Baryons2013
International Conference on the Structure of Baryons
June 24th - 28th 2013
Nucleon Sea Structure and
the Five-Quark Components
Wen-Chen Chang
Institute of Physics, Academia Sinica, Taiwan
Jen-Chieh Peng
University of Illinois at Urbana-Champaign, USA
1
Outline
• Evidences of nucleon sea
• Flavor Asymmetry of light sea quarks
• Structure of strange quarks
• Intrinsic sea quarks in light-front 5q model
• Sea quarks in lattice-QCD
• Prospect
• Conclusion
2
Deep Inelastic Scattering
Q2 :Four-momentum transfer
x : Bjorken variable (=Q2/2Mn)
n : Energy transfer
M : Nucleon mass
W : Final state hadronic mass
d 2
  Mott [W2 (n , Q 2 )  2W1 (n , Q 2 ) * tan 2 ( / 2)]
'
d dE
  Mott [ F2 ( x, Q 2 ) / n  2 F1 ( x, Q 2 ) / M * tan 2 ( / 2)]
•Scaling
•Valence quarks
•Quark-antiquark pairs
3
Sum Rules
N : expectation value of number of quarks.
J.I. Friedman, Rev. Mod. Phys. Vol. 63, 615 (1991)
4
Gottfried Sum Rule
SG  I 2p  I 2n
1
  [( F2p ( x )  F2n ( x )) / x ] dx
0
1 1
2 1 p
p
p
  dx (uv  d v )   (u ( x )  d p ( x )) dx
3 0
3 0
1

(if u p  d p )
3
J.I. Friedman, Rev. Mod. Phys. Vol. 63, 615 (1991)
Assume a symmetric quark-antiquark sea,
GSR is only sensitive to valance quarks.
5
Gottfried Sum Measured by NMC
SG is significantly lower than 1/3 !
SG = 0.235 ± 0.026
New Muon Collaboration (NMC), Phys. Rev. D50 (1994) R1
6
Explanations for the NMC result
• Uncertain extrapolation for 0.0 < x < 0.004
• Charge symmetry violation (un  d p, dn  u p )
• u ( x)  d ( x) in the proton
1
 (d ( x)  u ( x)) dx  0.148  0.04
0
Need independent methods to check the d  u asymmetry,
and to measure its x-dependence !
7
Drell-Yan Process
Acceptance in Fixed-target Exps.
d
4 2 1
2

e
[q( xt )q( xb )  q( xt )q( xb )]

dxbdxt 9 xb xt s
 pd
|x
pp
2
b
 x t


d ( xb )
1


1
4u( xb )   d ( xt )  1  d ( xt ) 

1 
  1 

2
d ( xb ) d ( xt )   u( xt )  2  u( xt ) 
 1  4u ( x ) u ( x ) 
b
t 

8
Light Anti-quark Flavor Asymmetry
 Naïve Assumption:
 NMC (Gottfried Sum Rule)
 NA51 (Drell-Yan, 1994)
NA 51 Drell-Yan
confirms
d(x) >u(x)
9
Light Anti-quark Flavor Asymmetry
 Naïve Assumption:
 NMC (Gottfried Sum Rule)
 NA51 (Drell-Yan, 1994)
 E866/NuSea (Drell-Yan, 1998)
10


Origin of u(x)d(x):
Perturbative QCD effect?
𝑞
G
𝑞
• Pauli blocking


• guu is more suppressed than gdd in the proton
since p=uud (Field and Feynman 1977)
• pQCD calculation (Ross, Sachrajda 1979)
• Bag model calculation (Signal, Thomas, Schreiber 1991)
• Chiral quark-soliton model (Pobylitsa et al. 1999)
• Instanton model (Dorokhov, Kochelev 1993)
• Statistical model (Bourrely et al. 1995; Bhalerao 1996)
• Balance model (Zhang, Ma 2001)
The valence quarks affect the gluon splitting.
11
 
Origin of u(x)d(x):
Non-perturbative QCD effect?
• Meson cloud in the nucleons (Thomas 1983, Kumano 1991):
Sullivan process in DIS.
p  N  ;   :  0 :    2 :1: 0
n
• Chiral quark model (Eichten et al. 1992; Wakamatsu 1992):
Goldstone bosons couple to valence quarks.
q  q ;   :  0 :    4 : 3 : 2

