Tranvserse Momentum and Spin:
an Experimental Overview
N.C.R. Makins
Outline
University of Illinois at Urbana-Champaign
& Josh Rubin,
the Animagician!
TMDs, SSAs, and
• Intro
the Collins & Sivers story
Fragmentation Function
• Collins
the “duct tape” of TMD analysis
• Transversity
the “3rd” PDF
function
• Sivers
parton orbital angular momentum
•
Boer-Mulders funcn & Cahn effect
Lq and kT with all new data!
N.C.R. Makins, SPIN2008, Oct 8, 2008
TMDs and SSAAs
Glossary:
Transverse Momentum Dependent PDFs & FFs
Single-Spin Azimuthal Asymmetries
A particular puzzle: Where does the proton spin come from?
q(x) = q↑(x) + q↓(x)
Δq(x) = q↑(x) − q↓(x)
1 1
= ΔΣ + ΔG + Lq + Lg
2 2
only three possibilities
➊ Quark
Z polarization
ΔΣ ≡
dx (Δu(x) + Δd(x) + Δs(x) + Δu(x) + Δd(x) + Δs(x)) ≈ 30% only
➋ Gluon Zpolarization
?
Lz ≡ Lq + Lg
?
ΔG ≡
dx Δg(x)
➌ Orbital angular momentum
In friendly, non-relativistic bound states like
atoms & nuclei (& constituent quark model),
particles are in eigenstates of L
Not so for bound, relativistic Dirac particles ...
Noble “l” is not a good quantum number
N.C.R. Makins, SPIN2008, Oct 8, 2008
Functions surviving on
integration over
Transverse Momentum
The others are sensitive to intrinsic kT in
the nucleon & in the fragmentation process
Mulders & Tangerman, NPB 461 (1996) 197
Distribution Functions
Weird #1
f1
=
g1 =
Fragmentation Functions
D1 =
g 1T =
G
1
=
G 1T =
h1 =
transversity
H1 =
f 1T =
Sivers
D1T =
Polarizing FF
h1 =
Boer-Mulders
H1 =
Collins
H 1L =
H 1T =
h 1L =
Weird #2
h 1T =
One T-odd function required to produce
Pretzelosity
single-spin asymmetries in SIDIS
N.C.R. Makins, SPIN2008, Oct 8, 2008
beam
target SIDIS xsec
Polarized
Measuring: Azimuthal Asymmetries
polnat leading
poln
order in 1/Q:
UU
1
cos(2φlh)
⊗ f1 =
⊗ h⊥
1 =
⊗ D1 =
⊗ H1⊥ =
UL
sin(2φlh)
⊗ h⊥
1L =
⊗ H1⊥ =
UT
sin(φlh + φlS )
⊗ h1 =
⊗ H1⊥ =
sin(3φlh − φlS )
⊗ h⊥
1T =
⊗ H1⊥ =
LL
1
⊗ g1 =
⊗ D1 =
LT
cos(φlh − φlS )
⊗ g1T =
⊗ D1 =
sin(φlh − φlS )
⊥
⊗ f1T
=
SIDIS, at
leading twist
⊗ D1 =
N.C.R. Makins, SPIN2008, Oct 8, 2008
Electro-Production of Hadrons with Tranvserse Target
Measure dependence of hadron production on two azimuthal angles
Electron beam defines
scattering plane
Target spin
transverse to beam
Azimuthal angles measured
around q vector ...
with respect to
scattering plane
φS = target spin orientation
φh
= hadron direction
N.C.R. Makins, SPIN2008, Oct 8, 2008
Fermilab E704:
p↑ p → πX at 400 GeV
π+
Analyzing Power
π-
AN =
1
π
π
Nleft
− Nright
π
π
Pbeam Nleft
+ Nright
Huge single-spin asymmetry !
0.6
!+
!0
!"
0.4
•
0.2
AN
+
Opposite sign for π = ud¯
−
than for π = d ū
• Effect larger for forward production
!S
· (!p
×!p )
• Observable:
odd under naive Time-Reversal
0
beam
-0.2
beam
π
-0.4
-0.6
0
0.2
0.4
0.6
x
0.8
1
Surprising observation! ..... Why?
F
N.C.R. Makins, SPIN2008, Oct 8, 2008
SSA’s
at high-energies
Single-Spin
Asymmetries
at Hard Scales
AN (Assuming A N =0.013)
Now
E704:confirmed
p↑p → πX at RHIC
at much higher energies
CNI
0.4
0.2
AN
SSA observables ∼ "J · (p"1 × p"2)
⇒ odd under naive time-reversal
0
0.6
π mesons
Total
π +energy
0.4
Collins
π0
Sivers
π−
Initial state twist-3
Final state twist-3
0.2
T-odd observables
STAR Run 6
Since QCD amplitudes are T-even, must arise
from interference between spin-flip and
non-flip amplitudes with different phases
0
-0.2
0.0 -0.4
-0.6
0.4 1.8 0.6
〈pT〉0= 1.0 0.2
1.1 1.3 1.5
2.1
-0.2
0
0.2
0.4
x
F
2.40.8
GeV/c 1
0.6
Suppressed
in pQCD
hard-scattering
Can’t
come from
perturbative
subprocess xsec:
√
• q helicity flip suppressed by mq / s
0.8
xF
π+
π-
• need αs-suppressed loop-diagram to
generate necessary phase
At hard (enough) scales, SSA’s must
arise from soft physics: T-odd distribution /
fragmentation functions
N.C.R. Makins, SPIN2008, Oct 8, 2008
SSA’s
at high-energies
Single-Spin
Asymmetries
at Hard Scales
AN (Assuming A N =0.013)
Now
E704:confirmed
p↑p → πX at RHIC
at much higher energies
CNI
0.4
0.2
AN
0
0.6
π mesons
Total
π +energy
0.4
Collins
π0
Sivers
π−
Initial state twist-3
Final state twist-3
0.2
T-odd observables
STAR Run 6
Since QCD amplitudes are T-even, must arise
from interference between spin-flip and
non-flip amplitudes with different phases
0
-0.2
0.0 -0.4
-0.6
0.4 1.8 0.6
〈pT〉0= 1.0 0.2
1.1 1.3 1.5
2.1
-0.2
0
0.2
0.4
x
F
SSA observables ∼ "J · (p"1 × p"2)
⇒ odd under naive time-reversal
Must be a spin-orbit structure
Suppressed
in pQCD
hard-scattering
come from
perturbative
subprocess xsec:
either in Can’t
the fragmentation
process
√
or within the proton itself
2.40.8
GeV/c 1
0.6
0.8
xF
π+
π-
• q helicity flip suppressed by mq / s
• need αs-suppressed loop-diagram to
generate necessary phase
At hard (enough) scales, SSA’s must
arise from soft physics: T-odd distribution /
fragmentation functions
N.C.R. Makins, SPIN2008, Oct 8, 2008
The Canonical Example:
Collins and Sivers
E704 Possible Mechanism #1: The “Collins Effect”
Need an ordinary distribution function ... transversity
h1(x)
Δq(x)
q(x)
... with a new, T-odd “Collins” fragmentation function
spin-orbit in fragmentation!
