b→s无粲衰变唯象研究及新物理探索
|
摘要
粒子物理的标准模型(Standard Model)是描述强相互作用和电弱相互作月丁的规范理论。它是迄今为止描述微观粒予相互作用规律的最完美的理论之一。然而，标准模型并不是完美无缺的，它所存在的某螳问题至今还没有得到合理的解决。这丧明粒子物理的际准模型并不是一个终极的理沦，它应该是某一能标下的一个低能有效理沦，这就为超出标准模型的新物理留出了发展的空间，即在更高的能标下应该有更基本的理论出现。重昧物理，尤其是B物理，是检验际准模型、探索CP破坏的起源以及寻找新物理的理想场所。因此，在近几十年来，对B介子衰变的研究成为一个非常热门和前沿的领域。
本文主要针对当前存在问题的一B介子衰变过程进行了详细的研究和分折，并适时引入新物理以寻求解决方案。．首先，我们简要慨述了粒子物理的际准模型，其中包括cKM矩阵和幺正三角形以及重正化群理论等基础内容。其次，我们回顾了与B介子衰变相关的低能有效哈密顿量，并详细介绍了QCD因子化方法。最后是我们论文的主体部分，其中包括下面几部分：
首先，在QCD因子化框架下，针对其巾旁观者和湮灭图贡献中存在的端点发散问题，我们采用一种新颖的红外有限的胶子传播子形式熏新计算了B→PP，PV衰变的旁观者和湮灭图振幅。存这部分，我们详细的讨论了该方案对旁观者和潭灭图贡献的大小和其中的强相位的影响。接着：结合最新的关于B→πK，πK~*和ρK衷变的实验数据，使用QCD因子化方法，我们对其存在的“πK puzzle”问题进行了研究。我们引入了一组模型无关的(赝-)标量耦台形式的算符(?)(1+γ_5)b(?)(?)(1 +γ_5)q (q=u,d)来解决这问题。我们的结果表明，在我们所拟合的新物理参数空间内，所有12个衰变道相关的物理可观测最都町以和实验结果达到很好的一致。很自然的，“πK puzzle”问题也得到了解决。
接着，我们详细地介绍了本文使用较多的非普适z'模型，并对于同洋的“πK puzzle”问题进行了进一步的研究。我们利用最新的实验数据对z'模型中的新物理参数进行了较以往更加严格的限制并分为五种情况对该新物理模型中的耦合进行了讨论。我们的结果表明，在该模型下，一个新的约为-86°的弱相位对解决“πK puzzle”问题起到关键作用。
同样是b→s过程的B_s-(?)_s混合，B_s→μ~+μ~－和B→X_sμ~+μ~-衰变对新物理也十分的敏感。最近的CDF和Do实验组的实验报告都指出了在B_s系统中存在着新的cP破坏的迹象。结合我们在代非普适z'模型中对B→πK,πK~*和ρK的研究结果，我们对B_s-(?)_s混合和B→X_sμ~+μ~-衰变过程进行研究，得到了较以往更加精确的b-s-Z'和μ-μ-Z'耦合的数值结果。我们发现B_s-(?)_s混合问题可以在代非普适Z'模型中得到解决，并且满足B→X_sμ~+μ~-衰变的实验限制。利用对B_s-(?)_s混合和B→X_sμ~+μ~-衰变过程的分析结果，为了寻求B→K~*μ~+μ~-衰变在低能区存在的前后不对称问题的解决方案，我们进一步对代非普适Z'模型的影响进行了研究，并得到了不同耦合形式之间的大小关系。但是，由于B→X_sμ~+μ~-对μ-μ-Z'耦合的严格限制，我们发现B→K~*μ~+μ~-衰变在低能区的前后不对称的理论预言可以在解s1(s2)中被z'贡献提高80％(50％)，但是仍然很难在(?)误差范围内和实验结果达到一致。
除了B介子系统，π,η→ι~+ι~-等一些已被理论和实验精确检验的衰变道也给我们检验新物理提供了优良的场所。最近HyperCP实验组声称在∑~+→pμ~+μ~-衰变中发现了一个质量为214.3Mev的中性标量介子P~0。这一粒子被指出有可能足次最小超对称模型(NMSSM)中的轻的CP为奇的希格斯A~0_1。对于这一问题，我们结合”π~0→e~+e~-，γγ，r→γA~0_1衰变和α_μ对NMSSM模型中的轻希格斯A~0_1进行了限制和研究。我们的结果表明，在低于7.8GeV的范围内并不能找到一个符合上述衰变限制的希格斯。并且，π~0→e~+e~-衰变中所存在的分支比问题也很难在NMSSM模型中解决。
The Standard Model (SM) of elementary particles is a theory based on the gauge group,which purports to describe the strong and electroweak interactions of fundamental parti-cles. Until now, it is the best theory for describing the dynamics of fundamental particles.However, the SM itself is not perfect, because there are also some problems that haven’tbeen solved reasonably yet, which indicates that the SM is not an ultimate theory but ane?ective theory at low scale. It provides room for developing new physics (NP) beyondthe SM, i.e. at the higher energy scale, there should exit some new and more basic theory.Heavy flavor physics, especially B physics, is a perfect region for testing SM, pursuingthe origin of the CP violation and searching for possible NP. Accordingly, the study ofB-meson decays is one of the currently very active researching fields.
In this thesis, we focus on some current very interesting puzzles in B meson decaysand pursue possible solutions with NP e?ects. Firstly, we briely introduce SM and somebasic concepts, including the CKM matrix, unitarity triangle, renormalization group andso on. Secondly, we review the low-energy e?ctive Hamiltonian relevant to B-mesondecays and various aspects of the QCD factorization approach. Finally, we present themain body of the thesis, which is composed of the following parts:
Firstly, within the QCD factorization framework, for B→PPˉPV processes, wequote a new infrared finite gluon propagator as an alternative to regulate the end-pointdivergency, which exist in the hard spectator corrections and annihilation contributins.In this part, we focus on the e?ects of such new scheme on the strength and strongphase in hard spectator corrections and annihilation contributions. Combining the up-to-date experiment measurment for B→πK,πK~*andρK decays, within the QCDfactorization framework, we analyze the existing“πK puzzle”. We introduce a group ofmodel independent (pseudo-)scalar operators (?)(1 +γ_5)b(?)(?)(1 +γ_5)q (q=u,d) for possiblesolution. Our numerical results show that, within the allowed NP parameter space, all of the obsevables of the twelve decays agree with the experimental data which implies thatthe“πK puzzle”coulde be resolved with the contribution of (peudo-)scalar operators.
After introducing a family nonuniversal Z' model in detail, we revisit the“πK puzzle”for possible solution within such a model. With the up-to-date experimental data, weperform a fit on the Z' couplings in five different cases. Our fitting results indicate thata new weak phase-86°, which is relevant to b-s-Z'coupling, is crucial to the obseved“πK puzzle”.
B_s-(?)_s mixing, B_s→μ~+μ~-and B→X_sμ~+μ~-decays, which also involve b→s transition, are sensitive to NP effects. Recently, both CDF and D0 collaborationsannounced a new CP violation evidence in B_s system. With the fitting results for afamily nonuniversal Z' couplings in B→πK,πK~*andρK decays, We study their effectson B_s-(?)_s mixing, B_s→μ~+μ~-and B→X_sμ~+μ~- decays, and get a more accurateb-s-Z'andμ-μ-Z' couplings than the previous works. We find the discrepancybetween the SM prediction and experimental measurment of B_s-(?)_s mixing could bebridged by Z' contribution without violating the bounds from the other decays. Motivatedby the observed mismatches between the SM prediction and experimental measurmentfor the forward-backward in B→K~* decay, which involvs b→s transion also, weperform a further analysis for a family nonuniversal Z' couplings’effects. We find theforward-backward in B→K~*μμdecay could be enhanced about 80%（50%）by Z'contributions at low q~2 regions in the allowed new coupling space. However, due to thestrong constaints from B→X_sμ~+μ~- on theμ-μ-Z' coupling, such result also can’tagree with the experimental data within 1σerror.
Besides B-meson system, some decays such asπ,η→ι~+ι~-, which have been measuredexactly, also provide a fertile ground for testing SM and possbile NP. Recently, HyperCPCollaboration has observed three events for the decayΣ+→pμ~+μ~-with a narrow rangeof dimuon masses, which may indicate that the decay proceeds via a neutral intermediatestate,Σ+→pP~0, P~0→μ~+μ~-, with a P~0 mass of 214.3±0.5MeV. This particle is treated as a candidate of the light CP-odd Higgs A_1~0 in next-to-mimimal supersymmetricstandrd model (NMSSM). Combiningπ~0→e~+e~-,γγ,Υ→γA~0_1 decays with a_μ, weperform a constraint on the light CP-odd Higgs A~0_1 and find that below 7.8GeV there isnot a suitable new pseudoscalar to fulfill the constraints. Moreover, the branching ratioproblem inπ~0→e~+e~- decays also can’t be resolved within NMSSM.
本文主要针对当前存在问题的一B介子衰变过程进行了详细的研究和分折，并适时引入新物理以寻求解决方案。．首先，我们简要慨述了粒子物理的际准模型，其中包括cKM矩阵和幺正三角形以及重正化群理论等基础内容。其次，我们回顾了与B介子衰变相关的低能有效哈密顿量，并详细介绍了QCD因子化方法。最后是我们论文的主体部分，其中包括下面几部分：
首先，在QCD因子化框架下，针对其巾旁观者和湮灭图贡献中存在的端点发散问题，我们采用一种新颖的红外有限的胶子传播子形式熏新计算了B→PP，PV衰变的旁观者和湮灭图振幅。存这部分，我们详细的讨论了该方案对旁观者和潭灭图贡献的大小和其中的强相位的影响。接着：结合最新的关于B→πK，πK~*和ρK衷变的实验数据，使用QCD因子化方法，我们对其存在的“πK puzzle”问题进行了研究。我们引入了一组模型无关的(赝-)标量耦台形式的算符(?)(1+γ_5)b(?)(?)(1 +γ_5)q (q=u,d)来解决这问题。我们的结果表明，在我们所拟合的新物理参数空间内，所有12个衰变道相关的物理可观测最都町以和实验结果达到很好的一致。很自然的，“πK puzzle”问题也得到了解决。
接着，我们详细地介绍了本文使用较多的非普适z'模型，并对于同洋的“πK puzzle”问题进行了进一步的研究。我们利用最新的实验数据对z'模型中的新物理参数进行了较以往更加严格的限制并分为五种情况对该新物理模型中的耦合进行了讨论。我们的结果表明，在该模型下，一个新的约为-86°的弱相位对解决“πK puzzle”问题起到关键作用。
同样是b→s过程的B_s-(?)_s混合，B_s→μ~+μ~－和B→X_sμ~+μ~-衰变对新物理也十分的敏感。最近的CDF和Do实验组的实验报告都指出了在B_s系统中存在着新的cP破坏的迹象。结合我们在代非普适z'模型中对B→πK,πK~*和ρK的研究结果，我们对B_s-(?)_s混合和B→X_sμ~+μ~-衰变过程进行研究，得到了较以往更加精确的b-s-Z'和μ-μ-Z'耦合的数值结果。我们发现B_s-(?)_s混合问题可以在代非普适Z'模型中得到解决，并且满足B→X_sμ~+μ~-衰变的实验限制。利用对B_s-(?)_s混合和B→X_sμ~+μ~-衰变过程的分析结果，为了寻求B→K~*μ~+μ~-衰变在低能区存在的前后不对称问题的解决方案，我们进一步对代非普适Z'模型的影响进行了研究，并得到了不同耦合形式之间的大小关系。但是，由于B→X_sμ~+μ~-对μ-μ-Z'耦合的严格限制，我们发现B→K~*μ~+μ~-衰变在低能区的前后不对称的理论预言可以在解s1(s2)中被z'贡献提高80％(50％)，但是仍然很难在(?)误差范围内和实验结果达到一致。
除了B介子系统，π,η→ι~+ι~-等一些已被理论和实验精确检验的衰变道也给我们检验新物理提供了优良的场所。最近HyperCP实验组声称在∑~+→pμ~+μ~-衰变中发现了一个质量为214.3Mev的中性标量介子P~0。这一粒子被指出有可能足次最小超对称模型(NMSSM)中的轻的CP为奇的希格斯A~0_1。对于这一问题，我们结合”π~0→e~+e~-，γγ，r→γA~0_1衰变和α_μ对NMSSM模型中的轻希格斯A~0_1进行了限制和研究。我们的结果表明，在低于7.8GeV的范围内并不能找到一个符合上述衰变限制的希格斯。并且，π~0→e~+e~-衰变中所存在的分支比问题也很难在NMSSM模型中解决。
The Standard Model (SM) of elementary particles is a theory based on the gauge group,which purports to describe the strong and electroweak interactions of fundamental parti-cles. Until now, it is the best theory for describing the dynamics of fundamental particles.However, the SM itself is not perfect, because there are also some problems that haven’tbeen solved reasonably yet, which indicates that the SM is not an ultimate theory but ane?ective theory at low scale. It provides room for developing new physics (NP) beyondthe SM, i.e. at the higher energy scale, there should exit some new and more basic theory.Heavy flavor physics, especially B physics, is a perfect region for testing SM, pursuingthe origin of the CP violation and searching for possible NP. Accordingly, the study ofB-meson decays is one of the currently very active researching fields.
