CTEQ-Jefferson Lab (CJ) collaborationhttp://www.jlab.org/CJ

Workshop on Deep Inelastic Scattering and Related Topics Birmingham, April 4, 2017

Wally Melnitchouk

Insights into sea quark asymmetriesfrom global PDF analysis

Outline

Evidence of sign change at large x?

constraint on at large x

New (preliminary) SeaQuest data

implications for pion cloud modelsand pion structure function extraction

asymmetry and chiral symmetry in QCD: a brief historyd� u

d� u

Asymmetries between various PDFs ( …) reveal nonperturbative structure of the nucleon

d� u, s� s, �u��d

Outlook

Light quark seaFrom perturbative QCD expect symmetric sea generatedby gluon radiation into pairs (if quark masses are the same)

qqqq

Thomas suggested that chiral symmetry of QCD (important at low energy)

should have consequences for antiquark PDFs in nucleon(measured at high energy)

+PV PVp n

⇡+

p

(ud)

d > u

since u and d quarks nearly degenerate,expect flavor-symmetric light-quark sea

d ⇡ u Ross, Sachrajda (1979)

A.W. Thomas (1984)

Light quark seaFirst clear experimental support for came from violationof Gottfried sum rule observed by NMC

d 6= u

1

x

(F p2 � F

n2 ) =

1

3(u+ � d

+) +2

3(u� d)

SG ⌘Z 1

0

dx

x

(F p2 � F

n2 ) = 0.235± 0.026

NMC (1991, 1994)

clear evidence for (or at least integrated value)d� u > 0

Light quark sea

strong enhancement of at x ~ 0.1 – 0.2, but intriguingbehavior at large x hinting at possible sign change of

d�

dx1dx2⇠

X

q

e

2q q(x1) q(x2) + (x1 $ x2)

�

pd

�

pp⇡ 1 +

d(x2)

u(x2)for x1 � x2

p

d, p

x dependence of asymmetry established in Fermilab E866 pp/pd Drell-Yan experiment

d� u

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

CTEQ4MNA 51

x

d_ / u_

E866 (2001)

dd� u

Light quark seaGeneral agreement with pion loop models

C CC C

C

p

�⇤

⇡+

n

(du)

e

y

(d� u)(x) =

Z 1

x

dy

y

f

⇡

+n

(y) q⇡v

(x/y)

splitting functionp ! ⇡+n

0 0.1 0.2 0.3x

–0.02

0

0.02

0.04

0.06

x(d

�u)

(a)

t mon

t exp

s exp

PV

Regge

Bishari (⇥0.5)k? cut

E866

0 0.1 0.2 0.3x

N

�

(b)

shape qualitatively reproduced bymost models (except at high x),but is there a direct connectionwith QCD?

Chiral EFT

Recently rigorous connection with QCD established viachiral effective field theory

L�N =gA2f�

⌅N�µ�5 ⌃⇤ · ⇧µ⌃⇥ ⌅N � 1

(2f�)2⌅N�µ ⌃⇤ · (⌃⇥ ⇥ ⇧µ⌃⇥)⌅NLe↵

Weinberg (1967)

lowest order interaction includespion rainbow and tadpole contributions

⇡N

matching quark- and hadron-leveloperators

yields convolution representation

Oµ1···µnq =

X

h

c(n)q/h Oµ1···µn

h

(d)(c)

(e)

(g)(f)

(a) (b)

contribute to d� u

Ji, WM, Thomas (2013)

q(x) =X

h

Z 1

x

dy

y

f

h

(y) qhv

(x/y)

Recently rigorous connection with QCD established viachiral effective field theory

f⇡(y) = f (on)(y) + f (�)(y) f (on)(y) =g2AM

2

(4⇡f⇡)2

Zdk2?

y(k2? + y2M2)

[k2? + y2M2 + (1� y)m2

⇡]2

F2

Splitting function for pion rainbow diagram has on-shelland -function contributions�

