Post on 20-Jul-2020
High-energy spin physics with hadron beams
Daniel Boer
University of Groningen
• Helicity distributions
• ∆q + ∆q → ∆Σ, spin crisis
• Spin sum rule, ∆g, Lz, Lqz, Lgz
• Polarized sea
• ∆u,∆d
• ∆s+ ∆s, ∆s−∆s
• Transversity
• Single spin asymmetries
• Qiu-Sterman effect, Sivers effect
• Spin effects in unpolarized hadrons
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 1
Helicity distributions
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 2
Polarized quark distributions
25 years ago high-energy spin physics entered new phase: polarized parton distributions
In 1988 the European Muon Collaboration (EMC) at CERN presented the firstexperimental result on ∆Σ, the sum of quark contributions to the proton spin:
∆Σ ≡ ∆u+ ∆d+ ∆s
Obtained from the asymmetry A1 in→e→p − →e ←p in polarized DIS (
→e→p → e′X)
∆q =∫dx∆q(x) = number of quarks and antiquarks with helicity +1
2 minus −12
∆q = (q+ − q−) + (q+ − q−)
with operator definition:
〈P, S|ψqγµγ5ψq(0)|P, S〉 = ∆q Sµ
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 3
Spin crisis
The sum of quark contributions to the proton spin:
∆Σ ≡ ∆u+ ∆d+ ∆s
Naively one expects ∆Σ = 1 and ∆s = 0
EMC [1988] obtained at 〈Q2〉 = 10.75 GeV2:
initially: ∆Σ = 0.02± 0.26 and ∆s = −0.23± 0.08
finally: ∆Σ = 0.12± 0.17 and ∆s = −0.19± 0.06
This was dubbed the “spin crisis” or “spin puzzle”
The quarks and antiquarks together contribute very little to the proton spin!
A surprisingly big role for the strange quarks
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 4
∆Σ at present
COMPASS experiment at CERN [2007]
∆Σ = 0.35± 0.03(stat.)± 0.05(syst.) Q2 = 3 GeV2
HERMES experiment at DESY [2007]
∆Σ = 0.330± 0.025(exp.)± 0.028(evol.)± 0.011(theo.) Q2 = 5 GeV2
25 years after EMC the conclusion remains essentially the same:
Only about 1/3 of the proton spin comes from the quark spin!
HERMES [2007]: ∆u = 0.84± 0.01, ∆d = −0.43± 0.01, ∆s = −0.09± 0.02
Recent lattice determination at Q2 = 7.4 GeV2(Bali et al., PRL 108 (2012) 222001)
∆ΣMS = 0.45(4)(9) and ∆sMS = −0.020(10)(4)
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 5
Spin Sum Rule
In general, one expects the following “spin sum rule” to hold
proton spin =1
2=
1
2∆Σ + ∆G+ Lz
Depending on the renormalization scheme, the three terms mix under changes of thescale in a controlled and known (NLO) way
It is known how to access ∆G(x) in experiments
∆G =
∫dx∆G(x) =
∫dx [G+ −G−]
Inclusive DIS is sensitive to ∆G(x) through Q2 dependence of the structure function g1:
gp/n1 (x,Q2) =
1
36
(4∆Σ± 3∆qNS
3 + ∆qNS8
)⊗(
1 +αs2π
∆Cq
)+
∑q
e2q
αs2π
∆G⊗∆Cg +O(α2s)
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 6
∆G(x) from inclusive DIS
Many groups have extracted fits of the polarized pdf’s from inclusive DIS (GRSV, BB,AAC, LSS, DNS, ...)
Important to be agnostic about sign of ∆G(x) and the shape
Neural net polarized pdfs: let shape be constrained by data rather than parameterizations
x-410 -310 -210 -110 1
) 02 (
x, Q
Σ ∆x
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
NNPDF Preliminary
NNPDFpol1.0
DSSV08
BB10
x-410 -310 -210 -110 1
) 02 g
(x,
Q∆x
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
NNPDF Preliminary
NNPDFpol1.0
DSSV08
BB10
NNPDFpol1.0 at Q20 = 1 GeV2
Nocera, Forte, Ridolfo, Rojo, arXiv:1206.0201
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 7
∆G from p p collisions
Polarized p p collisions at RHIC at√s = 200 GeV indicate ∆G(x) G(x)
ALL in jet production
STAR, arXiv:1106.5769
∫ 0.2
0.05
∆G(x,Q2 = 10 GeV2) = 0.13
DSSV, arXiv:1112.0904
→ Talk by Deshpande
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 8
Orbital angular momentum
Importance of Lz remains to be seen, through DVCS and other hard exclusive processes
Also at J-PARC (talks by Kawamura and Maas on January 15)
Theory developments on OAM in spin sum rule still ongoing
Is there a way to get at the orbital angular momentum of quarks and gluons separately?
