theoretical status of helicity-dependent parton densities · 2018. 11. 16. · theoretical status...

Theoretical status of helicity-dependent parton densitiesThe 21st International Symposium on Spin Physics

Emanuele R. Nocera

Universita degli Studi di Genova & INFN, Genova

Peking University - October 21, 2014

Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 1 / 25

Foreword

∆f (x ,Q2) = f⇒→(x ,Q2)− f⇒←(x ,Q2)

How do quarks (including sea quarks) and gluons carry the proton spin

S(µ) =1

2=∑f

⟨P;S |Jz

f (µ)|P; S⟩

=1

2

∫ 1

0

dx∆Σ(x , µ) +

∫ 1

0

dx∆g(x , µ) + Lz

All quantities depend on factorization scheme and scale µ

Spin decomposition is not unique (Y. Hatta, S1)

Very little of the proton spin is carried by quarks∫ 1

0

dx∆Σ =

∫ 1

0

dx∑

q=u,d,s

(∆q + ∆q) ∼ 30%

Quark and gluon longitudinal contributions ⇐⇒ longitudinal spin-dependent PDFs


Outline

1 Introduction

2 Impact of latest experimental results

pp collisions at RHICH: W±, π and jet productioninclusive DIS: COMPASS and JLAB

3 Recent theoretical progress

higher-twist correctionsall-order resummation, higher-order computations

4 Summary and outlook

DISCLAIMER

Emphasis on recent achievements in our knowledge of polarized PDFsin global QCD analyses

Apologies in advance for not discussing your favourite subject


1. Introduction


Probes of nucleon helicity structure

Guiding principle: factorization

e.g. DIS d∆σ =∑q,q,g

∆f (x ,Q2)⊗d∆σγ∗f (xP, αs(Q2)) d∆σγ∗f =

∞∑n=0

(αs

4π

)nd∆σ

(n)γ∗f

Reaction Partonic subprocess PDF probed x Q2 [GeV2]

`±{p, d, n} → `±X γ∗q → q∆q + ∆q

0.003 . x . 0.8 1 . Q2 . 70∆g

`±{p, d} → `±hX γ∗q → q∆u ∆u

0.005 . x . 0.5 1 . Q2 . 60∆d ∆d∆g

`±{p, d} → `±DX γ∗g → cc ∆g 0.06 . x . 0.2 ∼ 10

−→p −→p → jet(s)Xgg → qg

∆g 0.05 . x . 0.2 30 . p2T . 800

qg → qg

−→p p → W±XuL dR → W+ ∆u ∆u

0.05 . x . 0.4 ∼ M2WdL uR → W− ∆d ∆d

−→p −→p → πXgg → qg

∆g 0.05 . x . 0.4 1 . p2T . 200

qg → qg

Different processes constrain different PDFs, factorization is successful


Polarized vs unpolarized PDF determinations

1 Limited (x ,Q2) kinematic coverage

difficult to get ∆g from scaling violations in DIS and SIDIS→ additional direct probes of ∆g are needed (jets, open-charm)

need to use data down to Q2 = 1 GeV2

→ is perturbative QCD reliable?

→ how much higher twists affect the perturbative description of observables?

2 No neutrino DIS data

no quark-antiquark separation from inclusive DIS→ limited set of W± production data in pp collisions

→ SIDIS data require knowledge of fragmentation functions (extra uncertainties)

3 Sum rules on shaky (?) grounds

first moments of nonsinglet distributions ⇐⇒ hyperon decay constants→ some constraints on ∆s and ∆Σ at small-x values

→ is SU(3) symmetry broken?