0 0.2 0.4 0.6 0.8 1y

0

0.05

0.1

0.15

0.2

f(o

n)�

(y)

(b)t mon

t exp

s exp

PV

Regge

Bishari (scaled)k? cut

0 0.2 0.4 0.6 0.8 1y

0

0.1

0.2

0.3

f(o

n)N

(y)

(a)

UV regulator

f (�)(y) =

g2A4(4⇡f⇡)2

Zdk2? log

✓k2? +m2

⇡

µ2

◆�(y)F2

Chiral EFT

Recently rigorous connection with QCD established viachiral effective field theory

(d)(c)

(e)

(g)(f)

(a) (b)f⇡(y) = f (on)(y) + f (�)(y) f (on)(y) =

g2AM2

(4⇡f⇡)2

Zdk2?

y(k2? + y2M2)

[k2? + y2M2 + (1� y)m2

⇡]2

F2

f (�)(y) =

g2A4(4⇡f⇡)2

Zdk2? log

✓k2? +m2

⇡

µ2

◆�(y)F2

f (bub)(y) =8

g2Af (�)(y)

Bubble diagram contributes only at = 0 (hence x = 0)y

Salamu, Ji, WM, Wang (2015)

Splitting function for pion rainbow diagram has on-shelland -function contributions�

contributes to lowest moment, but not at x > 0

Chiral EFT

coefficients of leading nonanalytic (LNA) terms,reflecting infrared behavior, are model-independent!

Thomas, WM, Steffens (2000)

nonanalytic behavior vital for chiral extrapolation of lattice data on PDF moments from large

Detmold et al. (2001)

Expand moments of PDFs in powers of m⇡

QCD therefore predicts a nonzero asymmetry from loops⇡

m2⇡(GeV2)

Extraction of parton distributions from lattice QCD 5

0.150.200.250.30

!x1"u#d

0.150.200.250.30

!x1"u#d

0.02

0.06

0.10

0.14

!x2"u#d

0.02

0.06

0.10

0.14

!x2"u#d

0.000.020.040.06

!x3"u#d

0.000.020.040.06

!x3"u#d

0 0.2 0.4 0.6 0.8 1. 1.2mΠ2 !GeV2 "

Fig. 1. Moments of the unpolarized u − d distribution in the proton, for n = 1, 2 and 3. Latticedata10 include both quenched (solid symbols) and unquenched (open symbols) results. The solidline represents the full chiral extrapolation, while the inner (darkly shaded) error band showsvariation of µ by ± 20%, with the outer band (lightly shaded) showing the additional effects ofshifting the lattice data within the extent of their error bars. Linear extrapolations are indicatedby dashed lines, and the phenomenological values20 are shown as large stars at the physical pionmass.

bn is simply bnm2π) and bn is a third fitting parameter,7 are indistinguishable from

those in Fig. 1.Note that the majority of the data points (filled symbols) are obtained from

simulations employing the quenched approximation (in which background quarkloops are neglected) whereas Eq. (4) is based on full QCD with quark loop effectsincluded. On the other hand, recent calculations with dynamical quarks suggest thatat the relatively large pion masses (mπ > 0.5–0.6 GeV) where the full simulationsare currently performed, the effects of quark loops are largely suppressed, as the datain Fig. 1 (small open symbols) indicate. Further details of the lattice data,2,3,4,5

and a more extensive discussion of the fit parameters, can be found elsewhere.10

A similar analysis leads to analogous lowest order LNA parameterizations of themass dependence of the spin-dependent moments17

⟨xn⟩∆u−∆d = ∆an

!

1 + ∆cLNAm2π log

m2π

m2π + µ2

"

+ ∆bnm2

π

m2π + m2

b,n

, (6)

and

⟨xn⟩δu−δd = δan

!

