具有T宇称的最小黑格斯模型和左右双黑格斯模型的唯象研究
|
摘要
过去几十年标准模型理论预言和实验的吻合说明粒子物理标准模型是一个描述电弱相互作用的正确理论,但是我们仍然有理由相信标准模型只能是一个低能有效理论。而在更高的能标(大约TeV)一定会有新物理出现。在众多的新物理模型中,小Higgs理论和twin Higgs理论是重要的候选者,它们解决了标准模型中的不自然性等问题。具有T宇称的最小Higgs(LHT)模型和左右双Higgs(LRTH)模型是近年来被广泛关注的两个Higgs模型,它们避免了精细调节且为宇宙中的暗物质提供一个自然的候选者。基于已经运行的大型强子对撞机LHC和计划中的国际直线对撞机ILC这两个超高能对撞机的运行环境,结合一些具体的物理过程,本论文致力于具有T宇称的最小Higgs模型和左右双Higgs模型中的新物理粒子对物理测量可能存在的一些效应,研究内容包括以下方面：
首先,我们在LHC上研究了具有T宇称的最小Higgs模型对味改变top夸克产生过程pp→tc和pp→tV(V=γ,Z,g)的贡献,并对这些过程的截面在不同的新物理模型下进行了比较,探讨通过这些过程发现LHT模型存在迹象的可能性。研究发现在模型允许的最大参数范围内,过程pp→tc和pp→tg在LHT模型下的截面预言值有可能达到LHC的探测水平。如在LHC上能探测到这些味改变过程所产生的信号,这无疑是新物理存在的明显迹象。对截面的进一步精确测量,能够为人们了解LHT模型中的自由参数,尤其是镜像夸克质量,提供有用的信息。
其次,在ILC上研究了具有T宇称的最小Higgs模型中top-charm联合产生过程,并对它们的产生截面进行了比较,数值结果表明,三个过程的截面都随镜像夸克质量的增大而迅速增大。在模型允许的最大参数范围内,过程γγ→tc和e-γ→e-tc的截面或许可以达到ILC的探测水平。如果这些过程被探测到了,就会得到味改变耦合的一些信息,以便将LHT模型从其他新物理模型中区分出来；如果这些过程没有被探测到,我们可以给出镜像夸克质量的上限。另一方面,我们也对不同的新物理模型下的这几个过程进行了对比,产生截面大小的不同将有助于我们区分不同的新物理模型。
另外,Higgs粒子的研究是当今粒子物理学最重要的课题之一。LHC的一个重要历史使命就是寻找黑格斯粒子。在LHC上,Higgs玻色子分别与Z或W玻色子联合产生的过程qq'→Z(W)H是探索标准模型质量约为120 GeV Higgs粒子的最佳过程。我们计算了LRTH模型对这两个过程产生截面的相对修正,我们发现在LRTH下合理的参数范围内,LRTH模型对这两个过程可以有足够大的贡献,有可能达到LHC实验的探测范围。这些间接的物理信号对模型中的参数能提供有价值的信息,使人们能够进一步对模型进行鉴别。
In the past few decades, the remarkable agreement of experiments with theory testifies the validity of the Standard Model (SM) in describing the electroweak physics. However, we still have some reasons to believe that the SM can only be a low energy effective theory and there must be new physics at some higher energy scale around TeV. Among various new physics models, little higgs and twin higgs theory are important candidates. The two models can solve the hierarchy problem in the SM. The littlest Higgs model with T parity (LHT) and left-right twin Higgs model (LRTH) are the Higgs models which have attracted much attention in the past few years. They avoid fine-tuning and provide a natural candidate for cosmic dark matter. Basing on the running large hadron collider (LHC) and the planning international linear collider (ILC), we focus on the phenomenological effects of new particles in the LHT and LRTH models to some processes, which include the following aspects:
We first study the contributions of the LHT model to FC top quark production processes pp→tc and pp→tV(V=γ.Z,g) at the LHC and compare cross sections of these processes in different new physics models, and discuss the potential to observe the clue of the LHT model via these FC processes. The study showed that the prediction of the LHT model on processes pp→tc and pp→tg can achieve the LHC detection level with reasonable values of the parameters. The observation of these FC processes at the LHC is certainly the clue of new physics, and further precise measurements of the cross sections can provide useful information about the free parameters in the LHT model, specially about the mirror quark masses.
Next, we investigate the top-charm associated productions via e-γin the framework of the LHT model at the ILC and compared with the process e+e-(γγ)→tc. The numerical results showed that the cross sections of the processes increase sharply as the mirror quark masses increase, and in a large part of the allowed parameter space, the cross sections ofγγ→tc and e-γ→etc may reach the detectable level at the ILC. If these processes can be observed, some information about the FC couplings can be obtained in order to distinguish the LHT model from other new physics. If these FC processes are not to be observed, the upper limit on mirror quark masses can then be given. On the other hand, we also compare these productions in every new physics model. Due to the different values of the cross sections, the top-charm production also provides a good way to distinguish the LHT model from other new physics models.
In addition, Higgs physics is one of the most important topics in particle physics nowa-days. Searching for the Higgs boson is the primary goal of the LHC. At the LHC, Higgs-boson production in association with Z or W bosons, qq'→Z(W)H,is the most promising discov-ery channel for a SM Higgs particle with a mass around 120GeV. In this paper, we estimate the corrections of the LRTH model to these processes, and our numerical results showed that, with reasonable values of the parameters in the LRTH model, the LRTH model can generate significantly contributions to these processes, which might approach the observable threshold of the LHC experiments. People can get the valuable parameters information of the models and distinguish the new models through these indirect physical signals.
