Flavor Structure of the Nucleon Sea

in the Chiral Quark Soliton Model

Masashi Wakamatsu, Osaka University

1. Introduction

2. CQSM as a model of parton distribution functions (PDFs) in the nucleon

3. Flavor SU(3) CQSM and strange sea distributions in the nucleon

4. NuTeV anomaly and CSV parton distributions

5. Chiral-odd twist-3 distribution function e(x) and QCD vacuum structure

Plan of talk

6. Summary

“Mini-workshop on Lattice QCD and Hadron Physics”,

National Taiwan University, June 5-6, 2013

1. Introduction

Quantum Chromo Dynamics (QCD)

Color confinement (no free quarks, gluons) Asymptotic freedom

Chiral symmetry (Chiral Dynamics)

Nonperturbative QCD Perturbative QCD (pQCD)

hard to solve analytically !

Lattice QCD Effective models

established framework based on

• Factorization theorem

• Renormalization group

Deep-inelastic-scatterings (DIS) Hadron spectroscopy, Reactions, Structures

factorization theorem

• Standard approach to DIS physics

Soft part is treated as a black box, which should be determined via experiments !

We however believe that, even if this part is completely fixed by experiments,

one would still want to know why those PDFs take the form so determined !

• A complementary approach to DIS physics is necessary here to understand

hidden chiral dynamics of soft part, based on models or on lattice QCD

reasonable strategy !

PDFs

The nucleon structure function physics works out in a fine balance of the perturbative

and nonperturbative QCD.

key ingredient flavor structure of nucleon sea

Merits of CQSM over many other effective models of baryons :

parameter-free predictions for PDFs

Among a lot of models of baryons, the Chiral Quark Soliton Model (CQSM), first

proposed by Diakonov et al., would be the best model, at least as a model of internal

partonic structure of the nucleon and baryons.

2. CQSM as a model of parton distribution functions (PDFs) in the nucleon

• Its field theoretical nature enables reasonable estimation of antiquark distributions.

• It is a relativistic mean-field theory of quarks, with infinitely many Dirac-sea levels.

generate strong spin-isospin correlation in nucleon sea !

Biggest shortcoming of the model is a lack of explicit gluon degrees of freedom.

• The mean-field is of hedgehog-shape in harmony with

• Only 1 parameter of the model ( dynamically generated quark mass M ) is already

fixed from low energy phenomenology to be

What is Chiral Quark Soliton Model like ?

basis lagrangian

derivative expansion

effective meson action

based on instanton picture of the QCD vacuum

Soliton construction without using derivative expansion

M.F. Dirac equation

Hartree condition

breaks rotational symmetry

Energy of

Casimir energy

model needs regularization

where

Pauli-Villars regularization scheme

other observables

then

: uniquely fixed !

Skyrme model (Ellis-Karliner-Brodsky, 1988)

Chiral Quark Soliton Model (Wakamatsu-Yoshiki, 1991)

collective motion of quarks

in the rotating hedgehog M.F.

large quark OAM

A prominent physical consequence of the chiral soliton picture of the nucleon

small quark spin fraction !

In short, the nucleon of this model is a “rotating hedgehog”.

generate

(1) reproduces small quark spin fraction of proton consistent with EMC observation !

The past noteworthy attainments of CQSM for low energy baryon observables :

(2) reproduces large sigma term !

(3) resolves underestimation problem of in the Skyrme model !

• Still, most low energy baryon observables are insensitive to model differences !

• We shall demonstrate that the potential ability of CQSM manifests most clearly in

its predictions of internal partonic structure of the nucleon, especially in the flavor

structure of the sea quark distributions.

How to harmonize the two domains of QCD ? : nonperturbative and perturbative

matching problem

model predictions for PDFs empirically extracted PDFs

given at low given at high

relate through DGLAP (evolution) equation

• difficult to specify the exact initial (model) energy scale of evolution !

most effective models like MIT bag model :

Chiral Quark Soliton Model (CQSM) :

• This difference is sometimes important because of the diverging behavior of

the perturbative QCD running coupling constant at low energy scale !

QCD running coupling constant at the next-to-leading order (NLO)

pQCD is barely applicable !

~0.4

dangerous !