In this thesis, we focus on some current very interesting puzzles in B meson decaysand pursue possible solutions with NP e?ects. Firstly, we briely introduce SM and somebasic concepts, including the CKM matrix, unitarity triangle, renormalization group andso on. Secondly, we review the low-energy e?ctive Hamiltonian relevant to B-mesondecays and various aspects of the QCD factorization approach. Finally, we present themain body of the thesis, which is composed of the following parts:
Firstly, within the QCD factorization framework, for B→PPˉPV processes, wequote a new infrared finite gluon propagator as an alternative to regulate the end-pointdivergency, which exist in the hard spectator corrections and annihilation contributins.In this part, we focus on the e?ects of such new scheme on the strength and strongphase in hard spectator corrections and annihilation contributions. Combining the up-to-date experiment measurment for B→πK,πK~*andρK decays, within the QCDfactorization framework, we analyze the existing“πK puzzle”. We introduce a group ofmodel independent (pseudo-)scalar operators (?)(1 +γ_5)b(?)(?)(1 +γ_5)q (q=u,d) for possiblesolution. Our numerical results show that, within the allowed NP parameter space, all of the obsevables of the twelve decays agree with the experimental data which implies thatthe“πK puzzle”coulde be resolved with the contribution of (peudo-)scalar operators.
After introducing a family nonuniversal Z' model in detail, we revisit the“πK puzzle”for possible solution within such a model. With the up-to-date experimental data, weperform a fit on the Z' couplings in five different cases. Our fitting results indicate thata new weak phase-86°, which is relevant to b-s-Z'coupling, is crucial to the obseved“πK puzzle”.
B_s-(?)_s mixing, B_s→μ~+μ~-and B→X_sμ~+μ~-decays, which also involve b→s transition, are sensitive to NP effects. Recently, both CDF and D0 collaborationsannounced a new CP violation evidence in B_s system. With the fitting results for afamily nonuniversal Z' couplings in B→πK,πK~*andρK decays, We study their effectson B_s-(?)_s mixing, B_s→μ~+μ~-and B→X_sμ~+μ~- decays, and get a more accurateb-s-Z'andμ-μ-Z' couplings than the previous works. We find the discrepancybetween the SM prediction and experimental measurment of B_s-(?)_s mixing could bebridged by Z' contribution without violating the bounds from the other decays. Motivatedby the observed mismatches between the SM prediction and experimental measurmentfor the forward-backward in B→K~* decay, which involvs b→s transion also, weperform a further analysis for a family nonuniversal Z' couplings’effects. We find theforward-backward in B→K~*μμdecay could be enhanced about 80%（50%）by Z'contributions at low q~2 regions in the allowed new coupling space. However, due to thestrong constaints from B→X_sμ~+μ~- on theμ-μ-Z' coupling, such result also can’tagree with the experimental data within 1σerror.
Besides B-meson system, some decays such asπ,η→ι~+ι~-, which have been measuredexactly, also provide a fertile ground for testing SM and possbile NP. Recently, HyperCPCollaboration has observed three events for the decayΣ+→pμ~+μ~-with a narrow rangeof dimuon masses, which may indicate that the decay proceeds via a neutral intermediatestate,Σ+→pP~0, P~0→μ~+μ~-, with a P~0 mass of 214.3±0.5MeV. This particle is treated as a candidate of the light CP-odd Higgs A_1~0 in next-to-mimimal supersymmetricstandrd model (NMSSM). Combiningπ~0→e~+e~-,γγ,Υ→γA~0_1 decays with a_μ, weperform a constraint on the light CP-odd Higgs A~0_1 and find that below 7.8GeV there isnot a suitable new pseudoscalar to fulfill the constraints. Moreover, the branching ratioproblem inπ~0→e~+e~- decays also can’t be resolved within NMSSM.
引文
[1] S. L. Glashaw, Nucl. Phys. 22 (1961) 579.
[2] S. Weinberg,Phys. Rev.Lett. 19 (1967) 1264.
[3] A. Salam, in Elementary Particle Physics (Nobel Symposium N0.8)[J], edited by N. Svartholm (Almiqvistand Wisell, Stockholm (1968)), P367.
[4] S. W. Herb et al., Phys. Rev. Lett. 39 (1977) 252.
[5] Y. Kubota et al. [CLEO Collaboration], Nucl. Instrum. Meth. A 320 (1992) 66.
[6] D. Abbaneo et al. [ALEPH Collaboration], arXiv:hep-ex/0009052.
[7] F. Abe et al. [CDF Collaboration], Nucl. Instrum. Meth. A 271 (1988) 387; S. Abachi et al. [D0 Collabo-ration], Nucl. Instrum. Meth. A 338 (1994) 185.
[8] P. F. Harrison and H. R. Quinn [BABAR Collaboration], SLAC-R-0504.
[9] S. Mori et al. [Belle Collaboration], Nucl. Instrum. Meth. A 479 (2002)117.
[10] K. G. Wilson, Phys. Rev. 179 (1969) 1499 ; K. G. Wilson and W. Zimmermann, Comm. Math. Phys. 24(1972) 87 ; W. Zimmermann, in Proc. 1970 Brandeis Summer Institute in Theor. Phys. (Eds. S. Deser, M.Grisaru and H. Pendleton), MIT Press (1971) P396; Ann. Phys. 77 (1973) 570 ; E. Witten, Nucl. Phys. B120 (1977) 189 .
[11] K. G. Wilson, Phys. Rev. 179 (1969) 1499; K. G. Wilson and W. Zimmer-mann, Commun. Math. Phys.24 (1971) 87.
[12] E. Witten, Nucl. Phys. B 120 (1977) 189.
[13] A. Duncan, E. Eichten, J. Flynn, B. R. Hill, G. Hockney and H. Thacker, Phys. Rev. D 51 (1995) 5101.
[14] B. Y. Blok and M. A. Shifman, Sov. J. Nucl. Phys. 45 (1987) 135 [Yad. Fiz. 45 (1987) 211]; Sov. J. Nucl.Phys. 45 (1987) 301 [Yad.Fiz. 45 (1987) 478]; Nucl. Phys. B 389 (1993) 534.
[15] M. Beneke, G. Buchalla, M. Neubert and C. T. Sachrajda, Phys. Rev. Lett. 83 (1999) 1914; Nucl. Phys.B 591 (2000) 313.
[16] C. N. Yang and R. L. Mills, Phy. Rev. 96 (1954) 191.
[17] P. W. Higgs, Phys. Rev. Lett. 12 (1964) 132; Phys. Rev. 145 (1966) 1156.
[18] G.‘t Hooft, Nobel Lecture: A confrontation with infinity, Rev. Mod. Phys. 72 (2000) 333; M. Veltman,Nobel Lecture: From weak interactions to gravitation, Rev. Mod. Phys. 72 (2000) 341.
[19] S. L. Glashaw, J. Ilioponlos and L. Maiani, Phys. Rev. D 2 (1970) 1285.
[20] N. Cabibbo, Phys. Rev. Lett. 10 (1963) 531; M. Kobayashi and T. Maskawa, Prog. Theo. Phys. 49 (1973)652.
[21] For example, W. Marciano and H. Pagels, Phys Rep. 36C (1978) 137; A. J. Buras, Rev. Mod. Phys. 52(1980) 199; A. H. Muller, Phys Rep. 73C (1981) 237.
[22] H. D. Polizer, Phys Rep. 14C (1974) 129;
[23] C. Amsler et al. (Particle Data Group), Phys. Lett. B 667 (2008) 1
[24] H. Fritzsch and Z. Z. Xing, Phys. Lett. B413 (1997) 396.
[25] L. Wolfenstein, Phys. Rev. Lett. 51 (1983) 1945.
[26] J. Charles et al. (CKMfitter Group), Eur. Phys. J. C 41 (2005) 1; updated results and plots available at:http://ckmfitter.in2p3.fr..
[27] M. Bona et al. (UTfit Collaboration) JHEP 0507 (2005) 028; JHEP 0601 (2006) 081 ; online update at:http://www.utfit.org/.
[28] F. J. Dyson, Phys. Rev. D 75 (1949) 1736.
[29] W. Pauli and F. Villars, Rev. Mod. Phys. 21 (1949) 434.
[30] G.‘t Hooft and M. J. Veltman, Nucl. Phys. B 44 (1972) 189.
[31] G. Buchalla, A. G. Buras and M. E. Lautenbacher, Rev. Mod. Phys. 68 (1996) 1125; A. J. Buras, hep-ph/9806471.
[32] M. S. Chanowitz, M. Furman and I. Hinchli?e, Nucl. Phys. B 159 (1979) 225.
[33] P. Breitenlohner and D. Maison, Commun. Math. Phys. 52 (1977) 11 .
[34] A. J. Buras and P. H. Weisz, Nucl. Phys. B 33 (1990) 66.
[35] G.′t Hooft, Nucl. Phys. B 61 (1973) 455.
[36] W. A. Bardeen, A. J. Buras, D. W. Duke and T. Muta, Phys. Rev. D 18 (1978) 3998.
[37] G. C. Branco, L. Lavoura and J. P. Silva, CP Violation (Oxford University Press, Oxford, 1999); I. I. Bigiand A. I. Sanda, CP Violation (Cambridge University Press, Cambridge, 2000).
[38] Y. Nir, arXiv:hep-ph/0109090; arXiv:hep-ph/0208080; arXiv:hep-ph/0405091.