首先,我们在LHC上研究了具有T宇称的最小Higgs模型对味改变top夸克产生过程pp→tc和pp→tV(V=γ,Z,g)的贡献,并对这些过程的截面在不同的新物理模型下进行了比较,探讨通过这些过程发现LHT模型存在迹象的可能性。研究发现在模型允许的最大参数范围内,过程pp→tc和pp→tg在LHT模型下的截面预言值有可能达到LHC的探测水平。如在LHC上能探测到这些味改变过程所产生的信号,这无疑是新物理存在的明显迹象。对截面的进一步精确测量,能够为人们了解LHT模型中的自由参数,尤其是镜像夸克质量,提供有用的信息。
其次,在ILC上研究了具有T宇称的最小Higgs模型中top-charm联合产生过程,并对它们的产生截面进行了比较,数值结果表明,三个过程的截面都随镜像夸克质量的增大而迅速增大。在模型允许的最大参数范围内,过程γγ→tc和e-γ→e-tc的截面或许可以达到ILC的探测水平。如果这些过程被探测到了,就会得到味改变耦合的一些信息,以便将LHT模型从其他新物理模型中区分出来；如果这些过程没有被探测到,我们可以给出镜像夸克质量的上限。另一方面,我们也对不同的新物理模型下的这几个过程进行了对比,产生截面大小的不同将有助于我们区分不同的新物理模型。
另外,Higgs粒子的研究是当今粒子物理学最重要的课题之一。LHC的一个重要历史使命就是寻找黑格斯粒子。在LHC上,Higgs玻色子分别与Z或W玻色子联合产生的过程qq'→Z(W)H是探索标准模型质量约为120 GeV Higgs粒子的最佳过程。我们计算了LRTH模型对这两个过程产生截面的相对修正,我们发现在LRTH下合理的参数范围内,LRTH模型对这两个过程可以有足够大的贡献,有可能达到LHC实验的探测范围。这些间接的物理信号对模型中的参数能提供有价值的信息,使人们能够进一步对模型进行鉴别。
In the past few decades, the remarkable agreement of experiments with theory testifies the validity of the Standard Model (SM) in describing the electroweak physics. However, we still have some reasons to believe that the SM can only be a low energy effective theory and there must be new physics at some higher energy scale around TeV. Among various new physics models, little higgs and twin higgs theory are important candidates. The two models can solve the hierarchy problem in the SM. The littlest Higgs model with T parity (LHT) and left-right twin Higgs model (LRTH) are the Higgs models which have attracted much attention in the past few years. They avoid fine-tuning and provide a natural candidate for cosmic dark matter. Basing on the running large hadron collider (LHC) and the planning international linear collider (ILC), we focus on the phenomenological effects of new particles in the LHT and LRTH models to some processes, which include the following aspects:
We first study the contributions of the LHT model to FC top quark production processes pp→tc and pp→tV(V=γ.Z,g) at the LHC and compare cross sections of these processes in different new physics models, and discuss the potential to observe the clue of the LHT model via these FC processes. The study showed that the prediction of the LHT model on processes pp→tc and pp→tg can achieve the LHC detection level with reasonable values of the parameters. The observation of these FC processes at the LHC is certainly the clue of new physics, and further precise measurements of the cross sections can provide useful information about the free parameters in the LHT model, specially about the mirror quark masses.
Next, we investigate the top-charm associated productions via e-γin the framework of the LHT model at the ILC and compared with the process e+e-(γγ)→tc. The numerical results showed that the cross sections of the processes increase sharply as the mirror quark masses increase, and in a large part of the allowed parameter space, the cross sections ofγγ→tc and e-γ→etc may reach the detectable level at the ILC. If these processes can be observed, some information about the FC couplings can be obtained in order to distinguish the LHT model from other new physics. If these FC processes are not to be observed, the upper limit on mirror quark masses can then be given. On the other hand, we also compare these productions in every new physics model. Due to the different values of the cross sections, the top-charm production also provides a good way to distinguish the LHT model from other new physics models.
In addition, Higgs physics is one of the most important topics in particle physics nowa-days. Searching for the Higgs boson is the primary goal of the LHC. At the LHC, Higgs-boson production in association with Z or W bosons, qq'→Z(W)H,is the most promising discov-ery channel for a SM Higgs particle with a mass around 120GeV. In this paper, we estimate the corrections of the LRTH model to these processes, and our numerical results showed that, with reasonable values of the parameters in the LRTH model, the LRTH model can generate significantly contributions to these processes, which might approach the observable threshold of the LHC experiments. People can get the valuable parameters information of the models and distinguish the new models through these indirect physical signals.
引文
[1]S. L. Glashaw, Nucl. Phys.22,579 (1961); S. Weinberg, Phys. Rev. Lett.19,1264 (1967); A. Salam, in Elementary Particle Theory, (Nobel Symp. No.8) edited by N. Svartholm (Almqvist and Wicksell, Stockholm,1968), P367.
[2]P. W. Higgs, Phys. Rev. Lett.12,132 (1964); P. W. Higgs, Phys. Rev.145,1156 (1966);F. Englert, R. Brout, Phys. Rev. Lett.13,321 (1964); G. S. Guralnik, C. R. Hagen, T. W. B. Kibble, Phys. Rev. Lett.13,585 (1964).
[3]C. L. Bennett et al, Astrophys. J. Suppl.148,1 (2003).
[4]M. Kobayashi, T. Maskawa, Prog. Theor. Phys.49,652 (1973).
[5]M. Schmaltz, D. T.-Smith. Ann. Rev. Nucl. Part. Sci.55,229 (2005).
[6]Martin F. Sohnius. Phys. Rep.128,41 (1984); H. E. Haber and G. L. Kane, Phys. Rep.117,75 (1984); H. P. Nilles, Phys. Rep.110,1 (1984); A. H. Chamseddine, R. Arnowitt and P. Nath, Phys. Rev. Lett.49,970 (1982); R. Barbieri, S. Ferrara and C. A. Savoy, Phys. Lett. B 119,343 (1982); L. Hall. J. Lykken and S. Weinberg, Phys. Rev. D 27,2359 (1983):T. E. Clark, T. K. Kuo and N. Nakagawa, Phys. Lett. B 115,26 (1982); C. S. Aulakh and R. N. Mohapatra, Phys. Rev. D 28,217 (1983); K. S. Babu and R. N. Mohapatra, Phys. Rev. Lett.70,2845 (1993).
[7]T. P. Cheng and M. Sher, Phys. Rev. D 35,3484 (1987); L. J. Hall and S. Weinberg, Phys. Rev. D 48,979 (1993); D. Atwood, L. Reina and A. Soni, Phys. Rev. D 54,3296 (1996); D. Atwood, L. Reina and A. Soni, Phys. Rev. D 55,3156 (1997); L. Reina, hep-ph/9712426; M. Sher, hep-ph/9809590:D. Bowser-Chao, K. Cheung and W. Y. Keung, Phys. Rev. D 59,115006 (1999).
[8]E. Farhi and L. Susskind, Phys. Rept.74,277 (1981).