1
2=
1
2∆Σ + ∆G+ Lz
?=
1
2∆Σ + ∆G+ Lqz + Lgz
Jaffe & Manohar, 1990; Ji, 1997; Bashinsky & Jaffe, 1999; Chen et al., 2008; Wakamatsu, 2010; Leader,
2011; Hatta, 2011; Guo, Schmidt, 2012; Ji, Xiong, Yuan, 2012; Lorce, 2012
A gauge invariant and frame independent decomposition can be given, where each termcan be related to a measurable quantity (using GPDs to obtain Jq,g)
Intrinsically nonlocal operators, with some remaining debate about the uniqueness of Lq,gz
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 9
Polarized sea
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 10
Polarized sea from SIDIS
Unpolarized sea is far from symmetric: u 6= d; u+ d very different from s+ s; and
s− s is likely nonzero (NNPDF2.0: favored by fixed target DY data; NuTeV anomaly)
There are no reasons to expect the polarized sea to be more symmetric
Our present knowledge of the polarized sea comes from polarized SIDIS (~e ~p→ e′ hX)
SIDIS data allows for separate extractions of polarized quark and antiquark pdfs
Extractions of the helicity pdfs at next-to-leading order (NLO) with uncertainty estimates
DSSV: De Florian, Sassot, Stratmann, Vogelsang, PRL 101 (2008) 072001 & PRD 80 (2009) 034030
DSSV+: arXiv:1108.3955
Large dependence on fragmentation functions, which are quite uncertain still for kaons
LSS: Leader, Sidorov, Stamenov, PRD 82 (2010) 114018 & PRD 84 (2011) 014002 & arXiv:1212.3204
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 11
∆d−∆u
Chiral quark soliton model: d− u < |∆d−∆u|Efremov, Goeke, Pobylitsa, 2000; Goeke, Pobylitsa, Polyakov, Urbano, 2001
SIDIS data indicates |∆d−∆u| at least not much larger than d− u
DSSVDNSGRSV (val)
QSM
CTEQ x(d–-u
–)
DSSV 2=1DSSV 2/ 2=2%
x( u– - d
–)
x
-0.05
0
0.05
0.1
10 -3 10 -2 10 -1 1
x -210 -110 1
)
d - u
x(
-0.1
-0.05
0
0.05
0.1 COMPASS DSSV Bourrely-Soffer-Buccella Kumano-Miyama Wakamatsu
)u - d x(
COMPASS Collaboration, PLB 693 (2010) 227
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 12
∆s from SIDIS
COMPASS data extends the coverage down to x ' 5 × 10−3, almost an order ofmagnitude lower than the HERMES data used by DSSV in 2008
DSSV+arXiv:1108.3955
0
5
10
15
-0.02 0 0.02 0 0.02
2i
s1, [ 0.02-1.0 ]
DSSV+SIDISDIS
(a)
s1, [ 0.02-1.0 ]
all SIDIS dataHERMES K±
COMPASS K±
(b)
2i
s1, [ 0.001-0.02 ]
(c)0
5
10
15
-0.02 0 0.02
x > 0.02 data prefer slightly positive ∆s(x), DIS data large negative∫dx∆s(x)
COMPASS small x data favors small negative ∆s(x), so may indicate a node
Considerable ∆s(x) below x ∼ 10−3, where the asymmetry A1 is essentially zero (?!)
