x)
hq
1 (x)
legend
transverse and longitu
Table 2.1.: Pictorial representation and chiral properties of the
transverse longitudinal
nucleon spin
parton spin
TMDs - Pro
parton with transverse or longit
parton transverse momentum
nucleon with transverse or l
Proton goes out of
parton transverse
momentum
3

TRANSVERSE MOMENTUM
DEPENDENT FUNCTIONS
DF
σ
FF
fragmentation functions
f q
1 (x)
gq
1 (x)
hq
1 (x)
legend
nucleon spin
parton spin
TMDs - Pro
Proton goes out of
parton transverse
momentum
3

TRANSVERSE MOMENTUM
DEPENDENT FUNCTIONS
DF
σ
FF
Boer-Mulders DF
f q
1 (x)
gq
1 (x)
hq
1 (x)
legend
nucleon spin
parton spin
TMDs - Pro
Proton goes out of
parton transverse
momentum
3

TRANSVERSE MOMENTUM
DEPENDENT FUNCTIONS
DF
σ
FF
Boer-Mulders DF
Collins FF
f q
1 (x)
gq
1 (x)
hq
1 (x)
legend
nucleon spin
parton spin
TMDs - Pro
Proton goes out of
parton transverse
momentum
3

Francesca Giordano
f q
1 (x)
gq
1 (x)
hq
1 (x)
legend
nucleon spin
parton spin
TMDs - Pro
Proton goes out of
parton transverse
momentum
LEADING TWIST TERMS
implicit sum over quark ﬂavors
4

Francesca Giordano
LEADING AND
NEXT-TO-LEADING TWIST TERMS
f q
1 (x)
gq
1 (x)
hq
1 (x)
legend
nucleon spin
parton spin
TMDs - Pro
Proton goes out of
parton transverse
momentum
5

Francesca Giordano
LEADING AND
interaction dependent
terms neglected
f q
1 (x)
gq
1 (x)
hq
1 (x)
legend
nucleon spin
parton spin
TMDs - Pro
Proton goes out of
parton transverse
momentum
5

Francesca Giordano
LEADING AND
interaction dependent
terms neglected
+M2
Q2 C[
2
T
M2 f1D1 + ...]
f q
1 (x)
gq
1 (x)
hq
1 (x)
legend
nucleon spin
parton spin
TMDs - Pro
Proton goes out of
parton transverse
momentum
5

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
1 ]Boer-Mulders effect
kT
kT
Ph?
Ph? sT
sT
6

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
correlations between quark transverse spin &
transverse momentum
6

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
transverse momentum
SPIN Effect!
6

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
chiral odd chiral odd
chiral even!
}
transverse momentum
h?
1 H?
1
chiral odd functions
SPIN Effect!
6

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
transverse momentum
naive Time reversal odd
SPIN Effect!
6

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
Final State Interactions
transverse momentum
SPIN Effect!
6
u
FSI
u

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
transverse momentum
Spatial distortions due to
spin-orbit correlations
SPIN Effect!
6
u
FSI
u

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
transverse momentum
Collins FF H1 (z,kT
2) correlates transverse spin of fragm
and transverse momentum Ph of produced hadron h
““CollinsCollins--effect”effect”
h
h
q q
left-right (azimuthal) asymmetry in the direction
outgoing hadron
our observable: singleour observable: single--spinspin azimuthalazimuthal asymmasymm
Collins effect
SPIN Effect!
6
u
FSI
u

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
transverse momentum
Collins FF H1 (z,kT
2) correlates transverse spin of fragm
and transverse momentum Ph of produced hadron h
““CollinsCollins--effect”effect”
h
h
q q
left-right (azimuthal) asymmetry in the direction
outgoing hadron
our observable: singleour observable: single--spinspin azimuthalazimuthal asymmasymm
Collins effect
SPIN Effect!
access to Collins effect
6
u
FSI
u

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
transverse momentum
Cahn effect / C[f1D1]
Ph?
Ph?kT
kT
SPIN Effect!
7

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
transverse momentum
Ph?
Ph?kT
kT
kinematic effect generated by parton intrinsic
transverse motion
SPIN Effect!
7

