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Chiral Structure of Hadronic Currents. 陈华星 北京航空航天大学. April 21, 2014 武汉. Contents. Motivations Flavor structure of tetraquark Chiral structure of baryon Chiral structure of tetraquark Summary. 1. Motivation. Conventional mesons and baryons

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chiral structure of hadronic currents

Chiral Structure of Hadronic Currents

陈华星

北京航空航天大学

April 21, 2014 武汉

contents
Contents
  • Motivations
  • Flavor structure of tetraquark
  • Chiral structure of baryon
  • Chiral structure of tetraquark
  • Summary
1 motivation
1. Motivation
  • Conventional mesonsand baryons
  • QCD allows much richer hadron spectrum
  • Exotic hadrons:

glueballs ,

multiquarkstates ,

hybrids

molecularstates

1 motivation1
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)

2 tetraquark currents
2. Tetraquark Currents
  • The flavor structure of meson is

SU(3)F

  • The flavor structure of baryon is

SU(3)F

2 tetraquark currents1
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 currents2
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.

2 tetraquark currents3
2. Tetraquark Currents
  • We find that there are five independent currents for σ(600) JPC=0++ states:
3 chiral structure of baryon
3. Chiral structure of Baryon
  • Chiral structure of quark:
  • Chiral structure of meson
3 chiral structure of baryon1
3. Chiral structure of Baryon
  • Chiral structure of baryon

10

3 chiral structure of baryon2
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 baryon3
3. Chiral structure of Baryon
  • We can perform chiral transformations, and verify:

,

,

,

.

  • We can calculate their axial charges, such as:
3 chiral structure of baryon4
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 baryon5
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
4. Chiral structure of Tetraquark
  • Chiral structure of quark:
  • Chiral structure of tetraquark
4 chiral structure of tetraquark1
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.
4 chiral structure of tetraquark2
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

. ?

5 summary
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.
4 baryon masses
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