Pion cloud is a source of antiquarks in the protons and it lead to d>u.
12
d ( x)  u ( x) vs. Theoretical Models
13
Strange Quark in the Nucleon:
Deep-Inelastic Neutrino Scattering
n   s     c  X ; c  s    n 
n   s     c  X ; c  s    n 
14
Strange Quark in the Nucleon
(s  s )  0.5 * (u  d )
s( x)  s ( x)
CCFR, Z. Phys. C 65, 189 (1995)
15
Strange Quark Asymmetry
NuTeV, PRL 99, 192001 (2007)
Q 2  16 GeV 2
16
s(x)=s(x)?
• Meson Cloud Model (Signal and Thomas, 1987)
s( x )  s ( x ) at large x
• Chiral Field (Burkardt and Warr , 1992)
s( x )  s ( x ) at large x
• Baryon-Meson Fluctuation (Brodsky and Ma , 1996)
s( x )  s ( x ) at large x
• Perturbative evolution (Catani et al., 2004)
s( x )  s ( x ) at large x
17
Strange Content from Semi-Inclusive
Charged-Kaon DIS Production
( s ( x)  s ( x))  (u ( x)  d ( x))
Restoration of SU(3) symmetry
Q 2  2.5 GeV 2
HERMES, PLB 666, 446 (2008)
18
W and Z production at LHC
ATLAS, PRL 109, 012001 (2012)
0.5( s  s )
rs 
 1.000.25
0.28
d
19
Parton Distribution Functions of Protons
20
Short Range Structure of Hadron
Extrinsic Sea
Intrinsic Sea
Gluon splitting in leading twist
Gluon fusion & light quark
scattering (higher-twist)
Perturbative radiation
Non-perturbative dynamics
CP invariant
Possible CP non-invariant
Fast fluctuation
With a longer lifetime
Of small x
Of large x (valence-like)
Strong Q2 dependent
Small Q2 dependent
Hoyer and Brodsky, AIP Conf. Proc. 221, 238 (1990)
21
Intrinsic Sea Quarks in Light-Front 5q Fock
States
Brodsky, Hoyer, Peterson, Sakai (BHPS)
PLB 93,451 (1980); PRD 23, 2745 (1981)
| p  P3q | uud   P5 q | uudQQ 
mi2 2
P( x1 ,..., x5 )  N 5 (1   xi ) / [ m   ]
i 1
i 1 xi
5
5
2
p
The "intrinsic"-charm from | uudcc  is "valence"-like
and peak at large x unlike the "extrinsic" sea (g  cc )
“extrinsic”
“intrinsic”
The | uudcc  intrinsic-charm
can lead to large contribution
to charm production at large x
22
Experimental Evidences of
Intrinsic Charm
Gunion and Vogt, hep-ph/9706252
23
Global Fit by CTEQ
Pumplin, Lai, Tung, PRD 75, 054029 (2007)
No Conclusive Evidence…..
24
Search for the lighter “intrinsic”
quark sea
| p  P3q | uud   P5q | uudQQ 
No conclusive experimental evidence for
intrinsic-charm so far
Are there experimental evidences for the intrinsic
| uuduu , | uuddd , | uudss  5-quark states ?
2
Q
P5q ~ 1 / m
The 5-quark states for lighter quarks
have larger probabilities!
25
How to separate the “intrinsic sea”
from the “extrinsic sea”?
• Select experimental observables which have no
contributions from the “extrinsic sea”
• “Intrinsic sea” and “extrinsic sea” are expected to
have different x-distributions.
• Intrinsic sea is “valence-like” and is more abundant at
larger x.
• Extrinsic sea is more abundant at smaller x.
26
How to separate the “intrinsic sea”
from the “extrinsic sea”?
• Select experimental observables which have no
contributions from the “extrinsic sea”
• Investigate the x distribution of flavor non-singlet
quantities: d  u , d  u  s  s .
d  u has no contributi on from extrinsic sea ( g  q q)
and is sensitive to " intrinsic sea" only