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
transverse momentum
Ph?
Ph?kT
kT
transverse motion
hq
T i ! cos q
h ! cos H
h
SPIN Effect!
7

Francesca Giordano
BOER-MULDERS EFFECT
/ C[ h?
1 H?
kT
kT
Ph?
Ph? sT
sT
transverse momentum
Ph?
Ph?kT
kT
transverse motion
access to parton transverse momenta
hq
T i ! cos q
h ! cos H
h
SPIN Effect!
7

Francesca GiordanoFrancesca Giordano
HERMES @ HERA
8

Francesca Giordano
DESY
Francesca Giordano
HERMES @ HERA
8

Francesca Giordano
DESY
Francesca Giordano
HERMES @ HERA
27.6 GeV (e+/e-) lepton
beam off D/H target
8

Francesca Giordano
HERMES
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9

Francesca Giordano
HERMES
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Francesca Giordano
HERMES
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DIPOLE
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9

Francesca Giordano
HERMES
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27.6 GeV e±
beam
H/D target
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DIPOLE
DIPOLE
tracking detectors: momentum resolution <2.5%
9

Francesca Giordano
HERMES
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beam
H/D target
particle identification: lepton/hadron separation
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DIPOLE
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Francesca Giordano
HERMES
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beam
H/D target
RICH: discrimination between charged "/ K / p
particle identification: lepton/hadron separation
RICH
RICH
DIPOLE
DIPOLE
9

Francesca Giordano
ACCEPTANCE CORRECTION
w = (x, y, z, Ph?)
0
w[1 + 2hcos hiw + 2hcos 2 hiw]
10

Francesca Giordano
w = (x, y, z, Ph?)
n =
Z
L⇥0
w[1 + 2hcos ⇤hiw + 2hcos 2⇤hiw] acc
w, h
rad
w, h
dw
10

Francesca Giordano
w = (x, y, z, Ph?)
n =
Z
L⇥0
w, h
rad
w, h
dw
34
MC
RAD
MCMCMC
accLn εε=
MC
0σ

Generated in 4⇡
ωφωε dMC
RAD
),()
),(),( φωεφωε RADacc)2cos)( φωB ωd
Inside acceptance
MC
MC simulation of spectrometers to correct for
acceptance/QED radiation
10

Francesca Giordano
w = (x, y, z, Ph?)
n =
Z
L⇥0
w, h
rad
w, h
dw
34
MC
RAD
MCMCMC
accLn εε=
MC
0σ

Generated in 4⇡
ωφωε dMC
RAD
),()
Inside acceptance
MC
n =
Z
L⇥0
w, h
rad
w, h
dw
n =
Z
L⇥0
w
acc
w, h
rad
w, h
dw
10

Francesca Giordano
w = (x, y, z, Ph?)
n =
Z
L⇥0
w, h
rad
w, h
dw
34
MC
RAD
MCMCMC
accLn εε=
MC
0σ

Generated in 4⇡
ωφωε dMC
RAD
),()
Inside acceptance
MC
Not allowed!
n =
Z
L⇥0
w, h
rad
w, h
dw
n =
Z
L⇥0
w
acc
w, h
rad
w, h
dw
10

Francesca Giordano
w = (x, y, z, Ph?)
n =
Z
L⇥0
w, h
rad
w, h
dw
34
MC
RAD
MCMCMC
accLn εε=
MC
0σ

Generated in 4⇡
ωφωε dMC
RAD
),()
Inside acceptance
MC
Not allowed!
only if fully differential ratio (4D binning)
and only in the limit of inﬁnitely small bins
n =
Z
L⇥0
w, h
rad
w, h
dw
n =
Z
L⇥0
w
acc
w, h
rad
w, h
dw
10

Francesca Giordano
w = (x, y, z, Ph?)
(w)4-dimensional
n =
Z
L⇥0
w, h
rad
w, h
dw
Binning
900 kinematic bins x 12 -bins
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #
x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
unfolding
11

Francesca Giordano
w = (x, y, z, Ph?)
(w)4-dimensional
n =
Z
L⇥0
w, h
rad
w, h
dw
nborn= S 1
[n B0]
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
unfolding
11