[39] D. Fakirov and B. Stech, Nucl. Phys. B 133 (1978) 315 M. Bauer and B. Stech, Phys. Lett. B 152 (1985)380; M. Wirbel, B. Stech and M. Bauer, Z. Phys. C 29, 637 (1985); M. Bauer, B. Stech and M. Wirbel, Z.Phys. C 34, 103 (1987).
[40] H. Y. Cheng and B. Tseng, Phys. Rev. D 58 (1998) 094005;
[41] Y. H. Chen, H. Y. Cheng, B. Tseng and K. C. Yang, Phys. Rev. D 60 (1999) 094014; 62 (2000) 054029;A. Ali and C. Greub, Phys. Rev. D 57 (1998) 2996; A. Ali, G. Kramer and C. D. Lu, Phys. Rev. D 58(1998) 094009; 59 (1999) 014005.
[42] H. n. Li and G. Sterman, Nucl. Phys. B 381 (1992) 129;
[43] H. n. Li, Phys. Rev. D 52, 3958 (1994). H. n. Li and H. L. Yu, Phys. Rev. D 53, 2480 (1995).
[44] H. N. Li and H. L. Yu, Phys. Lett. B 353 (1995) 301; C. H. Chang and H. n. Li, Phys. Rev. D 55 (1997)5577; T. W. Yeh and H. n. Li, Phys. Rev. D 56 (1997) 1615; C. D. Lu, K. Ukai and M. Z. Yang, Phys. Rev.D 63 (2001) 074009.
[45] C. W. Bauer, S. Fleming and M. E. Luke, Phys. Rev. D 63 (2001) 014006; C. W. Bauer, S. Fleming,D. Pirjol and I. W. Stewart, Phys. Rev. D 63 (2001) 114020; C. W. Bauer and I. W. Stewart, Phys. Lett.B 516 (2001) 134; Phys. Rev. D 65 (2002) 054022.
[46] J. D. Bjorken, Nucl. Phys. Proc. Suppl. 11 (1989) 325 ; M. J. Dugan and B. Grinstein, Phys. Lett. B 255(1991) 583 .
[47] A. J. Buras and L. Silvestrini, Nucl. Phys. B 548 (1999) 293.
[48] G. P. Lepage and S. J. Brodsky, Phys. Lett. B 87 (1979) 359 ; G. P. Lepage and S. J. Brodsky, Phys. Rev.Lett. 43 (1979) 545 ; G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22 (1980) 2157 .
[49] S. J. Brodsky, Phys. Lett. B 243, 287 (1990); H. Simma and D. Wyler, Phys. Lett. B 272 (1991) 395 ; C.E. Carlson and J. Milana, Phys. Rev. D 49 (1992) 5908.
[50] N. Isgur and C. H. Llewellyn Smith, Nucl. Phys. B 317 (1989) 526 ; A. V. Radyushkin, Nucl. Phys. A 532(1991) 141.
[51] Y. Y. Keum, H. n. Li and A. I. Sanda, Phys. Lett. B 504 (2001) 6 ; Y. Y. Keum, H. n. Li and A. I. Sanda,Phys. Rev. D 63 (2001) 054008 ; Y. Y. Keum and H. n. Li, Phys. Rev. D 63 (2001) 074006 ; C. D. Lu¨,K. Ukai and M. Z. Yang, Phys. Rev. D 63 (2001) 074009 ; C. D. Lu¨and M. Z. Yang, Eur. Phys. J. C 23(2002) 275 Y. Y. Keum and A. I. Sanda, Phys. Rev. D 67 (2003) 054009.
[52] S. D. Genon and C. T. Sachrajda, Nucl. Phys. B 625 (2002) 239; Z. T. Wei and M. Z. Yang, Nucl. Phys.B 642, 263 (2002); S. D. Genon and C. T. Sachrajda, Nucl. Phys. B 650 (2003) 356.
[53] C. W. Bauer, D. Pirjol and I. W. Stewart, Phys. Rev. Lett. 87 (2001) 201806; C. W. Bauer, D. Pirjol,I. Z. Rothstein and I. W. Stewart, Phys. Rev. D 70 (2004) 054015; J. g. Chay and C. Kim, Phys. Rev. D68 (2003) 071502; Nucl. Phys. B 680 (2004) 302; A. R. Williamson and J. Zupan, Phys. Rev. D 74 (2006)014003 [Erratum-ibid. D 74 (2006) 03901].
[54] C. W. Bauer, D. Pirjol and I. W. Stewart, Phys. Rev. D 67 (2003) 071502.
[55] M. Ciuchini et al., Nucl. Phys. B 501 (1997) 271; Phys. Lett. B 515 (2001) 33; arXiv:hep-ph/0208048.
[56] C. W. Bauer, D. Pirjol, I. Z. Rothstein and I. W. Stewart, Phys. Rev. D 70 (2004) 054015; M. Beneke,G. Buchalla, M. Neubert and C. T. Sachrajda, Phys. Rev. D 72 (2005) 098501; C. W. Bauer, D. Pirjol,I. Z. Rothstein and I. W. Stewart, Phys. Rev. D 72 (2005) 098502.
[57] M. Beneke and T. Feldmann, Nucl. Phys. B 592, 3 (2001).
[58] V. M. Braun and I. E. Halperin, Z. Phys. C 44 (1989) 157 ; V. M. Braun and I. E. Halperin, Z. Phys. C48 (1990) 239 .
[59] A. G. Grozin and M. Neubert, Phys. Rev. D 55 (1997) 272.
[60] V. L. Chernyak and I. R. Zhitnitsky, Nucl. Phys. B 345 (1990) 137 .
[61] D. S. Du, D. S. Yang, and G. H. Zhu, Phys. Lett. B 488 (2000) 46; Phys. Lett. B 509 (2001) 263; Phys.Rev. D 64 (2001) 014036.
[62] H. Y. Cheng, and K. C Yang, Phys. Rev. D 63 (2001) 074011; Phys. Rev. D 64 (2001) 074004; Phys. Lett.B 511 (2001) 40.
[63] A. J. Buras, R. Fleischer, S. Recksiegel and F. Schwab, Phys. Rev. Lett. 92 (2004) 101804 ; Nucl. Phys. B697 (2004) 133; PoS HEP2005 (2006) 193.
[64] M. Beneke, G. Buchalla, M. Neubert, C. T. Sachrajda, Nucl. Phys. B 606 (2001) 245; M. Beneke andM. Neubert, Nucl. Phys. B 651 (2003) 225.
[65] M. Beneke and M. Neubert, Nucl. Phys. B 675 (2003) 333.
[66] T. Muta, A. Sugamoto, M. Z. Yang and Y. D. Yang, Phys. Rev. D 62 (2000) 094020; M. Z. Yang andY. D. Yang, Phys. Rev. D 62 (2000) 114019.
[67] H. N. Li, S. Mishima and A. I. Sanda, Phys. Rev. D 72 (2005) 114005.
[68] A. R. Williamson and J. Zupan, Phys. Rev. D 74 (2006) 014003.
[69] M. Gronau and J. L. Rosner, Phys. Rev. D 74 (2006) 057503; X. Q. Li and Y. D. Yang, Phys. Rev. D 73(2006) 114027 ; Phys. Rev. D 72 (2005) 074007; J. Chay, H. N. Li, arXiv: 0711.2953 [hep-ph]; C. W. Bauer,I. Z. Rothstein and I. W. Stewart, Phys. Rev. D 74 (2006) 034010; C. S. Kim, S. Oh, and C. Yu, Phys.Rev. D 72 (2005) 074005;
[70] S. Baek, JHEP 0607 (2006) 025; R. Arnowitt et al., Phys. Lett. B 633 (2006) 748; S. Khalil, Phys. Rev.D 72 (2005) 035007; Y. D. Yang, R. M. Wang, G. R. Lu, Phys. Rev. D 73 (2006) 015003; V. Barger,C. W. Chiang, P. Langacker and H. S. Lee, Phys. Lett. B 598 (2004) 218; W. S.Hou, M. Nagashima andA. Soddu, Phy. Rev. Lett. 95 (2005) 141601; W. S.Hou, M. Nagashima, G. Raz and A. Soddu, JHEP 0609(2006) 012; C. S. Kim, S. Oh and Y. W. Yoon, arXiv: 0707.2967 [hep-ph]; C. S. Kim, S. Oh, C. Sharma,R. Sinha and Y. W. Yoon Phys. Rev. D 76 (2007) 074019.
[71] S. W. Lin et al., Belle Collaboration, Nature 452 (2008) 332.
[72] B. Aubert et al., Babar Collaboration, Phys. Rev. Lett. 99 (2007) 021603.
[73] S. Chen et al., CLEO Collaboration , Phys. Rev. Lett. 85 (2000) 525.
[74] Michael Morello, CDF Collaboration, Nucl. Phys. Proc. Suppl. 170 (2007) 39.
[75] E. Barberio et al. (Heavy Flavor Averaging Group), arXiv: 0704.3575 [hep-ex]; and online update at:http://www.slac.stanford.edu/xorg/hfag.
[76] M. E. Peskin, Nature 452 (2008) 293.
[77] Th. Feldmann, M. Jung and Th. Mannel, arXiv: 0803.3729 [hep-ph].
[78] Th. Feldmann and T. Hurth, JHEP 0411 (2004) 037.
[79] J. M. Cornwall, Phys. Rev. D 26 (1982) 1453; J. Papavassiliou and J. M. Cornwall, Phys. Rev. D 44 (1991)1285.
[80] A. C. Aguilar, A. A. Natale and P. S. Rodrigues da Silva, Phys. Rev. Lett. 90 (2003) 152001; A. C. Aguilarand A. A. Natale, JHEP 0408 (2004) 057.
[81] L. Von Smekal, A. Hauck, and R. Alkofer, Phys. Rev. Lett. 79 (1997) 3591; R. Alkofer and L. Von Smekal,Phys. Rep. 353 (2001) 281; C. S. Fisher and R. Alkofer, Phys. Rev. D 67 (2003) 094020; R. Alkofer,W. Detmold, C. S. Fisher, and P. Maris, Nucl. Phys. Proc. Suppl. 141 (2005) 122.
[82] I. L. Bogolubsky, E. -M. Ilgenfritz, M. Mu¨ller Preussker and A. Sternbeck, PoS (LATTICE-2007) 290;A. Cucchieri and T. Mendes, PoS (LATTICE 2007) 297; P. O. Bowman et al., Phys. Rev. D 76 (2007)094505.
[83] Q. Chang, X. Q. Li and Y. D. Yang, JHEP 0706 (2007) 038.
[84] D. S. Du, J. Korean Phys. Soc. 45 (2004) S285; D. S. Du, Int. J. Mod. Phys. A 21 (2006) 658; D. S. Du,J. F. Sun, D. S. Yang and G. H. Zhu, Phys. Rev. D 67 (2003) 014023; D. S. Du, H. J. Gong, J. F. Sun,D. S. Yang and G. H. Zhu, Phys. Rev. D 65 (2002) 094025; D. S. Du, D. S. Yang and G. H. Zhu, Phys.Rev. D 64 (2001) 014036; Phys. Lett. B 509 (2001) 263; Phys. Lett. B 488 (2000) 46.