Recent determinations of polarized PDFs @ NLO

Fit Data sets Parton Distributions Uncertainties Latest update

AAC08 DIS, π0 ∆u+, ∆d+, ∆s+, ∆g Hessian ∆χ2 = 12.95 [arXiv:0808.0413]

BB10 DIS ∆u−, ∆d−, ∆q, ∆g Hessian ∆χ2 = 1 [arXiv:1005.3113]

LSS10 DIS, SIDIS ∆u+, ∆d+, ∆u, ∆d , ∆s, ∆g Hessian ∆χ2 = 1 [arXiv:1010.0574]

JAM13 DIS ∆u+, ∆d+, ∆u, ∆d , ∆s, ∆g Hessian ∆χ2 = 1 [arXiv:1310.3734]

DSSV++DIS, SIDIS,

∆u+, ∆d+, ∆u, ∆d , ∆s, ∆gHessian ∆χ2 = 1

[arXiv:1404.4293]π0, jets Lagr. mult. ∆χ2/χ2 = 2%

NNPDFpol1.1DIS, OC,

∆u+, ∆d+, ∆u, ∆d , ∆s, ∆g Monte Carlo [arXiv:1406.5539]W±, jets

PDF uncertainties stem from three sources

1 the underlying data, affected by statistical and (correlated) systematic errors

2 the theory used to describe them, based on the truncation of a perturbative series

3 the procedure used to extract PDFs from data

Available PDF sets are all based on item 2, but may differ significantly for items 1 and 3


2. Impact of latest experimental results


1) pp collisions at RHIC: W± production

AW−L ∼

∆ux1dx2

(1− cos θ)2 − ∆dx1ux2

(1 + cos θ)2

ux1dx2

(1− cos θ)2 − dx1ux2

(1 + cos θ)2

Longitudinal single- and double-spin asymmetries

AL =σ+ − σ−

σ+ + σ−ALL =

σ++ − σ+−

σ++ + σ+−

features

quark/antiquark separation at Q ∼ MW

no need of fragmentation functions

at RHIC, 〈x1,2〉 ' MW√se−ηl/2 ≈ [0.04, 0.4]

for W+, d ←→ d and ∆d ←→ ∆u

non-trivial positivity bound [arXiv:1104.2920]

1± ALL(yW ) > |AL(yW )± AL(−yW )|

no access to strangeness (W± + c required)

measurements

STAR + PHENIX (Z. Jinlong & F. Giordano)

much more to come from ongoing RHIC run



η lepton 2 1 0 1 2

0.5

0

0.5

= 2% error2χ/2

χ∆DSSV08 L0

W

+W

ν + ± e→ ± W→+p p=510 GeVs < 50 GeV

e

T25 < E

LA

Rel lumisyst

3.4% beam pol scale uncertainty not shown

+W

W

STAR Data CL=68%

DSSV08 RHICBOS

DSSV08 CHE NLO

LSS10 CHE NLO

[arX

iv:1

40

4.6

88

0]

| η lepton |0 0.5 1

0.5

0

0.5

+W

W

ν + ± e→ ± W→ p+p=510 GeVs < 50 GeV

e

T25 < E

LLA

DSSV08 CHE NLO

STAR Data CL=68%

6.5% beam pol scale uncertainty not shown [arX

iv:1

40

4.6

88

0]


AL =σ+ − σ−

σ+ + σ−ALL =

σ++ − σ+−

σ++ + σ+−

features



at RHIC, 〈x1,2〉 ' MW√se−ηl/2 ≈ [0.04, 0.4]



1± ALL(yW ) > |AL(yW )± AL(−yW )|


measurements





[Po

S(D

IS2

01

4)2

05

][P

oS

(DIS

20

14

)21

9]


AL =σ+ − σ−

σ+ + σ−ALL =

σ++ − σ+−

σ++ + σ+−

features



at RHIC, 〈x1,2〉 ' MW√se−ηl/2 ≈ [0.04, 0.4]



1± ALL(yW ) > |AL(yW )± AL(−yW )|


measurements





effects on ∆u and ∆d distributions

x

210

110

0.05

0.04

0.03

0.02

0.01

0

0.01

0.02

0.03

NNPDFpol1.1

=12χ∆DSSV08

positivity bound

)2=10 GeV2(x,Qu∆x

[arX

iv:1

40

6.5

53

9]

[Mar

coS

tra

tma

nn

,ta

lka

tD

IS2

01

3]

