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Adopting the electroweak standard model, We analyzd the framework forms of photon γ and neutral gauge boson Z0 mixing-loop chain propagators and the relevant renormalization. Based on this, We obtained the analytic results of renormalized γ and Z0 mixing-loop chain propagators composed of different physical loops that participate in electroweak interactions. In addition, We applied our result to an important type of lepton interaction in high energy physics: e+e-→μ+μ-, then obtained the analytic result of cross section via renormalized γ and Z0 mixing-loop chain propagators. Furthermore, we compared the result with a series of experimental results, and found that the result of this paper is in good agreement with the experimental results. This study would offer certain academic reference to the theoretical study and application of common complex propagators.
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Keywords:
- standard model /
- chain propagator /
- renormalization /
- radiation correction
[1] Weinberg S 1967 Phys. Rev. Lett. 19 1264
[2] Dyson F J 1952 Phys. Rev. 85 631
[3] ZHU H Y 1960 Quantum Field Theory (Beijing: Science Press) pp316—356(in Chinese) [朱洪元 1960 量子场论 (北京: 科学出版社) pp316—356]
[4] Dyson F J 1949 Phys. Rev. 75 486.
[5] Zhang Z C, Xu J, Fang Z Y, Gao F, Jiang Z F, Jiang M 2007 J. Chongqing Univ. 30 95 (in Chinese) [张忠灿、徐 进、方祯云、高 飞、蒋再富、蒋 敏 2007 重庆大学学报 30 95]
[6] Jiang M, Fang Z Y, Sang W L, Gao F 2006 Chin. Phys. Lett. 23 2681
[7] Denner A, Kraus E, Roth M 2004 Phys. Rev. D 70 033002
[8] Greub C, Liniger P 2001 Phys. Rev. D 63 054025
[9] Jack I, Jones D R T, Worthy L A 2007 Phys. Rev. D 75 045014
[10] Kidonakis N, Owens J M 2001 Phys. Rev. D 63 054019
[11] Qiang L, Li G J, Chong S L 2002 Phys. Rev. D 66 115008
[12] Jin L G, Li C S, Oakes R J, Zhu S H 2000 Phys. Rev. D 62 053008
[13] OPAL Collaboration 1997 Phys. Lett. B 391 221
[14] SLC 1982 Phys. Rev. Lett. 48 1701
[15] TASSO Collaboration 1988 Z. Phys. C 40 163
[16] Mark J. 1983 Phys. Rev. Lett. 50 1238
[17] JADE Collaboration 1986 Z. Physic C 30 371
[18] L3 Collaboration 1996 Phys. Lett. B 370 195
[19] LEP(ALEPH) 1997 Phys. Lett. B 399 329
[20] Particle Data Group 2008 Phys. Lett. B 667 125, 145
[21] Zhang Z C, Zhang Y, Fang Z Y, Jiang M, Sun H J, Gao F 2005 Chongqing Univ. 28 108 (in Chinese) [张忠灿、张 宇、方祯云、蒋 敏、孙红娟、高 飞 2005 重庆大学学报 28 108]
[22] Zhang Z C, Gao F, Fang Z Y, Zhang Y, Sun H J, Jiang M 2005 Chongqing Univ. 28 101 (in Chinese) [张忠灿、高 飞、方祯云 、张 宇、孙红娟、蒋 敏 2005 重庆大学学报 28 101]
[23] Pan Y, Wang K J, Fang Z Y, Wang X Y, Peng Q J 2008 Acta Phys. Sin. 57 4817 (in Chinese) [潘 宇、王凯俊、方祯云、汪先友、彭庆军 2008 57 4817]
[24] Dyson F J 1949 Phys. Rev. 75 486
[25] Salam A 1951 Phys. Rev. 82 217
[26] Weinberg S 1960 Phys. Rev. 118 838
[27] Zimmerman W 1968 Commun. Math. Phys. 11 1
[28] Bogoliubov N N, Parasiuk O S 1957 Acta Mah. 97 208
[29] Hepp K 1966 Comm. Math. Phys. 2 301
[30] Epstein H Glaser V 1973 Ann. Phys. 77 536
[31] ’t Hooft G 1971 Nucl. Phys. B 33 173
[32] Appelquist T 1969 Ann. of Phys. 54 27
[33] Bergére M C, Zuber J B 1974 Comm. Math. Phys. 35 113
[34] Bergére M C, Lam Y M P 1974 Comm. Math. Phys. 39 1
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[1] Weinberg S 1967 Phys. Rev. Lett. 19 1264
[2] Dyson F J 1952 Phys. Rev. 85 631
[3] ZHU H Y 1960 Quantum Field Theory (Beijing: Science Press) pp316—356(in Chinese) [朱洪元 1960 量子场论 (北京: 科学出版社) pp316—356]
[4] Dyson F J 1949 Phys. Rev. 75 486.