[85] D. Zwanziger, Phys. Rev. D 69 (2004) 016002; D. M. Howe andC. J. Maxwell, Phys. Lett. B 541 (2002)129; Phys. Rev. D 70 (2004) 014002; S. Furui and H. Nakajima, AIP Conf. Proc. 717, (2004) 685.
[86] S. Brodsky, S. Menke, C. Merino and J. Rathsman, Phys. Rev. D 67 (2003) 055008; A. C. Mattingly andP. M. Stevenson, Phys. Rev. D 49 (1994) 437; M. Baldicchi, G. M. Prosperi, Phys. Rev. D 66 (2002) 074008.
[87] F. Su, Y. D. Yang, G. R. Lu and H. J. Hao, Eur. Phys. J. C 44 (2005) 243; F. Su, Y. L. Wu, Y. D. Yangand C. Zhuang, Eur. Phys. J. C 48 (2006) 401; arXiv: 0705.1575 [hep-ph].
[88] A. A. Natale and C. M. Zanetti, arXiv: 0803.0154 [hep-ph].
[89] Q. Mason et al. (HPQCD Collaboration), Phys. Rev. D 73 (2006) 114501.
[90] A. Gray et al. (HPQCD Collaboration), Phys. Rev. Lett. 95 (2005) 212001.
[91] P. Ball and R. Zwicky, Phys. Rev. D 71 (2005) 014015; 71 (2005) 014029; Phys. Lett. B 633 (2006) 289.
[92] G. Eilam, M. Ladisa and Y. D. Yang, Phys. Rev. D 65 (2002) 037504.
[93] S. Baek, A. Datta, P. Hamel, O. F. Hernandez and D. London, Phys. Rev. D 72 (2005) 094008; S. Baekand D. London, Phys. Lett. B 653 (2007) 249.
[94] W. S. Hou, M. Nagashima and A. Suddu, Phys. Rev. Lett. 95 (2005) 141601.
[95] A. L. Kagan, Phys. Lett. B 601 (2004) 151.
[96] P. K. Das and K. C. Yang, Phys. Rev. D 71 (2005) 094002.
[97] H. Hatanaka and K. C. Yang, Phys. Rev. D 77 (2008) 035013.
[98] S. Nandi and A. Kundu, J. Phys. G 32 (2006) 835.
[99] M. Beneke, Phys. Lett. B 620 (2005) 143.
[100] G. Buchalla, G. Hiller, Y. Nir and G. Raz, JHEP 0509 (2005) 074.
[101] R. Fleischer, S. Jager, D. Pirjol and J. Zupan, arXiv: 0806.2900 [hep-ph].
[102] M. Gronau and J. Rosner, arXiv:0807.3080[hep-ph].
[103] James F. Hirschauer (BABAR Collaboration), talk presented at ICHEP08, the 34th International Confer-ence on High Energy Physics Philadelphia, Pennsylvania, July 30 - August 5, 2008.
[104] Jeremy P Dalseno (Belle Collaboration), talk presented ICHEP08.
[105] for example, M. Masip and A. Pomarol Phys. Rev. D 60 (1999) 096005.
[106] T. K. Kuo and N. Nakagawa, Phys. Rev. D 31 (1985) 1161;32 (1985) 306; K. K. Gan, Phys. Lett. B 209(1988) 95; E. Nardi, Phys. Rev. D 48 (1993) 1240; B. Holdom, Phys. Lett. B 339 (1994) 114; X. Zhang andB.-L. Young, Phys. Rev. D 51 (1995) 6584; B. Holdom and M. V. Ramana, Phys. Lett. B 365 (1996) 309.
[107] S. Chaudhuri, S.W. Chung, G. Hockney, and J. Lykken, Nucl. Phys. B 456 (1995) 89.
[108] G. Cleaver, M. Cvetiˇc, J.R. Espinosa, L. Everett, and P. Langacker, Nucl. Phys. B 525 (1998) 3; G. Cleaver,M. Cvetiˇc, J.R. Espinosa, L. Everett, P. Langacker, and J. Wang, Phys. Rev. D 59 (1999) 055005; 59 (1999)115003.
[109] G. Buchalla, G. Burdman, C. T. Hill and D. Kominis Phys. Rev. D 53 (1996) 5185; G. Burdman, K. D. Laneand T. Rador, Phys. Lett. B 514 (2001) 41; A. Martin and K. Lane, Phys. Rev. D 71 (2005) 015011.
[110] E. Nardi, Phys. Rev. D 48 (1993) 1240; J. Bernabeu, E. Nardi and D. Tommasini, Nucl. Phys. B 409(1993) 69; V. D. Barger, M. S. Berger and R. J. Phillips, Phys. Rev. D 52 (1995) 1663; M. B. Popovic andE. H. Simmons, Phys. Rev. D 62 (2000) 035002; T. G. Rizzo Phys. Rev. D 59 (1999) 015020.
[111] P. Langacher and M. Plu¨macher, Phys. Rev. D 62 (2000) 013006.
[112] M. S. Carena, A. Daleo, B. A. Dobrescu and T. M. P. Tait, Phys. Rev. D 70 (2004) 093009.
[113] T. G. Rizzo, hep-ph/0610104; arXiv: 0808.1906[hep-ph].
[114] V. Barger, C. W. Chiang, P. Langacker and H. S. Lee, Phys. Lett. B 598 (2004) 218.
[115] V. Barger, C. W. Chiang, P. Langacker and H. S. Lee, Phys. Lett. B 580 (2004) 186.
[116] K. Cheung, C. W. Chiang, N. G. Deshpande and J . Jiang, Phys. Lett. B 652 (2007) 285; J. H. Jeon,C. S. Kim, J. Lee and C. Yu Phys. Lett. B 636 (2006) 270; C. H. Chen and H. Hatanaka, Phys. Rev. D 73(2006) 075003.
[117] L. S. Durkin and P. Langacker, Phys. Lett. B 166 (1986) 436; P. Langacker and M. Luo, Phys. Rev. D 45(1992) 278.
[118] DELPHI Collaboration, P. Abreu et al., Z. Phys. C 65 (1995) 603; K.S. Babu and C. Kolda, The Z′Searches, in W. M. Yao, et al. [Particle Data Group], J. Phys. G 33 (2006) 1.
[119] J. Erler and P. Langacker, Phys. Lett. B 456 (1999) 68; Phys. Rev. Lett. 84 (2000) 212; J. Erler, P. Lan-gacker, S. Munir and E. R. Pena, arXiv: 0906.2435 [hep-ph]; E. Salvioni, G. Villadoro and F. Zwirner,arXiv: 0909.1320[hep-ph].
[120] N. S. Kroll, T. D. Lee, and B. Zumino, Phys. Rev. 157 (1967) 1376 ; B. Holdom, Phys. Lett. B 166 (1986)196 ; F. Del Aguila, M. Cvetiˇc and P. Langacker, Phys. Rev. D 52 (1995) 37; F. del Aguila, M. Masip,M. Perez-Victoria, Acta Phys. Polon. B 27 (1996) 1469; K. S. Babu, C. Kolda, and J. March-Russell,Phys. Rev. D 54 (1996) 4635.
[121] V M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 101 (2008) 241801.
[122] T. Aaltonen et al. (CDF Collaboration), Phys. Rev. Lett. 100 (2008) 161802.
[123] M. Bona et al., arXiv:0906.0953 [hep-ph]; M. Bona et al. (UTfit Collaboration); online update at:http://www.utfit.org/NP/NP.html.
[124] V. Niess (the CKM fitter group), talk at“Flavor Physics and CP Violation 2009”, Lake Placid, NY. onlineupdate at: http://ckmfitter.in2p3.fr/.
[125] V M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 97 (2006) 021802.
[126] H. Abulencia et al. (CDF Collaboration), Phys. Rev. Lett. 97 (2006) 242003.
[127] A. Lenz and U. Nierste, JHEP 0706 (2007) 072.
[128] Q. Chang, X. Q. Li and Y. D. Yang, JHEP 0905 (2009) 056.
[129] V. Barger, L. Everett, J. Jiang, P. Langacker, T. Liu and C. Wagner, JHEP12(2009) 048; arXiv:0902.4507[hep-ph].
[130] V. Barger, C. W. Chiang, J. Jiang, and P. Langacker, Phys. Lett. B596 (2004) 229.
[131] K. Cheung, C. W. Chiang, N. G. Deshpande and J. Jiang, Phys. Lett. B 652 (2007) 285.
[132] C. W. Chiang, R. H. Li and C. D. Lu, arXiv:0911.2399 [hep-ph]
[133] J. Hua, C. S. Kim, Y. Li, arXiv:1002.2532 [hep-ph].
[134] B. Aubert et al. (BABAR Collaboration), Phys. Rev. Lett. 93 (2004) 081802;
[135] M. Iwasaki et al. (Belle Collaboration), Phys. Rev. D 72 (2005) 092005.
[136] S. Glenn et al. (CLEO Collaboration), Phys. Rev. Lett. 80 (1998) 2289.
[137] A. J. Buras and M. Mu¨nz, Phys. Rev. D 52 (1995) 186.
[138] A. J. Buras and M. Mu¨nz, Phys. Lett. B 566 (2003) 115.
[139] A. J. Buras, arXiv:0904.4917 [hep-ph].
[140] T. Aaltonen et al. Phys. Rev. Lett. 100 (2008) 101802.
[141] Elvira Gamiz et al. (HPQCD Collaboration ), arXiv:0902.1815 [hep-lat].
[142] G. D’Ambrosio, G. F. Giudice, G. Isidori and A. Strumia, Nucl. Phys. B 645 (2002) 155.
[143] A. J. Buras, Acta. Phys. Polon. B bf 34 (2003) 5615.
[144] G. Buchalla and A. J. Buras, Nucl. Phys. B 400 (1993) 225.
[145] A. J. Buras E. Lautenbacher, M. Misiak and M. Mu¨nz, Nucl. Phys. B 423 (1994) 349.
[146] Y. Nir, Phys. Lett. B 221 (1989) 184.
[147] M. Misiak, Nucl. Phys. B393(1993) 23, Erratum-ibid B439(1995)461.
[148] M. Jezabek and J. H. Ku¨hn, Nucl. Phy. B320(1989)20.
[149] A. Ali, T. Mannel and T. Morozumi, Phys. Lett. B 273 (1991) 505.
[150] Z. Ligeti and M. B. Wise, Phys. Rev. D 53 (1996) 4937.
[151] A. Ali, G. Hiller, L. T. Handoko and T. Morozumi, Phys. Rev. D 55 (1997) 4105.
[152] F. Kru¨ger, L.M. Sehgal, Phys. Lett. B 380(1996)199.
[153] M. Beneke, G. Buchalla, M. Neubert and C. T. Sachrajda, Eur. Phys. J. C61(2009) 439.
[154] T. Huber, T. Hurth, and E. Lunghi, Nucl. Phys. B 802 (2008) 40; A. Ghinculov, T. Hurth, G. Isidori, andY. P. Yao, Nucl. Phys. B685(2004) 351.
[155] M. Bartsch, M. Beylich, G. Buchalla, and D. N. Gao, JHEP 0911 (2009) 011.
[156] C. Bobeth, G. Hiller and G. Piranishvili, JHEP 0807 106.