NNPDFpol1.1: W± 2�, SIDIS 4 DSSV08/++ : W± 4 , SIDIS 2�

start to test of what we know about light sea quarks from SIDIS with pions

looming (mild) tension between W± and SIDIS data?

are fragmentation function uncertainties underestimated?



effects on ∆u and ∆d distributions

x

310

210

110 1

0.05

0.04

0.03

0.02

0.01

0

0.01

0.02

0.03

)2=10 GeV2(x,Qd∆x

NNPDFpol1.1

=12χ∆DSSV08

positivity bound[a

rXiv

:14

06

.55

39

]

[Mar

coS

tra

tma

nn

,ta

lka

tD

IS2

01

3]

NNPDFpol1.1: W± 2�, SIDIS 4 DSSV08/++ : W± 4 , SIDIS 2�

start to test of what we know about light sea quarks from SIDIS with pions

looming (mild) tension between W± and SIDIS data?

are fragmentation function uncertainties underestimated?



effects on flavor asymmetry ∆u −∆d

x

310

210

110 1

0.08

0.06

0.04

0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

Sea asymmetry

)d∆ u∆NNPDFpol1.1 x(

)u dNNPDF2.3 x(

2=10 GeV2Q

[Po

S(D

IS2

01

4)2

04

]

x

310

210

110 1

0.08

0.06

0.04

0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

)d∆ u∆x(

NNPDFpol1.1

=12χ∆DSSV08

2=10 GeV2Q )ρπMC (

)ρMC (

)σπMC (

PB (ansatz)

CQSM

ST

[Po

S(D

IS2

01

4)2

04

]

the polarized asymmetry is sizable and comparable to the unpolarized asymmetry

polarized and unpolarized asymmetries have opposite sign→ large uncertainties, difficult to determine whether |∆u −∆d | > |u − d |the polarized asymmetry is positive, hence some models are likely to be disfavored→ more data are needed to discriminate between models


2) pp collisions at RHIC: jet and π production

Jet production

π production

Longitudinal double-spin asymmetry

ALL =σ++ − σ+−

σ++ + σ+−

features

at RHIC, 〈x1,2〉 ' 2pT√se−η/2 ≈ [0.05, 0.2]

qg and gg initiated subprocesses dominate(for most of the RHIC kinematics)

ALL sensitive to gluon polarization

cross sections are well described at NLO in pQCD

measurements

STAR (mainly jets) (Z. Chang & C. Dilk)

PHENIX (π production) (A. Manion & I. Yoon)

much more to come from ongoing RHIC run→ gaining precision→ di-jet measurements



(GeV/c)T

Parton Jet p5 10 15 20 25 30 35

LLA

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

| < 0.5η|

STAR 2009 Jet+X→p+p

=200 GeVs

(GeV/c)T

Parton Jet p5 10 15 20 25 30 35

LLA

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07STARBB10DSSVLSS10pLSS10NNPDF

| < 1η0.5 < |

6.5% scale uncertainty±from polarization not shown [a

rXiv

:14

05

.51

34

]

[GeV/c]T

p5 6 7 8 9 10 11 12

LL

A

0.1

0.05

0

0.05

0.1

0.15 g = g∆GRSV g = std∆GRSV

g = g∆GRSV DSSV

0πSTAR

+ X0π → p + p

= 200 GeVs < 2.0η0.8 <

6% Scale Uncertainty [arX

iv:1

30

9.1

80

0]


ALL =σ++ − σ+−

σ++ + σ+−

features

at RHIC, 〈x1,2〉 ' 2pT√se−η/2 ≈ [0.05, 0.2]




measurements






[arX

iv:1

40

2.6

29

6]

[arX

iv:1

40

9.1

90

7]


ALL =σ++ − σ+−

σ++ + σ+−

features

at RHIC, 〈x1,2〉 ' 2pT√se−η/2 ≈ [0.05, 0.2]




measurements






effects on ∆g distribution

x

310

210

110 1

0.2

0.15

0.1

0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

NNPDFpol1.1

=12χ∆DSSV08

positivity bound

)2=10 GeV2g(x,Q∆x

[arX

iv:1

40

6.5

53

9]