[9]C. T. Hill, Phys. Lett. B 345,483 (1995);hep-ph/9702320. K. Lane, E. Eichten, Phys. Lett. B 352, 382 (1995).
[10]I. Antoniadis. Phys. Lett. B246,377 (1990); P. Horava and E. Witten. Nucl. Phys. B460,506 (1996); ibid.. B475,94 (1996); E. Witten.. ibid., B471,135 (1996); J. D. Lykken. Phys. Rev. D54,3693 (1995):I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali. Phys. Lett. B436,257 (1998):N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali. Phys. Lett. B429,263 (1998); Phys. Rev. D59,086004 (1999); L. Randall and R. Sundrum. Phys. Rev. Lett.83,3370 (1999); ibid.83.4690 (1999); N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali. Sci. Am.283, (2):62 (2000); M. Quiros. arXiv:hep-ph/0606153.
[11]Particle Data Group, J. Phys. G.33,1 (2006).
[12]N. Arkani-Hamed. et al, JHEP 0208,021 (2002).
[13]Z. Chacko, H. S. Goh and R. Harnik, JHEP 0601,108 (2006).
[14]H. C. Cheng and I. Low, JHEP 0408,061 (2004).
[15]I. Low, JHEP 0410,067 (2004).
[16]J. Hubisz, P. Mcadc, Phys. Rev. D 71,035016 (2005).
[17]H. C. Cheng, I. Low and L. T. Wang, Phys. Rev. D 74,055001 (2006).
[18]H. S. Goh and S. F. Su, Phys. Rev. D 75,075010 (2007).
[19]http://public.web.cern.ch/public/en/LHC/Facts-en.html,CERN FAQ-LHC the guide; http://lhc.web.cern.ch/lhc/.
[20]http://www.linearcollider.org/
[21]Y. B. Liu, X. L. Wang, and H. M. Han, Europhys. Lett.81,31001 (2008).
[22]D. B. Kaplan, H. Georgi, Phys. Lett. B 136,183 (1984); D. B. Kaplan, H. Georgi, S. Dimopoulos, Phys. Lett. B 136,187 (1984); H. Georgi, D. B. Kaplan, Phys. Lett. B 145,216 (1984).
[23]N. A. Hamed, A. G. Cohen, H. Georgi, Phys. Rev. Lett.86,4757 (2001).
[24]K. Lane, Talk given at 31st International Conference on High Energy Physics (ICHEP 2002), Amsterdam, The Netherlands,24-31 Jul 2002. Amsterdam 2002, ICHEP 731.
[25]N. Arkani-Hamed, A. G. Cohen, H. Georgi, Phys. Lett. B 513,232 (2001); A. G. Cohen, T. Gregoire, J. G. Wacker, JHEP 0208,020 (2002); I. Low, W. Skiba, D. Smith, Phys. Rev. D 66, 072001 (2002).
[26]N. Arkani-Hamed, A. G. Cohen, E. Katz, A. E. Nelson, JHEP 0207,034 (2002); S. Chang, JHEP 0312,057 (2003); A. J. Buras, A. Poschenrieder and S. Uhlig, Nucl. Phys. B 716,173 (2005); A. J. Buras, A. Poschenrieder, S. Uhlig and W. A. Bardeen. JHEP 0611,062 (2006).
[27]T. Han, H. E. Logan, B. McElrath and L. T. Wang, Phys. Rev. D 67,095004 (2003):T. Han, H. E. Logan and L. T. Wang, JHEP 0601,099 (2006); M. Perelstein, Prog. Part. Nucl. Phys 58,247 (2007).
[28]S. R. Coleman and E. Weinberg, Phys. Rev. D 7,1888 (1973). R. Jackiw, Phys. Rev. D 9,1686 (1974).
[29]M. Perelstein, Prog. Part. Nucl. Nucl. Phys 58,247 (2007).
[30) J. Iliopoulos, C. Itzykson, A. Martin, Rev. Mod. Phys.47,165 (1975); Les Houches School 1976:0115; S. Y. Lee, A. M. Sciaccaluga, Nucl. Phys. B 96,435 (1975).
[31]C. Csaki, J. Hubisz, G. D. Kribs et al., Phys. Rev. D 67,115002 (2003); J. L. Hewett, F. J. Petriello, and T. G. Rizzo, JHEP 0310,062(2003).
[32]C. Csaki, J. Hubisz, G. D. Kribs et al, Phys. Rev. D 68,035009 (2003).
[33]M. C. Chen, S. Dawson, Phys. Rev. D 70,015003 (2004); W. Kilian and J. Reuter, Phys. Rev. D 70,015004 (2004).
[34]G. Marandella, C. Schappacher, and A. Strumia, Phys. Rev. D 72,035014 (2005).
[35]H. C. Cheng and I. Low, JHEP 0309,051 (2003).
[36]J. Hubisz, P. Meade, A. Noble and M. Perelstein, JHEP 0601.135 (2006); S. Matsumoto. T. Moroi and K. Tobe, Phys. Rev. D 78,055018 (2008).
[37]J. Hubisz, S. J. Lee, G. Paz, JHEP 0606,041 (2006).
[38]M. Blanke, A. J. Buras, A. Poschenrieder, C. Tarantino, S. Uhlig, A. Weiler, JHEP 0612,003 (2006).
[39]C. R. Chen, K. Tobe and C. P. Yuan, Phys. Lett. B 640,263 (2006).
[40]B. Pontecorvo, Sov. Phys. JETP 6,429 (1957); Sov. Phys. JETP 7,172 (1958):Z. Maki, M. Nakagawa, S. Sakata, Prog, Theor. Phys.28,870 (1962).
[41]M. Blanke, A. J. Buras, A. Poschenrieder, S. Recksiegel, C. Tarantino, S. Uhlig, A. Weiler, JHEP 0701,066 (2007).
[42]M. Blanke, A. J. Buras, A. Poschenrieder, S. Recksiegel, C. Tarantino, S. Uhlig, A. Weiler, Phys. Lett. B 646,253 (2007).
[43]Z. Chacko. H. S. Goh and R. Harnik, Phys. Rev. Lett.96,231802 (2006).
[44]J. C. Pati and A. Salam, Phys. Rev. D 10,275 (1974); R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11,566 (1975); R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11,2558 (1975).
[45]E. M. Dolle, S. F. Su, Phys. Rev. D 77,075013 (2008).