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 13
∆s− from SIDIS
∆s− can be nonzero too, but COMPASS data indicates it is not large
ss,
xx
-0.04-0.02
00.020.04
s xs x
x -210 -110
)
ss
- x(
-0.1
-0.05
0
0.05
0.1
COMPASS Collaboration, PLB 693 (2010) 227
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 14
Conclusions sea polarization
- |∆d−∆u| of similar size as d− u- Polarization of up sea distributions not large, down and strange polarization larger
- Lots of structure (and uncertainty) in polarized strange sea as function of x
DSSVPRL 101 (2008) 072001
RHIC: ∆u/u from AW−
L and ∆d/d from AW+
L
Future: more SIDIS data from JLab12 and perhaps an electron-ion collider (EIC)
Polarized high momentum beam in p p and p d Drell-Yan (ALL) at J-PARC allows studyof polarized sea at larger x values (x ∼ 0.25− 0.5) than at RHIC (talk by Goto)
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 15
Transversity
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 16
Transverse polarization
Transverse polarization allows to probe the transversity distributions: δq(x) = hq1(x)
∆q 6= δq due to relativistic effects and related to orbital angular momentum (OAM)
In quark models the difference is related to OAM via ‘pretzelosity’ h⊥(1)q1T (x):
∆q(x)− δq(x) = h⊥(1)q1T (x) = −L3
q(x)
Avakian, Efremov, Schweitzer, Yuan, PRD 78 (2008) 114024 & PRD 81 (2010) 074035
J. She, J. Zhu & B.Q. Ma, PRD 79 (2009) 054008
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 17
Transversity - definition & properties
h1(x): distribution of transversely polarized quarks inside a transversely polarized proton
Ralston & Soper, NPB 152 (1979) 109
It is a chiral-odd/helicity flip quantity:∫dλ
2πeiλx〈P, ST |ψ(0)L[0, λ]iσi+γ5ψ(λn−)|P, ST 〉 = SiT h1(x)
An interference between +12 and −1
2 helicity states:
1 1x x x x
+− +−
+− +−
δg(x)
+−
+− +−
+−
1h ( )x
There exists no gluon transversity distribution
Gluon effects inside a transversely polarized proton are suppressed (twist-3)
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 18
Transversity in DY
First suggestion was to measure h1 through the Drell-Yan process
ATT =σ(p↑ p↑ → ` ¯X)−σ(p↑ p↓ → ` ¯X)
σ(p↑ p↑ → ` ¯X)+σ(p↑ p↓ → ` ¯X)∝∑q
e2q h
q1(x1) hq1(x2)
Artru, Mekhfi, ZPC 45 (’90) 669; Jaffe, Ji, NPB 375 (’92) 527; Cortes, Pire, Ralston, ZPC 55 (’92) 409
However, polarized Drell-Yan is very demanding, still not done
RHIC is at present the only place that can do double polarized hadron scattering
An upper bound can be obtained by using Soffer’s inequality,
|h1(x)| ≤ 1
2[f1(x) + g1(x)]
The upper bound on ATT was shown to be small at RHIC (percent level)
Martin, Schafer, Stratmann & Vogelsang, PRD 60 (1999) 117502
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 19
ATT(QT) at J-PARC
Larger (maximum) asymmetries at J-PARC than at RHIC
√s = 10 GeV, Q = 2 GeV, y = 0, φ = 0
Kawamura, Kodaira & Tanaka, NPB 777 (2007) 203
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 20
Spin transfer asymmetry in p↑ p→ Λ↑ X
Transversity times its fragmentation analogue (H1(z)) can also arise: DNN ∝ h1H1
E704 Collaboration, Bravar et al., PRL 78 (1997) 4003
At E704 (√s ≈ 20 GeV) factorization is doubtful due to low pT <∼ 1.5 GeV
DNN at J-PARC probably equally large
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 21
Spin transfer asymmetry in µp↑→ µΛ↑X
COMPASS Collaboration, H. Kang, PoS DIS2010 (2010) 232
Small DNN in SIDIS indicates small Hu,d1 (z) and/or small hs1(x) in the measured range
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 22
Using pion angular distributions
Transversity can also be extracted by means of pion angular distributions:
• e p↑ → e′ πX (Collins ’93)
• e p↑ → e′ (π+ π−)X (Ji ’94; Collins, Heppelmann, Ladinsky ’94; Jaffe, Jin, Tang ’98; ...)