π
+
E704 effect:
π+
u
u
π
−
H1⊥(z, pT )
u
h1(x) ⊗ H1⊥(z, pT )
N.C.R. Makins, SPIN2008, Oct 8, 2008
E704 Possible Mechanism #2: The “Sivers Effect”
Need the ordinary fragmentation function
D1(z)
... with a new, T-odd “Sivers” distribution function
⊥
(x, kT )
f1T
Phenomenological model of Meng, Boros, Liang:
Forward π+ produced from orbiting valence-u quark by
recombination at front surface of beam protons
quark orbital motion!
u
E704 effect:
π
+
π
+
uv
d
⊥
(x, kT ) ⊗ D1(z)
f1T
N.C.R. Makins, SPIN2008, Oct 8, 2008
T-odd Distributionofvs
Fragmentation
Function
Electroproduction
Pions
with Transverse
Target
SIDIS xsec with transverse target polarization
has two similar terms:
th d!
o
b ve
er
s
b
sin(φlh + φlS ) ⇒ h1 =
⊗ H1⊥ =
⊥
sin(φlh − φlS ) ⇒ f1T
=
⊗ D1 =
seperate Sivers and Collins mechanisms
o
y
• (φlh − φlS ) = angle of hadron
S
'
S
!
!
relative to initial quark spin
•
"
c
"S
phqT
(φlh
φlS )
(φlh
l!
φS )
"h
+
=π+
−
=
hadron relative to final quark spin
'
x ( e-e plane )
#
*
N.C.R. Makins, SPIN2008, Oct 8, 2008
0.1
I
π+
Collins Moments for π+ π−
π
2 〈sin(φ+φS)〉UT
Sivers Moments for π+ π−
HERMES PRELIMINARY 2002-2005
lepton beam asymmetry, Sivers amplitudes
8.1% scale uncertainty
0.08
0.06
0.1
0.02
0.02
0
0
π-
0.04
0.02
0
HERMES PRELIMINARY 2002-2005
lepton beam asymmetry, Collins amplitudes
8.1% scale uncertainty
0.06
0.04
0.06
I
π+
0.08
0.04
π
2 〈sin(φ+φS)〉UT
2 〈sin(φ-φS)〉UT
2 〈sin(φ-φS)〉UT
Results from full 2002–2005 H↑ target data
0
π
-
-0.02
-0.04
-0.06
-0.02
-0.08
-0.04
-0.1
-0.06
0.1
0.2
0.3 0.2
x
0.3
0.4
0.5
0.6
0.2 0.4 0.6 0.8
z
1
Ph⊥ [GeV]
-0.12
0.1
0.2
0.3 0.2
x
0.3
0.4
0.5
0.6
0.2 0.4 0.6 0.8
z
1
Ph⊥ [GeV]
N.C.R. Makins, SPIN2008, Oct 8, 2008
Transversity
Photo-Album of our New Friends!
h1(x)
+
π
Collins
H1⊥(z, pT )
u
u
Boer-Mulders
+
π
⊥
h1 (x, kT )
u
uv
d
Sivers
⊥
f1T (x, kT )
Favored / Disfavored Frag Functions
u→π+
d→π−
Dfav ≡ D
=D
= ...
u→π−
d→π+
Ddis ≡ D
=D
= ...
N.C.R. Makins, SPIN2008, Oct 8, 2008
The Collins Fragmentation Function
⊥
H1 (z, pT )
Understanding the Collins Effect
The Collins function exists! ➡ spin-orbit correlations in π formation
Is the Artru mechanism responsible?
g
n
i
tr
S
nd del
u
L Mo
N.C.R. Makins, SPIN2008, Oct 8, 2008
Why are the Collins π− asymmetries so large?
+
AπCol
∼ δu · Hfavored
... expected: positive
AπCol ∼ δu · Hdisfavored ... expected:
−
$
2 !sin("+"S)#UT
Collins
DIS on proton target always dominated by u-quark scattering
0.1
+
$
HE
lep
8.1
0.08
0.06
0.04
zero
0.02
Limits on Transversity and Collins FF
0
Hdisfav / Hfav
$
2 !sin("+"S)#UT
probability
distribution CollinsFF
for Hd /Hf vs.isδrlarge & negative !
Data indicate
disfavored
$-
-0.02
-0.04
-0.06
-0.08
-0.1
-0.12
0.1
0.2
0.3 0.2
x
Map out solution space ...
find Hdisfav ≈ −Hfav
.
Gunar Schnell, HERMES Collaboration
0
δr ≈ δu/δd
Spin 2004 – Trieste, October 14th , 2004
– p. 16/18
N.C.R. Makins, SPIN2008, Oct 8, 2008
Interpretation
of Collins
Results
Interpretation
of Collins
Results
rtru model , based on
phenomenological
Lund string-fragmentation
model
Lund
model + 3P0 hypothesis
once more:
and 3P0 hypothesis for qq-pair formation
Subleading pion
heads out of page
L=1
"
struck
u
!
dd pair
leading π + = ud
...
heads down (into page)
because of L = 1
produced in string frag.
