Strangeness in the Nucleon:Overview

Ross YoungJefferson Lab

JLab Hall C 2005 Summer Workshop

Strange Overview

Origins of mass:Spin contributionsElectromagnetic currents:Lattice calculation

GsE & Gs

M

ms〈N|ss|N〉Δs

Origins of mass

Mass dynamically generated by quark-gluon interactionsWhat is the role of strange quarks?

Leinweber et al.mq∼ 5MeV mN ∼ 940MeV

ms〈N|ss|N〉 # 335±132MeVNelson & Kaplan PLB(1987)

MN,MΛ,MΣ,MΞGell-Mann–Okubo relation

∼MphysN −MSU(3)chiral limit

Nmeasures

ms〈N|ss|N〉 = ms∂MN

∂ms

∼ . . . s(D/ +ms)sQCD Lagrangian

evaluated at physical point!

Chiral Perturbation Theory

KNOWN: Low-energy behaviourUNKNOWN: Short distance effects

Low-energy constants

ms∂MN

∂ms= 113±108MeV

Borasoy & Meissner (1997)

Resonance saturation MODEL to determine

UNKNOWN!

High-order calculation

Strange Loops

What is the correction to the nucleon mass from this loop?Chiral phenomenology, excellent description of loop effects

msstrange quark

Lattice Results

0 0.1 0.2 0.3 0.4 0.5 0.6m Π2 !GeV2"

1

1.2

1.4

1.6

1.8

MB!GeV" Δ

N

Quenched

Dynamical

Differences described by chiral loops

RDY et al. PRD(2002)

Lattice Results

0 0.1 0.2 0.3 0.4 0.5 0.6m Π2 !GeV2"

1

1.2

1.4

1.6

1.8

MB!GeV" Δ

N

Quenched

Dynamical

Differences described by chiral loops

RDY et al. PRD(2002)

a0 a2 a4

N 1.23(1) 1.13(8) -0.35(12)

N(Q) 1.20(1) 1.10(8) -0.42(13)

D 1.40(3) 1.11(18) -0.56(25)

D(Q) 1.43(3) 0.76(21) -0.04(33)

mB = a0+a2m2π+a4m4π+Σ

Modelling Strangeness

Λ,Σ

K Dominant strange contributions in Kaon

cloud

mq msStrange Quark Mass

!80

!60

!40

!20

0

∆MNstrange!MeV"Local derivative

ms∂MN

∂ms! 16MeV

ms〈N|ss|N〉~5%

∼ 110MeV

Strange spin content

Polarised deep-inelastic scattering∫dxg1(x)

axial charge Δs=−0.10±0.04gA3F−Dhyperon decay Bass (2004)

Semi-inclusive reactionsΔs= 0.028±0.033±0.009

over measured range HERMES PRD(2005)

Electromagnetic Structure

Hot topic:SAMPLE, HAPPEX, MAINZ/A4, G0Parity-violating electron scattering (PVES)Elastic form factor measurements with polarised electron beam

GsE & Gs

MStrange form factors

GpZE,M =

14(G

pγE,M−Gnγ

E,M)− sin2θWGpγE,M−

14G

sE,M

PV asymmetry

Interference between and Z probesγ

APV =σR−σLσR+σL

=[−GFQ2

πα√2

]εGpγ

E GpZE + τGpγ

MGpZM − 1

2(1−4sin2θW)ε′GpγMG

pZA

ε(GpγE )2+ τ(Gpγ

M )2

Strangeness

Calculation of Anapole Moment

Zhu et al. PRD(2000)

Chiral perturbation theoryLow-energy constants determined by resonance saturation MODEL

Calculation of Anapole Moment

Zhu et al. PRD(2000)

Chiral perturbation theoryLow-energy constants determined by resonance saturation MODEL

SAMPLEPLB(2004)

Lattice Results

Dong et al. PRD(1998)Mathur & Dong NPB(2001)

Lewis et al. PRD(2003)

GsM =−0.36±0.20

GsM =−0.27±0.10

GsM(0.1GeV2) = +0.05±0.06

Leinweber et al. PRL(2005) GsM =−0.046±0.019

Charge Symmetry Constraint

Σ+=23u

Σ− 13sΣ+OΣ

Σ−=−13uΣ− 13s

Σ+OΣ

Σ+−Σ− = uΣ

p=23u

p− 13un+ON

n=−13up+

23u

n+ON

3ON=2p+n− up

uΣ(Σ+−Σ−)

3ON= p+2n− un

uΞ(Ξ0−Ξ−)

Lattice QCD

3ON=2p+n−up3ON=p+2n−un

Disconnected Loops

u,d,s=23lGu

M−13lGd

M−13lGs

MON =

lGuM = lGd

M

mu = mdQCD equality for

ON=−13(lGd

M+ lGsM)

