夸克传播子、QCD真空凝聚和夸克虚度
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摘要
研究完全穿衣服的夸克传播子是QCD研究中的一个非常重要的问题，它与精确的确定夸克的质量是密切相关的。夸克质量是标准模型的基本输入参数，准确地确定这些参数无论对于唯象的应用还是对于基本理论的应用都是极其重要的。本文首先简要地介绍了强相互作用的基本理论—QCD。接着在Dyson-Schwinger方程的理论框架内利用“彩虹”近似和不同的唯象的胶子传播子，研究了完全穿衣服的夸克传播子。我们求解了Dyson-Schwinger方程，并用它的解研究了非定域的夸克真空凝聚的结构，计算了各种定域的夸克真空凝聚值，定域的夸克胶子混合真空凝聚值和夸克在真空中的虚度。结果与格点规范、瞬子模型和文献中常用的经验值一致。同时，我们提出了一个参数化的夸克传播子来近似地描述Dyson-Schwinger方程的解。这个参数化的夸克传播子是解析的，在P~2的复平面上没有奇异点，因此在可观测量的计算中也没有夸克的产生域。我们用这个参数化的传播子重新地计算了前边提到的各种物理量，并与DSEs的解进行了比较。比较结果表明：参数化的夸克传播子是适用和可靠的，它给出了和Dyson-Schwinger方程一致的结果。最后，用我们得到的关于定域夸克的凝聚值和Gell-Mann-Oakes-Renner关系，成功地预言了轻夸克的流质量和Goldstone玻色子的质量，得到了实验上观测到的Goldstone玻色子的质量。显然，本文的物理思想和理论表述较好地描述了QCD的非微扰特征，为我们进一步研究打下了基础。
Study of fully dressed quark propagator is one of the most important issue in the investigation of QCD, since it is related to the determination of quark masses, which are fundamental QCD input parameters of Standard Model, and an accurate determination of these parameters is extremely important for both phenomenological and theoretical applications. We begin with a brief introduction to the strong interaction theory - QCD, and then study fully dressed quark propagator in the framework of Dyson-Schwinger Equations (DSEs) in the "Rainbow" approximation with three different phenomenological gluon propagators. We solve the DSEs and use its solutions to study the structure of non-local quark vacuum condensate and calculate local quark vacuum condensates, quark-gluon mixed vacuum condensates, and quark virtuality in the QCD vacuum. Our predictions are consistent with other model predictions such as Lattice QCD, Instanton Model and empirical values used widely in the literature. At the same time, we also propose a parameterized quark propagator to approach to the DSEs which is very complicated to be solved. The parameterization form of the fully dressed quark propagatoris is analytic everywhere in the finite complex p~2-plane and has no Lehmann representation, and hence there are no quark production thresholds in theoretical calculations of observables. We re-calculate all of the physics quantities mentioned above by use of the parameterized quark propagator and compared its predictions with those given by the solutions of DSEs. The results show that the parametrized form of quark propagator is an applicable and reliable approximation since its predictions are consistent with DSEs predictions and reproduces all physical quantities in an acceptable way. Finally, the current masses of light quarks and the masses of Goldstone bosons are also obtained by using our theoretical results on local vacuum condensates. The resulting agreements of the Golsdtone beson masses with their experimental data are quite good. Evidently, it shows that the physics idea and the formulated theory presented in this paper
are good for understanging non-perturbative feature of QCD.
Study of fully dressed quark propagator is one of the most important issue in the investigation of QCD, since it is related to the determination of quark masses, which are fundamental QCD input parameters of Standard Model, and an accurate determination of these parameters is extremely important for both phenomenological and theoretical applications. We begin with a brief introduction to the strong interaction theory - QCD, and then study fully dressed quark propagator in the framework of Dyson-Schwinger Equations (DSEs) in the "Rainbow" approximation with three different phenomenological gluon propagators. We solve the DSEs and use its solutions to study the structure of non-local quark vacuum condensate and calculate local quark vacuum condensates, quark-gluon mixed vacuum condensates, and quark virtuality in the QCD vacuum. Our predictions are consistent with other model predictions such as Lattice QCD, Instanton Model and empirical values used widely in the literature. At the same time, we also propose a parameterized quark propagator to approach to the DSEs which is very complicated to be solved. The parameterization form of the fully dressed quark propagatoris is analytic everywhere in the finite complex p~2-plane and has no Lehmann representation, and hence there are no quark production thresholds in theoretical calculations of observables. We re-calculate all of the physics quantities mentioned above by use of the parameterized quark propagator and compared its predictions with those given by the solutions of DSEs. The results show that the parametrized form of quark propagator is an applicable and reliable approximation since its predictions are consistent with DSEs predictions and reproduces all physical quantities in an acceptable way. Finally, the current masses of light quarks and the masses of Goldstone bosons are also obtained by using our theoretical results on local vacuum condensates. The resulting agreements of the Golsdtone beson masses with their experimental data are quite good. Evidently, it shows that the physics idea and the formulated theory presented in this paper
are good for understanging non-perturbative feature of QCD.
