pion structure from leading neutron electroproductionsu(2) ﬂavor asymmetry 50 reevaluation of the...

XXIV International Workshop on Deep-Inelastic Scattering and Related SubjectsDESY, Hamburg, April 13, 2016

Wally Melnitchouk

Pion structure fromleading neutron electroproduction

with Chueng Ji (NCSU), Josh McKinney (UNC),Nobuo Sato (JLab), Tony Thomas (Adelaide)

1

SU(2) flavor asymmetry

50 REEVALUATION OF THE GOTI'FRIED SUM R3

XXOc ~ Q.2

ICL

SG

0O0

Q' = 4 GeV'

x=0. The fit yields the values 0=0.20~0.03 and b=0.59+.0.06 and a contribution to SG of 0.013~0.005 (stat) forx(0.004. The quality of the fit is as good as that in Ref. [1]and the result is insensitive to the upper limit of the fittedrange (up to x=0.40).Summing the contributions from the measured and un-

measured regions we obtain for the Gottfried sum

SG=0.235 ~0.026.

Q. 10

Q.Q5II

)kI I I ~ I I I

0.01 0.10I I I I I I I

Q

FIG. 1. The difference F~z F2 (ful—l symbols and scale to theright) and J„'(F~z F2)dx/x —(open symbols and scale to the left) atQ =4 GeV, as a function of x from the present reevaluation(circles) and from Ref. [1] (triangles). The extrapolated result SGfrom the present vmrk and the prediction of the simple quark-partonmodel (OPM) are also shown.

uncertainty from the momentum calibration is reduced com-pared to that given in Table 2 of Ref. [1], while the othercontributions are unchanged.To evaluate the contributions to SG from the unmeasured

regions at high and low x, extrapolations of F2—Fz to x= 1and x=0 were made using the same procedures as describedin Ref. [1]. The contribution from the region x&0.8 is0.001~0.001. For the region x&0.004, the expressionax, appropriate for a Regge-like behavior, was again fittedto the data in the range 0.004&x&0.15 and extrapolated to

The error is the result of combining the statistical and sys-tematic errors in quadrature, and including the effect of the(correlated) systematic uncertainties on the extrapolations ofF2—F2 to x= 1 and x=0. This new value of SG agrees wellwith that in Ref. [1].However, the total error given here islarger than that quoted in Ref. [1]due to the more extensiveexamination of the systematic uncertainties. Nevertheless,the result for S& is significantly below the simple quark-parton model value of 1/3, so that the conclusions of Ref. [1)are unchanged.The evaluation of the Gottfried sum at higher Q requires

large extrapolations of the measured values of Fz/F~z at lowx, which rapidly reduces the accuracy of Fz —F2. For thisreason a precise determination of the Gottfried sum from theNMC data is restricted to Q around 4 GeV .

Bielefeld University, Freiburg University, Max Planck In-stitut Heidelberg, Heidelberg University, and Mainz Univer-sity were supported by Bundersministerium fur Forschungund Technologie. NIKHEF-K was supported in part byFOM, Vrije Universiteit Amsterdam and NWO. Soltan Insti-tute for Nuclear Studies and Warsaw University were sup-ported by KBN Grant No. 2 0958 9101.The work of D.S.was supported by the NSF and DOE.

[1]New Muon Collaboration, P. Amaudruz et al. , Phys. Rev. Lett.66, 2712 (1991).

[2] New Muon Collaboration, P. Amaudruz et al. , Phys. Lett. B295, 159 (1992); Report No. CERN-PPE/92-124, 1992 (un-published); erratum (unpublished); erratum (unpublished).

[3]New Muon Collaboration, P. Amaudruz et al. , Nucl. Phys.

8371, 3 (1992).[4]A. A. Akhundov et al. , Sov. J. Nucl. Phys. 26, 660 (1977); 44,

988 (1986); JINR-Dubna Report No. E2-10147, 1976 (unpub-lished); No. E2-10205, 1976 (unpublished); No. E2-86-104,1986 (unpublished); D. Bardin and N. Shumeiko, Sov. J. Nucl.Phys. 29, 499 (1979).

Z 1

0

dx

x

(F p2 � F

n2 ) =

1

3� 2

3

Z 1

0dx (d� u)

= 0.235(26)

violation of Gottfried sum rule

E866, PRD 64, 052002 (2001)

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_

σpd

2σpp≈

1

2

!