=lGs

M3

(1− lRsdlRsd

)

lRsd = lGsM/lGd

M = 0.139±0.042

Constraint on GMs

GsM=

(lRsd

1− lRsd

)[2p+n− u

p

uΣ(Σ+−Σ−)

]GsM=

(lRsd

1− lRsd

)[p+2n− un

uΞ(Ξ0−Ξ−)

]

GsM > 0

GsM < 0

Quark model

Lattice QCD

0.0 0.2 0.4 0.6 0.8 1.0m Π 2 !GeV2"

0.8

1.0

1.2

1.4

1.6

1.8

MN!GeV"

Chiral Extrapolation

Dipole

Leinweber, Thomas & RDY PRL(2004)

0.0 0.2 0.4 0.6 0.8 1.0m Π 2 !GeV2"

0.8

1.0

1.2

1.4

1.6

1.8

MN!GeV"

Chiral Extrapolation

Dipole

0.0 0.2 0.4 0.6 0.8 1.0m Π 2 !GeV2"

0.8

1.0

1.2

1.4

1.6

1.8

MN!GeV" Theta

Leinweber, Thomas & RDY PRL(2004)

0.0 0.2 0.4 0.6 0.8 1.0m Π 2 !GeV2"

0.8

1.0

1.2

1.4

1.6

1.8

MN!GeV"

Chiral Extrapolation

Dipole

0.0 0.2 0.4 0.6 0.8 1.0m Π 2 !GeV2"

0.8

1.0

1.2

1.4

1.6

1.8

MN!GeV" Theta

0.0 0.2 0.4 0.6 0.8 1.0m Π 2 !GeV2"

0.8

1.0

1.2

1.4

1.6

1.8

MN!GeV"

Monopole

Leinweber, Thomas & RDY PRL(2004)

0.0 0.2 0.4 0.6 0.8 1.0m Π 2 !GeV2"

0.8

1.0

1.2

1.4

1.6

1.8

MN!GeV"

Chiral Extrapolation

Dipole

0.0 0.2 0.4 0.6 0.8 1.0m Π 2 !GeV2"

0.8

1.0

1.2

1.4

1.6

1.8

MN!GeV" Theta

0.0 0.2 0.4 0.6 0.8 1.0m Π 2 !GeV2"

0.8

1.0

1.2

1.4

1.6

1.8

MN!GeV"

Monopole

0.0 0.2 0.4 0.6 0.8 1.0m Π 2 !GeV2"

0.8

1.0

1.2

1.4

1.6

1.8

MN!GeV"

Gaussian

Leinweber, Thomas & RDY PRL(2004)

Quenched Approximation

〈O〉 =∫DU OdetM[U ]exp(−SG[U ])

0 0.2 0.4 0.6 0.8m Π2 !GeV2"

1

1.2

1.4

1.6

1.8

MB!GeV"

0 0.2 0.4 0.6 0.8m Π2 !GeV2"

1

1.2

1.4

1.6

1.8

MB!GeV"

0 0.2 0.4 0.6 0.8m Π2 !GeV2"

1

1.2

1.4

1.6

1.8

MB!GeV"

0 0.2 0.4 0.6 0.8m Π2 !GeV2"

1

1.2

1.4

1.6

1.8

MB!GeV"

Chiral corrections

η′

B′

π,K

Quenched artefactDifferent contributions in Quenched QCD and QCD

u-quark in the proton

Magnetic Moments

Leinweber et al. PRL(2005)

Final Result

GsM =−0.046±0.019µN

Strange Signs

Lightest strange dof coupling to proton

pΛ,Σ0,Σ+

K+,K0s in mesons in baryon

|〈r2〉Es | > |〈r2〉Es | ⇒ 〈r2〉Es < 0

GsE > 0Try this at home:

Slowly creep up on a proton from a long distance,first strange thing you’ll see: a meson!K+

Summary

Strangeness in the nucleon is interestingNucleon mass ~-5% (maybe -30%)Momentum ~3%, Spin ~-10% (?maybe “+”)Electric/Magnetic form factors

work in progress

References

Nelson & Kaplan PLB192,193(1987)RDY et al. PRD66,094507(2002)

Borasoy & Meissner Ann.Phys.254,192(1997)Flambaum, RDY et al. PRD69,115006(2004)

Kaplan & Manohar NPB310,527(1988)Beck PRD39,3248(1989)

Kumar & Souder Prog.Part.Nucl.Phys.45,S333(2000)Zhu et al. PRD62,033008(2000)

SAMPLE Collaboration PLB583,79(2004)Leinweber, RDY et al. PRL94,212001(2005)

Leinweber, Thomas & RDY PRL92,242002(2004)