L = 1, S = 1 ⇒ J P = 0+
leading π+ = favored transition, heads into page
–) = page
leading π += subleading
favored transition,
particle heads
(prob πinto
disfavored transition,
subleading pcle (prob
) =ofdisfavored
transition, heads out of page
headsπ −
out
page
PerhapsH
Hdis ≈
likely
fav is not
≈−H
−H
is only
quitereasonable,
reasonablebut
after
all?
dis
fav
N.C.R. Makins, SPIN2008, Oct 8, 2008
Collins Effect in di-Hadron Correlations
In e+e- Annihilation into Quarks!
Collins effect in e+equark fragmentation
will lead to azimuthal
asymmetries in di-hadron
correlation measurements!
electron
q1
z2
q2
quark-2
spin
z1,2 relative pion
momenta
May 28th
quark-1
spin
positron
z1
Experimental requirements:
 Small asymmetries 
very large data sample!
 Good particle ID to high
momenta.
 Hermetic detector
Collins Asymmetries in Belle
20
Final Charm Corrected Results for
e+ e- π π X (29fb-1, off-resonance Data)
Phys.Rev.Lett.96:232002,2006
• Significant non-zero
asymmetries
• Rising behavior vs. z
• UL/C asymmetries about
40-50% of UL/L
asymmetries
• First direct measurements
of the Collins function
• UL/L data published
May 28th
Collins Asymmetries in Belle
21
2 "
!K
H1
In order to compare the Collins effect in SIDIS at HERMES
[17, 18] and in e+ e− -a
is, strictly speaking, necessary
to take into
the evolution
Collins Global
Fit: account
HERMES
& BELLEproperties of H1⊥ . Ho
ratifying to observe that within the range (22) the factor BGauss varies modera
3) and 25 % (at large z ∼ 0.6). Taking into account
1-σSchweitzer,
uncertainty
of the BE
Efremov,the
Goeke,
hep-ph/0603054
riation
in (22) z-dependent
we obtain the result in Fig. 7. The
of the preliminary
Fit BELLE
! (1/2)
(a) description
H
(z) at BELLE
(b)
1
Cunf
ndence of the
Collins
SSA
obtained
in
this
way
is
satisfactory.
results to
fav observation tha
0.2to our
good⊥(1/2)a
agreement observed
in
Fig.
7
gives
further
support
0.5
a
H1 data (z)
(z)
a z D1agreement.
E [20]
are=inCgood
Furthermore, we are 0.1
lead to the conclusion
ependence (21) is reasonable —0 given the accuracy of the 0data [17, 18, 20].
sin(φ+φS )
-0.1
Cfavrecall
= 0.15,that
Cunf in
= –0.45
lly, we
the expression for AUT
(z) certain
integrals over x
a
-0.2
= 0.023 at HERMES
[17,
fav
unf 18]-0.5where the used predictions for h1 (x) from the m
and so H1 ≈ −H1
-0.3
unf
-0.4
-0.5
S)(z)
Asin(!+!
UT
0
for proton
0
Cfav
0.5
(a)
0.2
0.4
0.6
0.8
S)(z) for proton
Asin(!+!
UT
z
(b)
0.2
FIG. 5: a. The two best fit solutions
for theHERMES
parameters
Ci in the Ansatz
(18) (indicated as discr
0
preliminary
Resulting
1-σ regions
as obtained from a fit to the BELLE data [20]. The solutions are symmetric with
0.15
⊥(1/2)a
-0.05
Collins
FF
(z) resulting
from Fig. 5 with the choic
indicated by a dashed line. b. The best fit for H1
0.1 HERMES
suggested
by fit
the analysis of the
also
-0.1
"+ experiment, see Sec. II.
"-
HERMES
data well
with XQSM
for h1
0.05
-0.15
0
-0.2
0.2
0.3
0.4
0.5
0.6
z
0.2
HERMES preliminary
0.3
0.4
0.5
0.6
z
N.C.R. Makins, SPIN2008, Oct 8, 2008
Final Charm Corrected Results for
e+ e- π π X (547 fb-1 ,on-resonance)
• Significance largely
increased
• Behavior unchanged
• Reduced systematics
• Precise measurement of
Collins asymmetries in e+e-
May 28th
Preliminary
NEW
Collins Asymmetries in Belle
23
Transversity
h1(x)
NewTransversity:
Spin-Structure
Transversity
δq(x)
TheFunction:
Third Structure
Function
Proton
Matrix
Elements
Forward
Helicity
Amplitudes
µ
vector charge !P S|ψγ ψ|P S"
!P S|ψγ µγ5ψ|P S"=
axial charge
tensor charge !P S|ψσ µν γ5ψ|P S"=
2
q
0
R1
0
R1
0
q
dx q(x) − q(x)
→ # valence quarks
dx ∆q(x) + ∆q(x)→ net quark spin
dx δq(x) − δq(x) → ???
q
~ Im
P
P
q(x) ∼
+
∆q(x) ∼
-
δq(x) ∼
=
R1
... but in
transverse
basis ...
(optical theorem
applied to DIS)
P
N.C.R. Makins, SPIN2008, Oct 8, 2008
Properties
Propertiesof
ofTransversity
Transversity
• In Non-Relativistic Case,
boosts and rotations commute:
δq(x) = ∆q(x)
... but bound quarks are highly relativistic in nature
• No Gluons
Angular momentum conservation: Λ − λ = Λ! − λ!
⇒ transversity has no gluon component
⇒ different Q2 evolution than ∆q(x)
• Chiral Odd
Helicity flip amplitudes occur only at
O(mq /Q) in inclusive DIS ...
mq
but they
are observable
tensor
charge = in e.g.
semi-inclusive
“pure valence”reactions
object
→ promising for LQCD
comparison?
?
N.C.R. Makins, SPIN2008, Oct 8, 2008
π
2 〈sin(φ+φS)〉UT
Collins Moments for pions from H↑
0.1
I
π+
HERMES PRELIMINARY 2002-2005
lepton beam asymmetry, Collins amplitudes
8.1% scale uncertainty
0.05
NEW
Chargedifference SSA
π
2 〈sin(φ+φS)〉UT
0
0.05
0
π
0
π
2 〈sin(φ+φS)〉UT
-0.05
π0
-0.05
Contribution from exclusive
ρ0 → π+π– largely cancels
-0.1
0.1
0.2
0.3 0.2 0.3 0.4 0.5 0.6
x
0.2 0.4 0.6 0.8 1
z
Ph⊥ [GeV]
N.C.R. Makins, SPIN2008, Oct 8, 2008
!
