Drell-Yan Process and Nucleon Spin
Jen-Chieh Peng
University of Illinois at Urbana-Champaign
SPIN 2008, University of Virginia, October 6-11, 2008
Outline
• Brief overview of TMDs and Drell-Yan• Recent Drell-Yan results from Fermilab E866
(Boer-Mulders functions) • Future prospects for Drell-Yan experiments
1
2
l l l
l
10-10
10-8
10-6
10-4
10-2
1
10 2
10 4
10 6
10 8
10 10
10 12
0.08 0.09 0.1 0.2 0.3 0.4 0.5 0.6
Complimentality between DIS and Drell-Yan
Both DIS and Drell-Yan cross sections are well described by NLO calculations
DIS Drell-Yan
0
2
4
6
8
10
12
14
16
1 10 102
103
104
105
x=0.65
x=0.40
x=0.25
x=0.18
x=0.13
x=0.08
x=0.05
x=0.032
x=0.02
x=0.013
x=0.008
x=0.005
x=0.0032
x=0.002
x=0.0013
x=0.0008
x=0.0005
x=0.00032
x=0.0002
x=0.00013
x=0.00008
x=0.00005
x=0.000032
(i=1)
(i=10)
(i=20)
Q2 /GeV2
F2+
c i(x)
NMC BCDMSSLAC
H1 94-97 e+p
H1 96-97 preliminary
NLO QCD Fit
ci(x)= 0.6 • (i(x)-0.4)
3
Three parton distributions describing quark’s transverse momentum and/or transverse spin
1) Transversity
2) Sivers function
3) Boer-Mulders function
=h1T
Correlation between and q Ns S⊥ ⊥
f1T =
Correlation between and q qs k⊥ ⊥
Correlation between and N qS k⊥ ⊥
h1 =
Three transverse quantities:1) Nucleon transverse spin
2) Quark transverse spin
3) Qaurk transverse mo
Three diff
me
er
ntum
ent correlations
N
q
q
S
s
k
⊥
⊥
⊥
⇒
×= 4
26 4
Qsxd πασ
),()(])1(1[ 211
,
22⊥∑−+ h
qqq PzDxfey
22 (1) 2
1 12,
22 (1) 2
1 12,
2 21 1
,
cos(2 )
sin(2 )
(1 ) ( ) ( , )4
| |
s
(1 ) ( ) ( , )4
| | (1 ) ( ) (in( )) ,
q qhq h
q qN h
q qhL q L h
q qN h
q
lh
lh
l lh
qhST q h
q qh
Py e h x H z Pz M M
PS y e h x H z Pz M MPS y e h x H z PzM
φ
φ
φ φ
⊥ ⊥⊥⊥
⊥ ⊥⊥⊥
⊥⊥⊥
+ −
−
+ − +
−
∑
∑
∑2 2 (1) 2
1 1,
32 (2) 2
1 13 2,
2 21 1
,
1| | (1 ) ( ) ( , )2
| | (1 ) ( ) ( , )61| | (1 ) ( ) ( , )21| | (1 )
sin( )
sin(3 )
co ( )2
s
q qhT q T h
q qN
q qhT q T h
q qN h
q qe L q h
q q
he T
N
l lh S
l lh S
l lh S
PS y y e f x D z PzM
PS y e h x H z Pz M M
S y y e g x D z P
PS y y ezM
φ φ
φ
φ
λ
λ
φ
φ
⊥⊥⊥
⊥ ⊥⊥⊥
⊥
⊥
−
−
+ − +
+ −
+ −
+ −−
∑
∑
∑
2 (1) 21 1
,
( ) ( , )q qq T h
q q
g x D z P ⊥∑
=f1
h1 =
h1L =
=h1T
f1T =
h1T =
=g1L
g1T =
Unpolarized
Polarized target
Polarziedbeam and
target
4SL and ST: Target Polarizations; λe: Beam Polarization
Sivers
Transversity
Boer-Mulders
Transversity and TMD PDFs are probed in Semi-Inclusive DIS
5
Transversity and TMD PDFs are also probed in Drell-Yan
1 1
1
- Unpolarized Drell-Yan:
- Single transverse spin asymmetry in polarized Drell