[157] For instance: N. G. Deshpande, J. Trampetic, Phys. Rev. Lett. 60 (1988) 2583 ; W. Jaus and D. Wyler,Phys. Rev. D 41 (1990) 3405; G. Burdman, Phys. Rev. D 52 (1995) 6400; P. Colangelo, F. De Fazio,P. Santorelli and E. Scrimieri, Phys. Rev. D 53 (1996) 3672 [Erratum-ibid. D 57 (1998) 3186]; T. M. Aliev,A. Ozpineci and M. Savci, Phys. Rev. D 56 (1997) 4260; D. Melikhov, N. Nikitin and S. Simula, Phys.Lett. B 430 (1998) 332; A. Ali, G. Kramer, G H Zhu, Eur. Phys. J. C 47 (2006) 625; C. Bobeth, G. Hiller,G. Piranishvili, JHEP 0807 (2008) 106.
[158] G. Burdman, Phys. Rev. D 57 (1998) 4254.
[159] M. Beneke, T. Feldmann and D. Seidel, Nucl. Phys. B 612 (2001) 25.
[160] A. J. Buras, M. Misiak, M. Munz and S. Pokorski, Nucl. Phys. B 424 (1994) 374.
[161] A. Ali, P. Ball, L. T. Handoko and G. Hiller, Phys. Rev. D 61 (2000) 074024.
[162] W. Altmannshofer, P. Ball, A. Bharucha, A. J. Buras, D. M. Straub and M. Wick, JHEP 0901 (2009) 019.
[163] For instance: C. Greub, A. Ioannissian and D. Wyler, Phys. Lett. B 346 (1995) 149; J. L. Hewett andJ. D. Wells, Phys. Rev. D 55 (1997) 5549; A. Ali, E. Lunghi, C. Greub,G. Hiller, Phys. Rev. D 66 (2002)034002; C. H. Chen and C. Q. Geng, Phys. Rev. D 66 (2002) 094018; T. Feldmann and J. Matias, JHEP0301 (2003) 074; G. Hiller, F. Kruger, Phys. Rev. D 69 (2004) 074020; F. Kruger and J. Matias, Phys.Rev. D 71 (2005) 094009; P. Colangelo, F. De Fazio, R. Ferrandes and T. N. Pham, Phys. Rev. D 73(2006) 115006; Y. G. Xu, R. M. Wang and Y. D. Yang, Phys. Rev. D 74 (2006) 114019; A. Hovhannisyan,W. S. Hou and N. Mahajan, Phys. Rev. D 77 (2008) 014016.
[164] B. Aubert et al. [BABAR Collaboration], Phys. Rev. D 79 (2009) 031102.
[165] B. Aubert et al. [BABAR Collaboration], Phys. Rev. Lett. 102 (2009) 091803.
[166] A. Ishikawa et al., Phys. Rev. Lett. 96 (2006) 251801.
[167] J. T. Wei et al. [BELLE Collaboration], Phys. Rev. Lett. 103 (2009) 171801.
[168] C. H. Chen, Phys. Lett. B 683 (2010) 160.
[169] A. K. Alok, A. Dighe, D. Ghosh, D. London, J. Matias, M. Nagashima and A. Szynkman, arXiv:0912.1382[hep-ph].
[170] K. G. Chetyrkin, M. Misiak and M. Munz, Phys. Lett. B 400 (1997) 206 [Erratum-ibid. B 425 (1998) 414].
[171] C. Bobeth, M. Misiak and J. Urban, Nucl. Phys. B 574 (2000) 291.
[172] C. Bobeth, A. J. Buras, F. Kru¨ger and J. Urban, Nucl. Phys. B 630 (2002) 87.
[173] T. Huber, E. Lunghi, M. Misiak and D. Wyler, Nucl. Phys. B 740 (2006) 105.
[174] C. Q. Geng and C. P. Kao, Phys. Rev. D 54 (1996) 5636.
[175] S. Drell, Nuov. Cim. XI (1959) 693.
[176] L. Bergstro¨m, Zeit. Phys. C 14 (1982) 129.
[177] K.S. Babu and E. Ma, Phys. Lett. B119 (1982) 449.
[178] L. Bergstr¨om, E. Masso, L. Ametller and A. Bramon, Phys. Lett. B 126 (1983) 117.
[179] Ll. Ametller, A. Bramon and E. Masso′Phys. Rev. D 48 (1993) 3388.
[180] M.J. Savage, M. Luke, and M.B. Wise, Phys. Lett. B291 (1992) 481.
[181] D. Go′mez Dumm and A. Pich Phys. Rev. Lett 80 (1998) 4633.
[182] M. Knecht, S. Peris and E. de Rafael Phys. Rev. Lett 83 (1999) 5230.
[183] A. E. Dorokhov and M. A. Ivanov, Phys. Rev. D 75 (2007) 114007.
[184] M. D. Scadron and M. Visinescu, Phys. Rev. D 29, (1984) 911; A. N. Kamal and L. C. Huah, Phys. Rev.D 32, (1985) 1744; G. Triantaphyllou, Mod. Phys. Lett. A 8, (1993) 1691.
[185] H. J. Behrend et al. (CELLO Collaboration), Zeit. Phys. C 49 (1991) 401.
[186] J. Gronberg et al. (CLEO Collaboration), Phys. Rev. D 57 (1998) 33.
[187] J. Fischer et al., Phys. Lett. B 73 (1978) 364.
[188] R. Niclasen, Ph.D Thesis, FERMILAB-THESIS-2006-12, UMI-32-07725. http:// lss. fnal. gov/ archive/thesis/ fermilab-thesis -2006-12. shtml.
[189] E. Abouzaid et al., KTeV Collaboration, Phys. Rev. D 75 (2007) 012004.
[190] A. E. Dorokhov and M. A. Ivanov, Eur. Phys. J. C 55 (2008) 193.
[191] A. E. Dorokhov and M. A. Ivanov, JETP Lett. 87 (2008) 531.
[192] W. Love, et al (CLEO Collaboration), arXiv:0807.2695 [hep-ex].
[193] B. Aubert, et al (BaBar Collaboration), arXiv:0808.0017 [hep-ex].
[194] H. P. Nilles, M. Srednicki and D. Wyler, Phys. Lett. B 120 (1983) 346; J. M. Frere, D. R. T. Jones andS. Raby, Nucl. Phys. B 222, (1983) 11; J. P. Derendinger and C. A. Savoy, Nucl. Phys. B 237, (1984)307; J. R. Ellis, J. F. Gunion, H. E. Haber, L. Roszkowski and F. Zwirner, Phys. Rev. D 39 (1989) 844;M. Drees, Int. J. Mod. Phys. A 4 (1989) 3635.
[195] G. Hiller, Phys. Rev. D 70 (2004) 034018.
[196] B. R. Martin, E. De Rafael and J. Smith, Phys. Rev. D 2, (1970) 179.
[197] M. Pratap and J. Smith, Phys. Rev. D 5, (1972) 2020; Z. K. Silagadze, Phys. Rev. D 74, (2006) 054003.
[198] H. K. Park, et al (HyperCP Collaboration), Phy. Rev. Lett. 94 (2005) 021801.
[199] X. G. He and J. Tandean, Phy. Rev. Lett. 98 (2007) 081802.
[200] X. G. He and J. Tandean and G. Valencia, JHEP 0806 (2008) 002.
[201] G. Valencia, arXiv:0805.3285 [hep-ph].
[202] X. G. He, J. Tandean and G. Valencia, Phys. Lett. B 631 (2005) 100.
[203] N. G. Deshpande, G. Eilam and J. Jiang, Phys. Lett. B 632 (2006) 212.
[204] J. F. Gunion, G. Gamberini and S. F. Novaes, Phys. Rev. D 38, (1988) 3481.
[205] G. W. Bennett et al. (Muon (g ? 2) Collaboration), Phys. Rev. D 73 (2006) 072003;
[206] M. Passera, W. J. Marciano and A. Sirlin, arXiv:0804.1142.
[207] F. Domingo and U. Ellwanger, JHEP 0807 (2008) 079.
[208] P. J. Franzini and F J. Gilman, Phys. Rev. D 32, (1985) 237; M. Drees and K. i. Hikasa, Phys. Rev. D 41,(1990) 1547; E. Fullana, M. A. Sanchis-Lozano, Phys. Lett. B 653 (2007) 67.
[209] M. Beneke, J. Rohrer, and D. Yang, Phys. Rev. Lett. 96 (2006) 141801.
[210] P. Ball and V. M. Braun, Phys. Rev. D 58 (1998) 094016; P. Ball, J. High Energy Phys. 09 (1998) 005;V. M. Braun and I. E. Filyanov, Z. Phys. C 48 (1990) 239; P. Ball, V. M. Braun, Y. Koike and K. Tanaka,Nucl. Phys. B 529 (1998) 323.
[211] M. Bander, D. Silverman and A. Soni, Phys. Rev. Lett. 43 (1979) 242.
[2] S. Weinberg,Phys. Rev.Lett. 19 (1967) 1264.
[3] A. Salam, in Elementary Particle Physics (Nobel Symposium N0.8)[J], edited by N. Svartholm (Almiqvistand Wisell, Stockholm (1968)), P367.
[4] S. W. Herb et al., Phys. Rev. Lett. 39 (1977) 252.
[5] Y. Kubota et al. [CLEO Collaboration], Nucl. Instrum. Meth. A 320 (1992) 66.
[6] D. Abbaneo et al. [ALEPH Collaboration], arXiv:hep-ex/0009052.
[7] F. Abe et al. [CDF Collaboration], Nucl. Instrum. Meth. A 271 (1988) 387; S. Abachi et al. [D0 Collabo-ration], Nucl. Instrum. Meth. A 338 (1994) 185.
[8] P. F. Harrison and H. R. Quinn [BABAR Collaboration], SLAC-R-0504.
[9] S. Mori et al. [Belle Collaboration], Nucl. Instrum. Meth. A 479 (2002)117.
[10] K. G. Wilson, Phys. Rev. 179 (1969) 1499 ; K. G. Wilson and W. Zimmermann, Comm. Math. Phys. 24(1972) 87 ; W. Zimmermann, in Proc. 1970 Brandeis Summer Institute in Theor. Phys. (Eds. S. Deser, M.Grisaru and H. Pendleton), MIT Press (1971) P396; Ann. Phys. 77 (1973) 570 ; E. Witten, Nucl. Phys. B120 (1977) 189 .
[11] K. G. Wilson, Phys. Rev. 179 (1969) 1499; K. G. Wilson and W. Zimmer-mann, Commun. Math. Phys.24 (1971) 87.
[12] E. Witten, Nucl. Phys. B 120 (1977) 189.
[13] A. Duncan, E. Eichten, J. Flynn, B. R. Hill, G. Hockney and H. Thacker, Phys. Rev. D 51 (1995) 5101.
[14] B. Y. Blok and M. A. Shifman, Sov. J. Nucl. Phys. 45 (1987) 135 [Yad. Fiz. 45 (1987) 211]; Sov. J. Nucl.Phys. 45 (1987) 301 [Yad.Fiz. 45 (1987) 478]; Nucl. Phys. B 389 (1993) 534.
[15] M. Beneke, G. Buchalla, M. Neubert and C. T. Sachrajda, Phys. Rev. Lett. 83 (1999) 1914; Nucl. Phys.B 591 (2000) 313.
[16] C. N. Yang and R. L. Mills, Phy. Rev. 96 (1954) 191.
[17] P. W. Higgs, Phys. Rev. Lett. 12 (1964) 132; Phys. Rev. 145 (1966) 1156.