[46]C. T. Hill and E. H. Simmons, Phys. Rept.381,235 (2003)[Erratum-ibid.390,553 (2004)]; C.-P. Yuan, hep-ph/0203088; E. Simmons, hep-ph/0211335; S. Willenbrock, hep-ph/0211067; D. Chakraborty, J. Konigsberg, D. Rainwater, hep-ph/0303092.
[47]J. Brau, Y. Okada, and N. Walker, arXiv:0712.1950; A. Djouadi et al., arXiv:0709.1893; N. Phinney, N. Toge, and N. Walker, arXiv:0712.2361; T. Behnke, C. damerell, J. Jaros, et al., arXiv:0712.2356.
[48]K. Abe et al., (ACFA Linear Collider Working Group), hep-ph/0109166.
[49]G. Eilam, J. L. Hewett, A. Soni, Phys. Rev. D 44,1473 (1991); B. Mele, S. Petrarca, A. Soddu, Phys. Lett. B 435 401 (1998); A. Cordero-Cid, J. M. Hernandez, G. Tavares-Velasco et al., Phys. Rev. D 73 094005 (2006):G. Eilam, M. Frank, I. Turan, Phys. Rev. D 73 053011 (2006).
[50]C. S. Li. R. J. Oakes, J. M. Yang, Phys. Rev. D 49,293 (1994); G. Couture, C. Hamzaoui, H. Konig, Phys. Rev. D 52,1713 (1995); J. L. Lopez, D. V. Nanopoulos, R. Rangarajan, Phys. Rev. D 56,3100 (1997); G. M. de Divitiis, R. Petronzio, L. Silvestrini, Nucl. Phys. B 504,45 (1997); J. M. Yang, B.-L. Young, X. Zhang, Phys. Rev. D 58,055001 (1998);J. J. Liu, C. S. Li, L. L. Yang, L. G. Jin, Phys. Lett. B 599,92 (2004); M. Frank and I. Turan, Phys. Rev. D 74,073014 (2006); J. M. Yang, C. S. Li, Phys. Rev. D 49,3412 (1994); J. Guasch, J. Sola, Nucl. Phys. B 562. 3 (1999); G. Eilam, A. Gcmintern. T. Han et al., Phys. Lett. B 510,227 (2001); J. L. Diaz-Cruz, H.-J. He, C.-P. Yuan, Phys. Lett. B 179.530 (2002); D. Delepine and S. Khalil, Phys. Lett. B 599,62 (2004).
[51]X. L. Wang. G. R. Lu, J. M. Yang et al., Phys. Rev. D 50,5781 (1994);C. X. Yue, G. R. Lu, Q. J. Xu et al., Phys. Lett. B 508,290 (2001); G. R. Lu, F. R. Yin, X. L. Wang, L. D. Wan, Phys. Rev. D68,015002 (2003); H. J. Zhang, arXiv:07120151.
[52]J. J. Cao, G. Eilam, M. Frank, K. Hikasa, G. L. Liu. I. Turan. and J. M. Yang, Phys. Rev. D 75. 075021 (2007).
[53]J. J. Liu, C. S. Li, L. L.Yang, L. G. Jin, Nucl. Phys. B 705,3 (2005):G. Eilam, M. Frank and I. Turan, Phys. Rev. D 74,035012 (2006):J. Guasch. W. Hollik, S. Oenaranda, J. Sola, Nucl. Phys. Proc. Suppl.157,152 (2006); D. Lopez-Val, J. Guasch,J. Sola, hcp-ph/07100587.
[54]J. Cao, Z. Xiong, J. M. Yang, Phys. Rev. D 67,071701 (2003); J. Cao, G. L. Liu, J. M. Yang, H. J. Zhang, Phys. Rev. D 76,014004 (2007):G. L. Liu and H. J. Zhang, hep-ph/07081553.
[55]J. Cao, Z. Xiong, and J. M. Yang, Nucl. Phys. B 651,87 (2003); C. S. Li, X. Zhang, and S. H. Zhu, Phys. Rev. D 60,077702 (1999).
[56]Z. H. Yu, H. Pietschmann, W. G. Ma, et.al., Eur. Phys. J. C 16,541 (2000).
[57]D. Atwood, L. Reina and A. Soni, Phys. Rev. D 53,1199 (1996):S. Bar-Shalom, G. Eilam, A. Soni and J. Wudka, Phys. Rev. Lett.79,1217 (1997); Phys. Rev. D 57,2957 (1998); D. Atwood, L. Reina and A. Soni, Phys. Rev. D 55,3156 (1997):W.-S. Hou, G.-L. Lin and C.-Y. Ma, Phys. Rev. D 56,7434 (1997); Y. Jiang, M. L. Zhou, W. G. Ma, et.al., Phys. Rev. D 57,4343 (1998); W. S. Hou and G. L. Lin, Phys. Lett. B 379,261 (1996).
[58]C. Yuc, Y. Dai, Q. Xu, G. Liu, Phys. Lett. B 525,301 (2002); C. Yue, G. R. Lu, J. Cao, J. Li, G. Liu, Phys. Lett. B 496,93 (2000).
[59]J. Cao, G. Liu, J. M. Yang, Eur. Phys. J. C 41,381 (2005).
[60]T. Han and J. L. Hewett, Phys. Rev. D 60,074015 (1999);J. A. Aguilar-Saavcdra, Phys. Lett. B 502,115 (2001); J. A. Aguilar-Saavedra, T. Riemann, hep-ph/0102197.
[61]S. Bar-Shalom and J. Wudka, Phys. Rev. D 60,094016 (1999); V. F. Obraztsov, S. R. Slabospitsky and O. P. Yushchenko, Phys. Lett. B 426,393 (1998):U. Mahanta and A. Ghosal, Phys. Rev. D 57,1735 (1998).
[62]H. J. He and C. P. Yuan, Phys. Rev. Lett.83,28 (1999); G. Burdman, Phys. Rev. Lett.83,2888 (1999); J. Cao, G. Liu, J. M. Yang, Phys. Rev. D 70,114035 (2004); F. Larios and F. Penunuri, Jour. Phys. G 30,895 (2004); X. L. Wang, Y. L. Yang, B. Z. Li, C. X. Yue, J. Y. Zhang, Phys. Rev. D 66,075009 (2002); X. L. Wang, B. Z. Li, Y. L. Yang, Phys. Rev. D 68,115003 (2003); W. Xu, X. L. Wang, Z. J. Xiao, Eur. Phys. J. C 51,891 (2007).