[5] Zhang Z C, Xu J, Fang Z Y, Gao F, Jiang Z F, Jiang M 2007 J. Chongqing Univ. 30 95 (in Chinese) [张忠灿、徐 进、方祯云、高 飞、蒋再富、蒋 敏 2007 重庆大学学报 30 95]
[6] Jiang M, Fang Z Y, Sang W L, Gao F 2006 Chin. Phys. Lett. 23 2681
[7] Denner A, Kraus E, Roth M 2004 Phys. Rev. D 70 033002
[8] Greub C, Liniger P 2001 Phys. Rev. D 63 054025
[9] Jack I, Jones D R T, Worthy L A 2007 Phys. Rev. D 75 045014
[10] Kidonakis N, Owens J M 2001 Phys. Rev. D 63 054019
[11] Qiang L, Li G J, Chong S L 2002 Phys. Rev. D 66 115008
[12] Jin L G, Li C S, Oakes R J, Zhu S H 2000 Phys. Rev. D 62 053008
[13] OPAL Collaboration 1997 Phys. Lett. B 391 221
[14] SLC 1982 Phys. Rev. Lett. 48 1701
[15] TASSO Collaboration 1988 Z. Phys. C 40 163
[16] Mark J. 1983 Phys. Rev. Lett. 50 1238
[17] JADE Collaboration 1986 Z. Physic C 30 371
[18] L3 Collaboration 1996 Phys. Lett. B 370 195
[19] LEP(ALEPH) 1997 Phys. Lett. B 399 329
[20] Particle Data Group 2008 Phys. Lett. B 667 125, 145
[21] Zhang Z C, Zhang Y, Fang Z Y, Jiang M, Sun H J, Gao F 2005 Chongqing Univ. 28 108 (in Chinese) [张忠灿、张 宇、方祯云、蒋 敏、孙红娟、高 飞 2005 重庆大学学报 28 108]
[22] Zhang Z C, Gao F, Fang Z Y, Zhang Y, Sun H J, Jiang M 2005 Chongqing Univ. 28 101 (in Chinese) [张忠灿、高 飞、方祯云 、张 宇、孙红娟、蒋 敏 2005 重庆大学学报 28 101]
[23] Pan Y, Wang K J, Fang Z Y, Wang X Y, Peng Q J 2008 Acta Phys. Sin. 57 4817 (in Chinese) [潘 宇、王凯俊、方祯云、汪先友、彭庆军 2008 57 4817]
[24] Dyson F J 1949 Phys. Rev. 75 486
[25] Salam A 1951 Phys. Rev. 82 217
[26] Weinberg S 1960 Phys. Rev. 118 838
[27] Zimmerman W 1968 Commun. Math. Phys. 11 1
[28] Bogoliubov N N, Parasiuk O S 1957 Acta Mah. 97 208
[29] Hepp K 1966 Comm. Math. Phys. 2 301
[30] Epstein H Glaser V 1973 Ann. Phys. 77 536
[31] ’t Hooft G 1971 Nucl. Phys. B 33 173
[32] Appelquist T 1969 Ann. of Phys. 54 27
[33] Bergére M C, Zuber J B 1974 Comm. Math. Phys. 35 113
[34] Bergére M C, Lam Y M P 1974 Comm. Math. Phys. 39 1
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