Francesca Giordano
w = (x, y, z, Ph?)
(w)4-dimensional
describes the acceptance &
smearing between adjacent bins
events smeared in the sample
from outside the acceptance
n =
Z
L⇥0
w, h
rad
w, h
dw
nborn= S 1
[n B0]
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
unfolding
11

Francesca Giordano
w = (x, y, z, Ph?)
(w)4-dimensional
describes the acceptance &
smearing between adjacent bins
events smeared in the sample
from outside the acceptance
n =
Z
L⇥0
w, h
rad
w, h
dw
A(1 + B cos h + C cos 2 h)
nborn= S 1
[n B0]
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
unfolding
11

Francesca Giordano
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
PION FIT & PROJECTION
w = (x, y, z, Ph?)
(w)4-dimensional
n =
Z
L⇥0
w, h
rad
w, h
dw
unfolding
z
x
y
Ph?
12

Francesca Giordano
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
0.023 0.042 0.078 0.145 0.27
0.3 0.45 0.6 0.7 0.85
0.2 0.3 0.4 0.5 0.6 0.75
0.05 0.2 0.35 0.5 0.7 1
PION FIT & PROJECTION
w = (x, y, z, Ph?)
(w)4-dimensional
n =
Z
L⇥0
w, h
rad
w, h
dw
unfolding
z
x
y
Ph?
12

Francesca Giordano
Boer-Mulders
Cahn
COS2 : PIONS
Final! / C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
13
arXiv:1204.4161

Francesca Giordano
Cahn expected ﬂavor blind
Boer-Mulders
Cahn
COS2 : PIONS
Final! / C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
13
arXiv:1204.4161

Francesca Giordano
different / amplitudes
Boer-Mulders effect
⇡+
⇡
Boer-Mulders
Cahn
COS2 : PIONS
Final! / C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
13
arXiv:1204.4161

Francesca Giordano
Boer-Mulders effect
⇡+
⇡
Boer-Mulders
Cahn
COS2 : PIONS
Final! / C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
SPIN Effect!13
arXiv:1204.4161

Francesca Giordano
Boer-Mulders effect
⇡+
⇡
Boer-Mulders
Cahn
Gamberg, Goldstein
Phys. Rev. D77:094016, 2008
COS2 : PIONS
Final! / C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
SPIN Effect!13
arXiv:1204.4161

Francesca Giordano
Boer-Mulders effect
⇡+
⇡
Boer-Mulders
Cahn
Zhang et al
Phys. Rev. D78:034035, 2008
Gamberg, Goldstein
Phys. Rev. D77:094016, 2008
COS2 : PIONS
Final! / C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
SPIN Effect!13
arXiv:1204.4161

Francesca Giordano
Boer-Mulders effect
⇡+
⇡
Boer-Mulders
Cahn
Barone et al
Phys. Rev. D78:045022, 2008
Zhang et al
Phys. Rev. D78:034035, 2008
Gamberg, Goldstein
Phys. Rev. D77:094016, 2008
COS2 : PIONS
Final! / C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
SPIN Effect!13
arXiv:1204.4161

Francesca Giordano
Boer-Mulders effect
⇡+
⇡
Boer-Mulders
Cahn
COS2 : PIONS
Final! / C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
Hydrogen vs Deuterium
SPIN Effect!14
arXiv:1204.4161

Francesca Giordano
Boer-Mulders effect
⇡+
⇡
Boer-Mulders
Cahn
COS2 : PIONS
Final! / C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
h?,u
1 ⇡ h?,d
1
Hydrogen vs Deuterium
SPIN Effect!14
arXiv:1204.4161

Francesca Giordano
Boer-Mulders effect
⇡+
⇡
COS : PIONS
Final!
/ 2M
Q C[ h?
1 H?
1
f1D1 + ....]
15
arXiv:1204.4161

Francesca Giordano
Cahn
Boer-Mulders
Boer-Mulders effect
⇡+
⇡
COS : PIONS
Final!
/ 2M
Q C[ h?
1 H?
1
f1D1 + ....]
15
arXiv:1204.4161