引文
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[2] Zhou Li-juan, Ping Rong-Gang, and Ma Wei-xing, Commun. Theor. Phys., Vol. 42 (2004) 875-883,
[3] L. Wolfenstein. Phys. Rev. Lett. 51(1983) 1945,
[4] M. Bochicchio, et al., Nucl. Phys. B268 (1983)331,
[5] C. J. Burden, C. D. Roberts, and M. J. Thomson, Phys. Lett. B371 (1996) 163,
[6] F. J. Dyson, Phys. Rev., 75 (1949) 1736,
[7] L. S. schwinger, Proc. Nat. Acad. Sci., Vol. 37 (1951) 452,
[8] C. D. Roberts, Prog. Part. Nucl. Phys. 45 (2000) 511
[9] W. Greiner, A. Schafer, Quantum Chromodynamics, Springer (1994),
[10] Adnan bashir, Alfredo Raya, arxiv: hep-ph/0411310,
[11] C. Itzykson and J. B. Zuber, Quantum Field Theory, McGraw-Hill, New York (1986),
[12] G. C. Wick, Phys. Rev. 961 (1954) 1124,
[13] P. C. Tandy, Prog. Part. Nucl. Phys. 39 (1997) 117,
[14] R. T. Cahill and C. D. Roberts. Phy. Rev. D32 (1985) 2419,
[15] L. S. Kissliner, "2004 Review of Light Cone Field Theory", ArXiv: hep-ph/9401248 vl, 30 Jan. 2004,
[16] D. C. Curtis and M. R. Pennington, Phys. Rev. D 42 (1990) 2165,
[17] R. Jackiw and K. Jahnson, Phys. Rev. D8 (1973) 2386,
[18] C. D. Roberts and A. G. williams, Prog. Part. Nucl. Phys., Vol. 33 (1994) 477,
[19] L. S. Kislliner and T. Meissner, Phys. Rev. C53 (1998) 1528,
[20] M. R. Frank and T. Meiesner, Phys. Rev. C53(1996)2410,
[21] L. S. Kisslinger, et al. arxiv: hep-ph/9906457,
[22] Wang Zhi-gang, arxiv: hep-ph/0204157,
[23] K. Wilson, On Products of Quantum Field Operators at short distances. Cornell Press, Cornell (1964) (sec. 4. 1),
[24] V. A. Novikov, M. A. Shiman, V. I. Vainshtein, M. B. Voloshin, and V. I. Zakharov, Nucl. Phys. B237 (1984) 525,
[25] A. E. Dorokhov, S. V. Mikhailov, Physics of Particles and Nuclei (suppl. ), Vol. 32 (2001) 554,
[26] V. Lubicz, Nucl. Phy. (proc. Suppl. ) B94 (2001) 116,
[27] Naxison S 1989 QCD Spectral Sum Rules (World Scientific, Singapore),
[28] Kremer M and Schierholz G 1987 Phys. Lett. B 194 283,
[29] Polyakov M V and Weiss C 1996 Phys. Lett. B 387 841,
[30] Zong H S, Wu X H, Lu X F, Chang C H and Zhao E G arxiv: hep-ph/0109122
[31] M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175 (1968) 2195,
[32] L. Kisslinger, M. Aw. Harry, and D. Linsuain, Phys. Rey. C60 (1999) 065204-1
[33] H. Leutwyler, Phy. Lett. B378 (1996) 313
[34] M. Jamin, J. A. Oller, and A. Pich, Eur. Phys. J. C24 (2002) 237.
[35] Bentez M. A., Barnett R. M., and Caso C., Particle Data Group, Particle properties data booklet, April (1990) from Review of Particle Properties ", Phys. Lett. B239 (1990) April.