Chiral Structure of Hadronic Currents

陈华星北京航空航天大学

April 21, 2014 武汉

Contents1. Motivations2. Flavor structure of tetraquark3. Chiral structure of baryon4. Chiral structure of tetraquark 5. Summary

1. MotivationConventional mesons and baryonsQCD allows much richer hadron spectrumExotic hadrons: glueballs , multiquark states , hybrids molecular states

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

Exotic in structure: hadron molecule

tetraquark, pentaquark

Λ(1405), X(3872)

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

The flavor structure of baryon is SU(3)F

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

2. Tetraquark 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 δAB and λAB, we can obtain singlet and octet, respectively.

Meson Currents

Diquark Currents

2. Tetraquark Currents We find that there are five independent

currents for σ(600) JPC=0++ states:

Fierz Transformations

Chiral Transformation

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

𝟏

𝟏⨁𝟖𝟖

𝑞𝛾5𝑞=𝑞𝐿𝑞𝑅−𝑞𝑅𝑞𝐿∈[(3 ,3 )⨁ (3 ,3 )]𝑞𝛾𝜇𝑞=𝑞𝐿𝛾𝜇𝑞𝐿+𝑞𝑅𝛾𝜇𝑞𝑅∈ [ (1,1 ) ] , [ (8 ,1 )⨁ (1 ,8 )]

3. Chiral structure of Baryon• Chiral structure of baryon

𝟏

𝟏⨁𝟖𝟖

10

𝟏𝟎

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.

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

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:

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:

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

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 , and chiral transformations.

• The different chiral transformation may be reasons for the anomaly.

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 isovector vector and axial-vector local tetraquark currents of quantum numbers

. ?

5. SummaryWe 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 pseudoscalar tetraquark 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.

Thank you very much!

4. Baryon masses• We assume that their masses originate

from three different sources:

1. bare mass term 2. electromagnetic terms 3. spontaneous chiral symmetry breaking terms