Gluon momentum fraction at the low energy scale

empirical

Short remark on the antiquark distributions (for unpolarized distribution)

where

one can prove

for longitudinally polarized distribution

we have

Parameter free predictions of

SU(2) CQSM for 3 twist-2 PDFs

• unpolarized PDFs

• longitudinally polarized PDFs

• transversities (chiral-odd)

totally different behavior of

the Dirac-sea contributions

in different PDFs !

Isoscalar Isovector

3 valence quarks

Dirac-sea quarks

Isoscalar unpolarized PDF

positivity

sea-like soft component

antiquark

Isovector unpolarized PDF

- NMC observation -

Dirac sea

Isoscalar longitudinally polarized PDF

New COMPASS data

deuteron

sign change in

low region !

model predicts

CQSM

CQSM prediction for in comparison with new COMPASS and HERMES fits

Old data

New data

Isovector longitudinally polarized PDF

CQSM predicts

This means that antiquarks gives sizable

positive contribution to Bjorken sum rule

Compare ! Remember the model prediction

anti-correlation of spin and isospin (?)

imbedded the hedgehog configuration

consistent with CQSM !

A global fit including polarized pp data at RHIC

• D. Florian, R. Sassot, M. Strattmann, W. Vogelsang, Phys. Rev. D80, 034030 (2009).

DSSV fit versus CQSM predictions

DSSV fit versus CQSM predictions

FNAL and J-PARC projects for measuring polarized sea-quark distributions

private communication with Xiaodong Jiang

Drell-Yan longitudinally polarized beam-target double-spin asymmetry

asymmetry between the spin-aligned and spin-anti-aligned D-Y cross sections

leading order formula

CQSM prediction corresponding to FNAL, JPARC kinematics

chance to measure !

from Xiaodong Jiang, private communication

sizable magnitude

The iso-singlet combination of unpolarized TMD PDF

A prominent feature of the CQSM prediction is self-evident from the shape of the already-

shown x-distribution, obtained after integrating over the transverse momentum .

Positivity of

antiquark dist.

Other interesting prediction of CQSM

: M. W., Phys. Rev. D79 (2009) 094028.

remember a dominant role of vacuum-polarized

Dirac-sea quarks in the small region !

frequently used factorized ansatz for TMD PDFs

drastically broken !

average transverse momentum (square) for quarks and antiquarks

antiquarks have harder component in -distribution !

large contribution to the z-component of OAM ?

CQSM

Transversities (versus longitudinally polarized distributions)

Our particular interest is the difference between

The most important quantities characterizing these are their 1st moments, called

Understanding of isospin dependencies is a key to disentangle

nonperturbative chiral dynamics contained in the PDFs

(A) Non-Relativistic (or Constituent or SU(6)) quark model

(B) MIT bag model

in both of NQM & MIT bag model

Well-known basic facts about axial and tensor charges

Important observation common shortcoming !

CQSM gives totally different predictions !

3 quark model cannot resolve EMC observation ?

Pasquini et al.

Caution about strong scale dependence of transversity around model energy scales

• M. W., Phys. Rev. D79 (2009) 014033.

from SDIS

Anselmino

scale independent ! nearly scale independent !

safer comparison of various model predictions for scale independent ratios

tensor-charge ratio axial-charge ratio

• M. W., Phys. Rev. D79 (2009) 014033.

Anselmino HERMES

Short summary on the transversity distributions

When one compares the model predictions for transversities with the empirical ones

extracted from high-energy SDIS measurements, one must be very careful about the

strong scale-dependence of transversities in the nonperturbative low energy domain.

Model predictions are very sensitive to the starting energy scale of evolution !

A safer comparison would therefore be made for the ratios like

which are scale-independent, because of the flavor-independent nature of evolution

equations for chiral-odd transversities, which does not couple to gluons !

3. flavor SU(3) CQSM and strange sea distribution in the nucleon

model lagrangian

with

basic dynamical assumptions

(1) lowest energy classical solution is obtained by embedding of SU(2)

hedgehog configuration.

(2) quantization of soliton rotational motion in SU(3) collective coordinate space.