!
↑
Collins!"##$%&'(&)**+,-$+&'π
Moments for pions & kaons from D'.
9)#($!,+&:
($$!1+:'+,"#
/+01+234546
NEW
:&;<*7'=
et
g
tar y!
D ke
is
Deuterium results ≈ 0 show
π+
!"#$%!&'(')&')*($!+,,",&!&-".#/!&%&'+0(')*!+,,",&
!sin(φ
+
φ
)"
⊥
S H ∼ 4δuv − δdv
H1,disfav
!!*"#&)1+,(2$%!&0($$+, −
=!−1
!&0($$!(&%00+',)+&/!*"07(')2$+!.)'-!8
!sin(φ + φS)"πH ∼ −4δuv + δdv
⊥
H1,fav
!
!
+
!sin(φ + φS)"πD ∼ 3δuv + 3δdv
!
!3$+(1)#4!-(1,"#5!&)0)$(
h1,uv ≈ −h1,dv
N.C.R. Makins, SPIN2008, Oct 8, 2008
N.C.R. Makins, SPIN2008, Oct 8, 2008
Introduction Collins effect in SIDIS and e + e − Sivers effect Single spin asymmetries in Drell-Yan processes Conclusions
Preliminary results
NEW
global fit
sin(φh +φS )
sin(φh +φS +π)
2002−2005
π+
0.1
0.1
COMPASS
0.1
2003−2004
h
HERMES
preliminary
sin (φ + φ + π)
π0
0.1
COMPASS AUT
S
0
−0.1
0.1
−0.1
AUT
−0.1
π+
0
−0.1
−0.1
−0.1
0.1
0.1
0
0
sin (φ + φ + π)
0.05
π−
0.1
S
h
0
0
−0.05
π−
−0.1
0
0.1
0.2
0.3
0.4
0.5
x
−0.05
−0.05
−0.1
−0.1
0.6 0
0.2
0.4
0.6
0.8
01
z
AUT
AUT
sin (φh + φS)
AUT
sin (φh + φS)
AUT
sin (φh + φS)
HERMES AUT
0.2
0.4
0.6
0.8
1
1.2
PT (GeV)
Alexei Prokudin Stony Brook University, October 3-4 2008
0
−0.1
−0.1
−2
10
01
−1
10
x
−0.1
0.5
01
z
0.5
1
1.5
PT (GeV)
11
Introduction Collins effect in SIDIS and e + e − Sivers effect Single spin asymmetries in Drell-Yan processes Conclusions
Preliminary results
BELLE cos(2ϕ0 )
0.2
BELLE cos(ϕ1 + ϕ2 )
0.2 < z1 < 0.3
0.2
0.3 < z1 < 0.5
0.1
0.05
0
−0.05
−0.05
0.2
0.5 < z1 < 0.7 0.2
0.15
0.15
A0(z1, z2)
A12(z1, z2)
0.1
0.1
0.1
0.05
0.05
0
0
−0.05
0.4
0.6
0.8
z2
0.15
0.1
0.1
0.05
0
−0.05
0.2
0.5 < z1 < 0.7 0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
0
−0.05
−0.05
0.2
0.2
0.4
0.6
z2
Alexei Prokudin Stony Brook University, October 3-4 2008
0.7 < z1 < 1
−0.05
0.2
0.8
0.3 < z1 < 0.5
−0.05
0.7 < z1 < 1
A12(z1, z2)
A0(z1, z2)
0.15
0.2 < z1 < 0.3
NEW
0.4
0.6
0.8
z2
0.2
0.4
0.6
0.8
z2
14
Introduction Collins effect in SIDIS and e + e − Sivers effect Single spin asymmetries in Drell-Yan processes Conclusions
Transversity
This is the extraction of
transversity from new
experimental data.
NEW
x ΔT u(x, k )
0.5
x ΔT u(x)
0.4
0.3
0.2
0.1
0
x ΔT d(x)
0.1
0.05
0
−0.05
−0.1
−0.15
−0.2
0.4
x = 0.1
0.3
0.2
0.1
Compared to ∆χ2 = 1
error estimate of
PRD75:054032,2007
0
−0.1
x ΔT d(x, k )
−0.1
Compared to previous
extraction
PRD75:054032,2007
0.5
0.1
0.05
0
−0.05
−0.1
x = 0.1
−0.15
0.2
0.4
0.6
0.8
1
x
−0.2
0
0.2
0.4
0.6
0.8
k (GeV)
Alexei Prokudin Stony Brook University, October 3-4 2008
1
∆T u(x) > 0 and
∆T d(x) < 0 The errors
are diminished
significantly.
∆T u(x) became larger
than that of the previous
fit.
20
Predictions from the global analysis, Collins
Update of the analysis with the most recent
COMPASS Deuteron3'HERMES Proton3'BELLE e+ e- -.+.
NEW
SS
A
P ↑
M
H
CO 007 !
2 ata
d
!"#$%&&'()*+*,'-.+.'/*)'01'.,-'023'45+0'+06'very last ()6-57+5*,8'*/'
%,869:5,*'6+'.9;'( DIS08 by A.Prokudin. )
S. Levorato, Transversity 2008 May 28-31 - Ferrara, Italy
25
Introduction Collins effect in SIDIS and e + e − Sivers effect Single spin asymmetries in Drell-Yan processes Conclusions
Tensor charges
+0.04
2 = 0.8 GeV2
∆T u = 0.54+0.07
,
∆
d
=
−0.23
at
Q
T
−0.09
−0.05
x F > 0.1
our result
1
Quark-diquark model:
Cloet, Bentz and Thomas
PLB 659, 214 (2008), Q 2 = 0.4 GeV2
1
2
CQSM:
