EFFECTIVE-POTENTIAL STUDY OF DYNAMICAL CHIRAL SYMMETRY BREAKING IN QUANTUM CHROMODYNAMICS

ZHU Chao-Yuan; HU Shi-Ke

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2024年10月30日

Chinese Physics C> 1987, Vol. 11> Issue(4) : 451-461

EFFECTIVE-POTENTIAL STUDY OF DYNAMICAL CHIRAL SYMMETRY BREAKING IN QUANTUM CHROMODYNAMICS

ZHU Chao-Yuan ^, ,
HU Shi-Ke

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Abstract：
Starting from QCD lagrangian with massless fermions and using the bilinear external sources, we derive the effective potential as a functional of composite operators, i.e.,functional of fermion propagator and gluon propagator, and then derive the Dyson--Schwinger equation for the propagators. There exist two sets of solution, the chiral-symmetry solution and chiralbreaking solution. By studying the asympotic solution of equation, we find that for the coupling constant beyond a critical value (α=1/4), a chiral-breaking solution is found, while for α<1/4 the chiral-symmetry consetrves. Using the asympotic behavior of the quark self-energy and the experimantal value for π ion decay constant f_π, we estimate the dynamical generated quark mass value, which is in agreement with the values obtained from other theoretical and experimental methods. Significance of the results are discussed.

References

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G. Jona-Lasinio, Nuovo Cimento.; 34(1964), 1790; S. Coleman and E. Weinberg, Phys. Rev.,D7(1973),1888.[2] R. Jackiw, Phys. Rev., D9(1974), 1686.[3] J. Cornwall, R. Jackiw and E. TombouIis, Phys. Rev., DIO(1974), 2428.[4] R. W. Haymaker and J. Perez-Mercader, Phys, Rev., D27(1983), 1353.[5] K. T. Mahanthappa and J. Randa., Phys. Rev., D27(1983), 2500,[6] H. Pagels,and S.Stokar, Phys. Rev., D20(1979), 2947.[7] Lay-Nam Chang,Ngee-Pong Chang, Phys. Rev., D29(1984), 312.

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ZHU Chao-Yuan and HU Shi-Ke. EFFECTIVE-POTENTIAL STUDY OF DYNAMICAL CHIRAL SYMMETRY BREAKING IN QUANTUM CHROMODYNAMICS[J]. Chinese Physics C, 1987, 11(4): 451-461.

ZHU Chao-Yuan and HU Shi-Ke. EFFECTIVE-POTENTIAL STUDY OF DYNAMICAL CHIRAL SYMMETRY BREAKING IN QUANTUM CHROMODYNAMICS[J]. Chinese Physics C, 1987, 11(4): 451-461. shu

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Received: 1900-01-01
Revised: 1900-01-01

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1.
沈阳化工大学材料科学与工程学院沈阳 110142

EFFECTIVE-POTENTIAL STUDY OF DYNAMICAL CHIRAL SYMMETRY BREAKING IN QUANTUM CHROMODYNAMICS

ZHU Chao-Yuan ^,
HU Shi-Ke

Corresponding author: ZHU Chao-Yuan,

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1987-08-05

Abstract: Starting from QCD lagrangian with massless fermions and using the bilinear external sources, we derive the effective potential as a functional of composite operators, i.e.,functional of fermion propagator and gluon propagator, and then derive the Dyson--Schwinger equation for the propagators. There exist two sets of solution, the chiral-symmetry solution and chiralbreaking solution. By studying the asympotic solution of equation, we find that for the coupling constant beyond a critical value (α=1/4), a chiral-breaking solution is found, while for α<1/4 the chiral-symmetry consetrves. Using the asympotic behavior of the quark self-energy and the experimantal value for π ion decay constant f_π, we estimate the dynamical generated quark mass value, which is in agreement with the values obtained from other theoretical and experimental methods. Significance of the results are discussed.