Jlab page 1

Roper from 2+1 Flavor Clover Roper from 2+1 Flavor Clover Fermions and Chiral DynamicsFermions and Chiral Dynamics

• Roper resonances from quenched approximation and Roper resonances from quenched approximation and 2+1 flavor Clover fermions 2+1 flavor Clover fermions

• Roper wavefunctions from overlap Roper wavefunctions from overlap

• Flavor-singlet and flavor-octec Flavor-singlet and flavor-octec ΛΛ (1/2 (1/2--))

• Attempt to understand the underline chiral dynamicsAttempt to understand the underline chiral dynamics

QCD Collaboration: A. Alexandru, Y. Chen, T. Doi, S.J. Dong, T. Draper, F .X. Lee, K.F. Liu, D. Mankame, X.F. Meng, N. Mathur, T. Streuer

Lattice 2008, July 15, 2008

B.G. Lasscock et al, PRD76, 054510 (2007)

Sequential Empirical Bayes Method Fitting of CSSM DataY. Chen

Glasgow, 2005, page 4

Overlap fermion on quenched 16^3 x 28 lattices

In the chirally improved fermion calculation (a=0.119 fm), the flavor-octet and flavor-singlet Λ(1/2-) are inverted.

Roper and N for Quenched Wilson and Clover at L ~ 2.4 fm

Radial excitationRadial excitation? ? • Roper is seen on the lattice with Roper is seen on the lattice with three-quarkthree-quark interpolation interpolation

field.field.• Weight :Weight :

|<0|<0||OONN||R R >|>|2 2 >> |<0|<0||OONN||NN>|>|2 2 >> 0 0 (point source, point sink)(point source, point sink)

∑∑ψψ(x)(x) ∑∑OONN(x(x) ) ∑∑ψψ(y)(y)

∑∑ψψ(z)(z) Point sink Wall sourcePoint sink Wall source

<0<0||OONN(0)|N(0)|N>> <<N| ∑N| ∑ψψ(x) ∑(x) ∑ψψ(y) ∑(y) ∑ψψ(z)|0 (z)|0 >> >> 00 However,However, <0<0||OONN(0)|R(0)|R>> <R<R| ∑| ∑ψψ(x) ∑(x) ∑ψψ(y) | ∑(y) | ∑ψψ(z)|0 (z)|0 >> << 00

2S

q4q State?

1S

Glasgow, 2005, page 9

Bethe-Salpeter Bethe-Salpeter WavefunctionWavefunction

r

+r

as )()(

limit, icrelativist-nonat 0)()(

*

*

qNRRN

NRRN

mrrdrO

rrdrO

Glasgow, 2005, page

10

Nucleon and Roper wavefunctions for mπ = 633 MeV

ORN = 0.30

Glasgow, 2005, page

11

Roper and Nucleon Wavefunctions at mRoper and Nucleon Wavefunctions at mππ = 438 MeV = 438 MeV

OORNRN = 0.59 = 0.59

S11 and Roper for Clover Fermions

Λ(1/2+) and Λ(1/2-) Singlet and Octect

Λ(1/2+) and Λ(1/2-) Singlet and Octect

a Roper S11 Λ(1/2-)

Singlet

Λ(1/2-)

Octet

Quenched

Overlap

0.2 fm √ √ √ √

Quenched

CI

0.12 fm

? √ ? ?

Quenched

Wilson

0.05 fm

? √ ? ?

Quenched

Clover

0.09 fm

√ ? ? ?

2+1FlavorClover

0.12 fm

√ √ √ √

ConclusionConclusion

Baryon Spectrum is sensitive to Baryon Spectrum is sensitive to fermion actions at finite a.fermion actions at finite a.Dynamical fermion has a large effect Dynamical fermion has a large effect on Son S11 11 and both singlet and octet and both singlet and octet ΛΛ(1/2(1/2--) for the Clover action.) for the Clover action.

In addition to chiral logs in mIn addition to chiral logs in mππ and mand mKK, , Roper and Roper and ΛΛ(1/2(1/2--) are good cases to ) are good cases to study chiral dynamics with different study chiral dynamics with different fermion actions.fermion actions.