1 +d(xt)

u(xt)

"

Z 1

0dx (d� u) = 0.118± 0.012

xb � xt

DIS

DY

One of the seminal discoveries of last 25 years has beenthe SU(2) flavor asymmetry in the proton sea, d 6= u

NMC, PRD 50, 1 (1994)

2

SU(2) flavor asymmetry

paradigm shift - nucleon not simply3 valence quarks + homogenous sea!qq

vital role played by nonperturbative dynamics,e.g. chiral symmetry breaking & nucleon’s pion cloud

asymmetry actually predicted a decade earlierfrom “Sullivan” process A.W. Thomas, PLB 126, 97 (1983)

C C

C C

C

p

�⇤

⇡+

n

(du)

e(d� u)(x) =

Z 1

x

dy

y

f

⇡

+n

(y) q⇡v

(x/y)

pion momentum distribution in nucleon,or “splitting function”p ! ⇡+n

One of the seminal discoveries of last 25 years has beenthe SU(2) flavor asymmetry in the proton sea, d 6= u

y

3

Chiral effective theory

pseudoscalar interaction often used for simplicity -results generally different from pseudovector theory

gA = 1.267

f� = 93 MeV

L�N =gA2f�

⌅N�µ�5 ⌃⇤ · ⇧µ⌃⇥ ⌅N � 1

(2f�)2⌅N�µ ⌃⇤ · (⌃⇥ ⇥ ⇧µ⌃⇥)⌅N

Weinberg, PRL 18, 88 (1967)

term + higher order+ �NN= �g⇡NN N i�5~⌧ · ~⇡ N

Splitting function can be computed in chiral effective theory of QCD (e.g. chiral perturbation theory)

At lowest order, effective (low-energy) Lagrangian⇡N

4


Coupling of e.m. current to nucleon dressed by pions

(d)(c)

(e)

(g)(f)

(a) (b)

Kroll-Ruderman(for gauge invariance)

tadpole

N rainbow

bare wfn renormalization

rainbow⇡

bubble⇡

Ji, WM, Thomas, PRD 88, 076005 (2013)

5


Coupling of e.m. current to nucleon dressed by pions

(d)(c)

(e)

(g)(f)

(a) (b)

tadpole

N rainbow

bare wfn renormalization

rainbow⇡

bubble⇡

contribute to d� u

Kroll-Ruderman(for gauge invariance)

Ji, WM, Thomas, PRD 88, 076005 (2013)

6

(d)(c)

(e)

(g)(f)

(a) (b)

Pion splitting functionsSplitting function for pion rainbow diagramhas on-shell and -function contributions

(a) (b) (c)

k

p�

f⇡(y) = f (on)(y) + f (�)(y)

equivalent inPV & PS theories

singular = 0 termonly in PV theory

y

y =k+

p+

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

f (bub)(y) =8

g2Af (�)(y)

y

Salamu, Ji, WM, WangPRL 114, 122001 (2015)

f (on)(y) =g2AM

2

(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

7

Infrared behavior is model independent

leading nonanalytic (LNA) structure of moments

Thomas, WM, Steffens, PRL 85, 2892 (2000)

Pion splitting functions

Z 1

0dx (

¯

d� u) =

(3g

2A � 1)

(4⇡f⇡)2

m

2⇡ log(m

2⇡/µ

2) + analytic in m

2⇡

can only be generated by pion loops - nonzero cloud contribution predicted by QCD!

⇡

vital e.g. for chiral extrapolation of lattice data

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.PRL 87, 172001 (2001)

8

Ultraviolet-divergent integrals for point-like particles

Finite size of nucleon provides natural scale to regularize integrals, but does not prescribe form of regularization

freedom in choosing regularization prescription

F = exp

⇥(t�m2

⇡)/⇤2⇤

cutoffk?

monopole in t ⌘ k2 = �k2? + y2M2

1� yF =

✓⇤2 �m2

⇡

⇤2 � t

◆F = ⇥(⇤2 � k2?)

exponential in t

exponential in s =k2? +m2

⇡

y+

k2? +M2

1� yF = exp

⇥(M2 � s)/⇤2

⇤

F =

1� (t�m2

⇡)2

(t� ⇤2)2

�1/2Pauli-Villars

F = y�↵⇡(t)exp

⇥(t�m2

⇡)/⇤2⇤

Regge


BishariF = y�↵⇡(t)

9

Detailed shape of splitting function depends on regularization, but common general features

e.g. on-shell function

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)

sharp cutoffs

At x > 0, only on-shell part contributes


(d� u)(x) = [2f (on) ⌦ q

⇡v ](x)

10

Flavor asymmetry

0 0.1 0.2 0.3x

–0.02

0

0.02

0.04

0.06x(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)

with exception of cutoff and Bishari models,all others give reasonable fits, �2 . 1.5

k?

large-x asymmetry to be probed by FNAL SeaQuest expt.

E866 data can be fitted with range of regulators.d� u

hni⇡N = 3

Z1

0

dy f (on)

N (y)

average pion “multiplicity”

⇠ 0.25� 0.3

11

Flavor asymmetryE866 data can be fitted with range of regulators.d� u

Is pion cloud the only explanation for the asymmetry?

are there other data that can discriminatebetween different mechanisms?

semi-inclusive production of “leading neutrons” (LN)

at HERA!

12

Leading neutron production at HERA

ZEUS

00.20.40.60.81

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

00.10.20.30.40.5

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

simultaneous fit never previously been performed

ZEUS & H1 collaborations measured spectra of neutronsproduced at very forward angles,

xL ⇡ 1� y

✓n < 0.8 mrad

can data be described within same frameworkas E866 flavor asymmetry?