These transversity measurements involve new fragmentation functions:
• Collins function H⊥1 (z, kT ), extractable from e+ e− → π+ π− X
• DiFF H<)1 (z,M2
ππ), extractable from e+ e− → (π+ π−)jet 1 (π+ π−)jet 2X
The required data available from B-factories (BELLE, BABAR)
R. Seidl et al., BELLE Collaboration, PRL ’06; PRD ’08; I. Garzia, for BaBar, at Transversity 2011
Vossen et al., BELLE Collaboration, PRL 107 (2011) 072004
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 23
First transversity extraction using Collins effect
Extraction of hq1(x) = ∆Tq(x) at Q2 = 2.4 GeV2
from HERMES, COMPASS & BELLE data
Anselmino et al., PRD 75 (2007) 054032 & arXiv:0812.4366
It shows:
hq1(x) ≈ fq1 (x)
3
About half its maximally allowed value (blue line)
Similar in size as ∆q(x) (dashed)
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 24
Transversity extraction from DiFF asymmetries
Consistent with a 2nd extraction using different method & different SIDIS & e+e− dataBacchetta, Courtoy, Radici, arXiv:1212.3568
0.0
0.2
0.4
0.01 0.10x
x h1uV(x)-x h1
dV(x)/4
fit
data HERMES
data COMPASS
0.01 0.02 0.05 0.10 0.20 0.50 1.00-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
x
x h1uv HxL
0.01 0.02 0.05 0.10 0.20 0.50 1.00-0.3
-0.2
-0.1
0.0
0.1
0.2
x
x h1dHxL
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 25
Single spin asymmetries
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 26
Transverse spin structure
The transverse spin case can be asymmetric around the momentum direction
Use high energy scattering p p→ πX as an eye:
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 27
Left-right asymmetries
Krueger et al., 1999; Ep = 22 GeV
Similar at J-PARC with Ep = 30 GeV
Distribution of produced particles is highly asymmetric in p↑ p→ πX and p↑ p→ πX[Fermilab: E704 (’91 & ’96) & BNL: AGS (’99); STAR (’02); BRAHMS (’05)]
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 28
Single spin asymmetries
SSA persist out to high energies (√s = 200 GeV, RHIC)
What is the explanation on the quark-gluon level?
The asymmetry in the partonic hard scattering is tiny
Two suggestions:
- higher twist effect in a collinear factorization approach (Qiu-Sterman effect)
- transverse momentum effect (Sivers effect, Collins effect)
Qiu-Sterman effect and Sivers effect are related to each other
Boer, Mulders, Pijlman, 2003; Ji, Qiu, Vogelsang, Yuan, 2006
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 29
Qiu-Sterman effect
Qiu-Sterman effect proposed as a mechanism for single spin asymmetries in p↑ p→ πX
Qiu & Sterman ’91
The quark-gluon correlation function
TF (x, ST ) is a collinear twist-3 function
The resulting SSA is power suppressed p1
p
q
P P
k k
A A
PB BP
TF (x, ST )A+=0∝ F.T. 〈P, ST | ψ(0)
∫dη− F+α(η−) γ+ψ(ξ−) |P, ST 〉
Applicable at high-pT , when collinear factorization is justified
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 30
Single spin asymmetries in DY
SSA in p↑ p→ ` ¯X integrated over QT is not related to transversity
Qiu-Sterman effect yields:
AN ∝ sinφ`S1
Q
[sin 2θ
1 + cos2 θ
] ∑a e
2a
∫dxT aF (x, ST ) f a1 (Q2/xs)∑
a e2a
∫dx fa1 (x) f a1 (Q2/xs)
Hammon, Teryaev & Schafer, 1997; Boer, Mulders & Teryaev, 1998; Boer & Qiu, 2002;
Anikin & Teryaev, 2010; Zhou, Metz, 2010; Ma, Zhang, 2012
Asymmetry expression equally applies to p p↑ and π p↑ DY
Predictions for ADYN vary widely, from percent level to sizes larger than AπN of E704
Also differ in the xF dependence
Boros, Liang & Meng, 1995; Boer & Qiu, 2002
Its measurement would be very helpful to pinpoint the underlying mechanism
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 31
Sivers effect
Sivers effect was suggested to explain SSA in p↑ p→ πX
D. Sivers (’89/’90)
kT × ST
One needs to include transverse momentum in the partonic correlator Φ(x)→ Φ(x,kT )
Φ(x,kT ) =1
2f1(x,k2
T ) 6P +P ·(kT × ST )
2Mf⊥1T (x,k2
T ) 6P + ...
Highly nontrivial theoretically, relies on factorization of the process
It can effectively describe the p↑ p→ πX data, despite lack of factorization justification
Anselmino, Boglione, D’Alesio, Murgia, ... (’95-...)