1 + δcLNAm2π log

m2π

m2π + µ2

"

+ δbnm2

π

m2π + m2

b,n

, (7)

Extraction of parton distributions from lattice QCD 5

0.150.200.250.30

!x1"u#d

0.150.200.250.30

!x1"u#d

0.02

0.06

0.10

0.14

!x2"u#d

0.02

0.06

0.10

0.14

!x2"u#d

0.000.020.040.06

!x3"u#d

0.000.020.040.06

!x3"u#d

0 0.2 0.4 0.6 0.8 1. 1.2mΠ2 !GeV2 "

Fig. 1. Moments of the unpolarized u − d distribution in the proton, for n = 1, 2 and 3. Latticedata10 include both quenched (solid symbols) and unquenched (open symbols) results. The solidline represents the full chiral extrapolation, while the inner (darkly shaded) error band showsvariation of µ by ± 20%, with the outer band (lightly shaded) showing the additional effects ofshifting the lattice data within the extent of their error bars. Linear extrapolations are indicatedby dashed lines, and the phenomenological values20 are shown as large stars at the physical pionmass.

bn is simply bnm2π) and bn is a third fitting parameter,7 are indistinguishable from

those in Fig. 1.Note that the majority of the data points (filled symbols) are obtained from

simulations employing the quenched approximation (in which background quarkloops are neglected) whereas Eq. (4) is based on full QCD with quark loop effectsincluded. On the other hand, recent calculations with dynamical quarks suggest thatat the relatively large pion masses (mπ > 0.5–0.6 GeV) where the full simulationsare currently performed, the effects of quark loops are largely suppressed, as the datain Fig. 1 (small open symbols) indicate. Further details of the lattice data,2,3,4,5

and a more extensive discussion of the fit parameters, can be found elsewhere.10

A similar analysis leads to analogous lowest order LNA parameterizations of themass dependence of the spin-dependent moments17

⟨xn⟩∆u−∆d = ∆an

!

1 + ∆cLNAm2π log

m2π

m2π + µ2

"

+ ∆bnm2

π

m2π + m2

b,n

, (6)

and

⟨xn⟩δu−δd = δan

!

1 + δcLNAm2π log

m2π

m2π + µ2

"

+ δbnm2

π

m2π + m2

b,n

, (7)

0 1.21.00.80.60.2 0.4

exp

m2⇡ (GeV2)

Detmold et al. (2001)

Z 1

0dx (

¯

d� u) =

(3g

2A � 1)

(4⇡f⇡)2

m

2⇡ log(m

2⇡/µ

2) + analytic in m

2⇡

m⇡

hxiLNAu�d ⇠ m

2⇡ logm

2⇡

Chiral EFT

coefficients of leading nonanalytic (LNA) terms,reflecting infrared behavior, are model-independent!

Expand moments of PDFs in powers of m⇡

QCD therefore predicts a nonzero asymmetry from loops⇡

Bali et al. (2014)

Z 1

0dx (

¯

d� u) =

(3g

2A � 1)

(4⇡f⇡)2

m

2⇡ log(m

2⇡/µ

2) + analytic in m

2⇡

Chiral EFT

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0 0.05 0.1 0.15 0.2 0.25

hxiM

Su�d(2

GeV

)

m

2⇡ [GeV2]

RQCD Nf = 2RBC/UKQCD (‘10), (‘13) Nf = 2 + 1

LHPC (‘12) Nf = 2 + 1ETMC (‘13) Nf = 2 + 1 + 1

ETMC (‘13) Nf = 2

Thomas, WM, Steffens (2000)

nonanalytic behavior vital for chiral extrapolation of lattice data on PDF moments from large m⇡

Constraints from leading neutronsDrell-Yan data can be described with range of UV regulators (shapes of pion splitting functions)

d� u

d

3�

LN

dx dQ

2dy

⇠ F

LN(3)2 (x,Q2

, y) = f⇡(y)F⇡2 (x/y,Q

2)

semi-inclusive production of “leading neutrons” at HERAcan discriminate between different shapes