[63]C. S. Huang, X. H. Wu and S. H. Zhu, Phys. Lett. B 452,143 (1999); C.-H Chang et al., Phys. Lett. B 313,389 (1993); A. Axelrod, Nucl. Phys. B 209,349 (1982):M. Clements et al., Phys. Rev. D 27,570 (1983); V. Ganapathi et al., Phys. Rev. D 27,579 (1983); G. Eilam, Phys. Rev. D 28,1202 (1983).
[64]H. S. Hou, Phys. Rev. D 75,094010 (2007).
[65]C. X. Yue, J. Wen, J. Y. Liu, W. Liu, Chin. Phys. C 33,89 (2009).
[66]X. L. Wang, H. L. Jin, Y. J. Zhang, Y. H. Xi, Nucl. Phys. B 807,210 (2009).
[67]X. L. Wang, Y.J. Zhang, H. L. Jin, Y. H. Xi. Nucl. Phys. B 810,226 (2009).
[68]Y. J. Zhang. G. R. Lu, X. L. Wang, Phys. Rev. D 83,074016 (2011).
[69]M. Blanke, A. J. Buras, A. Poschenrieder, JHEP 0701,066 (2007).
[70) J. Pumplin. A. Belyaev, J. Huston, et.al., JHEP 0602,032 (2006).
[71]张闯.γ光子对撞机[J].现代物理知识,2000,12(4)：19-21：傅恩生.光子对撞机研究进展[J].激光与光电子学进展,2004,41(2)：24-29.
[72]G. Jikia, Nucl. Phys. B374,83 (1992); O. J. P. Eboli, M. C. Gonzalez-Garcia, F. Halzen, S.F. Novaes, Phys. Rev. D 47,1889 (1993); K. M. Cheung, Phys. Rev. D 47,3750 (1993).
[73]K. Hagiwara and D. Zeppenfeld, Nucl. Phys. B 313,560 (1989); V. Barger, T. Han and D.Zeppenfeld, Phys. Rev. D 41,2782 (1990).
[74]J. Hubisz, S. J. Lee and G. Paz, JHEP 0606,041 (2006).
[75]J. Hubisz, P. Meade, A. Noble, et.al., JHEP 0601,135 (2006).
[76]T. Han, R. D. Peccei, and X. Zhang, Nucl. Phys. B 454,527 (1995); L. Chikovani and T. Djobava, hep-ex/0205016; M. Beneke et al., hep-ph/0003033; T. Han, K. Whisnant, B. L. Young, and X. Zhang, Phys. Rev. D 55,7241 (1997).
[77]T. Stelzer, Z. Sullivan, and S. Willenbrock, Phys. Rev. D 58,094021 (1998); T. Han, M. Hosch, K. Whisnant, B. L. Young, and X. Zhang, Phys. Rev. D 58,073008 (1998).
[78]F. del Aguila and J. A. Aguilar-Saavedra, Nucl. Phys. B576,56 (2000).
[79]Y. Jiang, M. L. Zhou, W. G. Ma, et.al., Phys. Rev. D 57,4343 (1998); W. S. Hou and G. L. Lin, Phys. Lett. B 379,261 (1996).
[80]D. Atwood, L. Reina and A. Soni, Phys. Rev. D 53,1199 (1996); S. Bar-Shalom, G. Eilam, A. Soni, et.al., Phys. Rev. Lett.79,1217 (1997):Phys. Rev. D 57,2957 (1998):D. Atwood, L. Reina and A. Soni, Phys. Rev. D 55,3156 (1997); W. S. Hou, G. L. Lin and C. Y. Ma, Phys. Rev. D 56, 7434 (1997).
[81]K. J. Abraham, K. Whisnant, B. L. Yang, Phys. Lett. B 419,381 (1998).
[82]S. L. Glashow, D. V. Nanopoulos, and A. Yildiz, Phys. Rev. D 18,5 (1978); A. Stange, W. Marciano, and S. Willenbrock. Phys. Rev. D 50,7 (1994).
[8.3]M. L. Ciccolini, S. Dittmaier, and and M. Kramer, Phys. Rev. D 68,073003 (2003); O. Brein, M. Ciccolini, S. Dittmaier, A. Djouadi, R. Harlander and M.Kramer, hep-ph/0402003.
[84]M. Y. Hussein, Nucl. Phys. B 174,55 (2007).
[85]Y. J. Zhang, G. R. Lu, unpublished.
[86]M. Carena,.1. S. Conway, H. E. Habcr. et.al. (R.cport of the Tcvatron Higgs working group), hep-ph/0109166.
[87]A. Stange, W. J. Marciano and S.Willenbrock, Phys. Rev. D 49,1354 (1994); Phys. Rev. D 50, 4491 (1994).
[88]A. Stange and W. Marciano, Phys. Rev. D 50,7 (1994).
[89]J. M. Butterworth, A. R. Davison, M. Rubin, G. P. Salam, Phys. Rev. Lett.100,242001 (2008).
[90]M. Clements et al., Phys. Rev. D 27,570 (1983); A. Axelrod, Nucl. Phys. B209,349 (1982); G. Passarino and M. Veltman, Nucl. Phys. B 160,151 (1979).
[2]P. W. Higgs, Phys. Rev. Lett.12,132 (1964); P. W. Higgs, Phys. Rev.145,1156 (1966);F. Englert, R. Brout, Phys. Rev. Lett.13,321 (1964); G. S. Guralnik, C. R. Hagen, T. W. B. Kibble, Phys. Rev. Lett.13,585 (1964).
[3]C. L. Bennett et al, Astrophys. J. Suppl.148,1 (2003).
[4]M. Kobayashi, T. Maskawa, Prog. Theor. Phys.49,652 (1973).
[5]M. Schmaltz, D. T.-Smith. Ann. Rev. Nucl. Part. Sci.55,229 (2005).
[6]Martin F. Sohnius. Phys. Rep.128,41 (1984); H. E. Haber and G. L. Kane, Phys. Rep.117,75 (1984); H. P. Nilles, Phys. Rep.110,1 (1984); A. H. Chamseddine, R. Arnowitt and P. Nath, Phys. Rev. Lett.49,970 (1982); R. Barbieri, S. Ferrara and C. A. Savoy, Phys. Lett. B 119,343 (1982); L. Hall. J. Lykken and S. Weinberg, Phys. Rev. D 27,2359 (1983):T. E. Clark, T. K. Kuo and N. Nakagawa, Phys. Lett. B 115,26 (1982); C. S. Aulakh and R. N. Mohapatra, Phys. Rev. D 28,217 (1983); K. S. Babu and R. N. Mohapatra, Phys. Rev. Lett.70,2845 (1993).