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 32
Sivers TMD
Sivers effect is described by a transverse momentum dependent distribution (TMD)
Theoretical definition not straightforward: modified/improved over the years
Collins, 1993 & 2002; Belitsky, Ji & Yuan, 2003; Ji, Ma & Yuan, 2005; Collins 2011
Factorization of scattering processes in terms of TMDs is established for semi-inclusiveDIS and Drell-Yan, but not for p p→ πX (subleading twist)
For a short summary see J.C. Collins, arXiv:1107.4123
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 33
Sivers effect in SIDIS
Sivers effect leads to an unsuppressed sin(φh−φS) asymmetry in e p↑ → e′ hX ∝ f⊥1TD1
Boer & Mulders ’98
SIDIS
e p→ e′ hX
Clearly observed by HERMES (PRL 2009) and COMPASS (PLB 2010)
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 34
Sivers TMD
The proper theoretical definition of the Sivers TMD is not unique
It involves Wilson lines that turn out to depend on the process!
P ·(kT × ST ) f⊥[C]1T (x,k2
T ) ∝ F.T. 〈P, ST |ψ(0)LC[0, ξ] γ+ψ(ξ)|P, ST 〉∣∣ξ=(ξ−,0+,ξT )
LC[0, ξ] = P exp
(−ig
∫C[0,ξ]
dsµAµ(s)
)
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 35
Process dependence of Sivers TMD
Gauge invariant definition of TMDs in semi-inclusive DIS contains a future pointingWilson line (FSI), whereas in Drell-Yan (DY) it is past pointing (ISI)Brodsky, Hwang & Schmidt ’02; Collins ’02; Belitsky, Ji & Yuan ’03
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 36
Process dependence of Sivers TMD
Time reversal invariance relates the Sivers functions of SIDIS and Drell-Yan
This is a calculable process dependence, which yields the relation (Collins ’02):
(f⊥1T )SIDIS = −(f⊥1T )DY to be tested
The more hadrons are observed, the more complicated the end result (ISI and FSI)
Bomhof, Mulders & Pijlman ’04
TMD factorization fails for processes like p p→ h1 h2X
Collins & Qiu ’07; Collins ’07; Rogers & Mulders ’10; Buffing & Mulders ’11
This does not cast doubt on the above sign relation
Experimental test needs to mind possible Q2 & flavor dependent nodes in x and/or kT
Boer ’11; Kang, Qiu, Vogelsang, Yuan ’11
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 37
Process dependence of TMDs
After taking Mellin moments and Bessel weighting (Boer, Gamberg, Musch, Prokudin, 2011),the well-defined quantity 〈kT × ST 〉(n, bT ) – the average transverse momentum shiftorthogonal to ST –, can be evaluated on the lattice (Musch et al., 2011)
SIDIS DY
Sivers-Shift, u-d - quarks
Ζ`
= 0.39,
ÈbT È = 0.12 fm,mΠ = 518 MeV
-10 -5 0 5 10 ¥-¥-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
ΗÈvÈ Hlattice unitsL
mN
f 1T¦@1
DH1L
f 1@1DH
0LHG
eVL
This is the first ‘first-principle’ demonstration that the Sivers function is nonzero
It clearly corroborates the sign change relation!
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 38
Sivers effect in Drell-Yan
Experimental test of Sivers effect in Drell-Yan is highly desired (sin(φ− φS)f⊥1T f1)
-0.1
0
0.1
0.2
0 0.2 0.4 0.6 0.8
ANsi
n(φ γ
-φS)
xF
JPARC: p↑ p
0<y<14<M<5 Ep=50 GeV
0
0.05
0.1
0.15
0 0.2 0.4 0.6 0.8
ANsi
n(φ γ
-φS)
xF
RHIC: p↑ p
√s=200 GeV0<y<34<M<9 GeV
Anselmino et al. ’09
p↑p DY studies kinematically largely complementary to SIDIS data (careful about nodes)
These predictions take into account the process dependence of the Sivers function
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 39
Spin effects in unpolarized hadrons
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 40
Spin averaged scattering of protons
z
P1 2P h φ
lepton plane (cm)
θ
l’
l
1
σ
dσ
dΩ∝(
1 + λ cos2 θ + µ sin 2θ cosφ+ν
2sin2 θ cos 2φ
)The O(αs) Lam-Tung relation:
1− λ− 2ν = 0
Large deviations from the Lam-Tungrelation were observed in πN DY
NA10 (’86/’88) & E615 (’89)
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 41
Failure of collinear pQCD treatment
With collinear parton densities, only higher order gluon emission can generate deviationsfrom Lam-Tung
Deviation from Lam-Tung relation in NNLO O(α2s) pQCD is (at least) an order of
magnitude smaller and of opposite sign
Brandenburg, Nachtmann & Mirkes ’93; Mirkes & Ohnemus ’95
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 42
Angular asymmetry requires helicity flip
The cos 2φ asymmetry arises from an interference between +1 and −1 photon helicities
L
L
R
RL
L R
R
+
This requires transversely polarized quark-antiquark annihilation
Transversely polarized quarks inside unpolarized hadrons
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 43
Spin structure of unpolarized protons
Non-collinear quarks can be polarized inside unpolarized protons!