Francesca Giordano
Cahn
/01&"#2'3" 456785988:.#;88<
=>?"#/01&"#@" $A67A5A.#;885
!"
x
-1
10
UU
〉)
h
φcos(〈2
-0.2
-0.1
0
0.1
−
π
+π
y
0.4 0.6 0.8
-0.2
-0.1
0
0.1 Xπe→e p
z
0.4 0.6
-0.2
-0.1
0
0.1
[GeV]⊥h
P
0.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1 HERMES preliminary
#$%φ& '$()*+,-$. [ ]...
2
1111
cos
+−−∝ ⊥⊥
DfHh
Q
M
F h
UU Cφ
!"#$%&'()*%+#', -(".#
/01&"#2'3" 456785988:.#;88<
=>?"#/01&"#@" $A67A5A.#;885
Fcos h
UU / C[h?
1 H?
1 f1D1+....]Fcos h
UU / C[h?
1 H?
1 f1D1+....]
Cahn only
Too large!

x
-1
10
UU
〉)
h
φcos(〈2
-0.2
-0.1
0
0.1
−
π
+π
y
0.4 0.6 0.8
-0.2
-0.1
0
0.1 Xπe→e p
z
0.4 0.6
-0.2
-0.1
0
0.1
[GeV]⊥h
P
0.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1 HERMES preliminary
φ  [ ]...
2
1111
cos
+−−∝ ⊥⊥
DfHh
Q
M
F h
UU Cφ
 
 
 
Boer-Mulders
Boer-Mulders effect
⇡+
⇡
COS : PIONS
Final!
/ 2M
Q C[ h?
1 H?
1
f1D1 + ....]
15
arXiv:1204.4161

Francesca Giordano
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
KAON FIT & PROJECTION
(w)4-dimensional
unfolding
z
x
y
Ph?
16

Francesca Giordano
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
KAON FIT & PROJECTION
0.042 0.078 0.145 0.27
0.3 0.45 0.6 0.7
0.3 0.4 0.5 0.6
0.2 0.35 0.5 0.7
(w)4-dimensional
unfolding
z
x
y
Ph?
16

COS2 KAONS & PIONS
Final! / C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
17
arXiv:1204.4161

COS2 KAONS & PIONS
Final!
Boer-Mulders
Cahn
/ C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
17
arXiv:1204.4161

COS2 KAONS & PIONS
Final!
Boer-Mulders
Cahn
/ C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
No predictions for Kaons!
17
arXiv:1204.4161

COS2 KAONS & PIONS
Final!
Boer-Mulders
Cahn
/ C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
No predictions for Kaons! Favored dominance for & .
same sign
K+
⇡+
?
17
arXiv:1204.4161

COS2 KAONS & PIONS
Final!
Boer-Mulders
Cahn
/ C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
same sign
K+
⇡+
?
fully sea object!
both favored&unfavored fragmentation
K
17
arXiv:1204.4161

COS2 KAONS & PIONS
Final!
Boer-Mulders
Cahn
/ C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
same sign
K+
⇡+
?
fully sea object!
K
Non trivial!
17
arXiv:1204.4161

COS2 KAONS & PIONS
Final!
Boer-Mulders
Cahn
/ C[ h?
1 H?
1
+
2
T
Q2
f1D1 + ....]
same sign
K+
⇡+
?
fully sea object!
K
Non trivial!
Collins FF for kaons
soon from Belle
17
arXiv:1204.4161

Francesca Giordano
COS KAONS & PIONS
Final!
Similar trends for Pion-Kaon
/ 2M
Q C[ h?
1 H?
1
f1D1 + ....]
18
arXiv:1204.4161

Francesca Giordano
COS KAONS & PIONS
Final!
Similar trends for Pion-Kaon ?
Cahn
Boer-Mulders
/ 2M
Q C[ h?
1 H?
1
f1D1 + ....]
18
arXiv:1204.4161

Francesca Giordano
MULTI-D RESULTS
http://durpdg.dur.ac.uk
First 6 bins
19

Francesca Giordano
MULTI-D RESULTS
First 6 bins
1st x bin
20

Francesca Giordano
MULTI-D RESULTS
First 6 bins
1st x bin
2nd x bin
20

Francesca Giordano
MULTI-D RESULTS
First 6 bins
1st x bin
2nd x bin
3rd x bin
20

Francesca Giordano
MULTI-D RESULTS
First 6 bins
1st x bin
2nd x bin
3rd x bin 4th x bin
20