0 0.2 0.4 0.6 0.8y

0

0.05

0.1

0.15

0.2

r/�

xL

(a)

x = 8.50 ⇥ 10�4

Q2 = 60 GeV2

0 0.2 0.4 0.6y

0

0.02

0.04

0.06

0.08

0.1

FLN

(3)

2

(b)

x = 1.02 ⇥ 10�3

Q2 = 24 GeV2 ycut

0.1

0.2

0.3

0.4

0.5

0.6

ZEUS

H1

10�4 10�3

x

10�2

10�1

100F

LN

(3)

2(⇥

2i) Q2 = 7 GeV2

10�4 10�3

x

Q2 = 15 GeV2

10�3 10�2

x

Q2 = 30 GeV2

10�3 10�2

x

10�2

10�1

100

FLN

(3)

2(⇥

2i) Q2 = 60 GeV2

10�3 10�2

x

Q2 = 120 GeV2

10�2 10�1

x

Q2 = 240 GeV2

0 0.1 0.2 0.3

y

0

0.05

0.1

0.15

FLN

(3)

2

Q2 = 480 GeV2

x = 0.032

0 0.1 0.2 0.3

y

Q2 = 1000 GeV2

x = 0.032

y = 0.06

y = 0.15

y = 0.21

y = 0.27

HERA+E866 fit

ZEUS

H1

McKinney, Ji, WM, Sato (2016)

best fit to combined ZEUS/H1 & DY datafor t-dependent exponential regulator

0 0.1 0.2 0.3 0.4 0.5 0.6ycut

0

0.5

1

1.5

2

⇤(G

eV)

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6ycut

0

0.2

0.4

0.6

hni ⇡

N

(b)

t mon

t exp

s exp

PV

Regge

Bisharik? cut

E866

0.1 0.2 0.3 0.4 0.5 0.6ycut

0

1

2

3

4

5

�2 do

f

(a)

ZEUS + H1t mon

t exp

s exp

PV

Regge

Bisharik? cut

0.1 0.2 0.3 0.4 0.5 0.6ycut

(b)

ZEUS + H1 + E866

Drell-Yan data can be described with range of UV regulators (shapes of pion splitting functions)

d� u

d

3�

LN

dx dQ

2dy

⇠ F

LN(3)2 (x,Q2

, y) = f⇡(y)F⇡2 (x/y,Q

2)

semi-inclusive production of “leading neutrons” at HERAcan discriminate between different shapes

Constraints from leading neutrons

hni⇡N = 3

Z1

0

dy f (on)

N (y)

average pion “multiplicity”

⇠ 0.3

10�3 10�2

x⇡

0

0.2

0.4

0.6

F⇡ 2

(a)

ycut

Q2 = 10 GeV2

0.1

0.2

0.3

0.4

0.5

0.6

10�3 10�2

x⇡

(b)ycut = 0.3

t mon

t exp

s exp

PV

Regge

Bishari

10�3 10�2

x⇡

(c)

HERA+E866 fit

GRS

SMRS

x⇡ = x/y

F⇡ 2

constrain shape of at from combined HERA + Drell-Yan fit

F⇡2 10�4 . x⇡ . 0.03

global analysis under way of HERA LN,Drell-Yan + pd/pp (+ upcomingJLab TDIS data) to determine pion PDFsat all x

⇡N

C. Keppel (Thu 9:40 am —WG1)

Drell-Yan data can be described with range of UV regulators (shapes of pion splitting functions)

d� u

d

3�

LN

dx dQ

2dy

⇠ F

LN(3)2 (x,Q2

, y) = f⇡(y)F⇡2 (x/y,Q

2)

semi-inclusive production of “leading neutrons” at HERAcan discriminate between different shapes

Constraints from leading neutrons

Sign change at large x?

