Nucleon and Roper on the Nucleon and Roper on the LatticeLattice

Y. Chen

Institute of High Energy Physics, CAS, China

Collaborating with

S.J. Dong, T. Draper, I. Horvath, F.X. Lee, K.F. Liu, N. Mathur, S. Tamhankar, and J.B. Zhang

(Kentucky Lattice Group)

IntroductionIntroduction

• Roper resonance has been well established as a four-star state in Particle Data Table.

• A radial excited state of the nucleon? Same quantum number

• Parity reversal cannot be easily interpreted. Roper(1440) and (1535)

• A pentaquark candidate? (Jaffe-Wilczek, PRL91, 232003, 2003)

• Hybrid?

• Nonperturbative Method ------ Lattice QCD

11S

Simulation DetailsSimulation Details

• lattice, quenched approximation

• Iwasaki gauge action ( improved)

overlap fermion action (chiral symmetry, improved)• The lattice spacing is set by • The lowest quark mass gives • 80 Configurations to do the statistics.• Nucleon mass spectrum is simulated. (hep-lat/0306199)• Nucleon and Roper wave functions are calculated.

28163

fma )3(200.0 fMeVm 180

)( 2aO

)(aO

Mass and spectral weights

: hadron masses to be extracted : spectral weights

hadron matrix elements wave functions

tm

nn

tm

n

nn eWenRtTr 2

)(0)0()(

nmnW

Nucleon Mass SpectrumNucleon Mass Spectrum

Point-source point-sink correlation function are calculated and analyzed.

Nucleon interpolation field operator

Constrained curve fitting--------- “Sequential Empirical Bayes”(SEB)hep-lat/0405001(Kentucky Group)

Roper mass and S11(1535) mass tends to cross over as quark mass decreases.

Chiral symmetry may play a role for this crossover. Flavor-spin interaction

takes place due to the Goldstone boson exchange (L.Y. Glozman and D.O. Riska, Phys. Rep. 268, 263(1996) )

)()()()( 5 xuxdCxux cbaTabc

Nucleon and Roper WavefunctionsNucleon and Roper Wavefunctions

Coulomb gauge fixed Wall-source point sink correlation funct

ions are calculated and analyzed. The spectrum is similar to that of point

source. The spectral weights of Roper are negat

ive for both heavy and light quark masses.

Wall-source means, qualitatively

This hints that a radial node.

)()0,(0 xNx N

0)(4)( **

23 rdrrxxdNN

)(* rN

Spatially extended sink operator

where , Nucleon two-point functions are calculated in Coulomb

gauge.

where and

)()()()( 215121 xuxdCxuxx cbaTabc ，

),( 11 txx

),( 22 txx

tm

n

nennRtRTr 0)0()(0)0,0(),(

21 xxR

)()(0 RnR n

Wavefunctions are fitted by the variational function form

which are motivated from the non-relativistic potential

model.

The r.m.s radius of nucleon can be estimated as

Light Quark RegionLight Quark Region

Point-source correlation function behaves bad at this quark mass.

Therefore,

Wall-source correlation function is used to extracte the wavefunctions

There is an additional minus sign in the Roper wavefunction, due to the wall source effect.

The Roper wavefunction has a radial node.

The behavior of the roper wave function is a little bit puzzling.

Ghost StateGhost State

In quenched approximation, the Z-graph goes to the hairpin-graph which results in a ghost state.

However, the spectral weight of

the ghost is much smaller than that of the Roper, at this quark mass.

It seems that the ghost can not

account for the strange behavior of the Roper wave function completely.

SummarySummary The simulation of nucleon spectrum turns out that the Roper mass and

the mass of S11(1535) tend to cross over as quark mass goes down. Our result support the notion that

Heavy quark Light quark SU(6) ----transition--- dynamics dominated color-spin by chiral symmetry

The Roper wavefunction has definitely a radial node in medium quark region ( ). At lower quark mass, there is a hint the node also exists, but further work is needed.

R.M.S radius of nucleon is about 0.7 fm, which seems insensitive to the quark mass, when quark mass is not too high.

MeVm 400