Boer & Mulders, 1998
For unpolarized hadrons:
Φ(x,kT ) =M
2
f1(x,k2
T )6PM
+ h⊥1 (x,k2T )i6kT 6PM2
Possibly large due to chiral symmetry breaking
=h1⊥ +
LRL R
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 44
Lattice calculation
〈kT×sT 〉(n, bT ), the average transverse momentum shift orthogonal to a given transversepolarization of quarks inside an unpolarized proton, and hence h⊥1 is clearly nonzeroMusch et al., 2011
SIDIS DY
Boer-Mulders Shift, u-d - quarks
Ζ`
= 0.39,
ÈbT È = 0.36 fm,mΠ = 518 MeV
-10 -5 0 5 10 ¥-¥
-0.2
-0.1
0.0
0.1
0.2
ΗÈvÈ Hlattice unitsL
mN
h 1¦@1
DH1L
f 1@1DH
0LHG
eVL
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 45
Transverse quark polarization
This can explain the anomalous unpolarized Drell-Yan data from CERN and Fermilabfrom the 1980s
(1− λ− 2ν) ∝ h⊥1 (π)h⊥1 (N)
Fit h⊥1 to data by assuming
Gaussian kT dependence
Boer, 1999
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]
Many model calculations of h⊥1 and its asymmetries have been performedGoldstein & Gamberg ’02, ’07; Boer, Brodsky & Hwang ’03
Lu & Ma ’04, ’05; Barone, Lu & Ma ’07; Zhang, Lu, Ma & Schmidt ’08
Courtoy, Scopetta & Vento ’09; Lu & Schmidt ’09
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 46
Hadron type dependence
Asymmetry for p p and p d expected to be smaller, as confirmed by Fermilab dataFNAL-E866/NuSea Collaboration, L.Y. Zhu et al. ’07 & ’09
Asymmetry for p p expected to be very similar to π p (both have valence antiquarks)
Although this depends on the kinematics too of course:
0 0.2 0.4 0.6 0.8x
F
0
0.05
0.1
0.15
0.2
ν
J-PARC: pp Ep
= 50 GeV
0.2 0.4 0.6 0.80.00
0.05
0.10
0.15
XF
PANDA s=30 GeV2
Lu & Schmidt ’10
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 47
Lam-Tung on resonance
Usually Drell-Yan data is taken in the safe region Q = 4− 12 GeV, cutting out the Υ
Vector particles yield same asymmetries in qq channelAnselmino, Barone, Drago & Nikolaev, 2004
NA10 data (1986) on the Υ is compatible with thatabove/below it, but inconclusive about LT violation
E866 data (2008): Υ produced from gg mainly
Very interesting to test LT at J-PARC on the J/ψ
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 48
Sign change of h⊥1
How about measuring the sign change of h⊥1 ?
(h⊥1 )SIDIS = −(h⊥1 )DY
Chiral-odd functions always appear in pairs, hence not straightforward
Restricting to valence quarks & assuming up-quark dominance, it is possible through:
• (e p↑ → e′ hX)/(e p→ e′ hX) ∝ hu1/h⊥u [+]1
• (π− p↑ → `¯X)/(π− p→ `¯X) ∝ hu1/h⊥u [−]1 (or p p↑ → `¯X ∝ h⊥u [−]
1 hu1)
Including d-quarks requires many more observables, using e+e− and p p collisions andexploiting Λ↑ and dihadron (DiFF) final states
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 49
The polarized Drell-Yan process
In the case of one transversely polarized hadron beam:
dσ
dΩ dφS∝ 1 + cos2 θ + sin2 θ
[ν2
cos 2φ− ρ |ST | sin(φ+ φS)]
+ . . .