[7]T. P. Cheng and M. Sher, Phys. Rev. D 35,3484 (1987); L. J. Hall and S. Weinberg, Phys. Rev. D 48,979 (1993); D. Atwood, L. Reina and A. Soni, Phys. Rev. D 54,3296 (1996); D. Atwood, L. Reina and A. Soni, Phys. Rev. D 55,3156 (1997); L. Reina, hep-ph/9712426; M. Sher, hep-ph/9809590:D. Bowser-Chao, K. Cheung and W. Y. Keung, Phys. Rev. D 59,115006 (1999).
[8]E. Farhi and L. Susskind, Phys. Rept.74,277 (1981).
[9]C. T. Hill, Phys. Lett. B 345,483 (1995);hep-ph/9702320. K. Lane, E. Eichten, Phys. Lett. B 352, 382 (1995).
[10]I. Antoniadis. Phys. Lett. B246,377 (1990); P. Horava and E. Witten. Nucl. Phys. B460,506 (1996); ibid.. B475,94 (1996); E. Witten.. ibid., B471,135 (1996); J. D. Lykken. Phys. Rev. D54,3693 (1995):I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali. Phys. Lett. B436,257 (1998):N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali. Phys. Lett. B429,263 (1998); Phys. Rev. D59,086004 (1999); L. Randall and R. Sundrum. Phys. Rev. Lett.83,3370 (1999); ibid.83.4690 (1999); N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali. Sci. Am.283, (2):62 (2000); M. Quiros. arXiv:hep-ph/0606153.
[11]Particle Data Group, J. Phys. G.33,1 (2006).
[12]N. Arkani-Hamed. et al, JHEP 0208,021 (2002).
[13]Z. Chacko, H. S. Goh and R. Harnik, JHEP 0601,108 (2006).
[14]H. C. Cheng and I. Low, JHEP 0408,061 (2004).
[15]I. Low, JHEP 0410,067 (2004).
[16]J. Hubisz, P. Mcadc, Phys. Rev. D 71,035016 (2005).
[17]H. C. Cheng, I. Low and L. T. Wang, Phys. Rev. D 74,055001 (2006).
[18]H. S. Goh and S. F. Su, Phys. Rev. D 75,075010 (2007).
[19]http://public.web.cern.ch/public/en/LHC/Facts-en.html,CERN FAQ-LHC the guide; http://lhc.web.cern.ch/lhc/.
[20]http://www.linearcollider.org/
[21]Y. B. Liu, X. L. Wang, and H. M. Han, Europhys. Lett.81,31001 (2008).
[22]D. B. Kaplan, H. Georgi, Phys. Lett. B 136,183 (1984); D. B. Kaplan, H. Georgi, S. Dimopoulos, Phys. Lett. B 136,187 (1984); H. Georgi, D. B. Kaplan, Phys. Lett. B 145,216 (1984).
[23]N. A. Hamed, A. G. Cohen, H. Georgi, Phys. Rev. Lett.86,4757 (2001).
[24]K. Lane, Talk given at 31st International Conference on High Energy Physics (ICHEP 2002), Amsterdam, The Netherlands,24-31 Jul 2002. Amsterdam 2002, ICHEP 731.
[25]N. Arkani-Hamed, A. G. Cohen, H. Georgi, Phys. Lett. B 513,232 (2001); A. G. Cohen, T. Gregoire, J. G. Wacker, JHEP 0208,020 (2002); I. Low, W. Skiba, D. Smith, Phys. Rev. D 66, 072001 (2002).
[26]N. Arkani-Hamed, A. G. Cohen, E. Katz, A. E. Nelson, JHEP 0207,034 (2002); S. Chang, JHEP 0312,057 (2003); A. J. Buras, A. Poschenrieder and S. Uhlig, Nucl. Phys. B 716,173 (2005); A. J. Buras, A. Poschenrieder, S. Uhlig and W. A. Bardeen. JHEP 0611,062 (2006).
[27]T. Han, H. E. Logan, B. McElrath and L. T. Wang, Phys. Rev. D 67,095004 (2003):T. Han, H. E. Logan and L. T. Wang, JHEP 0601,099 (2006); M. Perelstein, Prog. Part. Nucl. Phys 58,247 (2007).
[28]S. R. Coleman and E. Weinberg, Phys. Rev. D 7,1888 (1973). R. Jackiw, Phys. Rev. D 9,1686 (1974).
[29]M. Perelstein, Prog. Part. Nucl. Nucl. Phys 58,247 (2007).
[30) J. Iliopoulos, C. Itzykson, A. Martin, Rev. Mod. Phys.47,165 (1975); Les Houches School 1976:0115; S. Y. Lee, A. M. Sciaccaluga, Nucl. Phys. B 96,435 (1975).
[31]C. Csaki, J. Hubisz, G. D. Kribs et al., Phys. Rev. D 67,115002 (2003); J. L. Hewett, F. J. Petriello, and T. G. Rizzo, JHEP 0310,062(2003).
[32]C. Csaki, J. Hubisz, G. D. Kribs et al, Phys. Rev. D 68,035009 (2003).
[33]M. C. Chen, S. Dawson, Phys. Rev. D 70,015003 (2004); W. Kilian and J. Reuter, Phys. Rev. D 70,015004 (2004).
[34]G. Marandella, C. Schappacher, and A. Strumia, Phys. Rev. D 72,035014 (2005).
[35]H. C. Cheng and I. Low, JHEP 0309,051 (2003).
[36]J. Hubisz, P. Meade, A. Noble and M. Perelstein, JHEP 0601.135 (2006); S. Matsumoto. T. Moroi and K. Tobe, Phys. Rev. D 78,055018 (2008).
[37]J. Hubisz, S. J. Lee, G. Paz, JHEP 0606,041 (2006).
[38]M. Blanke, A. J. Buras, A. Poschenrieder, C. Tarantino, S. Uhlig, A. Weiler, JHEP 0612,003 (2006).