(3) perturbative treatment of SU(3) breaking term.

some typical predictions of the SU(3) CQSM

(A) longitudinally polarized strange quark distributions

LSS NLO fits

at

negative polarization

separate contributions of

One finds that

consistent with the physical

picture of kaon cloud model

Note the apparent asymmetry

Brodsky-Ma, 1996

Signal-Thomas, 1987

asymmetry of unpolarized strange sea

This is also consistent with the

picture of kaon cloud model

Note the asymmetry

s-quark has valence-like

harder component ?

Comparison with the recent unbiased PDF fits based on neural-network framework

4. NuTeV anomaly and charge-symmetry-violating (CSV) parton distribution functions

NuTeV measured the Paschos-Wolfenstein ratio

The result shows significant deviation from the predictions of the standard model :

Main QCD corrections to the P-W ratio

where

Theoretical analyses for charge symmetry violating PDFs

Recent review : J.T. Londergan, J.C. Peng, and A.W. Thomas, Rev. Mod. Phys. 82 (2010)

(1) Sather’s ansatz : Phys. Lett. B274 (1992) 433

supplemented with simple quark model like MIT bag model

CSV valence quark distribution

with

(2) “QED splitting” : MRST (2005), Glueck, Delgado, and Reya (2005)

“QED evolution” process

CSV is radiatively generated through

(3) CQSM with perturbative treatment of u-d quark mass difference

Sather’s ansatz

The CQSM predictions are much smaller than those based on Sather’s ansatz !

The two effects tend to cancel !

CSV sea-quark distributions

Short summary on the CSV effects in PDFs

• The conclusion of Londergan et al’s analyses based on Sather’s ansats is that

the CSV effects in the PDFs gives main ingredients to resolve NuTeV anomaly.

• According to the SU(3) CQSM, the CSV effects to the Paschos-Wolfenstein ratio

is much smaller than the effects of strangle quark asymmetry.

• The CSV sea-quark distributions predicted by the SU(3) CQSM due to the

up- and down-quark mass difference is of opposite sign as predicted

by the “QED splitting” effects, and they tend to cancel !

chiral-odd

• M. W. and Y. Ohnishi, Phys. Rev. D67 (2003) 114011.

• Y. Ohnishi and M. W., Phys. Rev. D69 (2004) 114002 .

5. Chiral-odd twist-3 distribution function and QCD vacuum structure

Why is it interesting ?

M.Burkardt and Y.Koike (2002)

What is the physical origin of this peculiar delta-function singularity ?

theoretical definition of PDF e(x)

with

measures light-cone correlation of scalar type

existence of delta-function singularity in indicates

long-range (infinite-range) correlation

Within the CQSM, we could analytically confirm this behavior

• M. W. and Y. Ohnishi, Phys. Rev. D67 (2003) 114011.

• P. Schweitzer, Phys. Rev. D67 (2003) 114010.

We found the existence of this infinite-range correlation is inseparably connected with

nontrivial vacuum structure of QCD

spontaneous cSB and nonvanishing vacuum quark condensate

Why does vacuum property come into a nucleon (baryon) observable ?

related to extraordinary nature of the scalar quark density of the nucleon

CQSM prediction for the nucleon scalar quark density

3 valence

total

Dirac sea vacuum quark

condensate

We need sophisticated numerical method to calculate containing d(x)

Y. Ohnishi and M. W., Phys. Rev D69 (2004) 114002

We find that

where

with small

1st moment sum rule for isoscalar e(x)

numerically

dominant

With this gives

reproduce fairly large pN sigma term

[Cf.] nucleon scalar charge in the MIT bag model

However, because of the normalization condition

we find the inequality

quark models with only 3 valence quark degrees

freedom cannot reproduce large pN sigma term !

compare

then

Short summary on e(x)

(1) delta-function singularity in chiral-odd twist-3 distribution e(x) is

a rare manifestation of nontrivial vacuum structure of QCD in baryon observable

(2) existence of this singularity can in principle be observed as

violation of pN sigma-term sum rule of

need precise experimental information on this quantity in wider range of x.

especially in small x region

• A CLASS collaboration proposal, H. Avakian et al.

This singularity would not exist, if the quark condensate is an in-hadron property and not

a properties of QCD vacuum, as Brodsky and Schrock are recently claiming.

6. Summary

Probably, the CQSM is the most successful model of the nucleon structure functions.