Boer-Mulders
-Yan:
cos functions:
Sivers functions:
Transversity
(2 )
( ) ( )
distributio
DY
DYN T q q q
d h h
A f x f x
σ φ⊥ ⊥
⊥
∝
∝
1 1
- Double transverse spin asymmetry in polarized Drell-Yan:
Drell-Yan and SIDIS involve different combinations of TMDs Drell-Yan does not require
ns:
kno
( ) (
wledge of the fra
)DYTT q qA h x h x
••
∝
gmentation functions T-odd TMDs are predicted to change sign from DIS to DY
(Boer-Mulders and Sivers functions) Remains to be tested experimenta ! lly
•
Boer-Mulders functions from unpolarized Drell-Yan
1
10
10 2
10 3
10 4
10 5
2 4 6 8 10 12 14 16
J/ψ
ψ′
ϒ
ϒ′ ϒ″
Mass (GeV/c2)
Cou
nts/
0.1
GeV
/c2
800 andGeV p d X p p Xµ µ µ µ+ − + −+ → + →
(E605/772/789/866)
~ 200,000 high-mass Drell-Yan events
6
Drell-Yan decay angular distributions
z
P1 2P h φ
lepton plane (cm)
θ
l’
l
Θ and Φ are the decay polar and azimuthal angles of the µ+ in the dilepton rest-frame
*1 2
*( )h h x l l q qxγ γ+ −+ → + → + + →+
Collins-Soper frameA general expression for Drell-Yan decay angular distributions:
2 21 3 1 cos sin 2 cos sin cos 24 2
ddσ νλ θ µ θ φ θ φ
σ π⎛ ⎞⎛ ⎞ ⎡ ⎤ ⎡ ⎤= + + +⎜ ⎟⎜ ⎟ ⎢ ⎥ ⎢ ⎥Ω⎝ ⎠⎝ ⎠ ⎣ ⎦ ⎣ ⎦
*"Naive" Drell-Yan (transversely polarized , no transverse mo 1, 0, 0mentum)
γλ µ ν= = =→
1, 0, 0λ µ ν≠ ≠ ≠In general :7
Drell-Yan decay angular distributions
z
P1 2P h φ
lepton plane (cm)
θ
l’
l
Θ and Φ are the decay polar and azimuthal angles of the µ+ in the dilepton rest-frame
Collins-Soper frameA general expression for Drell-Yan decay angular distributions:
2 21 3 1 cos sin 2 cos sin cos 24 2
ddσ νλ θ µ θ φ θ φ
σ π⎛ ⎞⎛ ⎞ ⎡ ⎤ ⎡ ⎤= + + +⎜ ⎟⎜ ⎟ ⎢ ⎥ ⎢ ⎥Ω⎝ ⎠⎝ ⎠ ⎣ ⎦ ⎣ ⎦
Reflect the spin-1/2 nature of quarks (analog of the Callan-Gross relation in DI
Ins
Lam-Tung relation:
ensitive to QCD - S
c)
orrection
2
s
1 λ ν−
=
−
−
8
Decay angular distributions in pion-induced Drell-Yan
Z. Phys.
37 (1988) 545
T0 and increases with pν ν≠
Dashed curves are from pQCD
calculations
NA10 π- +W
9
Decay angular distributions in pion-induced Drell-YanPhys. Rev. D 39 (1989) 92
1, 0, 0 and they vary with , , andTm p xµµ πλ µ ν≠ ≠ ≠
E615 Data 252 GeV π- + W
λ λ λ
µ µ µ
ν ν ν
2(GeV/c )mµµ xπ (GeV/c)Tp
10
Decay angular distributions in pion-induced Drell-YanIs the Lam-Tung relation violated?
140 GeV/c 194 GeV/c 286 GeV/c
Data from NA10 (Z. Phys. 37 (1988) 545)
11
Violation of the Lam-Tung relation suggests interesting new origins (Brandenburg, Nachtmann, Mirkes, Brodsky, Khoze, Muller, Eskolar, Hoyer,Vantinnen, Vogt, etc.)
