The Quest for the spin of the proton ! or

1DIS - Madrid, April 2009 E.C. Aschenauer

The Quest for the spin of the proton !or

“You think you understand something?Now add spin…” - R. Jaffe

Nobel Prize, 1943: "for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton" mp = 2.5 nuclear magnetons, ± 10% (1933)

Otto Stern Proton spins are used to image the structure and function of the human body

using the technique of magnetic resonance imaging.

Paul C. Lauterbur

Sir Peter Mansfield

Nobel Prize, 2003: "for their discoveries concerning magnetic resonance imaging"

The Spin of the Proton

E.C. Aschenauer

2DIS - Madrid, April 2009


How do the partons contribute

E.C. Aschenauer

SqDq

DG

Lg

SqLq

dq1Tf

SqDq

DG

Lg

SqLq dq1Tf

Is the proton looking like this?

“Helicity sum rule”

12h= P,12 |JQCD

z |P,12 = 12q

∑ Sqz+Sgz+ Lqzq∑ +Lgz

total u+d+squark spin

angular momentum

gluonspin Where do we stand

solving the “spin puzzle” ?

Dq & DG contributions to the proton spin

E.C. Aschenauer


γ*

u,d,s,gpolarized DISSqDq, DG

γ*

u,d,s

p,K

polarized SIDISDqf

polarized pp scattering

Dqf, DG

u,d,s,g

u,d,s,gu,d,s,g

p,Kjet

Existing data from:

to extract polarized PDFs! a “global QCD analysis” is required !

all processes tied together: universality of pdfs & Q2 – evolution

each reaction provides insights into different aspects and kinematics

in NLO DSSV PRL101:072001,2008

Inclusive World data


new

: input to the old GRSV-analysis: input to the DIS & SIDIS – analysis by DNS

Inclusive DIS-Data:

Semi-Inclusive World Data


not in DNS Semi-inclusive DIS-Data:


includes all world data from DIS, SIDIS and pp Kretzer FF favor SU(3) symmetric sea, not so for KKP, DSS DS ~25-30% in all cases

D. De Florian et al. arXiv:0804.0422 NLO @ Q2=10 GeV2

NLO FIT to World Data

KretzerKKP

c2DIS c2

SIDIS Duv DuDdv Dd Ds Dg DS

206206

225231

0.940.70 -0.26

-0.340.087-0.049

-0.11-0.055

-0.045-0.051

0.310.28

DSSV 0.813 -0.458 0.036 -0.115 -0.057 0.242

Polarized Strangeness


Driven by SIDISK-AsymmetriesK-FFdominated by

Driven bySU(3); (3F-D)

New Results from

isoscaler method AK++K- & Aincl

“Purity” Method using FFInput : A1,d , A1,d

p +

, A1,dp−

, A1,dK+

, A1,dK−

Results are completely consistent with Hermessea quark polarizations ~ 0


More on Strangeness PDF Kaon multiplicities from Deuterium target

strange quark sea in proton and neutron identical fragmentation simplifies

Only assumptions used: isospin symmetry between proton and neutron charge-conjugation invariance in fragmentation

.( ) 4 ( ) ( )K K K K Kds un trD z dz D z dz D z dz

+ - + -+ +- = +

( ) 2 ( )strangK K K

seD z dz D z dz+ -+=

.( ) ( ) ( ) ( )( ) /( ) / 5 ( ) 2 ( )

nK

str strangKK

DiseQ x D z dz S x D z dzdN x dx

dN x dx Q x S x- +

=+

Fit x-dependence of multiplicitiesusing PDFs from CTEQ-6

dotted:CTEQ-6L & fit ( )K

SD z dz( )K

QD z dzdashed:

solid:S(x)=Q(x): CTEQ-6L & DSS

1 2/ (1 )a x ax e x- - -

s(x) + sbar(x)

dashed-dotted:

€

D sK(z )dz

The Gluon Polarization


unpolarised cross sections nicely reproduced in NLO pQCD

in NLO

RHIC: many sub-processes with a dominant gluon contribution high-pT jet, pion, heavy quark, …

RHIC Data


STARGRSV curves with cone radius 0.7 and -0.7 < < 0.9

2005 jet data: PRL 100, 232003 (2008)

2005: PRD 76, 051106

2006: arXiv:0810.0694

p0 @ 200 GeV

The Gluon Polarization


x RHIC range0.05· x · 0.2

small-x0.001· x · 0.05

large-xx ¸ 0.2

Dg(x) very small at medium x best fit has a node at x ~ 0.1 huge uncertainties at small x

small-x behavior completely unconstrained

Dg(x) small !?Dg(x) dx

0.