[18] G.‘t Hooft, Nobel Lecture: A confrontation with infinity, Rev. Mod. Phys. 72 (2000) 333; M. Veltman,Nobel Lecture: From weak interactions to gravitation, Rev. Mod. Phys. 72 (2000) 341.
[19] S. L. Glashaw, J. Ilioponlos and L. Maiani, Phys. Rev. D 2 (1970) 1285.
[20] N. Cabibbo, Phys. Rev. Lett. 10 (1963) 531; M. Kobayashi and T. Maskawa, Prog. Theo. Phys. 49 (1973)652.
[21] For example, W. Marciano and H. Pagels, Phys Rep. 36C (1978) 137; A. J. Buras, Rev. Mod. Phys. 52(1980) 199; A. H. Muller, Phys Rep. 73C (1981) 237.
[22] H. D. Polizer, Phys Rep. 14C (1974) 129;
[23] C. Amsler et al. (Particle Data Group), Phys. Lett. B 667 (2008) 1
[24] H. Fritzsch and Z. Z. Xing, Phys. Lett. B413 (1997) 396.
[25] L. Wolfenstein, Phys. Rev. Lett. 51 (1983) 1945.
[26] J. Charles et al. (CKMfitter Group), Eur. Phys. J. C 41 (2005) 1; updated results and plots available at:http://ckmfitter.in2p3.fr..
[27] M. Bona et al. (UTfit Collaboration) JHEP 0507 (2005) 028; JHEP 0601 (2006) 081 ; online update at:http://www.utfit.org/.
[28] F. J. Dyson, Phys. Rev. D 75 (1949) 1736.
[29] W. Pauli and F. Villars, Rev. Mod. Phys. 21 (1949) 434.
[30] G.‘t Hooft and M. J. Veltman, Nucl. Phys. B 44 (1972) 189.
[31] G. Buchalla, A. G. Buras and M. E. Lautenbacher, Rev. Mod. Phys. 68 (1996) 1125; A. J. Buras, hep-ph/9806471.
[32] M. S. Chanowitz, M. Furman and I. Hinchli?e, Nucl. Phys. B 159 (1979) 225.
[33] P. Breitenlohner and D. Maison, Commun. Math. Phys. 52 (1977) 11 .
[34] A. J. Buras and P. H. Weisz, Nucl. Phys. B 33 (1990) 66.
[35] G.′t Hooft, Nucl. Phys. B 61 (1973) 455.
[36] W. A. Bardeen, A. J. Buras, D. W. Duke and T. Muta, Phys. Rev. D 18 (1978) 3998.
[37] G. C. Branco, L. Lavoura and J. P. Silva, CP Violation (Oxford University Press, Oxford, 1999); I. I. Bigiand A. I. Sanda, CP Violation (Cambridge University Press, Cambridge, 2000).
[38] Y. Nir, arXiv:hep-ph/0109090; arXiv:hep-ph/0208080; arXiv:hep-ph/0405091.
[39] D. Fakirov and B. Stech, Nucl. Phys. B 133 (1978) 315 M. Bauer and B. Stech, Phys. Lett. B 152 (1985)380; M. Wirbel, B. Stech and M. Bauer, Z. Phys. C 29, 637 (1985); M. Bauer, B. Stech and M. Wirbel, Z.Phys. C 34, 103 (1987).
[40] H. Y. Cheng and B. Tseng, Phys. Rev. D 58 (1998) 094005;
[41] Y. H. Chen, H. Y. Cheng, B. Tseng and K. C. Yang, Phys. Rev. D 60 (1999) 094014; 62 (2000) 054029;A. Ali and C. Greub, Phys. Rev. D 57 (1998) 2996; A. Ali, G. Kramer and C. D. Lu, Phys. Rev. D 58(1998) 094009; 59 (1999) 014005.
[42] H. n. Li and G. Sterman, Nucl. Phys. B 381 (1992) 129;
[43] H. n. Li, Phys. Rev. D 52, 3958 (1994). H. n. Li and H. L. Yu, Phys. Rev. D 53, 2480 (1995).
[44] H. N. Li and H. L. Yu, Phys. Lett. B 353 (1995) 301; C. H. Chang and H. n. Li, Phys. Rev. D 55 (1997)5577; T. W. Yeh and H. n. Li, Phys. Rev. D 56 (1997) 1615; C. D. Lu, K. Ukai and M. Z. Yang, Phys. Rev.D 63 (2001) 074009.
[45] C. W. Bauer, S. Fleming and M. E. Luke, Phys. Rev. D 63 (2001) 014006; C. W. Bauer, S. Fleming,D. Pirjol and I. W. Stewart, Phys. Rev. D 63 (2001) 114020; C. W. Bauer and I. W. Stewart, Phys. Lett.B 516 (2001) 134; Phys. Rev. D 65 (2002) 054022.
[46] J. D. Bjorken, Nucl. Phys. Proc. Suppl. 11 (1989) 325 ; M. J. Dugan and B. Grinstein, Phys. Lett. B 255(1991) 583 .
[47] A. J. Buras and L. Silvestrini, Nucl. Phys. B 548 (1999) 293.
[48] G. P. Lepage and S. J. Brodsky, Phys. Lett. B 87 (1979) 359 ; G. P. Lepage and S. J. Brodsky, Phys. Rev.Lett. 43 (1979) 545 ; G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22 (1980) 2157 .
[49] S. J. Brodsky, Phys. Lett. B 243, 287 (1990); H. Simma and D. Wyler, Phys. Lett. B 272 (1991) 395 ; C.E. Carlson and J. Milana, Phys. Rev. D 49 (1992) 5908.
[50] N. Isgur and C. H. Llewellyn Smith, Nucl. Phys. B 317 (1989) 526 ; A. V. Radyushkin, Nucl. Phys. A 532(1991) 141.
[51] Y. Y. Keum, H. n. Li and A. I. Sanda, Phys. Lett. B 504 (2001) 6 ; Y. Y. Keum, H. n. Li and A. I. Sanda,Phys. Rev. D 63 (2001) 054008 ; Y. Y. Keum and H. n. Li, Phys. Rev. D 63 (2001) 074006 ; C. D. Lu¨,K. Ukai and M. Z. Yang, Phys. Rev. D 63 (2001) 074009 ; C. D. Lu¨and M. Z. Yang, Eur. Phys. J. C 23(2002) 275 Y. Y. Keum and A. I. Sanda, Phys. Rev. D 67 (2003) 054009.
[52] S. D. Genon and C. T. Sachrajda, Nucl. Phys. B 625 (2002) 239; Z. T. Wei and M. Z. Yang, Nucl. Phys.B 642, 263 (2002); S. D. Genon and C. T. Sachrajda, Nucl. Phys. B 650 (2003) 356.
[53] C. W. Bauer, D. Pirjol and I. W. Stewart, Phys. Rev. Lett. 87 (2001) 201806; C. W. Bauer, D. Pirjol,I. Z. Rothstein and I. W. Stewart, Phys. Rev. D 70 (2004) 054015; J. g. Chay and C. Kim, Phys. Rev. D68 (2003) 071502; Nucl. Phys. B 680 (2004) 302; A. R. Williamson and J. Zupan, Phys. Rev. D 74 (2006)014003 [Erratum-ibid. D 74 (2006) 03901].
[54] C. W. Bauer, D. Pirjol and I. W. Stewart, Phys. Rev. D 67 (2003) 071502.
[55] M. Ciuchini et al., Nucl. Phys. B 501 (1997) 271; Phys. Lett. B 515 (2001) 33; arXiv:hep-ph/0208048.
[56] C. W. Bauer, D. Pirjol, I. Z. Rothstein and I. W. Stewart, Phys. Rev. D 70 (2004) 054015; M. Beneke,G. Buchalla, M. Neubert and C. T. Sachrajda, Phys. Rev. D 72 (2005) 098501; C. W. Bauer, D. Pirjol,I. Z. Rothstein and I. W. Stewart, Phys. Rev. D 72 (2005) 098502.
[57] M. Beneke and T. Feldmann, Nucl. Phys. B 592, 3 (2001).
[58] V. M. Braun and I. E. Halperin, Z. Phys. C 44 (1989) 157 ; V. M. Braun and I. E. Halperin, Z. Phys. C48 (1990) 239 .
[59] A. G. Grozin and M. Neubert, Phys. Rev. D 55 (1997) 272.
[60] V. L. Chernyak and I. R. Zhitnitsky, Nucl. Phys. B 345 (1990) 137 .
[61] D. S. Du, D. S. Yang, and G. H. Zhu, Phys. Lett. B 488 (2000) 46; Phys. Lett. B 509 (2001) 263; Phys.Rev. D 64 (2001) 014036.
[62] H. Y. Cheng, and K. C Yang, Phys. Rev. D 63 (2001) 074011; Phys. Rev. D 64 (2001) 074004; Phys. Lett.B 511 (2001) 40.
[63] A. J. Buras, R. Fleischer, S. Recksiegel and F. Schwab, Phys. Rev. Lett. 92 (2004) 101804 ; Nucl. Phys. B697 (2004) 133; PoS HEP2005 (2006) 193.
[64] M. Beneke, G. Buchalla, M. Neubert, C. T. Sachrajda, Nucl. Phys. B 606 (2001) 245; M. Beneke andM. Neubert, Nucl. Phys. B 651 (2003) 225.
[65] M. Beneke and M. Neubert, Nucl. Phys. B 675 (2003) 333.
[66] T. Muta, A. Sugamoto, M. Z. Yang and Y. D. Yang, Phys. Rev. D 62 (2000) 094020; M. Z. Yang andY. D. Yang, Phys. Rev. D 62 (2000) 114019.
[67] H. N. Li, S. Mishima and A. I. Sanda, Phys. Rev. D 72 (2005) 114005.
[68] A. R. Williamson and J. Zupan, Phys. Rev. D 74 (2006) 014003.
[69] M. Gronau and J. L. Rosner, Phys. Rev. D 74 (2006) 057503; X. Q. Li and Y. D. Yang, Phys. Rev. D 73(2006) 114027 ; Phys. Rev. D 72 (2005) 074007; J. Chay, H. N. Li, arXiv: 0711.2953 [hep-ph]; C. W. Bauer,I. Z. Rothstein and I. W. Stewart, Phys. Rev. D 74 (2006) 034010; C. S. Kim, S. Oh, and C. Yu, Phys.Rev. D 72 (2005) 074005;
[70] S. Baek, JHEP 0607 (2006) 025; R. Arnowitt et al., Phys. Lett. B 633 (2006) 748; S. Khalil, Phys. Rev.D 72 (2005) 035007; Y. D. Yang, R. M. Wang, G. R. Lu, Phys. Rev. D 73 (2006) 015003; V. Barger,C. W. Chiang, P. Langacker and H. S. Lee, Phys. Lett. B 598 (2004) 218; W. S.Hou, M. Nagashima andA. Soddu, Phy. Rev. Lett. 95 (2005) 141601; W. S.Hou, M. Nagashima, G. Raz and A. Soddu, JHEP 0609(2006) 012; C. S. Kim, S. Oh and Y. W. Yoon, arXiv: 0707.2967 [hep-ph]; C. S. Kim, S. Oh, C. Sharma,R. Sinha and Y. W. Yoon Phys. Rev. D 76 (2007) 074019.
[71] S. W. Lin et al., Belle Collaboration, Nature 452 (2008) 332.
[72] B. Aubert et al., Babar Collaboration, Phys. Rev. Lett. 99 (2007) 021603.