NEW FIT

DSSV*

DSSV

incl. 90% C.L. variations

Q2 = 10 GeV

2

RHIC x range

x∆g

x-0.2

-0.1

0

0.1

0.2

10-3

10-2

10-1

1

[arX

iv:1

40

4.4

29

3]

NNPDFpol1.1: jet data 2�, π data 4 DSSV++: jet data 2�, π 2�

first evidence of sizable gluon polarization

NNPDFpol1.1 and DSSV++ results in perfect agreement

most significant constraints come from STAR jet data from 2009 run

the gluon polarization remains largely uncertain outside the x-range probed by RHIC


3) More DIS data: COMPASSinclusive DIS (F. Kunne)

new measurement of Ap1 and gp

1 (2011)

beam energy increased to 200 GeV

lower values of x and higher values of Q2

[Po

S(D

IS2

01

4)2

06

]

open-charm production (K.Kurek)

idea: process receiving (dominant)contributions from γ∗g fusion

new evaluation of gluon polarization atLO with a neural network approach

[Po

S(D

IS2

01

4)2

11

]


3) More DIS data: JLABinclusive DIS: g1 at large x(P. Bosted)

new data on gp,d1 /F p,d

1 from CLAS

[arX

iv:1

40

4.6

23

1]

new data on An1 from Hall A

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 1A

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

1SLAC E142 SLAC E154

JLab E99117 HERMES

This Work RCQM

Statistical NJL

LSS (BBS) Avakian et al.

DSE (realistic)

DSE (contact)

[arX

iv:1

40

6.1

20

7]

inclusive DIS: g2

(S. Choi & M. Cummings)

measurement of g3He2 by JLAB Hall A

much more to come from JLAB Hall C

x

0 0.2 0.4 0.6 0.8 1

He

3 2g

2x

-0.01

-0.005

0

0.005

This Work (E = 4.7 GeV)

This Work (E = 5.9 GeV)

Global Analyses

E142

E154

E01-012 (Resonance)

E99-117

E97-103

He

3 2g

2x

-0.05

0

0.05

0.1Panel a)

Panel b)

[arX

iv:1

40

4.4

00

3]


3) More DIS data: JLAB

potential impact of JLAB data on longitudinal asymmetries

x

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.5

0

0.5

1

1.5

)2=4 GeV2(x,Qp

1A

E143

E155

HERMES

JLAB E93009

NNPDF

RCQM

Statistical

NJL

SU(6)breaking

x

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

0.5

0

0.5

1)2=4 GeV2(x,Qn

1A

E154

E155

HERMES

JLAB E99117

JLAB E06014

NNPDF

RCQM

Ava et al.

Statistical

LSS(BSS)

NJL

SU(6)breaking

JLAB data are much more precise than previous measurement

JLAB data cover the large-x region, up to x ∼ 0.7

JLAB data are expected to have significant impact in narrowing PDF uncertainties→ better determination of total up and down distributions→ possibility to test different models of nucleon structure in the valence region


3. Recent theoretical progress


1) Progress on inclusion of higher-twist corrections: JAM13

[arX

iv:1

31

0.3

73

4]

leading-twist factorization of g1 and g2 receives contributions from higher-twist terms

g1 = gτ=21 + gτ=3

1 + gτ=41 g2 = gτ=2

2 + gτ=32

→ gτ=22 can be related to gτ=2

1 via Wandzura-Wilckzek relation [PLB,72,195]

→ gτ=32 can be related to gτ=3

1 via Blumlein-Tkablaze identity [arXiv:hep-ph/9812478]

→ gτ=32 can be parametrized (using e.g. the form by Braun et al.) [arXiv:1103.1269]

→ gτ=41 can be parametrized as gτ=4

1 (x ,Q2) = h(x)/Q2 (D. Hui)higher twists to both g1 and g2 are included in JAM13

higher twist contributions are sizable and are needed for describing JLAB data properly