[39]C. R. Chen, K. Tobe and C. P. Yuan, Phys. Lett. B 640,263 (2006).
[40]B. Pontecorvo, Sov. Phys. JETP 6,429 (1957); Sov. Phys. JETP 7,172 (1958):Z. Maki, M. Nakagawa, S. Sakata, Prog, Theor. Phys.28,870 (1962).
[41]M. Blanke, A. J. Buras, A. Poschenrieder, S. Recksiegel, C. Tarantino, S. Uhlig, A. Weiler, JHEP 0701,066 (2007).
[42]M. Blanke, A. J. Buras, A. Poschenrieder, S. Recksiegel, C. Tarantino, S. Uhlig, A. Weiler, Phys. Lett. B 646,253 (2007).
[43]Z. Chacko. H. S. Goh and R. Harnik, Phys. Rev. Lett.96,231802 (2006).
[44]J. C. Pati and A. Salam, Phys. Rev. D 10,275 (1974); R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11,566 (1975); R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11,2558 (1975).
[45]E. M. Dolle, S. F. Su, Phys. Rev. D 77,075013 (2008).
[46]C. T. Hill and E. H. Simmons, Phys. Rept.381,235 (2003)[Erratum-ibid.390,553 (2004)]; C.-P. Yuan, hep-ph/0203088; E. Simmons, hep-ph/0211335; S. Willenbrock, hep-ph/0211067; D. Chakraborty, J. Konigsberg, D. Rainwater, hep-ph/0303092.
[47]J. Brau, Y. Okada, and N. Walker, arXiv:0712.1950; A. Djouadi et al., arXiv:0709.1893; N. Phinney, N. Toge, and N. Walker, arXiv:0712.2361; T. Behnke, C. damerell, J. Jaros, et al., arXiv:0712.2356.
[48]K. Abe et al., (ACFA Linear Collider Working Group), hep-ph/0109166.
[49]G. Eilam, J. L. Hewett, A. Soni, Phys. Rev. D 44,1473 (1991); B. Mele, S. Petrarca, A. Soddu, Phys. Lett. B 435 401 (1998); A. Cordero-Cid, J. M. Hernandez, G. Tavares-Velasco et al., Phys. Rev. D 73 094005 (2006):G. Eilam, M. Frank, I. Turan, Phys. Rev. D 73 053011 (2006).
[50]C. S. Li. R. J. Oakes, J. M. Yang, Phys. Rev. D 49,293 (1994); G. Couture, C. Hamzaoui, H. Konig, Phys. Rev. D 52,1713 (1995); J. L. Lopez, D. V. Nanopoulos, R. Rangarajan, Phys. Rev. D 56,3100 (1997); G. M. de Divitiis, R. Petronzio, L. Silvestrini, Nucl. Phys. B 504,45 (1997); J. M. Yang, B.-L. Young, X. Zhang, Phys. Rev. D 58,055001 (1998);J. J. Liu, C. S. Li, L. L. Yang, L. G. Jin, Phys. Lett. B 599,92 (2004); M. Frank and I. Turan, Phys. Rev. D 74,073014 (2006); J. M. Yang, C. S. Li, Phys. Rev. D 49,3412 (1994); J. Guasch, J. Sola, Nucl. Phys. B 562. 3 (1999); G. Eilam, A. Gcmintern. T. Han et al., Phys. Lett. B 510,227 (2001); J. L. Diaz-Cruz, H.-J. He, C.-P. Yuan, Phys. Lett. B 179.530 (2002); D. Delepine and S. Khalil, Phys. Lett. B 599,62 (2004).
[51]X. L. Wang. G. R. Lu, J. M. Yang et al., Phys. Rev. D 50,5781 (1994);C. X. Yue, G. R. Lu, Q. J. Xu et al., Phys. Lett. B 508,290 (2001); G. R. Lu, F. R. Yin, X. L. Wang, L. D. Wan, Phys. Rev. D68,015002 (2003); H. J. Zhang, arXiv:07120151.
[52]J. J. Cao, G. Eilam, M. Frank, K. Hikasa, G. L. Liu. I. Turan. and J. M. Yang, Phys. Rev. D 75. 075021 (2007).
[53]J. J. Liu, C. S. Li, L. L.Yang, L. G. Jin, Nucl. Phys. B 705,3 (2005):G. Eilam, M. Frank and I. Turan, Phys. Rev. D 74,035012 (2006):J. Guasch. W. Hollik, S. Oenaranda, J. Sola, Nucl. Phys. Proc. Suppl.157,152 (2006); D. Lopez-Val, J. Guasch,J. Sola, hcp-ph/07100587.
[54]J. Cao, Z. Xiong, J. M. Yang, Phys. Rev. D 67,071701 (2003); J. Cao, G. L. Liu, J. M. Yang, H. J. Zhang, Phys. Rev. D 76,014004 (2007):G. L. Liu and H. J. Zhang, hep-ph/07081553.
[55]J. Cao, Z. Xiong, and J. M. Yang, Nucl. Phys. B 651,87 (2003); C. S. Li, X. Zhang, and S. H. Zhu, Phys. Rev. D 60,077702 (1999).
[56]Z. H. Yu, H. Pietschmann, W. G. Ma, et.al., Eur. Phys. J. C 16,541 (2000).
[57]D. Atwood, L. Reina and A. Soni, Phys. Rev. D 53,1199 (1996):S. Bar-Shalom, G. Eilam, A. Soni and J. Wudka, Phys. Rev. Lett.79,1217 (1997); Phys. Rev. D 57,2957 (1998); D. Atwood, L. Reina and A. Soni, Phys. Rev. D 55,3156 (1997):W.-S. Hou, G.-L. Lin and C.-Y. Ma, Phys. Rev. D 56,7434 (1997); Y. Jiang, M. L. Zhou, W. G. Ma, et.al., Phys. Rev. D 57,4343 (1998); W. S. Hou and G. L. Lin, Phys. Lett. B 379,261 (1996).
[58]C. Yuc, Y. Dai, Q. Xu, G. Liu, Phys. Lett. B 525,301 (2002); C. Yue, G. R. Lu, J. Cao, J. Li, G. Liu, Phys. Lett. B 496,93 (2000).
[59]J. Cao, G. Liu, J. M. Yang, Eur. Phys. J. C 41,381 (2005).