1

∫ = −0.084@10GeV 2

d g = Δg(x,10GeV 2 ) dx0.05

0.2

∫


Compass & Hermes: The golden channels for Dg

Idea: Direct measurement of DGIsolate the photon gluon fusion process

detection of hadronic final states charmed mesons high pT pairs of hadrons

single high pT hadronsh±h±

h±

2 1Q 2 0.1Q

2 0.1Q 2 0.1Q

less sub-processes contributing more sub-processes contributing

higher statistics

less sub-processes contributing more sub-processes contributing

higher statistics + + + ..

|||| ||| |( ) ;B SigSig

gmeas i it i i

i tB

tog f AA p f A ff A

s= = + =

s

|| ||ˆ]1 [ meas

Sig

BgBgf

GA

aAG

f-

D=

Several possible contributions to the measured asymmetryMC needed to determine R and aLL

q

g

q

g qg

Important at Q2<0.1

h±h± vs. h±: h± more inclusive → pQCD NLO calculations (easier) possible

Dg from electro production


DSSV gluon agrees well with model-dependent “LO” extractions of Dg/g

not in global fit[NLO not available]

a future global NLO fit will use measured ALL not derived Dg/gneed first to check unpolarized cross section


Beyond form factors and quark distributions

E.C. Aschenauer

Generalized Parton Distributions

Proton form factors, transverse charge & current densities

Structure functions,quark longitudinalmomentum & helicity distributions

X. Ji, D. Mueller, A. Radyushkin (1994-1997)

Correlated quark momentum and helicity distributions in transverse space - GPDs

How to access GPDs?quantum number of final state selects different GPDs: theoretically very clean DVCS (g): H, E, H, E VM (r, w, f): H E info on quark flavors PS mesons (p, ): H E ~

~ ~

~

ρ0 2u+d, 9g/4ω 2u-d, 3g/4f s, g

ρ+ u-d

J/ψ g

p0 2Du+Dd 2Du-Dd

Jq

z =12

xdx H q + E q( )−1

1

⎛⎝

⎞⎠t→ 0

J q

z =12

Dqq∑ + Lq

z

q∑

12=Jq

z + Jgz =

12

Dqq∑ + Lq

z

q∑ + Jg

z

E.C. Aschenauer


W & t dependences: probe transition from soft hard regime

VM production @ small x

r f J/YU

s ~ Wd

steep energy dependence of s in presence of the hard scale

s ~ e-b|t|

universality of b-slope parameter: point-like configurations dominate

E.C. Aschenauer



HERMES / JLAB kinematics: BH >> DVCS

Deeply Virtual Compton Scattering DVCS

two experimentally undistinguishable processes:

DVCS Bethe-Heitler (BH)

p + D

( )* 2 2*~ | | | |BH DVCS DVC BS HB DVCSHd t t + t ts + t + t

isolate BH-DVCS interference term non-zero azimuthal asymmetries

€

ds / dpe dΩe dΩg(pb / GeV sr2 )

H, %H, E, %Emost clean channel for interpretation in terms of GPDs

can measure DVCS – cross section and I


HERMES: combined analysis of charge & polarization dependent data separation of interference term + DVCS2

DVCS

Beam Charge Asymmetry

~ Ac(n=0)cosΦ

~ Re[F1H]

higher twist

higher twist

s LU (Φ, Pl ,el ) = σ UU (Φ){1 + Pl ALUDVCS (Φ) + el Pl ALU

I + el AC (Φ)}

snI sin(nΦ)

n=1

2

∑ cnI cos(nΦ)

n=1

3

∑Beam Spin Asymmetry

~ Im[F1H]

DVCS

DVCS from &


Archiv: 0812.2517

only some appetizers on existing data lets see what theory says

Hermes BCA CLAS BSA

Hall A Hall A

different GPD parametrisations

Results from Theory


cont

ribu

tion

to

nucl

eon

spin

mp2 GeV2

LHPC Collab. hep-lat/0705.4295

Lattice:K. Kumericki & D. MuellerarXiv: 0904.0458

t=0

t=-0.3

First hints for a small Jq Lq

More insights to the proton - TMDs


Unpolarized distribution function q(x), G(x)

Helicity distribution function Dq(x), DG(x)

Transversity distribution function dq(x)

kr⊥q

Correlation between and rs⊥q

kr⊥q

Correlation between and rS⊥

N

Correlation between and rs⊥q

rS⊥

N

Sivers distribution functionf1T⊥

Boer-Mulders distribution functionh1⊥

Single Spin Asymmetries

Explore spin orbit correlations

peculiarities of f1T

chiral even naïve T-odd DFrelated to parton orbital

angular momentumviolates naïve universality of

PDFsQCD-prediction: f1T,DY = -f1T,DIS

Transverse Polarization Effects @ RHIC


Left-Right

Naive pQCD (in a collinear picture) predicts AN ~ mq/sqrt(s) ~ 0

However, large AN observed in forward pions / Kaons.