=Boer-Mulders function h1
κ1=0.47, MC=2.3 GeV
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.5 1 1.5 2 2.5 3
ν
QT [GeV]
221 12 2( , ) ( )T TkC HT
T HT C
M Mh x k c e f xk M
ααπ
−⊥ =+
12
1
1
1 represents a correlation between quark's and transverse spin in an unpolarized hadron (ana is a time-reversal odd, chiral-o
logous to Colldd TMD p
ins fuarton distributio
nction)n
T
h
h
h k⊥
⊥
⊥
•
•
•
1 1
1 1
can lead to an azimuthal dependence with h hf f
ν⊥ ⊥⎛ ⎞⎛ ⎞
∝ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
2 2
1 2 2 216( 4 )
T C
T C
Q MQ M
ν κ=+
Boer, PRD 60 (1999) 014012
ν>0 implies valence BM functions for pion and nucleon have same signs
Motivation for measuring decay angular distributions in p+p and p+d Drell-Yan
• No proton-induced Drell-Yan azimuthal decay angular distribution data
• Provide constraints on models explaining the pion-induced Drell-Yan data. (h1
is expected to be small for sea quarks. Some other models predict similar effects for p+N and π+N)
• Test of the Lam-Tung relation in proton-induced Drell-Yan
• Compare the decay angular distribution of p+pversus p+d (information on flavor dependence)
13
14
With Boer-Mulders function h1:
ν(π-W µ+µ-X)~ [valence h1(π)] * [valence h1
(p)]
ν(pd µ+µ-X)~ [valence h1(p)] * [sea h1
(p)]
Azimuthal cos2Φ Distribution in p+d Drell-YanLingyan Zhu et al., PRL 99 (2007) 082301
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3 3.5 4
pT (GeV/c)
ν
π- + W at 194 GeV/cπ- + W at 252 GeV/cp + d at 800 GeV/c
-0.1
-0.05
0
0.05
0.1
5 7.5 10 12.5 15mµµ (GeV/c2)
ν
-0.1
-0.05
0
0.05
0.1
0 0.2 0.4 0.6 0.8xF
ν
-0.1
-0.05
0
0.05
0.1
0.2 0.4 0.6 0.8x1
ν-0.1
-0.05
0
0.05
0.1
0.05 0.1 0.15 0.2x2
νν>0 suggests same sign for the valence and sea BM functions
What does this mean?• These results suggest that the Boer-Mulders
functions h1 for sea quarks are significantly
smaller than for valence quarks and have the same sign as valence quarks.
• A combined analysis of p+p and p+d, together with the π+p and π+d Drell-Yan cos(2Ф) data can lead to extraction of valence and sea Boer-Mulders functions.
15
Extraction of Boer-Mulders functions from p+d Drell-Yan
(B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt, arXiv:0803.1692)
Fit to the p+d Drell-Yan data
Satisfy the positivity bound
16
Extraction of Boer-Mulders functions from p+d Drell-Yan
(B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt, arXiv:0803.1692)
, 2 2 21 1
Parametrization of the BM functions:( , ) (1 ) ( ) exp( / )q c q
q BMh x p H x x f x p p⊥⊥ ⊥= − −
c3.99 3.83 0.91 -0.96 0.16 0.45 0.79
uH2 / dofχdH uH dH
2BMp
(in agreement with model calculations (bag-model, quark-diquark, relativistic CQM, Lattic
and ha
e)
ve the same sign and
and the picture g
similar magnitude
aiven by M. Burkar
nd dt)
u d
u
H H
H H
•
• are smaller by factor of 4 and have opposite signd 17
18
Quark-diquark Models for Boer-MuldersFunction h1
Recent quark-diquark model including axial-diquarks Gamberg, Goldstein & Schlegel, arXiv: 0708.0324.
B-M d-quark B-M u-quark Sivers d-quark Sivers u-quark
Same sign for the u and d quarks B-M functions
19
A simple explanation for the signs of the up- and down-quark Boer-Mulders functions
1) Transversity
1
1
1
1
11
From fits to SIDIS data,we know that1) transversity
2) Sivers function
3) Boer-Mulders function One expects
( ) 0
( ) 0
(
( ) 0
( 0
) )
)
( 0 0
T T
h u
f u
h u
h d
f d
h d
⊥
⊥
⊥
⊥
<
<
>
>
<<
Correlation between and q Ns S⊥ ⊥
2) Sivers function
Correlation between and N qS k⊥ ⊥
3) Boer-Mulders function
Correlation between and q qs k⊥ ⊥
Sea-quark Boer-Mulders Functions
20
0 1 2 3-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 0 1 2 3
140 GeV
ν
(a)
G eV QT
194 GeV
GeV
(b) QT
286 GeV
(c)G eVQT
1) Use quark-spectator-antiquark model to calculate pion B-M functions. Pion-induced Drell-Yan data are well reproduced.
(Lu and Ma, hep-ph/0504184)
2) Use pion-cloud model convoluted with the pionB-M function to calculate sea-quark B-M for proton.