Without introducing any free parameter, it reproduces all the characteristic features of

the known PDFs, especially those of the sea quark distributions, at least qualitatively.

The success is naturally connected with the fact that the model incorporates the

spontaneous cSB of the QCD vacuum and the associated Goldstone pions.

Still, an important difference with ordinary meson cloud model may be noteworthy !

Intuitively, the meson cloud model would not generate large spin polarization of sea

quarks, because pion carries no spin and heavier meson clouds are suppressed.

The large prediction of the CQSM for may be interpreted as the

manifestation of strong anti-correlation between spin and isospin imbedded in the hedgehog

configuration dictated by large-Nc QCD dynamics.

Remember that this strong anti-correlation is also the origin of very small quark spin

fraction of the nucleon !

At any rate, the experimental extraction of the flavor (or isospin) dependence of the

sea-quark PDFs is a key to disentangle

non-perturbative chiral dynamics of QCD

hidden in the nucleon structure functions.

summary of Lattice QCD predictions

Novel observation

(Cf.) prediction of SU(6)-like quark model

LHPC QCDSF-UKQCD

The 2nd nucleon spin crisis ?

7. Phenomenology of nucleon spin decomposition

[Caution] The energy scale dependence of

Thomas pointed out that the strong scale dependence of might resolve the

discrepancy.

• A. W. Thomas, Phys. Rev. Lett. 101 (2008) 102003.

We pointed out that the following asymptotic relation holds

• M. W. and Y. Nakakoji, Phys. Rev. D77 (2008) 074011.

Actually, this possibility was noticed earlier. [See eq.(92) of the following paper.]

which means that is large and negative at least in the asymptotic limit.

neutron beta-decay coupling constant

Leading-order evolution eq. for flavor nonsinglet channel

neutron beta-decay coupling constant !

Since right-hand-side becomes 0 as , we conclude that

This can be easily understood from the well-known evolution equations.

• X. Ji, J. Tang, and P. Hoodbhoy, Phys. Rev. Lett. 76 (1996) 740.

Thomas’ analysis

Thomas carried out an analysis of the proton spin contents in the context of the refined

cloudy bag (CB) model, and concluded that the modern spin discrepancy can well be

resolved in terms of the standard features of the nonperturbative structure of the nucleon,

i.e.

(1) relativistic motion of valence quarks

(2) pion cloud required by chiral symmetry

(3) exchange current contribution associated with the OGE hyperfine interactions

supplemented with QCD scale evolution.

• A. W. Thomas, Phys. Rev. Lett. 101 (2008) 102003.

strong scale dependence !

crossover around 0.5 GeV scale

The tendency is OK but the agreement with the Lattice QCD is not very good !

From Radici’s talk at QCD-N’12 (Bilbao)

In our opinion, to start the evolution from too low energy scale is dangerous, because

of the diverging behavior of the perturbative QCD running coupling constant.

We have estimated the orbital angular momentum of up and down quarks in the

proton as functions of the energy scale, by carrying out a downward evolution of

available information from high energy experimental data supplemented with the

Lattice QCD data, to find that remains to be large and negative even at

low energy scale of nonperturbative QCD !

uncertainty band

The discrepancy with quark models still appears to remain. How can it be solved ?

In recent few years, there have been intensive debate on the theoretical aspect of the

nucleon spin decomposition problem, which is still continuing.

In a series of paper (P.R. D81 (2010) 114010, D84 (2011) 037501, D85 (2012) 114039,

D85 (2012) 114039), we have clarified that there exist two kinds of quark and gluon

OAMs. Confining to the quark OAMs here, we have

An important fact is that the OAM corresponding to the Lattice QCD calculation and

the GPD analysis is the “mechanical” OAM not the “canonical” OAM.

Very roughly speaking, the quark OAM involved in Thomas’ theoretical analysis is a

counterpart of “canonical” OAM not the “mechanical” OAM.

with

Or, is it an indication of a big difference between “dynamical’’ & “canonical’’ quark OAM ?

Does the strong scale dependence of resolve the 2nd nucleon spin puzzle, as

Thomas claims ?

A key is a precise measurement of at a few GeV scale.

Thomas’ scenario

our scenario