Proposed mechanisms　 - Sivers 　 - Collins　 - twist-3 process - ...need correlations between particles (g-jet)to disentangle underlying process

Boer-Mulders


dsdxdydzdΦdP⊥

2 =2p a2

xyQ2y2

2(1−e)(1+ g2

2x)[ΦUU,T + 2e(1+e)cosΦΦUU

cosΦ +e cos(2Φ)Φuucos(2Φ)]Unpol. SIDIS cross section:

Boer-Mulders x Collins FF

remember Collins FF:H1fav⊥ (z)=−H1unfav

⊥ (z)

Boer-Mulders fct. for u and d quark seem to have same sign consistent with Fermi-lab DY-experiments E605++

h1,u⊥ =1d

⊥

K+ > 0 K- ~ 0 K+ > p+

importance of sea quarks? Deuterium ~ 0

u and d quark cancel


HERMES & COMPASS Measurements

ASivers ∝ f1T (x)D1(z)

Proton

Proton: Sivers moment:

p+ > 0 p- ~ 0

hep-ex/0802.2160Deuterium

Fit M. Anselmino et al. arXiv:0805.2677

Sivers function and OAM


Anselmino et al. arXiv:0809.2677

Model dependent statement:

(1−x)f1T⊥q(x)=−3

2MCΦasEq(x,0,0)

dx0

1

(1−x)f1T⊥q(x)=−32MCΦasκ q

anomalous magnetic moment:κu = 1.67κd = -2.03

x

Sivers fct. from fit to M. Burkardt et al.

Lattice: P. Haegler et al.lowest moment of distribution of unpol. q in transverse pol. protonand of transverse pol. quarks in unpol. proton

Conclusions


many avenues for further important measurements and theoretical developments

we have just explored the tip of the iceberg

you are here

Lq,g

DsDg

Dutot, Ddtot

Du, Dd

spin sum ruleThank you for your attention &to everybody, who helped preparing the talk, especially Werner and Marco


BACKUP SLIDES


good agreement with NLO-QCDPolarised opposite to proton spin

Polarized Quark Densities

Du(x) > 0

First complete separation of pol. PDFs without assumption on sea polarization

Polarised parallel to proton spinDd(x) < 0

Du(x), Dd(x) ~ 0 No indication for Ds(x) < 0 In measured range (0.023 – 0.6)

0.002 0.043uD =- 0.054 0.035dD =- 0.028 0.034sD =+

DSS: good global fit of all e+e-, ep, and pp hadron data


de Florian, Sassot, MSmain results:• results for p, K±, chg. hadrons• full flavor separation for Di

H(z) and DgH

• uncertainties (L.M.) well under control• fits all LEP, HERMES, SMC, RHIC, … data • supersede old fits based only on e+e- data

apart from cross-over trajectory (x=x) GPDs not directly

accessible: deconvolution needed ! (model dependent)

but only x and t accessible experimentally ),,( txH x

x is mute variable (integrated over):

GPD moments cannot be directly revealed,

extrapolations t 0 are model dependent +

++

-

1

1

),,(~ dxixtxHT DVCSex

x+

-

+-

1

1

),,(),,(~ tHidxx

txHP xxpxxe.g.

cross sections & beam-charge asymmetry ~ Re(T

DVCS )

beam or target-spin asymmetries ~ Im(T DVCS )

accessing GPDs: some caveats

t=0 q(x)x=0 q(x)

E.C. Aschenauer


detour: DSS kaon FF’s DiK(z)


RHIC pp data (BRAHMS,STAR) explain different Dg

smaller u & larger s-frag. required by SIDIS

note: some issues with K- data (slope!)await eagerly final HERMES data


DsUT ~ sinf∙Im{k(H - E) + … }

DsC ~ cosf ∙Re{ H + xH +… }~

DsLU ~ sinf∙Im{H + xH + kE}~

DsUL ~ sinf∙Im{H + xH + …}~

polarization observables:

DsUT

beam target

kinematically suppressed

H

H

H, E

~

different charges: e+ e- (only @HERA!):

H

DVCS ASYMMETRIES

x = xB/(2-xB ),k = t/4M2

( )* 2 2*~ | | | |BH DVCS DVC BS HB DVCSHd t t + t ts + t + t


[M. Burkardt, M. Diehl 2002]FT (GPD) : momentum space impact parameter space:

probing partons with specified long. momentum @transverse position b

T

polarized nucleon:

[x=0]

from lattice

What does theory tell

d-quarku-quark


Hermes: Charge and Beam Spin Asymmetry Heavy Targets

Beam Charge Asymmetry

Beam Spin Asymmetry

Why nuclear DVCS: constrain nuclear GPDs constrain models attempting

to describe nuclear matter neutron and proton matter distribution in nuclei

Beam: 27.5 GeV e±; <50>% polarizationTarget: (un)-polarized gas targets; <85%> polarizationLumi: pol: 5x1031 cm-2/s-1; unpol: 3x1032-33 cm-2/s-1

Data taking finished June 2007

36

The contemporary experiments

E.C. Aschenauer

DIS - Madrid, April 2009

SM1

SM2

6LiD Target

160 GeV μ

RICH

ECal & HCalμ Filter

Trigger-hodoscopes

SiliconMicromegas

SciFi

Gems

Drift chambers

StrawsMWPC

50 m

Beam: 160 GeV m: 80% polarizationTarget: 6LiD: 50% polarization (2002-2006) NH3: 80% polarisation (2007)Lumi: 5x1032 cm-2s-1

STAR Detector

Beams: √s=200 GeV pp; 50% polarizationLumi: 50 pb-1

The Quest for the spin of the proton ! or

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