[73] S. Chen et al., CLEO Collaboration , Phys. Rev. Lett. 85 (2000) 525.
[74] Michael Morello, CDF Collaboration, Nucl. Phys. Proc. Suppl. 170 (2007) 39.
[75] E. Barberio et al. (Heavy Flavor Averaging Group), arXiv: 0704.3575 [hep-ex]; and online update at:http://www.slac.stanford.edu/xorg/hfag.
[76] M. E. Peskin, Nature 452 (2008) 293.
[77] Th. Feldmann, M. Jung and Th. Mannel, arXiv: 0803.3729 [hep-ph].
[78] Th. Feldmann and T. Hurth, JHEP 0411 (2004) 037.
[79] J. M. Cornwall, Phys. Rev. D 26 (1982) 1453; J. Papavassiliou and J. M. Cornwall, Phys. Rev. D 44 (1991)1285.
[80] A. C. Aguilar, A. A. Natale and P. S. Rodrigues da Silva, Phys. Rev. Lett. 90 (2003) 152001; A. C. Aguilarand A. A. Natale, JHEP 0408 (2004) 057.
[81] L. Von Smekal, A. Hauck, and R. Alkofer, Phys. Rev. Lett. 79 (1997) 3591; R. Alkofer and L. Von Smekal,Phys. Rep. 353 (2001) 281; C. S. Fisher and R. Alkofer, Phys. Rev. D 67 (2003) 094020; R. Alkofer,W. Detmold, C. S. Fisher, and P. Maris, Nucl. Phys. Proc. Suppl. 141 (2005) 122.
[82] I. L. Bogolubsky, E. -M. Ilgenfritz, M. Mu¨ller Preussker and A. Sternbeck, PoS (LATTICE-2007) 290;A. Cucchieri and T. Mendes, PoS (LATTICE 2007) 297; P. O. Bowman et al., Phys. Rev. D 76 (2007)094505.
[83] Q. Chang, X. Q. Li and Y. D. Yang, JHEP 0706 (2007) 038.
[84] D. S. Du, J. Korean Phys. Soc. 45 (2004) S285; D. S. Du, Int. J. Mod. Phys. A 21 (2006) 658; D. S. Du,J. F. Sun, D. S. Yang and G. H. Zhu, Phys. Rev. D 67 (2003) 014023; D. S. Du, H. J. Gong, J. F. Sun,D. S. Yang and G. H. Zhu, Phys. Rev. D 65 (2002) 094025; D. S. Du, D. S. Yang and G. H. Zhu, Phys.Rev. D 64 (2001) 014036; Phys. Lett. B 509 (2001) 263; Phys. Lett. B 488 (2000) 46.
[85] D. Zwanziger, Phys. Rev. D 69 (2004) 016002; D. M. Howe andC. J. Maxwell, Phys. Lett. B 541 (2002)129; Phys. Rev. D 70 (2004) 014002; S. Furui and H. Nakajima, AIP Conf. Proc. 717, (2004) 685.
[86] S. Brodsky, S. Menke, C. Merino and J. Rathsman, Phys. Rev. D 67 (2003) 055008; A. C. Mattingly andP. M. Stevenson, Phys. Rev. D 49 (1994) 437; M. Baldicchi, G. M. Prosperi, Phys. Rev. D 66 (2002) 074008.
[87] F. Su, Y. D. Yang, G. R. Lu and H. J. Hao, Eur. Phys. J. C 44 (2005) 243; F. Su, Y. L. Wu, Y. D. Yangand C. Zhuang, Eur. Phys. J. C 48 (2006) 401; arXiv: 0705.1575 [hep-ph].
[88] A. A. Natale and C. M. Zanetti, arXiv: 0803.0154 [hep-ph].
[89] Q. Mason et al. (HPQCD Collaboration), Phys. Rev. D 73 (2006) 114501.
[90] A. Gray et al. (HPQCD Collaboration), Phys. Rev. Lett. 95 (2005) 212001.
[91] P. Ball and R. Zwicky, Phys. Rev. D 71 (2005) 014015; 71 (2005) 014029; Phys. Lett. B 633 (2006) 289.
[92] G. Eilam, M. Ladisa and Y. D. Yang, Phys. Rev. D 65 (2002) 037504.
[93] S. Baek, A. Datta, P. Hamel, O. F. Hernandez and D. London, Phys. Rev. D 72 (2005) 094008; S. Baekand D. London, Phys. Lett. B 653 (2007) 249.
[94] W. S. Hou, M. Nagashima and A. Suddu, Phys. Rev. Lett. 95 (2005) 141601.
[95] A. L. Kagan, Phys. Lett. B 601 (2004) 151.
[96] P. K. Das and K. C. Yang, Phys. Rev. D 71 (2005) 094002.
[97] H. Hatanaka and K. C. Yang, Phys. Rev. D 77 (2008) 035013.
[98] S. Nandi and A. Kundu, J. Phys. G 32 (2006) 835.
[99] M. Beneke, Phys. Lett. B 620 (2005) 143.
[100] G. Buchalla, G. Hiller, Y. Nir and G. Raz, JHEP 0509 (2005) 074.
[101] R. Fleischer, S. Jager, D. Pirjol and J. Zupan, arXiv: 0806.2900 [hep-ph].
[102] M. Gronau and J. Rosner, arXiv:0807.3080[hep-ph].
[103] James F. Hirschauer (BABAR Collaboration), talk presented at ICHEP08, the 34th International Confer-ence on High Energy Physics Philadelphia, Pennsylvania, July 30 - August 5, 2008.
[104] Jeremy P Dalseno (Belle Collaboration), talk presented ICHEP08.
[105] for example, M. Masip and A. Pomarol Phys. Rev. D 60 (1999) 096005.
[106] T. K. Kuo and N. Nakagawa, Phys. Rev. D 31 (1985) 1161;32 (1985) 306; K. K. Gan, Phys. Lett. B 209(1988) 95; E. Nardi, Phys. Rev. D 48 (1993) 1240; B. Holdom, Phys. Lett. B 339 (1994) 114; X. Zhang andB.-L. Young, Phys. Rev. D 51 (1995) 6584; B. Holdom and M. V. Ramana, Phys. Lett. B 365 (1996) 309.
[107] S. Chaudhuri, S.W. Chung, G. Hockney, and J. Lykken, Nucl. Phys. B 456 (1995) 89.
[108] G. Cleaver, M. Cvetiˇc, J.R. Espinosa, L. Everett, and P. Langacker, Nucl. Phys. B 525 (1998) 3; G. Cleaver,M. Cvetiˇc, J.R. Espinosa, L. Everett, P. Langacker, and J. Wang, Phys. Rev. D 59 (1999) 055005; 59 (1999)115003.
[109] G. Buchalla, G. Burdman, C. T. Hill and D. Kominis Phys. Rev. D 53 (1996) 5185; G. Burdman, K. D. Laneand T. Rador, Phys. Lett. B 514 (2001) 41; A. Martin and K. Lane, Phys. Rev. D 71 (2005) 015011.
[110] E. Nardi, Phys. Rev. D 48 (1993) 1240; J. Bernabeu, E. Nardi and D. Tommasini, Nucl. Phys. B 409(1993) 69; V. D. Barger, M. S. Berger and R. J. Phillips, Phys. Rev. D 52 (1995) 1663; M. B. Popovic andE. H. Simmons, Phys. Rev. D 62 (2000) 035002; T. G. Rizzo Phys. Rev. D 59 (1999) 015020.
[111] P. Langacher and M. Plu¨macher, Phys. Rev. D 62 (2000) 013006.
[112] M. S. Carena, A. Daleo, B. A. Dobrescu and T. M. P. Tait, Phys. Rev. D 70 (2004) 093009.
[113] T. G. Rizzo, hep-ph/0610104; arXiv: 0808.1906[hep-ph].
[114] V. Barger, C. W. Chiang, P. Langacker and H. S. Lee, Phys. Lett. B 598 (2004) 218.
[115] V. Barger, C. W. Chiang, P. Langacker and H. S. Lee, Phys. Lett. B 580 (2004) 186.
[116] K. Cheung, C. W. Chiang, N. G. Deshpande and J . Jiang, Phys. Lett. B 652 (2007) 285; J. H. Jeon,C. S. Kim, J. Lee and C. Yu Phys. Lett. B 636 (2006) 270; C. H. Chen and H. Hatanaka, Phys. Rev. D 73(2006) 075003.
[117] L. S. Durkin and P. Langacker, Phys. Lett. B 166 (1986) 436; P. Langacker and M. Luo, Phys. Rev. D 45(1992) 278.
[118] DELPHI Collaboration, P. Abreu et al., Z. Phys. C 65 (1995) 603; K.S. Babu and C. Kolda, The Z′Searches, in W. M. Yao, et al. [Particle Data Group], J. Phys. G 33 (2006) 1.
[119] J. Erler and P. Langacker, Phys. Lett. B 456 (1999) 68; Phys. Rev. Lett. 84 (2000) 212; J. Erler, P. Lan-gacker, S. Munir and E. R. Pena, arXiv: 0906.2435 [hep-ph]; E. Salvioni, G. Villadoro and F. Zwirner,arXiv: 0909.1320[hep-ph].
[120] N. S. Kroll, T. D. Lee, and B. Zumino, Phys. Rev. 157 (1967) 1376 ; B. Holdom, Phys. Lett. B 166 (1986)196 ; F. Del Aguila, M. Cvetiˇc and P. Langacker, Phys. Rev. D 52 (1995) 37; F. del Aguila, M. Masip,M. Perez-Victoria, Acta Phys. Polon. B 27 (1996) 1469; K. S. Babu, C. Kolda, and J. March-Russell,Phys. Rev. D 54 (1996) 4635.
[121] V M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 101 (2008) 241801.
[122] T. Aaltonen et al. (CDF Collaboration), Phys. Rev. Lett. 100 (2008) 161802.
[123] M. Bona et al., arXiv:0906.0953 [hep-ph]; M. Bona et al. (UTfit Collaboration); online update at:http://www.utfit.org/NP/NP.html.
[124] V. Niess (the CKM fitter group), talk at“Flavor Physics and CP Violation 2009”, Lake Placid, NY. onlineupdate at: http://ckmfitter.in2p3.fr/.
[125] V M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 97 (2006) 021802.
[126] H. Abulencia et al. (CDF Collaboration), Phys. Rev. Lett. 97 (2006) 242003.
[127] A. Lenz and U. Nierste, JHEP 0706 (2007) 072.
[128] Q. Chang, X. Q. Li and Y. D. Yang, JHEP 0905 (2009) 056.
[129] V. Barger, L. Everett, J. Jiang, P. Langacker, T. Liu and C. Wagner, JHEP12(2009) 048; arXiv:0902.4507[hep-ph].
[130] V. Barger, C. W. Chiang, J. Jiang, and P. Langacker, Phys. Lett. B596 (2004) 229.
[131] K. Cheung, C. W. Chiang, N. G. Deshpande and J. Jiang, Phys. Lett. B 652 (2007) 285.
[132] C. W. Chiang, R. H. Li and C. D. Lu, arXiv:0911.2399 [hep-ph]
[133] J. Hua, C. S. Kim, Y. Li, arXiv:1002.2532 [hep-ph].
[134] B. Aubert et al. (BABAR Collaboration), Phys. Rev. Lett. 93 (2004) 081802;
[135] M. Iwasaki et al. (Belle Collaboration), Phys. Rev. D 72 (2005) 092005.
