Chiral Structure of Hadronic Currents

1. Chiral Structure of Hadronic Currents 陈华星 北京航空航天大学 April 21, 2014 武汉

2. Contents • Motivations • Flavor structure of tetraquark • Chiral structure of baryon • Chiral structure of tetraquark • Summary

3. 1. Motivation • Conventional mesonsand baryons • QCD allows much richer hadron spectrum • Exotic hadrons: glueballs , multiquarkstates , hybrids molecularstates

4. 1. Motivation • Exotic in quantum numbers: mesons : JPC=0--,0+-,1-+,2+-, etc. baryons : S=+1 & B=1, I=5/2, etc. Candidates: π1(1400), π1(1600) and π1(2000)with IGJPC =1-1-+ Zc(3900), Zc(4020)charged charmonium • Exoticin structure: hadron molecule tetraquark, pentaquark Λ(1405), X(3872)

5. 2. Tetraquark Currents • The flavor structure of meson is SU(3)F • The flavor structure of baryon is SU(3)F

6. 2. Tetraquark Currents • Tetraquark is complicated: • For each state, there may exist more than one currents. • We try to do a systematical study on tetraquark currents. SU(3)F Flavor structure

7. 2. Tetraquark Currents Meson Currents • Scalar JP=0+ • Vector JP=1- • Tensor JP=1+- • Axial-vector JP=1+ • Pseudo-scalar JP=0- A, B are the flavor indices; a is the color index. By adding δABand λAB, we can obtain singlet and octet, respectively.

8. Diquark Currents

9. 2. Tetraquark Currents • We find that there are five independent currents for σ(600) JPC=0++ states:

10. Fierz Transformations

11. Chiral Transformation

12. 3. Chiral structure of Baryon • Chiral structure of quark: • Chiral structure of meson

13. 3. Chiral structure of Baryon • Chiral structure of baryon 10

14. 3. Chiral structure of Baryon • We investigate chiral properties of local fields of baryons consisting of three quarks with flavor SU(3) symmetry. We construct explicitly independent local three-quark fields: , , , , , , • where a,b,c are color indices, A,B,C are flavor indices, are totally symmetric tensors.

15. 3. Chiral structure of Baryon • We can perform chiral transformations, and verify: , , , . • We can calculate their axial charges, such as:

16. 3. Chiral structure of Baryon • We construct all SUL(3)xSUR(3)chirally invariant non-derivative one-pseudoscalar-meson-baryon interactions, i.e., all chiral-singlet Lagrangians made by baryons and mesons:

17. 3. Chiral structure of Baryon • We construct all SUL(3)xSUR(3)chirally invariant non-derivative one-vector-meson-baryon interactions, i.e., all chiral-singlet Lagrangians made by baryons and mesons:

18. 4. Chiral structure of Tetraquark • Chiral structure of quark: • Chiral structure of tetraquark

20. 4. Chiral structure of Tetraquark • We systematically studied the chiral structure of local scalar and pesudoscalar tetraquark currents that belong to the “non-exotic”tetraquark chiral multiplets. • We find that they transform differently from mesons under the chiral transformations, but transform in the same way as mesons under , andchiral transformations. • The different chiral transformation may be reasons for the anomaly.

21. 4. Chiral structure of Tetraquark • We investigate the chiral structure of local vector and axial-vector tetraquark currents that belong to the “non-exotic” tetraquark chiral multiplets. They transform in the same way as mesons: • We find that there is a one to one correspondence among all the isovectorvector and axial-vector local tetraquark currents of quantum numbers . ?

22. 5. Summary • We investigate the chiral structure of local baryon and non-local baryon fields, and study their chiral transformation properties. • We investigate the chiral structure of local scalar and pseudoscalartetraquark currents, and study their chiral transformation properties. • We investigate the chiral structure of local vector and axial-vector tetraquark currents, and study their chiral transformation properties.

23. Thank you very much!

24. 4. Baryonmasses • We assume that their masses originate from three different sources: 1. bare mass term 2. electromagnetic terms 3. spontaneous chiral symmetry breaking terms