0 0.1 0.2 0.3x

–0.02

0

0.02

0.04

0.06

x(d

�u)

(a)

t mon

t exp

s exp

PV

Regge

Bishari (⇥0.5)k? cut

E866

0 0.1 0.2 0.3x

N

�

(b)

E866 data has driven successful phenomenology throughinterplay of PDFs and chiral physics

… but lingering question of possible sign change of at high xd� u

sign change cannot be accommodated within chiral EFT frameworksince (negative) contribution << (positive) N contribution�

evidence for other mechanisms?

Sign change at large x?

conclusions based on LO analysis … how robust?

“Independent evidence for sign change at x ~ 0.3” from NMC d� u

Peng et al., PLB 736 (2014) 411

d� u ⌘ 1

2(uv � dv)�

3

2x(F p

2 � F

n2 )

Sign change at large x?

conclusions based on LO analysis … how robust?

“Independent evidence for sign change at x ~ 0.3” from NMC d� u

Peng et al., PLB 736 (2014) 411

d� u ⌘ 1

2(uv � dv)�

3

2x(F p

2 � F

n2 )

Sign change at large x?At higher order can easily generate zero crossing in

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

x

�0.04

�0.02

0.00

0.02

0.04

0.06

0.08

“x(d

�u)”

Q2 = 4 GeV2

CJ15 NLO

d � u

�

� ⌘ 1

2(uv � dv)�

3

2x(F p

2 � F

n2 )

with no asymmetry!d� u

“sign change”for NMC data

no evidence of sign change from DIS data!

Sign change at large x?At higher order can easily generate zero crossing in

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

x

�0.04

�0.02

0.00

0.02

0.04

0.06

0.08

“x(d

�u)”

Q2 = 4 GeV2

CJ15 NLO

d � u

�

� ⌘ 1

2(uv � dv)�

3

2x(F p

2 � F

n2 )

with no asymmetry!d� u

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

x

�0.04

�0.02

0.00

0.02

0.04

0.06

0.08

“x(d

�u)”

Q2 = 54 GeV2

CJ15 NLO

d � u

�

persists at E866kinematics

Preliminary data from SeaQuest (E906) Drell-Yan experimentat Fermilab shows no evidence for sign change

SeaQuest data consistent with E866 data up to x ~ 0.2,remains above unity up to x ~ 0.5

P. Reimer (2016)

Sign change at large x?

Results not significantly affected ifinclude nuclear corrections

0 0.1 0.2 0.3 0.4 0.5xN

0.6

0.8

1

1.2

1.4

σ p

d / 2σ

pp

free nucleonsmearingsmearing + off-shellSeaQuestEhlers, Accardi, Brady, WM (2014)

Consequences for chiral analysis?Sign change at large x?

0 0.1 0.2 0.3 0.4 0.5x

–0.02

0

0.02

0.04

0.06

x(d

�u)

t mon

t exp

s exp

PV

Regge

Bishari/2k? cut

0 0.1 0.2 0.3 0.4 0.5x

N

�E866

SeaQuest

Barry, Sato, WM et al. (2017)

including both E866 and preliminary SeaQuest data in fit …

Improved fit, but almostno effect on shape!

Preliminary

�2

dof

hni⇡N

E866 E866 + SeaQuest

1.2 0.8

0.85 0.85⇤ (GeV)

0.29 0.29

OutlookEagerly await final SeaQuest data!

settle question of sign change in at high xd� u

Combine “leading neutron” analysis with Drell-Yan datato constrain pion PDFs at low and high x

⇡N

upcoming “tagged DIS” experiment at JLab C. Keppel (Thu 9:40 am —WG1)

Extend to strangeness sector to analyze asymmetry within chiral SU(3) EFT framework

s� s

)2 (GeV2Q2 4 6 8 10 12

GSR

Inte

gral

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3

= 0.9066max= 0.0040 xminx = 0.9066max= 0.0040 xminx

•••

••

•

•• NMC

CJ17 reanalysis

Niculescu et al. (2016)