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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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 2 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 3 / 25
1. Introduction
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 4 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 5 / 25
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?
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 6 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 7 / 25
2. Impact of latest experimental results
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 8 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 9 / 25
1) pp collisions at RHIC: W± production
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]
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 9 / 25
1) pp collisions at RHIC: W± production
[Po
S(D
IS2
01
4)2
05
][P
oS
(DIS
20
14
)21
9]
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 9 / 25
1) pp collisions at RHIC: W± production
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?
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 10 / 25
1) pp collisions at RHIC: W± production
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?
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 10 / 25
1) pp collisions at RHIC: W± production
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 11 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 12 / 25
2) pp collisions at RHIC: jet and π production
(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]
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 12 / 25
2) pp collisions at RHIC: jet and π production
[arX
iv:1
40
2.6
29
6]
[arX
iv:1
40
9.1
90
7]
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 12 / 25
2) pp collisions at RHIC: jet and π production
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 13 / 25
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
]
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 14 / 25
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]
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 15 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 16 / 25
3. Recent theoretical progress
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 17 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 18 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 19 / 25
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)
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 20 / 25
4. Summary and outlook
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 21 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 22 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 22 / 25
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-
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 23 / 25
Opportunities at a future EIC
[arX
iv:1
40
9.1
63
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 24 / 25
Opportunities at a future EIC
-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
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 24 / 25
Opportunities at a future EIC
∫∆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
all uncertainties for ∆χ2=9
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
all uncertainties for ∆χ2=9
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]
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
(X. Jiang)
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 24 / 25
Opportunities at a future EIC
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]
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 24 / 25
Opportunities at a future EIC
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]
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
More in S11 parallel session
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 24 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 25 / 25
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 25 / 25
5. Backup
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 1 / 3
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
NLO QCD, NNPDFpol1.1
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 2 / 3
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
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
NLO QCD, NNPDFpol1.1
[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
NLO QCD, NNPDFpol1.1
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 2 / 3
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
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<
NLO QCD, NNPDFpol1.1
[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
NLO QCD, NNPDFpol1.1
π
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 2 / 3
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]
[arX
iv:1
40
2.6
29
6]
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 2 / 3
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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 3 / 3
Effects of open-charm production at COMPASS
[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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 3 / 3
Effects of open-charm production at COMPASS
[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
Emanuele R. Nocera (UNIGE) Helicity-dependent PDFs October 21, 2014 3 / 3
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