Toru T. Takahashi with Teiji Kunihiro ・ Why N*(1535)? ・ Lattice QCD calculation ・ Result TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAA Lattice QCD study of g_A of N*(1535) with two flavors of dynamical quarks

Why lattice QCD ?

Introduction Nuclear or Hadron Physics Quantum Chromodynamics Quantum manybody system SU(3) gauge theory Hadrons proton neutron …… Quarks (fund. rep.) Mesons ,….. Gluons (adjoint rep.) GAP!! Strong coupling nature of QCD Analytic study is still difficult Lattice QCD calculation Want to understand the hadron dynamics in terms of QCD

Why N*(1535) ?

・ Importance of strange quarks in N*(1535) ・ It’s chiral structure Baryon sector in the linear sigma model Two types of chiral realization 1)One may naively expect that nucleons become massless as indicated using linear sigma mode.  Naïve assignment 2) DeTar and Kunihiro in 1989, Schafer and Shuryak in 1995  They showed the possibility that nucleons are massive even in the chiral-restored phase.  Mirror assignment

Chiral symmetry The original QCD lagrangian has a (approx.) global symmetry. ( SU(3)_R x SU(3)_L invariant )  chirality This symmetry spontaneously broken to SU(3)_v and NG bosons appear.

Baryons are fermions composed of quarks. ? How are baryons transformed ?? Naively, Q + Q + Q Naïve assignmentMirror assingment  Naïve  Mirror

Naïve and mirror assignment We hereby consider the situation where linear combinations of two nucleon fields construct physical N and N*. There are two possible realizations for N 1 and N 2. NAÏVE and MIRROR N1 and N2 is the original states of N and N*

Naïve assignment Under the SU(2) L xSU(2) R transformation, Let us consider two nucleon fields. Chiral partner in

Mirror assignment Under the SU(2) L xSU(2) R transformation, In this case, we consider two nucleon fields, We can introduce chirally invariant mass term! They can be massive even near the chirally restored phase! diagonalization belong to the same multiplet and are chiral partners of each other.

Naive Mirror Mixing between N1 and N2 σ is responsible for mass generation. σ is responsible for mass splitting. They can be massive in restored phase. Massterm! Taken from the paper by D.Jido, Y.Nemoto, M.Oka, A.Hosaka

Naive Mirror 逆符号  diagonalization Off-diagonal coupling vanishes. (in the soft pion limit, where we can neglect the derivative coupling.) is small. Consistent?

Couplings are related in the mirror assignment. We can distinguish one from another even in the chiral-broken phase…? gA for N(1535) is negative  Mirror assignment positive  Naïve assignment All we have to do is to investigate the sign of gA for N(1535)

Lattice QCD

g_A in Lattice QCD Lattice QCD SIMPLY provides us with vacuum expectation values of OPERATORS. RECIPE 1.Construct or choose the interpolating field which couples to N(1535) 2. Compute the ratio of 2- and 3- point correlations here couples to the state

PROBLEMS in lattice QCD calculations CONTAMINATION of Signals N(1535) is accompanied by N(1650) lying just 100MeV above. N(1535) can decay. Lattices are usually 4D torus-type.

Signals in Lattice QCD Difficulty in the lattice QCD calculation We suffer from the contaminations of the other scattering state. Energy of the ground state Correlation between operators Euclidean time evolution by exp(-Ht) Creation at t=0 Annihilation at t=T N(1650) N(1535)

We need to separate signals. Signals in Lattice QCD Remember pentaquark ! We employ two different types of operators.  Diagonalize the 2x2 correlation matrix and separate the signals!

PROBLEMS in lattice QCD calculations CONTAMINATION of Signals N(1535) can decay. Lattices are usually 4D torus-type. N(1535) is accompanied by N(1650) lying just 100MeV above.

Contaminations from scattering states Infinite volume N(1535) N(1650) πN threshold N(1535) N(1650) πN threshold Finite volume & Heavy quark masses N(1535) N(1650) πN threshold Our setups πN-scattering states do not bother us! It is quite difficult to extract higher-excited state signals! It implies the volumes and the quark masses are far from realistic ones.

PROBLEMS in lattice QCD calculations CONTAMINATION of Signals Lattices are usually 4D torus-type. N(1535) is accompanied by N(1650) lying just 100MeV above. N(1535) can decay.

Imaginary time dir. 4D torus is harmful ??? N* N + πN + πN + πN + π What we want We do not have Let us consider 2-point functions We impose Dirichlet boundary for quarks!

PROBLEMS in lattice QCD calculations CONTAMINATION of Signals N(1535) is accompanied by N(1650) lying just 100MeV above. N(1535) can decay. Lattices are usually 4D torus-type.

16^3 x 32 lattice with two flavors of dynamical quarks The renormalization-group improved gauge action at β=1.95 The mean field improved clover quark action with the clover coefficient c_SW=1.530  Lattice size = (2.5fm)^3 x (5.0fm) Hopping parameter κ=0.1375, ,  pion mass = 1.16 GeV, GeV, GeV Simulation parameters The quarks are heavier than the realistic ones. Generated by CP-PACS

Masses - chiral extrapolation - N(940) 1204( 4) MeV N(1440) 2019(141) MeV N(1535) 1642(32) MeV N(1650) 1815(49) MeV Diagonalization processes seem to work well.

Lattice QCD results  1.00 gV and gA for N(940) gV for N(1535)  1.26 preliminary

Lattice QCD results gA for N(1535) preliminary

Lattice QCD results Relative sign is -  mirror assignment Relative sign is +  naïve assignment Even the relative sign is quark-mass-dependent.  Finite size effect ? (2.5 fm)^3 may be small for N(1535)  Transition from naïve to mirror sea quark effect in the light-quark region ? Model prediction

Summary We have studied the axial charge of N(1535) using lattice QCD. g_A for N(1535) seems small as | g_A| ～ 0.2. Even the sign is quark-mass-dependent. The absolute value is quite small.  “Naïve” only with Yukawa terms is not likely? u- and d- contributions are individually quite small. Analysis on a large lattice 2+1 dynamical calculations Possible mixture of mirror and naïve assignments ?