M. Wakamatsu, PLB B 653 (2007) 398.
Q 2 = 0.3 GeV2
2
3
Lattice QCD:
M. Gockeler et al.,
Phys.Lett.B627:113-123,2005 , Q 2 =
GeV2
3
4
4
QCD sum rules:
Han-xin He, Xiang-Dong Ji,
PRD 52:2960-2963,1995, Q 2 ∼ 1 GeV2
ΔT u
ΔT d
Alexei Prokudin Stony Brook University, October 3-4 2008
22
NEW
2-D moments for
π :
x-Q correlation
2
Collins
Contalbrigo Marco
±
Sivers
Transverse Spin Physics at HERMES
SPIN2008, Charlottesville, 07-10-2008
NEW
π
2-D Collins moments for
z vs Ph
x vs z
Contalbrigo Marco
±
Transverse Spin Physics at HERMES
┴
SPIN2008, Charlottesville, 07-10-2008
Transversity from the
Interference Fragmentation Function
h1(x)
Two-hadron SIDIS
Explicit dependence on transverse momentum of
hadron Ph┴
Convolution of two unknown functions
Trans. component of relative momentum survives
integration over the Ph┴ of pair
Collinear kinematics (factorization)
Simple product of unknown functions
Limited statistic power
Contalbrigo Marco
Transverse Spin Physics at HERMES
SPIN2008, Charlottesville, 07-10-2008
Azimuthal 2π-moment
Evidence of a T-odd and chiral-odd dihadron FF
No evidence of the
sign-change at the ρ0 mass
Contalbrigo Marco
Jaffe et al. Phys.Rev.Lett.80,1166
(1998)
Bacchetta and Radici
hep-ph/0608037
Transverse Spin Physics at HERMES
SPIN2008, Charlottesville, 07-10-2008
!"#$%&'(#)$*+,--./(0.+
"#!$!%&'(&('!)*+&,,(.(/0!+1!02(!(3(10!02(!04%!2*'&%1,!4+02!02(!2+52(,0!&(.*0+3(!(1(&56!$7
8(*,%1-!9%&!.(*'+15!2*'&%1!)*+&,!*1!(12*1/(:(10!%;!02(!,+51*.!+,!
)&('+/0('7!<*'&%1,!4+02!2+52(&!(1(&56!:*6!/*&&6!:%&(!+1;%&:*0+%1!*=%>0!
02(!)%.*&+$*0+%1!%;!02(!;&*5:(10+15!?>*&@7
π!"#$%!&''&(#$)!*%+,-)!
!
π!"#$%!(+.)!*%+,-)!
NEW
!
N.C.R. Makins, SPIN2008, Oct 8, 2008
!"#$%&'(#)$*+,--./(0.+
Κ/π !"# π$%&'()*&+,,+-().&/*!01.&
!
NEW
Κ/π !"# π$%&'()*&-!2.&/*!01.&
"#$%!&'(')&')*($!+,,-,&!&.-/#0!&%&'+1(')*!+,,-,&!*-#&)2+,(3$%!&1($$+,4
!
N.C.R. Makins, SPIN2008, Oct 8, 2008
vs invariant mass of the pair
NEW
Systematic errors
Polarization 5%
Relative lumi. 5x10-4
No systematic effects
detected from bunch
shuffling
promising
for RHIC
future
Consistent with 0, despite the second bin of π0h- pairs and the
last bin of h+h- pairs are 2σ from 0
10/07/2008
42
The Sivers Function
⊥
f1T (x, kT )
The Leading-Twist Sivers Function: Can it Exist in DIS?
⊥
A T-odd function like f1T
must arise from
interference ... but a distribution function
is just a forward scattering amplitude,
how can it contain an interference?
q
2
q
q
P
P
~ Im
P
Brodsky, Hwang, & Schmidt 2002
can interfere
with
and produce
a T-odd effect!
(also need Lz != 0)
It looks like higher-twist ... but no , these are soft gluons
= “gauge links” required for color gauge invariance
Such soft-gluon reinteractions with the soft wavefunction are
final (or initial) state interactions ... and may be
process dependent !
new universality issues
e.g. Drell-Yan
N.C.R. Makins, SPIN2008, Oct 8, 2008
opUnderstanding
h
ks 4
r
o 00
W
to er 2
n
m
Heisenberg
Picture
Field
Theory
m
TreRigorous
Su
the Sivers Asymmetry
Schroedinger
“Cartoons”Picture
Model of Meng,
Chou, Yang
+
π
uv
d
Requires:
● rescattering via gauge link
● interference effect involving
L=0 and L=1 states
Theoretical synthesis of fieldtheoretic analysis (rigour) and
phenomenological thinking (intuition)
N.C.R. Makins, SPIN2008, Oct 8, 2008
π
2 〈sin(φ-φS)〉UT
Sivers Moments for pions from H↑ Data
I
+
π
HERMES PRELIMINARY 2002-2005
lepton beam asymmetry, Sivers amplitudes
8.1% scale uncertainty
0.1
Chargedifference SSA
NEW
0.05
π
2 〈sin(φ-φS)〉UT
0
0.1
0
π
0.05
π
2 〈sin(φ-φS)〉UT
0
0.05
π-
0
isolates valence
-0.05
0.1
0.2
0.3 0.2 0.3 0.4 0.5 0.6
x
0.2 0.4 0.6 0.8 1
z
Ph⊥ [GeV]
N.C.R. Makins, SPIN2008, Oct 8, 2008
!"#$%&'(&)**$+%"$&'π!',!
NEW
D target
with RICH
9)#($!,+&:$'&/
($$!1+:'+,"#!1('(
-$./$01232454672
8&9:*5';<=>
!"#$%!&'(')&')*($!+,,",&!&-".#/!&%&'+0(')*!+,,",&
!!*"#&)1+,(2$%!&0($$+,
!!&0($$!(&%00+',)+&/!*"07(')2$+!.)'-!8
!
!
!
3$+(1)#4!-(1,"#5!&)0)$(,6
So what is the sign of L?
Connection to nucleon anomalous magnetic moment
• Consitituent quark model (CQM) says Δu = +4/3, Δd = –1/3
does a great job of explaining the proton anomalous
• CQM
magnetic moment, via µ ∼ e /m Δq
p
∑
q
q
q
we know that the current quarks are not as polarized as in
• ...thebutCQM
... and they are relativistic: must involve L ≠ 0
q
• Missing piece must come from ∑ e L and must be positive
• Therefore L must be positive and L negative
q q
q
u
d
Numerous models give Lu > 0 and Ld < 0
i.e. quark angular momentum shared between spin and L
in transverse
case, that is!
Lattice & GPD calculations give opposite
predictions in longitudinal-spin case
N.C.R. Makins, SPIN2008, Oct 8, 2008
Phenomenology: Sivers Mechanism
Many models
predict Lu > 0 ...