Francesca Giordano
MULTI-D RESULTS
First 6 bins
1st x bin
2nd x bin
3rd x bin 4th x bin 5th x bin
20

Francesca Giordano
MULTI-D RESULTS
First 6 bins
1st x bin
2nd x bin
HYDROGEN, .
⇡+
DEUTERIUM, .
⇡+
20

Francesca Giordano
MULTI-D RESULTS
First 6 bins
1st x bin
2nd x bin
HYDROGEN, .
⇡+
HYDROGEN, .
⇡
DEUTERIUM, .
⇡+
DEUTERIUM, .
⇡
HYDROGEN, .KHYDROGEN, .
K+
DEUTERIUM, .KDEUTERIUM, .
K+
HYDROGEN, .
HYDROGEN, .
DEUTERIUM, .
DEUTERIUM, .
h+
h+
h
h
20

Francesca Giordano
MULTI-D RESULTS
First 6 bins
1st x bin
2nd x bin
HYDROGEN, .
⇡+
HYDROGEN, .
⇡
DEUTERIUM, .
⇡+
DEUTERIUM, .
⇡
HYDROGEN, .KHYDROGEN, .
K+
DEUTERIUM, .KDEUTERIUM, .
K+
HYDROGEN, .
HYDROGEN, .
DEUTERIUM, .
DEUTERIUM, .
THERE’S
AN EASIER WAY!
h+
h+
h
h
20

Francesca Giordano
A USEFUL TOOL
http://www-hermes.desy.de/cosnphi/
New!
21

Francesca Giordano
Binning
900 kinematic bins x 12 - bins
Binning
Binning
Binning
Binning
Binning
Binning
Binning
Binning
x 0.02 0.04 0.08 0.15 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1 6Ph?
A USEFUL TOOL
New!
z
x
y
Ph?
22

Francesca Giordano
A USEFUL TOOL
New!
23

Francesca Giordano
UU
cos22
-0.2
-0.1
0
0.1
+h
x
-1
10
UU
cos22
-0.2
-0.1
0
0.1
-
h
y
0.4 0.6 0.8
z
0.4 0.6 0.8
e h Xe p
[GeV]hP
0.2 0.4 0.6 0.8 1 1.2
Systematic errors not shown
Systematic errors not shown
A USEFUL TOOL
New!
23

Francesca Giordano
PIONS: MORE PROJECTIONSFull z-dependence
24

Francesca Giordano
PIONS: MORE PROJECTIONSFull z-dependence Full -dependencePh?
24

Francesca Giordano
KAONS: MORE PROJECTIONS
Larger z-dependence Larger -dependencePh?
25

Francesca Giordano
SUMMARY
To date provides the most complete data
set available for Boer-Mulders and Cahn effects!
 
  



2009 Madrid, 26-30 April 2009
26

Francesca Giordano
Different behavior for with respect to pions:
large signals and same sign for modulation: indication of
same sign for favored/unfavored strange Collins fragmentation
functions?
K+
/K
cos 2 h
SUMMARY
 
  



2009 Madrid, 26-30 April 2009
26

Francesca Giordano
functions?
K+
/K
cos 2 h
Differences between :
evidence of a non-zero Boer-Mulders function:
conﬁrms opposite sign for favored and unfavored pion Collins
+
/
SUMMARY
 
  



2009 Madrid, 26-30 April 2009
26

Francesca Giordano
functions?
K+
/K
cos 2 h
+
/
Similar results for deuterium & hydrogen data
suggest a Boer-Mulders function with same sign for u and d quark
SUMMARY
 
  



2009 Madrid, 26-30 April 2009
26

Francesca Giordano
functions?
K+
/K
cos 2 h
+
/
Thank you!
Similar results for deuterium & hydrogen data
suggest a Boer-Mulders function with same sign for u and d quark
SUMMARY
 
  



2009 Madrid, 26-30 April 2009
26

F Giordano: spin-dependent effects in spin-averaged DIS

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F Giordano: spin-dependent effects in spin-averaged DIS