Asymmetries of quark sea in nucleon - MENU 2013 - 13th...

Asymmetries of quark sea in nucleon

Harleen Dahiya

Department of PhysicsDr. B.R. Ambedkar National Institute of Technology

Jalandhar

13th International Conference on Meson-Nucleon Physics andthe Structure of the Nucleon (MENU 2013)

RomeSeptember 30- October 4, 2013

H Dahiya (NITJ) Asymmetries of quark sea in nucleon MENU 2013 1 / 22

Outline

1 Internal structure of the baryons

2 Chiral Constituent Quark Model

3 Sea Quark Distribution

4 Gottfried Sum Rule

5 Results

6 Summary and Conclusions


Internal structure of the baryons

Naive Quark Model

Internal Structure: The knowledge of internal structure of nucleon interms of quark and gluon degrees of freedom in QCD provide a basis forunderstanding more complex, strongly interacting matter.

Knowledge has been rather limited because of confinement and it is stilla big challenge to perform the calculations from the first principles ofQCD.

Naive Quark Model is able to provide a intuitive picture andsuccessfully accounts for many of the low-energy properties of thehadrons in terms of the valence quarks.



Proton Spin Problem: The driving question

1988 European Muon Collaboration (Valence quarks carry 30% ofproton spin)Naive Quark Model contradicts this results (Based on Pure valencedescription: proton = 2u + d)"Proton spin crisis"

Confirmed by the measurements of polarized structure functions ofproton in the deep inelastic scattering (DIS) experiments by SMC,E142-3 and HERMES experiments.

Provides evidence that the valence quarks of proton carry only a smallfraction of its spin suggesting that they should be surrounded by anindistinct sea of quark-antiquark pairs.

Bjorken Sum Rule: ∆3 = ∆u −∆dEllis-Jaffe Sum Rule: ∆8 = ∆u + ∆d − 2∆s(Reduces to ∆8 = ∆Σ when ∆s = 0)



Flavor Structure

Several interesting facts revealed regarding the flavor distributionfunctions.

The conventional expectation that the quark sea perhaps can beobtained through the perturbative production of the quark-antiquarkpairs by gluons produces nearly equal numbers of u and d .1991 NMC result: Asymmetric nucleon sea (d > u)Confirmed by E866 and HERMESGottfried Sum Rule: IG = 1

3 + 23

∫ 10 [u(x)− d(x)]dx = 0.254± 0.026

Confirmed by the Drell-Yan experiments measuring a large quark seaasymmetry ratio d/u. Study of the quark sea is intrinsically anonperturbative phenomena and it is still a big challenge to performthese calculations from the first principles of QCD.



Quark Sea

Flavor and spin structure of the nucleon is not limited to u and d quarksonly.

The measured quark sea asymmetry established that the study of thestructure of the nucleon is intrinsically a nonperturbative phenomena.

Non-perturbative effects explained only through the generation of “quarksea”



Non-perturbative regime

Recently, a wide variety of accurately measured data have beenaccumulated forstatic properties of hadrons: masses, electromagnetic moments, chargeradii etc.low energy dynamical properties: scattering lengths and decay rates etc.

These lie in the non perturbative range of QCD.

The direct calculations of these quantities form the first principle of QCDare extremely difficult: they require non-perturbative methods.

Techniques such as lattice gauge theory, QCD sum rules, and a widevariety of models have been developed to study this extremelyinteresting energy regime.



Pion Cloud Mechanism

quark sea is believed to originate from process such as virtual pionproduction.

It is suggested that in the deep inelastic lepton-nucleon scattering, thelepton probe also scatters off the pion cloud surrounding the targetproton. The π+(du) cloud, dominant in the process p → π+n, leads toan excess of d sea.

However, this effect should be significantly reduced by the emissionssuch as p → ∆++ + π− with π−(ud) cloud. Therefore, the pion cloudidea is not able to explain the significant d > u asymmetry.

This approach can be improved upon by adopting a mechanism whichoperates in the interior of the hadron.


Chiral Constituent Quark Model


χCQM initiated by Weinberg and developed by Manohar and Georgi toexplain the successes of NQM.

"Quark sea" generation q± → GB0 + q′

∓ → (qq′) + q

′

∓

Incorporates confinement and chiral symmetry breaking.