M. Burkardt: Chromodynamic lensing
Electromagnetic coupling ~ (J0 + J3) stronger for oncoming quarks
We observe
u mostly over here
l
l π+
!sin(φh − φS)#UT
−
>0
(and opposite for π )
FSI kick
π+
∴ for φlS = 0, φlh = π/2 preferred
Model agrees!
D. Sivers: Jet Shadowing
Parton energy loss considerations suggest
quenching of jets from
“near” surface of target
➡ quarks from “far” surface should dominate
+
π
uv
d
Opposite sign to data ...
N.C.R. Makins, SPIN2008, Oct 8, 2008
Sivers Global Fit: HERMES & COMPASS
PHYSICAL REVIEW D 72, 054028 (2005)
VERSE-SPIN ASYMMETRIES: FROM . . .
0.2
π+
Sivers AN
HERMES PRELIMINARY
For convenience:
(not corrected for acceptance and smearing)
0.15
Vogelsang & Yuan,
PRD 72 (2005) 054028
⊥,q
(x)
qT (x) ≡ f1T
Fit HERMES AUT to Sivers funcn of form:
0.1
0.05
(1/2)
(1/2)
uT (x)
d
(x)
= Su x(1 − x), T
= Sd x(1 − x)
u(x)
u(x)
0
π0.05
● assume no antiquark Sivers func: qT (x) = 0
● unpol PDFs = GRV-LO, unpol FFs = Kretzer
0
-0.05
0
0.1
0.2
LSANG AND FENG YUAN
xB
0.3
0.4
0.2
0.3
0.4
Su = −0.81 ± 0.07, Sd = 1.86 ± 0.28
0.6
0.7
zh 0.5
PHYSICAL REVIEW D 72, 054028 (2005)
ine). Sivers SSA fit to the HERMES data [10]; see text. The bands correspond to the 1-" error of the fitted
Sivers
0.1 data
that the
haveAnot
N yet been corrected for acceptance and smearing.
Fits COMPASS deuterium data well!
-0
tained from the fit. In [37], the asymme-0.1transverse momentum of the hadron
ith the
e fit. Both fits find a large d quark Sivers
-0.2
posite
sign relative to the u-quark one. We
ed that
ourPositive
fit results
for the Sivers func-0.3
hadrons (COMPASS)
ent with these fits within the current large
here we notice that the Sivers function in
posite0.1sign compared to ours and to the
ions’’-0[40].
SS Collaboration also has measured the
y [12],
-0.1 separately for positively and negaadrons, produced off a deuteron target. To
-0.2 with their data, we assume that the
parison
are mostly pions. We calculate the Sivers
"
hadrons region of the
and !Negative
in the kinematic
!! -0.3
riment, using-2 the above fitted Sivers
funcxB 10-1
10
tions for u and d quarks, and compare to their data for
leading positive and negative hadrons, respectively. We
show this comparison in Fig. 3. One can see that our
calculations based on fits to the HERMES data are also
consistent with the COMPASS data, within error bars. We
note that for the kinematical region of the COMPASS
experiment, our predicted Sivers asymmetries for a deuteron target are very small, except in the large-x valence
region. The smallness of the Sivers asymmetry is again
related to cancellations between u and d contributions,
which for deuterons enter in a different combination than
for a proton target. It will be very interesting to check these
predictions with future COMPASS data for a proton target.
Thanks to the higher Q2 , such data would also help in
confirming the leading-twist nature of the Sivers and
Collins
asymmetries.
0.2
0.4
0.6
0.8
1
But a surprise! Sd >> Su!
e.g., large-NC expectation: uT (x) ≈ −dT (x)
Hmm ... Su actually reflects uT + d T /4
... Sd actually reflects dT + 4uT
z
Could Sivers (and L) be large for antiquarks?
N.C.R. Makins, SPIN2008, Oct 8, 2008
The Sivers effect for
kaons and jets
⊥
f1T (x, kT )
h
2 〈sin(φ-φS)〉UT
Sivers moments
for Kaons from
full 2002–05
Hydrogen data
0.25
III
K+
π+
HERMES PRELIMINARY 2002-2005
lepton beam asymmetry, Sivers amplitudes
8.1% scale uncertainty
0.2
0.15
0.1
0.05
Sivers K+
much larger than
for π+ !
h
2 〈sin(φ-φS)〉UT
0
-
0.15
K
π
0.1
0.05
0
-0.05
-0.1
-0.15
0.1
0.2
0.3 0.2
x
0.3
0.4
0.5
0.6
0.2 0.4 0.6 0.8
z
1
Ph⊥ [GeV]
–
Effect about equal for K– = su and π– = du → note: same antiquark ...
+
Effect seems larger for K+ = us than π+ = ud at x ≈ 0.1 ... !
→ significant antiquark Sivers functions? and strongly flavor-dependent?
N.C.R. Makins, SPIN2008, Oct 8, 2008
!"#$%&'()#'
π$$*+,-(.#",/$0#$12%324
!"#$%&'%()*
+("*,-**
./01/2*
2%3#"4*
54677#'"%#
4*
5$*+,-(.#",/$0#$12%324
56$7+089&/#0#",/$7(/.#",/'
!"#$%&#!''(
-.%/012.034&#!''(#5#62..%.%#
Elena Boglione
)*+!,
!"#$%&'()#'
π$$+,-.(/#"-0$1#$2345677
-'($,.&,*)!+*'!
π#!!/01-233!
3,4('5!
%5677(&',(5!
!"#!!$%&%!
%'(!)*&!
+,&&($
*$$+,-.(/#"-0$1#$2345677
!"#$%&#!''(
)*%+,-.*,/0&#!''(#1#2.**%*%#
Elena Boglione
345!6
!"#$%&'("&)%"*+)",-'.+-/)",-&
Note:
• large d-quark Sivers
Sivers
• antiquark
needed to explain data
Sivers saturated
• anti-s
to positivity bounds
$"&'()&$**+
,-(./01-/23)&$**+&4&51--(-(&
Elena Boglione
!"#$%
Predictions: Sivers
NEW
O.+68+'
()6-59+5*,'
*/'
%,867:5,*'
6+'.7;
possible
discrepancy?