[60]T. Han and J. L. Hewett, Phys. Rev. D 60,074015 (1999);J. A. Aguilar-Saavcdra, Phys. Lett. B 502,115 (2001); J. A. Aguilar-Saavedra, T. Riemann, hep-ph/0102197.
[61]S. Bar-Shalom and J. Wudka, Phys. Rev. D 60,094016 (1999); V. F. Obraztsov, S. R. Slabospitsky and O. P. Yushchenko, Phys. Lett. B 426,393 (1998):U. Mahanta and A. Ghosal, Phys. Rev. D 57,1735 (1998).
[62]H. J. He and C. P. Yuan, Phys. Rev. Lett.83,28 (1999); G. Burdman, Phys. Rev. Lett.83,2888 (1999); J. Cao, G. Liu, J. M. Yang, Phys. Rev. D 70,114035 (2004); F. Larios and F. Penunuri, Jour. Phys. G 30,895 (2004); X. L. Wang, Y. L. Yang, B. Z. Li, C. X. Yue, J. Y. Zhang, Phys. Rev. D 66,075009 (2002); X. L. Wang, B. Z. Li, Y. L. Yang, Phys. Rev. D 68,115003 (2003); W. Xu, X. L. Wang, Z. J. Xiao, Eur. Phys. J. C 51,891 (2007).
[63]C. S. Huang, X. H. Wu and S. H. Zhu, Phys. Lett. B 452,143 (1999); C.-H Chang et al., Phys. Lett. B 313,389 (1993); A. Axelrod, Nucl. Phys. B 209,349 (1982):M. Clements et al., Phys. Rev. D 27,570 (1983); V. Ganapathi et al., Phys. Rev. D 27,579 (1983); G. Eilam, Phys. Rev. D 28,1202 (1983).
[64]H. S. Hou, Phys. Rev. D 75,094010 (2007).
[65]C. X. Yue, J. Wen, J. Y. Liu, W. Liu, Chin. Phys. C 33,89 (2009).
[66]X. L. Wang, H. L. Jin, Y. J. Zhang, Y. H. Xi, Nucl. Phys. B 807,210 (2009).
[67]X. L. Wang, Y.J. Zhang, H. L. Jin, Y. H. Xi. Nucl. Phys. B 810,226 (2009).
[68]Y. J. Zhang. G. R. Lu, X. L. Wang, Phys. Rev. D 83,074016 (2011).
[69]M. Blanke, A. J. Buras, A. Poschenrieder, JHEP 0701,066 (2007).
[70) J. Pumplin. A. Belyaev, J. Huston, et.al., JHEP 0602,032 (2006).
[71]张闯.γ光子对撞机[J].现代物理知识,2000,12(4)：19-21：傅恩生.光子对撞机研究进展[J].激光与光电子学进展,2004,41(2)：24-29.
[72]G. Jikia, Nucl. Phys. B374,83 (1992); O. J. P. Eboli, M. C. Gonzalez-Garcia, F. Halzen, S.F. Novaes, Phys. Rev. D 47,1889 (1993); K. M. Cheung, Phys. Rev. D 47,3750 (1993).
[73]K. Hagiwara and D. Zeppenfeld, Nucl. Phys. B 313,560 (1989); V. Barger, T. Han and D.Zeppenfeld, Phys. Rev. D 41,2782 (1990).
[74]J. Hubisz, S. J. Lee and G. Paz, JHEP 0606,041 (2006).
[75]J. Hubisz, P. Meade, A. Noble, et.al., JHEP 0601,135 (2006).
[76]T. Han, R. D. Peccei, and X. Zhang, Nucl. Phys. B 454,527 (1995); L. Chikovani and T. Djobava, hep-ex/0205016; M. Beneke et al., hep-ph/0003033; T. Han, K. Whisnant, B. L. Young, and X. Zhang, Phys. Rev. D 55,7241 (1997).
[77]T. Stelzer, Z. Sullivan, and S. Willenbrock, Phys. Rev. D 58,094021 (1998); T. Han, M. Hosch, K. Whisnant, B. L. Young, and X. Zhang, Phys. Rev. D 58,073008 (1998).
[78]F. del Aguila and J. A. Aguilar-Saavedra, Nucl. Phys. B576,56 (2000).
[79]Y. Jiang, M. L. Zhou, W. G. Ma, et.al., Phys. Rev. D 57,4343 (1998); W. S. Hou and G. L. Lin, Phys. Lett. B 379,261 (1996).
[80]D. Atwood, L. Reina and A. Soni, Phys. Rev. D 53,1199 (1996); S. Bar-Shalom, G. Eilam, A. Soni, et.al., Phys. Rev. Lett.79,1217 (1997):Phys. Rev. D 57,2957 (1998):D. Atwood, L. Reina and A. Soni, Phys. Rev. D 55,3156 (1997); W. S. Hou, G. L. Lin and C. Y. Ma, Phys. Rev. D 56, 7434 (1997).
[81]K. J. Abraham, K. Whisnant, B. L. Yang, Phys. Lett. B 419,381 (1998).
[82]S. L. Glashow, D. V. Nanopoulos, and A. Yildiz, Phys. Rev. D 18,5 (1978); A. Stange, W. Marciano, and S. Willenbrock. Phys. Rev. D 50,7 (1994).
[8.3]M. L. Ciccolini, S. Dittmaier, and and M. Kramer, Phys. Rev. D 68,073003 (2003); O. Brein, M. Ciccolini, S. Dittmaier, A. Djouadi, R. Harlander and M.Kramer, hep-ph/0402003.
[84]M. Y. Hussein, Nucl. Phys. B 174,55 (2007).
[85]Y. J. Zhang, G. R. Lu, unpublished.
[86]M. Carena,.1. S. Conway, H. E. Habcr. et.al. (R.cport of the Tcvatron Higgs working group), hep-ph/0109166.
[87]A. Stange, W. J. Marciano and S.Willenbrock, Phys. Rev. D 49,1354 (1994); Phys. Rev. D 50, 4491 (1994).
[88]A. Stange and W. Marciano, Phys. Rev. D 50,7 (1994).
[89]J. M. Butterworth, A. R. Davison, M. Rubin, G. P. Salam, Phys. Rev. Lett.100,242001 (2008).
[90]M. Clements et al., Phys. Rev. D 27,570 (1983); A. Axelrod, Nucl. Phys. B209,349 (1982); G. Passarino and M. Veltman, Nucl. Phys. B 160,151 (1979).