[136] S. Glenn et al. (CLEO Collaboration), Phys. Rev. Lett. 80 (1998) 2289.
[137] A. J. Buras and M. Mu¨nz, Phys. Rev. D 52 (1995) 186.
[138] A. J. Buras and M. Mu¨nz, Phys. Lett. B 566 (2003) 115.
[139] A. J. Buras, arXiv:0904.4917 [hep-ph].
[140] T. Aaltonen et al. Phys. Rev. Lett. 100 (2008) 101802.
[141] Elvira Gamiz et al. (HPQCD Collaboration ), arXiv:0902.1815 [hep-lat].
[142] G. D’Ambrosio, G. F. Giudice, G. Isidori and A. Strumia, Nucl. Phys. B 645 (2002) 155.
[143] A. J. Buras, Acta. Phys. Polon. B bf 34 (2003) 5615.
[144] G. Buchalla and A. J. Buras, Nucl. Phys. B 400 (1993) 225.
[145] A. J. Buras E. Lautenbacher, M. Misiak and M. Mu¨nz, Nucl. Phys. B 423 (1994) 349.
[146] Y. Nir, Phys. Lett. B 221 (1989) 184.
[147] M. Misiak, Nucl. Phys. B393(1993) 23, Erratum-ibid B439(1995)461.
[148] M. Jezabek and J. H. Ku¨hn, Nucl. Phy. B320(1989)20.
[149] A. Ali, T. Mannel and T. Morozumi, Phys. Lett. B 273 (1991) 505.
[150] Z. Ligeti and M. B. Wise, Phys. Rev. D 53 (1996) 4937.
[151] A. Ali, G. Hiller, L. T. Handoko and T. Morozumi, Phys. Rev. D 55 (1997) 4105.
[152] F. Kru¨ger, L.M. Sehgal, Phys. Lett. B 380(1996)199.
[153] M. Beneke, G. Buchalla, M. Neubert and C. T. Sachrajda, Eur. Phys. J. C61(2009) 439.
[154] T. Huber, T. Hurth, and E. Lunghi, Nucl. Phys. B 802 (2008) 40; A. Ghinculov, T. Hurth, G. Isidori, andY. P. Yao, Nucl. Phys. B685(2004) 351.
[155] M. Bartsch, M. Beylich, G. Buchalla, and D. N. Gao, JHEP 0911 (2009) 011.
[156] C. Bobeth, G. Hiller and G. Piranishvili, JHEP 0807 106.
[157] For instance: N. G. Deshpande, J. Trampetic, Phys. Rev. Lett. 60 (1988) 2583 ; W. Jaus and D. Wyler,Phys. Rev. D 41 (1990) 3405; G. Burdman, Phys. Rev. D 52 (1995) 6400; P. Colangelo, F. De Fazio,P. Santorelli and E. Scrimieri, Phys. Rev. D 53 (1996) 3672 [Erratum-ibid. D 57 (1998) 3186]; T. M. Aliev,A. Ozpineci and M. Savci, Phys. Rev. D 56 (1997) 4260; D. Melikhov, N. Nikitin and S. Simula, Phys.Lett. B 430 (1998) 332; A. Ali, G. Kramer, G H Zhu, Eur. Phys. J. C 47 (2006) 625; C. Bobeth, G. Hiller,G. Piranishvili, JHEP 0807 (2008) 106.
[158] G. Burdman, Phys. Rev. D 57 (1998) 4254.
[159] M. Beneke, T. Feldmann and D. Seidel, Nucl. Phys. B 612 (2001) 25.
[160] A. J. Buras, M. Misiak, M. Munz and S. Pokorski, Nucl. Phys. B 424 (1994) 374.
[161] A. Ali, P. Ball, L. T. Handoko and G. Hiller, Phys. Rev. D 61 (2000) 074024.
[162] W. Altmannshofer, P. Ball, A. Bharucha, A. J. Buras, D. M. Straub and M. Wick, JHEP 0901 (2009) 019.
[163] For instance: C. Greub, A. Ioannissian and D. Wyler, Phys. Lett. B 346 (1995) 149; J. L. Hewett andJ. D. Wells, Phys. Rev. D 55 (1997) 5549; A. Ali, E. Lunghi, C. Greub,G. Hiller, Phys. Rev. D 66 (2002)034002; C. H. Chen and C. Q. Geng, Phys. Rev. D 66 (2002) 094018; T. Feldmann and J. Matias, JHEP0301 (2003) 074; G. Hiller, F. Kruger, Phys. Rev. D 69 (2004) 074020; F. Kruger and J. Matias, Phys.Rev. D 71 (2005) 094009; P. Colangelo, F. De Fazio, R. Ferrandes and T. N. Pham, Phys. Rev. D 73(2006) 115006; Y. G. Xu, R. M. Wang and Y. D. Yang, Phys. Rev. D 74 (2006) 114019; A. Hovhannisyan,W. S. Hou and N. Mahajan, Phys. Rev. D 77 (2008) 014016.
[164] B. Aubert et al. [BABAR Collaboration], Phys. Rev. D 79 (2009) 031102.
[165] B. Aubert et al. [BABAR Collaboration], Phys. Rev. Lett. 102 (2009) 091803.
[166] A. Ishikawa et al., Phys. Rev. Lett. 96 (2006) 251801.
[167] J. T. Wei et al. [BELLE Collaboration], Phys. Rev. Lett. 103 (2009) 171801.
[168] C. H. Chen, Phys. Lett. B 683 (2010) 160.
[169] A. K. Alok, A. Dighe, D. Ghosh, D. London, J. Matias, M. Nagashima and A. Szynkman, arXiv:0912.1382[hep-ph].
[170] K. G. Chetyrkin, M. Misiak and M. Munz, Phys. Lett. B 400 (1997) 206 [Erratum-ibid. B 425 (1998) 414].
[171] C. Bobeth, M. Misiak and J. Urban, Nucl. Phys. B 574 (2000) 291.
[172] C. Bobeth, A. J. Buras, F. Kru¨ger and J. Urban, Nucl. Phys. B 630 (2002) 87.
[173] T. Huber, E. Lunghi, M. Misiak and D. Wyler, Nucl. Phys. B 740 (2006) 105.
[174] C. Q. Geng and C. P. Kao, Phys. Rev. D 54 (1996) 5636.
[175] S. Drell, Nuov. Cim. XI (1959) 693.
[176] L. Bergstro¨m, Zeit. Phys. C 14 (1982) 129.
[177] K.S. Babu and E. Ma, Phys. Lett. B119 (1982) 449.
[178] L. Bergstr¨om, E. Masso, L. Ametller and A. Bramon, Phys. Lett. B 126 (1983) 117.
[179] Ll. Ametller, A. Bramon and E. Masso′Phys. Rev. D 48 (1993) 3388.
[180] M.J. Savage, M. Luke, and M.B. Wise, Phys. Lett. B291 (1992) 481.
[181] D. Go′mez Dumm and A. Pich Phys. Rev. Lett 80 (1998) 4633.
[182] M. Knecht, S. Peris and E. de Rafael Phys. Rev. Lett 83 (1999) 5230.
[183] A. E. Dorokhov and M. A. Ivanov, Phys. Rev. D 75 (2007) 114007.
[184] M. D. Scadron and M. Visinescu, Phys. Rev. D 29, (1984) 911; A. N. Kamal and L. C. Huah, Phys. Rev.D 32, (1985) 1744; G. Triantaphyllou, Mod. Phys. Lett. A 8, (1993) 1691.
[185] H. J. Behrend et al. (CELLO Collaboration), Zeit. Phys. C 49 (1991) 401.
[186] J. Gronberg et al. (CLEO Collaboration), Phys. Rev. D 57 (1998) 33.
[187] J. Fischer et al., Phys. Lett. B 73 (1978) 364.
[188] R. Niclasen, Ph.D Thesis, FERMILAB-THESIS-2006-12, UMI-32-07725. http:// lss. fnal. gov/ archive/thesis/ fermilab-thesis -2006-12. shtml.
[189] E. Abouzaid et al., KTeV Collaboration, Phys. Rev. D 75 (2007) 012004.
[190] A. E. Dorokhov and M. A. Ivanov, Eur. Phys. J. C 55 (2008) 193.
[191] A. E. Dorokhov and M. A. Ivanov, JETP Lett. 87 (2008) 531.
[192] W. Love, et al (CLEO Collaboration), arXiv:0807.2695 [hep-ex].
[193] B. Aubert, et al (BaBar Collaboration), arXiv:0808.0017 [hep-ex].
[194] H. P. Nilles, M. Srednicki and D. Wyler, Phys. Lett. B 120 (1983) 346; J. M. Frere, D. R. T. Jones andS. Raby, Nucl. Phys. B 222, (1983) 11; J. P. Derendinger and C. A. Savoy, Nucl. Phys. B 237, (1984)307; J. R. Ellis, J. F. Gunion, H. E. Haber, L. Roszkowski and F. Zwirner, Phys. Rev. D 39 (1989) 844;M. Drees, Int. J. Mod. Phys. A 4 (1989) 3635.
[195] G. Hiller, Phys. Rev. D 70 (2004) 034018.
[196] B. R. Martin, E. De Rafael and J. Smith, Phys. Rev. D 2, (1970) 179.
[197] M. Pratap and J. Smith, Phys. Rev. D 5, (1972) 2020; Z. K. Silagadze, Phys. Rev. D 74, (2006) 054003.
[198] H. K. Park, et al (HyperCP Collaboration), Phy. Rev. Lett. 94 (2005) 021801.
[199] X. G. He and J. Tandean, Phy. Rev. Lett. 98 (2007) 081802.
[200] X. G. He and J. Tandean and G. Valencia, JHEP 0806 (2008) 002.
[201] G. Valencia, arXiv:0805.3285 [hep-ph].
[202] X. G. He, J. Tandean and G. Valencia, Phys. Lett. B 631 (2005) 100.
[203] N. G. Deshpande, G. Eilam and J. Jiang, Phys. Lett. B 632 (2006) 212.
[204] J. F. Gunion, G. Gamberini and S. F. Novaes, Phys. Rev. D 38, (1988) 3481.
[205] G. W. Bennett et al. (Muon (g ? 2) Collaboration), Phys. Rev. D 73 (2006) 072003;
[206] M. Passera, W. J. Marciano and A. Sirlin, arXiv:0804.1142.
[207] F. Domingo and U. Ellwanger, JHEP 0807 (2008) 079.
[208] P. J. Franzini and F J. Gilman, Phys. Rev. D 32, (1985) 237; M. Drees and K. i. Hikasa, Phys. Rev. D 41,(1990) 1547; E. Fullana, M. A. Sanchis-Lozano, Phys. Lett. B 653 (2007) 67.
[209] M. Beneke, J. Rohrer, and D. Yang, Phys. Rev. Lett. 96 (2006) 141801.
[210] P. Ball and V. M. Braun, Phys. Rev. D 58 (1998) 094016; P. Ball, J. High Energy Phys. 09 (1998) 005;V. M. Braun and I. E. Filyanov, Z. Phys. C 48 (1990) 239; P. Ball, V. M. Braun, Y. Koike and K. Tanaka,Nucl. Phys. B 529 (1998) 323.
[211] M. Bander, D. Silverman and A. Soni, Phys. Rev. Lett. 43 (1979) 242.