27


Data of d(x)-u(x)
vs. Light-Front 5q Fock States
uuddd
5
P
P
uuduu
5
 0.118
• The data are in good
agreement with the 5q
model after evolution
from the initial scale μ
to Q2=54 GeV2
• The difference of these
two 5-quark
components could be
determined.
Chang and Peng, PRL 106, 252002 (2011)
28
How to separate the “intrinsic sea”
from the “extrinsic sea”?
• “Intrinsic sea” and “extrinsic sea” are expected to
have different x-distributions
• Intrinsic sea is “valence-like” and is more abundant at
larger x
• Extrinsic sea is more abundant at smaller x
An example is the s( x )  s ( x ) distributi on
29

Data of x(s(x)+s(x))
vs. Light-Front 5q Fock States
uudss
5
P
 0.024
Chang and Peng, PLB 704, 197 (2011)
 are
• The x(s(x)+s(x))
from HERMES kaon
SIDIS data at <Q2>=2.5
GeV2.
• The data seem to
consist of two
components.
• Assume data at x>0.1
are originated from the
 5intrinsic |uudss>
quark state.
30
How to separate the “intrinsic sea”
from the “extrinsic sea”?
• Select experimental observables which have no
contributions from the “extrinsic sea”
• Investigate the x distribution of flavor non-singlet
quantities: d  u , d  u  s  s .
d  u  s  s has no contributi on from extrinsic sea ( g  q q)
and is sensitive to " intrinsic sea" only
31



Data of x(d(x)+u(x)-s(x)-s(x))
vs. Light-Front 5q Fock States
uuduu
5
P
P
uuddd
5
 2P
uudss
5
  from
•
The
d(x)+u(x)
 0.314
CTEQ 6.6.

• The s(x)+s(x) from
HERMES kaon SIDIS
data at <Q2>=2.5 GeV2.
u d ss
~ P5uuduu  P5uuddd  2 P5uudss
(not sensitive to extrinsic sea)
Chang and Peng, PLB 704, 197 (2011)
32
Extraction of various 5qcomponents for light quarks
P5uudss  0.024
P5uuddd  P5uuduu  0.118
uuddd
5
P
 0.240; P
uuduu
5
P5uuduu  P5uuddd  2P5uudss  0.314
 0.122; P
uudss
5
 0.024
33
Constituent 5q model
Riska and Zou, PLB 636, 265 (2006)
proton =
Puud uud + Pss [uuds] s
Axial Form Factor GAs  GEs   GMs
GAs
q2
Dominate configuration of [uuds] s is 3 P0 [4]FS [22]F [22]S
Pss  10  15%
34
Constituent 5q model
Kiswandhi, Lee, Yang, PLB 704, 373 (2011)
proton =
Puud uud + Pss [uuds] s
Axial Form Factor GAs  GEs   GMs
q2
Two dominate configurations of [uuds] s are
3
P0 [4]FS [22]F [22]S and 3 P0 [31]FS [211]F [22]S .
Pss  0.025  0.058%
35
Extended Chiral Constituent 5q model
(complete configurations)
Use 3 P0 version for the transition
coupling between 3q and 5q states.
Strong interplays among different components with (very) large cancellations.
An and Saghai, PRC 85, 055203 (2012); 1306.3041 (2013)
36
Comparison of 5q Probabilities



P(uu)
P(dd)
P(ss)

P(cc)
0.198
0.148
0.093
0.011
Bag model;
Donoghue and Golowich, PRD15, 3421 (1977)
0.003
Light-cone 5q model;
Hoffmann and Moore, ZPC 20, 71 (1983)
0.009
Meson cloud model;
Navarra et al., PRD 54, 842 (1996)
0.250
0.250
0.050
References
0.10 0.15
Constituent 5q model;
Riska and Zou, PLB 636, 265 (2006)
0.122
0.240
0.024
Light-front 5q model;
Chang and Peng, this work (2011)
0.098
0.216
0.057
Extended chiral constituent quark model;
An and Saghai, PRC 85, 055203 (2012)
37
Diagrams of Nucleon Hadronic
Tensor in Path-Integral Formalism
W n
1

N
2 M NV
Connected Diagram
d 3 x iqx
 2 e J v ( x, t1 ) J  (0, t2 ) N
Disconnected Diagram
38
Connected and Disconnected Sea
Liu and Dong, PRL 72, 1790 (1994)