13

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


ZEUS H1

d

3�

LN

dx dQ

2dy

⇠ F

LN(3)2 (x,Q2

, y)

Measured LN differential cross section (integrated over )p?

for exchange⇡2f (on)

N (y)F⇡2

(x/y,Q2)

quality of fit depends on range of fittedy

r =d�LN

d�inc

e.g.

14

At large y, non-pionic mechanisms contribute(e.g. heavier mesons, absorption)


0

0.02

0.04

0.06

0.08

0.5 0.6 0.7 0.8 0.9 1z

(1/σ

inc)

dσp→

n / d

z

qT2 < 0.04 GeV2

π

a~

1

ρ+a2

Q2 > 2 GeV2H1 2009ZEUS 2007

Kopeliovich et al., PRD 85, 114025 (2012)

0

0.2

0.4

0.6

0.8

1

0.6 0.7 0.8 0.9 1

Kab

s

z

light-cone R2lc = 0.2 GeV-2

γ∗ p → n X 10 < Q2 < 100 GeV2

γ p → n X Q2 < 0.02 GeV2

(= 1-y) (= 1-y)

D’Alesio, Pirner, EPJA 7, 109 (2000)

To reduce model dependence, fit the value of up to which data can be described in terms of exchange

ycut⇡

15

Fit requires higher momentum pions with increasing


ycut

values from fit to E866 data only

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

larger values of more in conflict with E866 dataycut

16


Combined fit to HERA LN and E866 Drell-Yan data

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

McKenney, N. Sato, WM, C. JiPRD 93, 700205 (2016)

17


Combined fit to HERA LN and E866 Drell-Yan data

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

best fits for largest number of points afforded byt-dependent exponential (and t monopole) regulators

# pts = 54 108 266187McKenney, N. Sato, WM, C. JiPRD 93, 700205 (2016)

18

10�4 10�3

x

10�2

10�1

100

FLN

(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, NPB 637, 3 (2002) NPB 776, 1 (2007)


Fit to ZEUS LN spectra for (t-dependent exponential)ycut = 0.3

19

10�4 10�3

x

10�2

10�1

FLN

(3)

2(⇥

2i) Q2 = 7.3 GeV2

10�3 10�2

x

Q2 = 11 GeV2

10�3 10�2

x

Q2 = 16 GeV2

10�3 10�2

x

10�2

10�1

FLN

(3)

2(⇥

2i) Q2 = 24 GeV2

10�3 10�2

x

Q2 = 37 GeV2

10�3 10�2

x

Q2 = 55 GeV2

10�2 10�1

x

10�2

10�1

FLN

(3)

2(⇥

2i) Q2 = 82 GeV2 y = 0.095

y = 0.185

y = 0.275

HERA+E866 fit


Fit to H1 LN spectra for (t-dependent exponential)ycut = 0.3

H1, EPJC 68, 381 (2010)

�2

dof

= 1.27

for 202 (187+15) points

20

Extracted pion structure function

stable values of at from combined fitF⇡2 4⇥10�4 . x⇡ . 0.03

shape similar to GRS fit to Drell-Yan data (for ),but smaller magnitude

⇡N x⇡ & 0.2

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

⌘ ⇠ log(logQ2)

a = a0 + a1⌘F

⇡2 = N x

a⇡ (1� x⇡)

b,

McKenney, N. Sato, WM, C. JiPRD 93, 700205 (2016)

21

Predictions at TDIS kinematics

0 0.02 0.04 0.06 0.08 0.1

x

0

0.01

0.02

0.03

0.04

FLP

(3)

2(a)

y = 0.1

y = 0.2

HERA JLab

t exp (ycut = 0.3)

t exp (ycut = 0.2)

t mon (ycut = 0.2)

10�3 10�2 10�1

x⇡

0

0.02

0.04

0.06

0.08

0.1

0.12

(b)

sea

total

y = 0.2

HERA ⇡N DY

HERA + E866 fit

SMRS

GRS

JLab TDIS (“tagged” DIS, ) experimentcan fill gap in coverage between HERAand Drell-Yan kinematics⇡N

x⇡

McKenney, N. Sato, WM, C. JiPRD 93, 700205 (2016)F

LP(3)2 = f⇡�p(y)F

⇡2 (x⇡, Q

2)

e d ! e p pX

22

Outlook

Combined analysis can be extended by includingalso Drell-Yan data⇡N

Generalize parametrization by fitting individualpion valence and sea quark PDFs, rather than F⇡

2

constrain large- regionx⇡ (x⇡ & 0.2)

Ultimate goal will be to use all data sensitive topion structure (including TDIS, EIC?) to constrainpion PDFs over full range 10�4 . x⇡ . 1

23

pion structure from leading neutron electroproductionsu(2) ﬂavor asymmetry 50 reevaluation of the...

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