2) Progress on all-order resummation

DIS: Hall A data [arXiv:nucl-ex/0405006] SIDIS: G. Karayan data [arXiv:hep-ex/0407032]

[arX

iv:1

30

4.1

37

3]

[arX

iv:1

30

4.1

37

3]

resummation of large logarithm corrections to spin asymmetries in DIS and SIDIS

asymmetries are rather insensitive to the inclusion of resummed higher-order terms

modest decrease of spin asymmetries at fairly high x values, more pronounced for SIDIS

most relevant for JLAB kinematics, important for future high statistic JLAB12


3) Progress on higher-order computations (MS scheme)

linear scale logarithmic scale

-0.3

-0.2

-0.1

0

0.1

0.2

0 0.2 0.4 0.6 0.8 1x

d ∆q

S /

d

ln

µ

2

LO

NLO

NNLO

∗ 1/(1-x)

2

x

d ∆g /

d

ln

µ

2

M, αS

= 0.3, N

f = 3

∗ 1/(1-x)

4

-0.3

-0.2

-0.1

0

0.1

0.2

0 0.2 0.4 0.6 0.8 1-0.01

0

0.01

0.02

0.03

10-4

10-3

10-2

10-1

x

d ∆q

S /

d

ln

µ

2

LO

NLO

NNLO

x

d ∆g /

d

ln

µ

2

M, αS

= 0.3, N

f = 3

0

0.02

0.04

0.06

0.08

10-4

10-3

10-2

10-1

[arX

iv:1

40

9.5

13

1]

NNLO (three-loop) corrections to spin-dependent splitting functions have been computed

NNLO corrections to the splitting functions are small outside the region of small x

corrections to the evolution of the PDFs can be unproblematic down to x ≈ 10−4

QCD analyses of polarized PDFs are now feasible up to NNLO accuracy→ only in a FFN scheme (VFN would require non-trivial unknown matching conditions)→ only including DIS data (coefficient functions are know at NNLO only for DIS)


4. Summary and outlook


A new standard of spin-dependent PDF

1996 [arXiv:hep-ph/9512406]

x

310

210

110 1

0.2

0.1

0

0.1

0.2

0.3

0.4 u∆x

GS96positivity bound

2=10 GeV2Q

x

310

210

110 1

0.25

0.2

0.15

0.1

0.05

0

0.05

0.1

0.15

d∆x

x

310

210

110 1

1.2

1

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

g∆x

x

310

210

110 1

0.05

0.04

0.03

0.02

0.01

0

0.01

0.02

0.03

u∆x

x

310

210

110 1

0.05

0.04

0.03

0.02

0.01

0

0.01

0.02

0.03

d∆x

x

310

210

110 1

0.06

0.04

0.02

0

0.02s∆x

Polarized PDFs took the first steps


A new standard of spin-dependent PDF

2014 [arXiv:1406.5539]

x

310

210

110 1

0.2

0.1

0

0.1

0.2

0.3

0.4 u∆x

NNPDFpol1.1

GS96positivity bound

2=10 GeV2Q

x

310

210

110 1

0.25

0.2

0.15

0.1

0.05

0

0.05

0.1

0.15

d∆x

x

310

210

110 1

1.2

1

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

g∆x

x

310

210

110 1

0.05

0.04

0.03

0.02

0.01

0

0.01

0.02

0.03

u∆x

x

310

210

110 1

0.05

0.04

0.03

0.02

0.01

0

0.01

0.02

0.03

d∆x

x

310

210

110 1

0.06

0.04

0.02

0

0.02s∆x

Polarized PDFs are coming of adult age now


Achievements & open issues

achievements

new data are improving the accuracy of PDFs determined in global QCD analysesthere is evidence for a positive gluon polarization in the x region covered by RHIC dataa determination of ∆u and ∆d distributions from W data is now possible∫ 1

10−3dx∆Σ(x , 10GeV2) = 0.25± 0.10

∫ 0.5

0.05dx∆g(x , 10GeV2) = 0.23± 0.07

open issues

uncertainties coming from the small-x unmeasured region dominate∫ 1

0dx∆Σ(x , 10GeV2) = 0.18± 0.21

∫ 1

0dx∆g(x , 10GeV2) = 0.03± 3.24

is there mounting tension between inclusive DIS and (kaon) SIDIS data?

