KN phase shifts in chiral quark model

F. Huang, Z.Y. Zhang, Y.W. Yu

(Institute of High Energy Physics, Beijing,

China)

Motivations Formulation

The model Determination of parameters

Results discussions Summary

Outline

Motivations• To extend our model to study BM

interactionso NPQCD effect is important; QCD-inspired

models are still neededo Our model works well for NN and NYo To extend our model to study BM

interactions; Start with KN in which annihilation is simple

• To get a better understanding of KN

interactiono Most of previous works based on CQM failed

to accurately reproduce the KN phase shiftso Can we reproduce KN phase shifts in our

model ?

Formulation (1) the modelThe Hamiltonian of KN system

Generalize the idea of SU(2) σ model to SU(3)f case

Clearly, HIch is invariant under the infinitesimal

chiral SU(3)LSU(3)R transformation.

From HIch, the SU(3) chiral-field-induced

quark-quark potentials can be derived

For KN, there are alsoqq interactions

For KN system,qq can only annihilate into kaon

Ck is adjusted to fit the mass of kaon

The exchange diagrams forqq

The annihilation diagrams forqq

Formulation (2) parameters fitting

• Input: bu=0.5 fm, mu=313 MeV, ms=470 MeV

• The chiral field coupling constant

• Mesons’ masses: experimental values Except mσ (adjustable parameter), mσ=675 MeV

• Λ-1=0.18 fm, close to chiral symmetry breaking scale

• gu and gs, determined by mΔ-mN and mΣ-mΛ

• Parameters of Vconf, fitted by baryons’ masses and their stability conditions

We consider the mixing between the flavor singlet and octet mesons

The mixing of scalar meson is still an open problem

About the mixing angle

PS= –23

Ⅰ S≈ 35Ⅱ S= –18

Y.B. Dai, Y.L. Wu, hep-ph/0304075

Model parametersmσ 980=׳ MeV, m=980 MeV

mε=980 MeV, mσ=675 MeV

m=138 MeV, m=495 MeV

m=549 MeV, mη 957=׳ MeV

Λ=1100 MeV

The masses of baryons

Results discussions• RGM calculation

• Conventional notation LI 2J

About the mixing of σ0 and σ8

The attraction of σ is reduced in both of these two cases

Ⅰ S≈ 35Ⅱ S= –18

We took two possible values of S

Influence of the annihilation

The numerical phase shifts scarcely have changes when we omit the annihilation part entirely.

The annihilation part coming form S-channel acts in the very short range, so it plays a non-significant role in KN scattering process.

The annihilation diagrams forqq

Comparing with recent RGM study

S. Lemaire et al, NPA 714 (2003) 265

gluon+++confinement, RGM calculation

Summary

The chiral SU(3) quark model is extended to includeq

KN scattering process is studied using RGM

Our results achieve a considerable improvement on theoretical phase shifts comparing with others’ worksA reasonable interaction between K and N

can be obtained from the chiral SU(3) quark model when the mixing of σ0 and σ8 is

considered and mσ is taken to be 675 MeV

The end

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