S
S
A
P
M H↑
O
C 007
2 ata
d
!"#$%&&'()*+*,'-.+.'/*)'01'.,-'023'45+0'+06'7.+68+'()6-59+5*,'*/'%,867:5,*'6+'.7;
#;'%,867:5,*'6+'.7;'<<&5=6)8'>//69+'/*)'$5*, .,-'?.*, $)*-@9+5*,'5,'&6:52A,97@85=6'B66('A,67.8+59''
&9.++6)5,C3DD'''.)E5=FGHGI;JKLL'M06(2(0N;
S. Levorato, Transversity 2008 May 28-31 - Ferrara, Italy
26
Origins of SSA in p↑+p → π+X at RHIC
STAR: arXiv:hep-ex/0801.2990
accepted for publication in PRL
π0→γγ
RUN-6
Hints of Sivers function
universality?
How to separate Sivers and
Collins contributions?
Origins of SSA in p↑+p → π+X at RHIC
STAR Preliminary
Jet-like
cluster
RUN-8
20x times increase in
acceptance
Towards Jet-like AN
to isolate Sivers contributions
Universality of kTT-dependent
Universality
-dependentFunctions
Functions
e+e− Annihilation
SIDIS
Drell-Yan
These proceses
have similar
gauge-link
topology:
Expectation: T-odd functions will change sign between
spacelike (SIDIS) and time-like (e+e− and DY) processes
Sivers
BELLE sign-change
e+e− Experiment
Analysis
of Collins
from between
high-statistics
BELLE
data in progress!
effect
should function
change sign
SIDIS
and DY
•••Sivers
Critical for
providing
normalization
point
for SIDISatand
pp data ∼ h H
new
prospect:
measure with
photon-jet
RHIC
• Exciting
1
Universality of E704 / RHIC
p↑p → πX not yet clear ...
⊥
1
3 “soft blobs” ...
gauge-link topology
more complex
N.C.R. Makins, SPIN2008, Oct 8, 2008
The Boer-Mulders function
⊥
h1 (x, kT )
... and the Cahn effect ...
The Cahn Effect
Cahn, PLB 78 (1978) 269
A cos(Φ) modulation in the unpolarized xsec for SIDIS
➡ kinematic effect for massless eq→eq scattering due to parton kT
Volume 78B, number 2,3
k’
PHYSICS LETTERS
parton kT → Φ=180°
q-vector
slide = lepton
scattering:(2p
plane
<cos2,>ep
(1
photon–target
TheCM
expressions
frame for charg
beam k
parton kT → Φ=0°
Fig. 1. Electron-patton scattering in the center of mass of the
(in the approximation in
cleon are ignored) is obta
#2 qua
action to left-handed
kT
(12).φ Thus we f
√from eq.cos
!photon and the target proton.#The
!
2 incident electron
virtual
"
2
2 momentum, k,kTand the final electron momentum k' lie2 in the
σ ∝ s + u x-z
∝ plane.
1 −The momentum
1 − ytransfer
cos φ q = k+- (1
− y) the 1 −
k'
defines
Q
Q 1−y
in eq systemnegative z-axis. The parton initially has momentum p, with z
% ~ (1 component equal to a fraction, x, of the proton momentum,
Φ=180°
higher
s,u
in beam-quark
P. The preferred:
transverse component
of the
parton
momentum makes system
o - ~ (1 - y ) 2higher
( 1 - (2pz/
an azimuthal
~ with the
x-axis in the x-y
plane. The hadrons
reflected
in angle
azimuthal
distribution
of produced
order
probability of scattering depends on ~ since tile invariants !
s
"
√- p)2 are ~ dependent. See eqs. (11) 2k2 In the
!= (k + "
p)2 and u = (k'
(1valence
− y) quark app
T
2kT(12). (2
1 − yis reflected in!cos
and
This−
~ y)
dependence
'the final
hadron
2φ" =
!cos φ" = − distribution.
2
2
Q
1
+
(1
−
y)
2
Q
1 + (1 − y)
(cos ~ ) p = -(2p!/Q) (1
(2p±/Q)x/1-y
N.C.R. Makins, SPIN2008, Oct 8, 2008
First DIS data with charge-separated hadrons!
!#$%& !
cos(Φ) moment for
positive hadrons
!"#$
"
!;)1 !
2# cos(" )!
h UU
!18& !
0.2
#$%&'
()*+,
-./0*+1
#$%&2
NEW
5*$62
3'()*+2,2
7)/$+89$:8)&
-./0*+14
"
"
0.2
0.2
0.2
0.1
0.1
0.1
0
0
0
-0.1
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.2
-0.3
-0.3
-0.3
-0.3
0.1
+
h
Hydrogen
Deuterium
!#$%& !
0
!18& !
"
10-1
x
"
1
0.4
0.6
0.8 0.2
y
0.4
0.6
0.8
z
1
!"
HERMES Preliminary
#$%&'
()*+,
-./0*+1
0.2
charge-separation + different targets may offer
insight into <kT> for different quark flavours
0.4
0.6
5*$62
Ph [GeV]
7)/$+89$:8)&
N.C.R. Makins, SPIN2008, Oct 8, 2008
!"#$%&'(")*+',-*.-/"&0
)22-2(%(:-I'%J2)%(EJE,(E,FJ*%-'*;
#$%&'()*+,'-.%#$%/-0*,-').%&$%12-345,'.%6$%7823
942$%1:;($%<$%&%=>.%=?=@=A>%B!CC?D
5-)(%'-E%,'F*45)%/-)2%G%#4*5)2(%F-'E2,H4E,-'
!"
Wolfgang Käfer, Traversity08 @ Ferrara
-./0*+14
Cahn effect for negative hadrons
!#$%& !
#$%&'
()*+,
-./0*+1
cos(Φ) moment for!"#$
negative hadrons
"
NEW
!8(0 !
!18& !
"#$%3
9&'()*3+3
5*$62
,-./)*0:
7)/$+89$:8)&
"
"
2# cos(" )!
h UU
!"
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0
0
0
0
-0.1
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.2
-0.3
-0.3
-0.3
0.1
-0.3
h !#$%& !"
-
Hydrogen
Deuterium
!05% !