→ DIS data ⇒ negative x∆s→ SIDIS data ⇒ changing sign x∆s→ new, very precise, JLAB data (DIS)point to negative x∆s [arXiv:14101657]

→ simmetry breaking? (F.-C. Cao)

need for a better knowledge of FF→ new data are now available(F. Kunne, G. Karayan)→ global QCD analyses are ongoing

x

310

210

110 1

0.04

0.03

0.02

0.01

0

0.01

0.02 s∆x

NNPDFpol1.1

=12χ∆DSSV08 positivity bound

2=10 GeV2Q

directly from SIDIS-

indirectly from DIS-


Opportunities at a future EIC

[arX

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9.1

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3]

requirements & features

large kinematic reach→ high-energy collider

precision of electromagnetic probes→ electron beams

spin→ polarized hadron beams

versatility→ heavy ion beams

deliverables observables what we learn

∆g scaling violations in DIS gluon contribution to proton spin

∆q, ∆q SIDIS for pions and kaonsquark contribution to proton spin;

flavor asymmetry ∆u −∆d ; strangeness ∆s

gW−1 , gW−

5 inclusive CC DIS at high Q2 flavor separation at medium x and high Q2



-0.04

-0.02

0

0.02

0.04

-0.04

-0.02

0

0.02

0.04

-0.04

-0.02

0

0.02

0.04

10-2

10-1

1

DSSV

DSSV+ & EIC 5×100, 5×250

all uncertainties for ∆χ2=9

x∆u–

x∆d–

x∆s–

x

Q2 = 10 GeV

2

x∆g

x

-0.2

-0.1

-0

0.1

0.2

0.3

10-2

10-1

1

[arX

iv:1

20

6.6

01

4]

expected impact of EIC data

dramatic reduction of uncertaintiesof both PDFs and their moments

accurate determination of ∆g viascaling violations in DIS

accurate determination of ∆u, ∆dvia SIDIS and CC DIS

access to unknown electroweakstructure functions via CC DIS





gW−1 , gW−




∫∆Σ(x,Q2) dx

1

0.001

∫∆g(x

,Q2)

dx

1

0.0

01

Q2 = 10 GeV

2

DSSV+

EIC

EIC

5×1005×250

20×250


BN

L E

IC S

cien

ce T

ask F

orc

e

-1

-0.5

0

0.5

1

0.3 0.35 0.4 0.45

[arX

iv:1

20

6.6

01

4]

χQSM CTEQ6 x(d–-u

–)

DSSV

DSSV+ & EIC 5×100, 5×250


x(∆u– -∆d

–)

x

-0.05

0

0.05

0.1

10-3

10-2

10-1

1

[arX

iv:1

20

6.6

01

4]





gW−1 , gW−


(X. Jiang)



0

2

4

6

8

10

-0.06 -0.04 -0.02 0

0

2

4

6

8

10

-0.04 -0.02 0 0.02

0

2

4

6

8

10

-0.26 -0.24 -0.22 -0.2 -0.18

∆χ2

DSSV+

CC DIS

∫∆d(x,Q2) dx

1

0.05

∆χ2

∫∆u(x,Q2) dx

1

0.05

Q2 = 10 GeV

2

DSSV ∆χ2

∆χ2

∫∆d(x,Q2) dx

1

0.05

∆χ2

∫∆u(x,Q2) dx

1

0.05

0

2

4

6

8

10

0.6 0.62 0.64 0.66

[arX

iv:1

30

9.5

32

7]

0

1

2

3

AL

AW ,p

+ cx=0.013 (c=0)

0.02 (0.2)

0.032 (0.4)

0.05 (0.6)

0.08 (0.8)

0.125 (1.0)

0.2 (1.2)

0.31 (1.4)

0.47 (1.6)

0.7 (1.8)