Assuming u-quark dominance and Gaussian kT -dependence for h⊥1 :
ν ∝ 2h⊥1 h⊥1
ρ ∝ h1 h⊥1
ρ ≈√ν
2
hu1fu1≈ 6%
0 0.2 0.4 0.6 0.8x
F
0
0.05
0.1
0.15
0.2
ν
J-PARC: pp Ep
= 50 GeV
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 50
Pion or kaon induced DY
Measurement of ν and ρ with only one polarized beam offers a probe of transversity
Comparison of π± p↑ Drell-Yan would provide valuable information on the flavordependence of h1 and h⊥1
Especially π+p↑ is of interest, since no data yet and it provides information on the
d-quark ratio h⊥d/p1 /h
d/p1 , without suppression by a charge-squared factor
Using the input on h⊥1 from for example unpolarized p p Drell-Yan would allow for an
extraction of h1 from π±p↑ Drell-Yan
Kp↑ DY allows to investigate h1 for sea quarks, since h⊥s/K1 not expected to be small
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 51
Summary of transverse spin asymmetries
-0.1
0
0.1
0.2
0 0.2 0.4 0.6 0.8
ANsi
n(φ γ
-φS)
xF
JPARC: p↑ p
0<y<14<M<5 Ep=50 GeV
0 0.2 0.4 0.6 0.8x
F
0
0.05
0.1
0.15
0.2
ν
J-PARC: pp Ep
= 50 GeV
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 52
Conclusions for high-energy spin physics with hadron beams
• Polarized sea
• SIDIS data unclear about ∆s(x), kaon fragmentation functions, and SU(3) breaking
• Better ∆u, ∆d, ∆s±∆s determinations needed, also from hadronic collisions
• Transversity
• First extractions of h1 through Collins and DiFF methods are roughly compatible
• Indicates hq1 is about half its allowed maximum and similar in size to gq1 = ∆q
• Need to learn much more about h1 using hadronic collisions: ATT , ATT (QT ), DNN
• SSA
• Various single spin asymmetries turn out (AπN) or are expected (ADYN ) to be large
• Various mechanisms proposed, TF : sinφ`S, f⊥1T : sin(φ`h−φ`S), h⊥1 , H⊥1 : sin(φ`h+φ`S)
• Disentangling mechanisms and testing TMD formalism needs hadronic collisions
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 53
Back-up Slides
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 54
0
0.2
0.4
0.6
0.8
-0.5 0 0.5
x 2
xF
COMPASS: π p↑
4<M<9 GeVEπ=160 GeV
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8
x 1
xF
JPARC: p↑ p
4<M<5 GeVEp=50 GeV
0<y<1
-0.1
0
0.1
0.2
0 0.2 0.4 0.6 0.8
ANsi
n(φ γ
-φS)
xF
JPARC: p↑ p
0<y<14<M<5 Ep=50 GeV
0
0.2
0.4
0.6
0.8
0 0.2 0.4 0.6 0.8
x 1
xF
RHIC: p↑p
0<y<34<M<9 GeV√s=200 GeV
0
0.05
0.1
0.15
0 0.2 0.4 0.6 0.8
ANsi
n(φ γ
-φS)
xF
RHIC: p↑ p
√s=200 GeV0<y<34<M<9 GeV
0
0.05
0.1
0.15
4 6 8 10
ANsi
n(φ γ
-φS)
M (GeV)
RHIC: p↑ p
0<y<3√s=200 GeV
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 55
Azimuthal spin asymmetries
The left-right asymmetry in p↑ p→ πX is actually a sinφS asymmetryNikola Poljak, for the STAR collaboration, arXiv:0901.2828
SSA in Drell-Yan:
dσ
dΩ dφS∝ 1 + cos2 θ+
ν
2cos 2φ+Ah⊥1
|ST | sin(φ+ φS) +Af⊥1T|ST | sin(φ− φS) + . . .
Transversity asymmetry: Ah⊥1∝ h1h
⊥1
Sivers asymmetry: Af⊥1T∝ f⊥1Tf1
There is also a sin(3φ− φS) asymmetry which is ∝ h⊥1Th⊥1 (pretzelosity)
A link between pretzelosity and orbital angular momentum of quarks found in models:
L3q = −
∫dxh
⊥(1)q1T (x)
J. She, J. Zhu & B.Q. Ma, ’09; Avakian, Efremov, Schweitzer & Yuan, ’10
KEK theory center workshop on Hadron physics with high-momentum hadron beams at J-PARC in 2013 – D. Boer, January 18, 2013 56