High-energy spin physics with hadron beams€¦ · Efremov, Goeke, Pobylitsa, 2000; Goeke,...

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


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


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


∆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)


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)


∆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


∆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


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


Polarized sea


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


∆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


∆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 (?!)


∆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


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)


Transversity


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


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)


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


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


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


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


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


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)


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


Single spin asymmetries


Transverse spin structure

The transverse spin case can be asymmetric around the momentum direction

Use high energy scattering p p→ πX as an eye:


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)]


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


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


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


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-...)


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


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)


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)

)


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


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


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!


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


Spin effects in unpolarized hadrons


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)


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


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


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


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


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


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


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


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


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


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


Summary of transverse spin asymmetries

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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


Back-up Slides


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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


High-energy spin physics with hadron beams€¦ · Efremov, Goeke, Pobylitsa, 2000; Goeke,...

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Transcript of High-energy spin physics with hadron beams€¦ · Efremov, Goeke, Pobylitsa, 2000; Goeke,...