“Justifies” the idea of constituent quarks and scope of the modelextended in the context of “proton spin crisis”



Methodology

“Quark sea” generation q± → GB0 + q′

∓ → (qq′) + q

′

∓

L = g8q(

Φ + ζ η′√

3I)

q = g8q (Φ′) q

Φ′ =

π0√

2+ β η√

6+ ζ η

′√

3π+ αK +

π− − π0√

2+ β η√

6+ ζ η

′√

3αK 0

αK− αK 0 −β 2η√6

+ ζ η′√

3

Φ′ = φuuuu + φud dd + φusss ϕud ud ϕusus

ϕdudu φduuu + φdd dd + φdsss ϕdsdsϕsusu φsd sd φsuuu + φsd dd + φssss



Transition probabilities

φuu = φdd =1

2+β

6+ζ

3, φss =

2β

3+ζ

3, φus = φds = φsu = φsd = −

β

3+ζ

3,

φdu = φud = −1

2+β

6+ζ

3, ϕud = ϕdu = 1 , ϕus = ϕds = ϕsu = ϕsd = α .

The parameter a(= |g8|2) denotes the transition probability of chiral fluctuation ofthe splittings u(d) → d(u) + π+(−), whereas α2a, β2a and ζ2a respectivelydenote the probabilities of transitions of u(d) → s + K−(o),u(d , s) → u(d , s) + η, and u(d , s) → u(d , s) + η

′.

The quark sea content of the baryon can be calculated in χCQM by substitutingfor every constituent quark q →

∑Pqq + |ψ(q)|2, where

∑Pq is the transition

probability of the emission of a GB from any of the q quark and |ψ(q)|2 is thetransition probability of the q quark.


Sea Quark Distribution

Octet baryons

For p(uud)u = a(2φ2

uu + φ2du + ϕ2

du), d = a(2φ2ud + 2ϕ2

ud + φ2dd ) and

s = a(2φ2us + 2ϕ2

us + φ2ds + ϕ2

us)

For Σ+(uus)

u = a(2φ2uu + φ2

su + ϕ2su), d = a(2φ2

ud + 2ϕ2ud + φ2

sd + ϕ2sd ) and

s = a(2φ2us + 2ϕ2

us + φ2ss)

For Σ0(uds)

u = a(φ2uu + φ2

du + φ2su + ϕ2

du + ϕ2su), d = a(φ2

ud + φ2dd + φ2

sd + ϕ2ud + ϕ2

sd )

and s = a(φ2us + φ2

ds + φ2ss + ϕ2

us + ϕ2ds)

For Ξ0(uss)

u = a(φ2uu + 2φ2

su + 2ϕ2su), d = a(φ2

ud + ϕ2ud + 2φ2

sd + 2ϕ2sd ) and

s = a(φ2us + ϕ2

us + 2φ2ss)


Sea Quark Distribution

x−dependence in χCQM

F B2 (x) = x

∑u,d,s

e2q[qB(x) + qB(x)] ,

F B1 (x) =

12x

F B2 (x) ,

where eq is the charge of the quark q (eu = 23 and ed = es = − 1

3 ). Interms of the quark distribution functions, the structure function F2 for anybaryon can be expressed as

F B2 (x) =

49

x(uB(x) + uB(x)) +19

x(dB(x) + dB(x) + sB(x) + sB(x)) .

x−dependence is phenomenologically incorporateduB(x) = uB(1− x)10, dB(x) = dB(1− x)7, sB(x) = sB(1− x)8.Flavor structure of the baryon is given as

qB(x) = qBval(x) + qB(x) ,

where q = u,d , s.H Dahiya (NITJ) Asymmetries of quark sea in nucleon MENU 2013 13 / 22

Gottfried Sum Rule

The Gottfried integrals

The Gottfried integral IpnG in terms of the sea quarks

IpnG =

∫ 1

0

F p2 (x)− F n

2 (x)

xdx =

13

+23

∫ 1

0

[up(x)− dp(x)

]dx .