, 21 ( , )u
th x k⊥ , 21 ( , )d
th x k⊥(Lu, Ma, Schmidt, hep-ph/0701255)
Extraction of Boer-Mulders functions from p+d Drell-Yan
(B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt, Private communication)
Set I: , have same signsSet II: , have opposite signs
u d
u d
H HH H
Predict larger values of ν for p+p than for p+d21
New results on the Azimuthal cos2Φ Distribution in p+p Drell-Yan
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.5 1 1.5 2 2.5 3 3.5 4
pT (GeV/c)
ν
p + d at 800 GeV/c
p + p at 800 GeV/c
Prediction of p+p
• p+p is similar to p+d but larger
22
23
New results on the Azimuthal cos2Φ Distribution in p+p Drell-Yan
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.5 1 1.5 2 2.5 3 3.5 4
pT (GeV/c)
ν
p + d at 800 GeV/c
p + p at 800 GeV/c
2 2
2 2
:/
31 /2
T
T
PQCDP Q
P Qν =
+
• PQCD is important at large pT
• A global fit to all pion and proton data is needed 24
Future prospect for Drell-Yan experiments• Fermilab p+p, p+d, p+A
– Unpolarized beam and target• RHIC
– Polarized p+p collision• COMPASS
– π-p and π-d with polarized targets• FAIR
– Polarized antiproton-proton collision• J-PARC
– Possibly polarizied proton beam and target25
Fermilab E906 dimuon experiment (Geesaman, Reimer et al., expected to run ~2010-2011)
• BM functions can be measured at larger x
• Azimuthal angular distributions of J/Ψ 26
Polarized proton beam at J-PARC ?• Polarized proton beam at J-PARC with
– Polarized H¯ source– RF dipole at 3 GeV RCS– Two 30% partial snakes at 50 GeV Main Ring
Pol. H- Source
180/400 MeV Polarimeter
Rf Dipole
25-30% Helical Partial Siberian Snakes
pC CNI Polarimeter
Extracted BeamPolarimeter
30 GeV50 GeV
27
Outstanding questions to be addressed by future Drell-Yan experiments
• Does Sivers function change sign between DIS and Drell-Yan?
• Does Boer-Mulders function change sign between DIS and Drell-Yan?
• Are all Boer-Mulders functions alike (proton versus pion Boer-Mulders functions)
• Flavor dependence of TMD functions• Independent measurement of transversity
with Drell-Yan28
Summary
29
• The Drell-Yan process compliments the SIDIS as a powerful independent tool for measuring transversity and TMD PDFs.
• First results on azimuthal decay angular distributions on unpolarized p-p or p-d Drell-Yan are now available.
• Pronounced cos2Φ azimuthal dependence previously observed in pion-induced Drell-Yan is not observed in p-por p-d Drell-Yan
• These results suggest that the Boer-Mulders functions h1
for sea quarks are smaller than for valence quarks.• Future Drell-Yan experiments at Fermilab, J-PARC and
other facilities can provide new information (flavor dependence of valence and sea, opposite sign for SIDIS and D-Y) on Boer-Mulders and other TMDs.
BACKUP SLIDES
30
Polarized Drell-Yan experiment at J-PARC• Experimental condition
– higher beam intensity is possible for unpolarizedliquid H2 target, or nuclear target
• 5×1012 ppp = 2.5×1012×2sec in 1pulse (5sec) possible?
– PYTHIA simulation• 75% polarization beam• 120 days, beam on target
5×1017 (with 50% duty factor)• ~5% reaction target• 10000 fb-1 luminosity• mass 4 – 5 GeV/c2
31
4 < Mµ+µ- < 5 GeVintegrated over qT
red liquid H2 targetblue nuclear target
analyzingmagnet
liquid H2
targetnucleartarget
64cm
127cm51cmpolarizedbeam
New results on the Azimuthal cos2Φ Distribution in p+p Drell-Yan
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3 3.5 4
pT (GeV/c)
ν
π- + W at 194 GeV/cπ- + W at 252 GeV/cp + d at 800 GeV/c
p + p at 800 GeV/cp + p/d at 800 GeV/c
• p+p is similar to p+d
• A global fit to all pion and proton data is needed 32
Nuclear modification of spin-dependent PDF?
EMC effect for g1(x)
Bentz, Cloet et al., arXiv:0711.0392
Very difficult to measure !
Easier to measure the nuclear modification of Boer-Mulders functions (only unpolarizedtargets are required)?
(suggested by Gary Goldstein)33
Decay angular distributions for p+d Drell-Yan at 800 GeV/c
2 21 3 1 cos sin 2 cos sin cos 24 2
ddσ νλ θ µ θ φ θ φ
σ π⎛ ⎞⎛ ⎞ ⎡ ⎤ ⎡ ⎤= + + +⎜ ⎟⎜ ⎟ ⎢ ⎥ ⎢ ⎥Ω⎝ ⎠⎝ ⎠ ⎣ ⎦ ⎣ ⎦
0
0.5
1
1.5
2λ
-0.2
-0.1
0
0.1
0.2µ
-0.2
-0.1
0
0.1
0.2ν
-1
-0.5
0
0.5
1
0 0.5 1 1.5 2 2.5 3 3.5 4pT (GeV/c)
2ν-(
1-λ)
p+d at 800 GeV/c
34
<λ> 1.07±0.07<µ> 0.04±0.013<ν> 0.03±0.01
<2ν-1+λ> -0.13±0.07
No significant azimuthalasymmetry in p+d Drell-Yan!