"
10-1
x
1
0.4
0.6
0.8 0.2
y
0.4
0.6
0.8
z
1
"#$%&
HERMES Preliminary
'()*+
,-./)*0
1)#23
4(.#*56#75(%
0.2
0.4
0.6
Ph [GeV]
apparent discrepancy for h– ! ... different kinematics ...?
!!
N.C.R. Makins, SPIN2008, Oct 8, 2008
Φ)
(2
s
co
The Boer-Mulders distribution function
⊥
h⊥
(x,
k
)
⊗
H
T
1
1 (z, pT ) → cos(2φ) modulation
Boer-Mulders: correlation between Sq and Lq
assume Su // Lu
u
➌ FSI kick
back to
remnant
➋ γ* absorbed
90°
0°
➊ oncoming quarks
scatter most ...
h1 sets spin direc’s
➍ Collins!
favoured
u → π+
< cos 2φ> negative
disfavoured u → π–
< cos 2φ> positive
180°
Expected sign of Boer-Mulders
Widely expected that h1 has the same sign for u and d
• Transversity: h
> 0 h1,d < 0
→ same as g1,u and g1,d in NR limit
1,u
• Sivers:
f1T
,u
<0
f1T
,d
u
>0
d
→ relatn to anomalous magnetic moment*
f1T ,q κq where κu ≈ +1.67 κd ≈ –2.03
values achieve κp,n = Σq eq κq with u,d only
• Boer-Mulders: should follow that h
1
,u
u
and h1
→ relatn to tensor magnetic moment*
→ possible analogue to Sokolov-Ternov?
but these
TMDs are all
independent
!!su · !S p" = +0.5 !!lu · !S p" = +0.5 !!su ·!lu" = 0
,d
d
<0 !
u
d
* Burkardt PRD72 (2005) 094020;
Barone et al PRD78 (1008) 045022;
N.C.R. Makins, SPIN2008, Oct 8, 2008
First charge-separated data #1: HERMES
Φ)
2#cos(2" )!
h UU
(2
s
co
0.2
⊥
h⊥
(x,
k
)
⊗
H
T
1
1 (z, pT ) → cos(2φ) modulation
0.2
0.2
0.2
0.1
0.1
0.1
0
0
0
0
-0.1
-0.1
-0.1
-0.1
+
h
0.1
-0.2
Hydrogen
Deuterium
10-1
-0.2
2#cos(2" )!
h UU
x
0.2
1
0.4
0.6
-0.2
0.8 0.2
y
0.4
0.6
0.8
-0.2
1
z
0.2
0.2
0.2
0.1
0.1
0.1
0
0
0
0
-0.1
-0.1
-0.1
-0.1
0.1
-0.2
-
h
Hydrogen
Deuterium
10-1
-0.2
x
1
0.4
0.6
-0.2
0.8 0.2
y
0.4
0.6
0.8
-0.2
1
z
HERMES Preliminary
NEW
0.2
0.4
0.6
Ph [GeV]
HERMES Preliminary
0.2
0.4
0.6
Ph [GeV]
→ u-quark dominance ...
• hydrogen
→ opposite signs for h and h due to Collins favored-vs-disfav
• deuterium ≈ hydrogen values! can we understand?
+
–
N.C.R. Makins, SPIN2008, Oct 8, 2008
Back-of-envelope estimates for <cos(2Φ)>(x)
for convenience
π+
!cos(2φ)"H
4δuv − δdv
∼
4u + ηd + 4ηū + d¯
!cos(2φ)"πH ∼
A.U.
−
2
Boer-Mulders
cos(2φ)
−4δuv + δdv
4ηu + d + 4ū + ηd¯
Hydrogen
Deuterium
D1,disfav
η≡ R
" 0.35
D1,fav
= −1
−3δuv − 3δdv
¯
(4η + 1)(u + d) + (4 + η)(ū + d)
−
π+ (solid)
π- (dash)
2
0
0
-1
-1
η = 0.35
Model: h1,q⊥ = -q for all flavours q
-1
⊥
H1,fav
!cos(2φ)"πD ∼
1
10
R
3δuv + 3δdv
¯
(4 + η)(u + d) + (4η + 1)(ū + d)
+
1
-2
⊥
H1,disfav
!cos(2φ)"πD ∼
A.U.
δq(x) ≡
Using
h⊥
1,q(x)
R
R
-2
x
Boer-Mulders
cos(2φ)
Hydrogen
Deuterium
π+ (solid)
π- (dash)
η = 0.35
Model: h1,q⊥ = -q for u,ubar h1,q⊥ = -1.6q for d,dbar
10
-1
x
Hydrogen–Deuterium similarity → same sign for Boer-Mulders u & d!
N.C.R. Makins, SPIN2008, Oct 8, 2008
First charge-separated data #2: COMPASS
!"#$%&'(")*+',-*.-/"&0
NEW
COMPASS cos(2Φ)
well explained by
dominant
Cahn effect !
ry t
e
v ren
fe re!
f
i
d ctu
pi
... while Cahn
contribution seems
small at HERMES !
Challenge
for theory!
123+$%*#4'526$%789-*4'32:2;+'
+$<-=>?@?A2B?!A'C(#DED(F
,%,+/
G+(*
3%#$';8/9#$&
D:GH
#$$%$&'&(%)*'+$#'&,+,-&,-.+/'%*/0
!"
Wolfgang Käfer, Traversity08 @ Ferrara
Summary: Newest Highlights in Transverse Spin
New COMPASS results 2007 H↑ target & 2003-04 D↑ with RICH
• D↑ target essential complement to HERMES H↑
Collins: confirms HERMES results @ higher scales
• H↑
• H↑ Sivers: consistent with zero → unexpected
New BELLE results on Collins and (soon) many other
fragmentation functions essential to analysis of DIS and pp data
First charge-separated data on cos(Φ) and cos(2Φ)
from HERMES and COMPASS
effect more-or-less as expected for h+
• Cahn
effect discrepancy for h– betw HERMES & COMPASS
• Cahn
from HERMES agrees with Boer-Mulders expections
• cos(2Φ)
cos(2Φ) from COMPASS indicates dominant Cahn contribution!
Many new results skipped ... please see C.Aidala → pp,
J.C.Peng →DY ... and all the other fabulous talks at SPIN08!
N.C.R. Makins, SPIN2008, Oct 8, 2008