LO

NLO

∆d/d→1

x=0.013 (c=0)0.02 (0.2)

0.032 (0.4)

0.05 (0.6)

0.08 (0.8)

0.125 (1.0)

0.2 (1.2)

0.31 (1.4)

0.47 (1.8)

0.7 (2.6)

AL

AW ,n

- c

Q2 [GeV

2]

-3

-2

-1

0

102

103

104

[arX

iv:1

30

9.5

32

7]





gW−1 , gW−




0

2

4

6

8

10

-0.06 -0.04 -0.02 0

0

2

4

6

8

10

-0.04 -0.02 0 0.02

0

2

4

6

8

10

-0.26 -0.24 -0.22 -0.2 -0.18

∆χ2

DSSV+

CC DIS

∫∆d(x,Q2) dx

1

0.05

∆χ2

∫∆u(x,Q2) dx

1

0.05

Q2 = 10 GeV

2

DSSV ∆χ2

∆χ2

∫∆d(x,Q2) dx

1

0.05

∆χ2

∫∆u(x,Q2) dx

1

0.05

0

2

4

6

8

10

0.6 0.62 0.64 0.66

[arX

iv:1

30

9.5

32

7]

0

1

2

3

AL

AW ,p

+ cx=0.013 (c=0)

0.02 (0.2)

0.032 (0.4)

0.05 (0.6)

0.08 (0.8)

0.125 (1.0)

0.2 (1.2)

0.31 (1.4)

0.47 (1.6)

0.7 (1.8)

LO

NLO

∆d/d→1

x=0.013 (c=0)0.02 (0.2)

0.032 (0.4)

0.05 (0.6)

0.08 (0.8)

0.125 (1.0)

0.2 (1.2)

0.31 (1.4)

0.47 (1.8)

0.7 (2.6)

AL

AW ,n

- c

Q2 [GeV

2]

-3

-2

-1

0

102

103

104

[arX

iv:1

30

9.5

32

7]





gW−1 , gW−


More in S11 parallel session


Take away message

Spin experiments continue to produce high impact results(STAR, PHENIX, COMPASS, JLAB)

Theory efforts and global QCD fits try to keep up interesting physics questionsin gluon/sea quark regime

The next (last?) chapter in the tale of the proton spin will begin with an EIC


5. Backup


Predictions for single-hadron production asymmetry

AHLL =

σ++ − σ+−

σ++ + σ+−=

∑a,b,c=q,q,g fa ⊗ fb ⊗ DH

c ⊗∆σcab∑

a,b,c=q,q,g fa ⊗ fb ⊗ DHc ⊗ σc

ab

PHENIX [arXiv:0810.0701] [arXiv:0810.0694] [arXiv:1402.6296] STAR [arXiv:1309.1800]

[GeV]T

p2 4 6 8 10

0.04

0.03

0.02

0.01

0

0.01

0.02

0.03

0.04 0π

LLA

=200 GeVs

NLO QCD, NNPDFpol1.1

[GeV]T

p1 1.5 2 2.5 3 3.5 4

0.04

0.03

0.02

0.01

0

0.01

0.02

0.03

0.04 0π

LLA

=62.4 GeVs


Good agreement between experimental data and theoretical predictions

Experimental uncertainties are larger than than those of the corresponding predictions

We expect a slight impact on the gluon PDF from these data



AHLL =

σ++ − σ+−

σ++ + σ+−=


c ⊗∆σcab∑


ab


[GeV]T

p0.5 1 1.5 2 2.5 3 3.5 4

0.02

0.01

0

0.01

0.02

0.03

0.04

0.05

0.06+

hLL

A

=62.4 GeVs


[GeV]T

p0.5 1 1.5 2 2.5 3 3.5 4

0.02

0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

hLLA

=62.4 GeVs







AHLL =

σ++ − σ+−

σ++ + σ+−=


c ⊗∆σcab∑


ab


[GeV]T

p4 5 6 7 8 9 10 11 12

0.1

0.05

0

0.05

0.1

0.15 0π

LLA

=200 GeVs

<2.0η0.8<


[GeV]T

p2 4 6 8 10 12 14 16

0.02

0.01

0

0.01

0.02

0.03π

LLA

=200 GeVs

|<0.38η|

0π+π


π






AHLL =

σ++ − σ+−

σ++ + σ+−=


c ⊗∆σcab∑


ab


[arX

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2.6

29

6]