• qds(x)=qds(x), where q=u, d, s; s(x)=s(x)
 ds

ds
• u (x)=d (x)
• qcs(x)=qcs(x), where q=u, d
 cs

 cs

• Origin of u(x) d(x): u (x) d (x)
• Small-x behaviors:
• qvalence(x) , qcs(x)
• qds(x) x-1
x-1/2
How do we separate these two components?
39
Ratio of Momentum Fraction between
s and u in DI by Lattice QCD
Connected Insertion (CI)
Doi, et al. PoS LATTICE2008:163, 2008
Disconnected Insertion (DI)
40
Connected Sea
u CS ( x)  d CS ( x)
u CS ( x)  d CS ( x)
 (u ( x)  d ( x))  (u DS ( x)  d DS ( x))
1
 (u ( x)  d ( x))
 ( s ( x)  s ( x)) HERMES
CT10
R
d ( x)  u ( x)
 (d CS ( x)  u CS ( x))  (d DS ( x)  u DS ( x))
 (d CS ( x)  u CS ( x))
Liu, Chang, Cheng and Peng, PRL 109, 252002 (2012)
41
Small-x Behaviors of CS and DS
Small-x behavior:
•Valence and CS x-1/2
•DS x-1
Liu, Chang, Cheng and Peng, PRL 109, 252002 (2012)
42
Moments of Nucleon Sea
Q 2  2.5 GeV 2
Momentum fraction of u+d is about
equally divided between CS and DS.
Liu, Chang, Cheng and Peng, PRL 109, 252002 (2012)
43
“Connected, Disconnected Sea” VS.
“Intrinsic, Extrinsic sea”
Connected Sea
(u, d quarks only)
Intrinsic Sea:
•Non-perturbative
•Origin of flavor asymmetry of light sea quarks
•With x^-1/2 small-x behavior from the Reggeon
exchange
Disconnected Sea
(u, d quarks and
heavy quarks)
Intrinsic Sea:
•Non-perturbative
•Peaked at medium x (~ 0.1)
•Meson cloud or the Reggeon exchange
Extrinsic Sea:
•Perturbative
•At small x
•With x^-1 small-x behavior from the Pomeron
exchange
44
Future Prospect (Experimental)
• Light sea quarks:
• E906/SeaQuest at FNAL: flavor asymmetry of d-bar/u-bar at
large x region.
• MINERνA at FNAL: x-dependence of nuclear effects for sea
quarks.
• JLAB-12 GeV: transverse spatial distribution of sea quarks.
• Kaon-induced DY experiment at J-PARC: s and s-bar.
• Electron-Ion Collider (EIC): sea quark distributions and their
spin structure.
• Heavy sea quarks:
• Open-charm production at forward rapidity, e.g. fixed-target
experiment at LHC.
• Higgs production at large xF at LHC.
45
 
d/u From E906/SeaQuest at FNAL
Ratio of Drell-Yan cross sections
(in leading order—E866 data analysis confirmed
in NLO)
 Global NLO PDF fits which
include E866 cross section
ratios agree with E866
results
 Fermilab E906/Drell-Yan will
extend these
measurements and reduce
statistical uncertainty.
 E906 expects systematic
uncertainty to remain at
approx. 1% in cross section
ratio.
46
Future Prospect (Theoretical)
• Intrinsic sea for hyperons and mesons?
• Intrinsic gluons in the nucleons?
• Connection between the 5-quark model and the
meson-cloud model?
• Connection between the 5-quark model and lattice
QCD?
• Spin-dependent observables of intrinsic sea?
47
Conclusion
• Using DIS, Drell-Yan and SIDIS processes, the
structure of sea quarks in the nucleon are explored.


• Themeasured x distributions of (d-u), (s+s) and

 could be reasonably described by the
(u+d-s-s)
light-front 5q Fock states. The probabilities of the
intrinsic 5q states of light sea quarks are extracted.
• The intrinsic or valence-like sea quarks are deeply
connected with the non-perturbative QCD. More
accurate data will be available in the coming
experiments at FNAL, JLAB, LHC, J-PARC and EIC.
48