Normalization conditions used∫ 1

0up

val(x)dx = 2 ,∫ 1

0dp

val(x)dx = 1 ,∫ 1

0sp

val(x)dx = 0 ,

∫ 1

0un

val(x)dx = 1 ,∫ 1

0dn

val(x)dx = 2 ,∫ 1

0sn

val(x)dx = 0 ,∫ 1

0dn(x)dx =

∫ 1

0up(x)dx ,

∫ 1

0un(x)dx =

∫ 1

0dp(x)dx ,∫ 1

0sn(x)dx =

∫ 1

0sp(x)dx .


Gottfried Sum Rule

The Gottfried Integrals

Gottfried integrals in terms of the sea quarks

IΣ+Σ0

G ≡∫ 1

0

F Σ+

2 (x)− F Σ0

2 (x)

xdx

=13

+29

∫ 1

0

[4uΣ+

(x) + dΣ+

(x)− 4uΣ0(x)− dΣ0

(x)]

dx ,

IΣ0Σ−

G ≡∫ 1

0

F Σ0

2 (x)− F Σ−

2 (x)

xdx

=13

+29

∫ 1

0

[4uΣ0

(x) + dΣ0(x)− 4dΣ+

(x)− uΣ+

(x)]

dx ,

IΞ0Ξ−

G ≡∫ 1

0

F Ξ0

2 (x)− F Ξ−

2 (x)

xdx =

13

+23

∫ 1

0

[uΞ0

(x)− dΞ0(x)]

dx .

A flavor symmetric sea leads to the Gottfried sum rule IG = 13 with

uB=dB.


Results


Results

In the figure, we have shown the variation of the sea quark distributionsxu(x), xd(x) and xs(x) with the Bjorken scaling variable x for p(uud),Σ+(uus), Σ0(uds) and Ξ0(uss).One can easily find out that

dp(x) > up(x) > sp(x), dΣ+

(x) > uΣ+

(x) ≈ sΣ+

(x),

dΣ0(x) > uΣ0

(x) > sΣ0(x), dΞ0

(x) > uΞ0(x) > sΞ0

(x),

As the sea quarks do not contribute at higher values of x , therefore wehave taken the region x = 0− 0.5. Beyond this x region the contributionof the sea quarks should be completely dominated by the valencequarks. The difference between the various sea distributions is observedto be maximum at x ≈ 0.1. As the value of x increases, the differencebetween the sea contributions decreases.


Results


Results

These quantities not only provide important constraint on a model thatattempts to describe the origin of the quark sea but also provide a directdetermination of the presence of significant amount of quark sea in thelow x region.

When x is small dB(x)− uB(x) asymmetries are large implying thedominance of sea quarks in the low x region.

At the values x > 0.3, d − u tends to 0 implying that there are no seaquarks in this region.

The case of Σ0 is particularly interesting because of its flavor structurewhich has equal numbers of u, d and s quarks in its valence structure.

Unlike the other octet baryons, where the d(x)− u(x) asymmetrydecreases continuously with the x values, the asymmetry in this casefirst increases and then for values of x > 0.1 it decreases.


Results

The Gottfried sum rules for the case of Σ+, Σ0, and Ξ0 should readIΣ+Σ0

G = 13 , IΣ0Σ−

G = 13 and IΞ0Ξ−

G = 13 if the quark sea was symmetric.

However, due to the d(x)− u(x) asymmetry in the case of octetbaryons, a lower value of the Gottfried integrals is obtained.

The quality of numerical agreement can be assessed only after the datagets refined.


Results

Application Potential

The present calculations suggest few important pointsDecomposition of various measurable quantities into thecontributions from valence and sea components.Contribution of strange quarks in the nucleon which do not appearexplicitly in most quark model descriptions of the nucleon and therole played by non-valence flavors in understanding the nucleoninternal structure.What is the role played by non-valence flavors in understandingthe nucleon internal structure?


Summary and Conclusions

Summary and Conclusions

The results obtained for the quark distribution functions reinforce ourconclusion that χCQM is able to generate qualitatively as well asquantitatively the requisite amount of quark sea.

This phenomenological analysis strongly suggests an important role forthe quark sea at low value of x .

New experiments aimed at measuring the flavor content of the otheroctet baryons are needed for profound understanding of thenonperturbative properties of QCD.

At leading order, the model envisages constituent quarks, the Goldstonebosons (π,K , η mesons) as appropriate degrees of freedom.


Asymmetries of quark sea in nucleon - MENU 2013 - 13th...

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