Effects of open-charm production at COMPASS

Virtual photon-nucleon asymmetry for open-charm production[arXiv:1212.1319]

AγN→D0X =∆g ⊗∆σγg ⊗ DH

c

g ⊗ σγg ⊗ DHc

FEATURES

∆g is probed directly through the photon-gluon fusion process(in DIS ∆g is mostly probed through scaling violations instead)

the fragmentation functions for heavy quarks are computable in perturbation theory(and only introduce a very moderate uncertainty in the fit)

EXPERIMENTAL MEASUREMENT

COMPASS (2002-2007) [arXiv:1211.6849]

Experiment Set Ndatχ2/Ndat

NNPDFpol1.0 DSSV08 AAC08 BB10

COMPASS 45 1.23 1.23 1.27 1.25COMPASS K1π 15 1.27 1.27 1.43 1.38COMPASS K2π 15 0.51 0.51 0.56 0.55COMPASS K3π 15 1.90 1.90 1.81 1.82



[GeV]0D

Tp

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.25

4

3

2

1

0

1

2

3

DSSV08

AAC08

BB10

NNPDFpol1.0

πCOMPASS K1

πCOMPASS K2

πCOMPASS K3 < 30 [GeV]0

DE

X0 D→ N γ

LLA

[GeV]0D

Tp

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.25

4

3

2

1

0

1

2

3

DSSV08

AAC08

BB10

NNPDFpol1.0

πCOMPASS K1

πCOMPASS K2

πCOMPASS K3 < 50 [GeV]0

D30 < E

X0 D→ N γ

LLA

[GeV]0D

Tp

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.25

4

3

2

1

0

1

2

3

DSSV08

AAC08

BB10

NNPDFpol1.0

πCOMPASS K1

πCOMPASS K2

πCOMPASS K3 > 50 [GeV]0

DE

X0 D→ N γ

LLA

Data are affected by large uncertainties w.r.t. the uncertainty due to PDFsThey do not show a clear trend

Experiment Set Ndatχ2/Ndat

NNPDFpol1.0 DSSV08 AAC08 BB10

COMPASS 45 1.23 1.23 1.27 1.25COMPASS K1π 15 1.27 1.27 1.43 1.38COMPASS K2π 15 0.51 0.51 0.56 0.55COMPASS K3π 15 1.90 1.90 1.81 1.82



[GeV]0D

Tp

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.25

4

3

2

1

0

1

2

3

NNPDFpol1.0

NNPDFpol1.0 RW

πCOMPASS K1

πCOMPASS K2

πCOMPASS K3 < 30 [GeV]DE

X0 D→ N γ

LLA

[GeV]0D

Tp

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.25

4

3

2

1

0

1

2

3

NNPDFpol1.0

NNPDFpol1.0 RW

πCOMPASS K1

πCOMPASS K2

πCOMPASS K3 < 50 [GeV]D30 < E

X0 D→ N γ

LLA

[GeV]0D

Tp

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.25

4

3

2

1

0

1

2

3

NNPDFpol1.0

NNPDFpol1.0 RW

πCOMPASS K1

πCOMPASS K2

πCOMPASS K3 > 50 [GeV]DE

X0 D→ N γ

LLA

The impact of open-charm data from COMPASS is mostly negligible,as we notice from the value of the χ2/Nndat and the reweighted observable

Experiment Set Ndat χ2/Ndat χ2rw/Ndat

COMPASS 45 1.23 1.23COMPASS K1π 15 1.27 1.27COMPASS K2π 15 0.51 0.51COMPASS K3π 15 1.90 1.89


theoretical status of helicity-dependent parton densities · 2018. 11. 16. · theoretical status...

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