pQCD方案下双Higgs模型与B_s→PP衰变过程的研究
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摘要
众所周知,B介子的研究,无论是理论研究还是实验测量,对检验标准模型和寻找新物理信号有着重要意义。目前,人们已经对标准模型下B介子的衰变做了广泛的研究,本文中我们主要研究的是Bs介子衰变到两个赝标介子(Bs→P2P3)的一类衰变。我们分别计算了13个具体衰变的的衰变分枝比和CP破坏的标准模型预言及其在双Higgs模型下的新物理修正
在论文的综述部分,我们首先讨论了标准模型的局限性,介绍了建立新物理模型的动机。在第二章,我们对标准模型及双Higgs模型做了简要的介绍和讨论。在第三章中,我们首先对B物理研究的基本理论框架做了简单介绍,然后对B介子衰变过程强子矩阵元计算的各种因子化方法做了介绍和比较,最后重点介绍了pQCD因子化方案在Bs介子两体衰变中的运用。
第四章是论文的工作部分。我们首先对双Higgs模型III下的Wilson系数进行了计算,结果表明双Higgs模型III对于Wilson系数Ci(i=3～10)的修正非常小,可以忽略。主要的修正来自于色磁偶贡献C8g。
在第四章,我们采用pQCD因子化方案,计算了13个Bs→P2P3衰变道的衰变分枝比和CP破坏的新物理修正,并对其作了分析。目前Bs的衰变只有少数衰变道有实验测量值。对于部分衰变道的分枝比,只要在双Higgs模型下选择适合的参数,理论预言值和实验测量值就可以很好的符合。通过分析,我们发现：(a)对于没有色磁企鹅图贡献的四个衰变道,模型Ⅲ的修正非常小。(b)对于那些色磁企鹅图贡献为主的衰变道的衰变分枝比,模型Ⅲ可以给出30%～190%的增强。
第四章中,我们还在标准模型和双Higgs模型III的理论框架下计算了13个衰变道的直接CP破坏,并发现：(a)四个没有色磁企鹅图贡献的衰变道,双Higgs模型III的贡献依然很小。(b)在其他9个衰变道中,除了B8→K+π-,新物理修正都使直接CP破坏的模减小,衰变道Bs→K+K-的减幅最大,达到-57%。(c)只有Bs→K+π-衰变道,新物理修正使其直接CP破坏相比标准模型有24%的增强。
第四章的最后,我们还计算了时间相关的衰变道的混合CP破中可观测量Sf,Hf。对于所有13个衰变道,新物理修正对Sf,Hf的影响都不大。
最后一章中,我们对全文进行了总结,并对未来几年B物理研究做了讨论和展望。
As is well known, the theoretical studies and experimental measurements of the two-body charmless hadronic B and Bs meson decays provide a good opportunity for testing the standard model (SM), probing CP violation and searching for possible new physics(NP) beyond SM. Actually the comprehensive studies of the B meson system in the framework of the standard model have been undertaken frequently by using different factorization methods. In this paper, by employing the pQCD factorization, we calculated the new physics contributions, in the two-Higgs-doublet models, to the branching ratios and CP-violating asymmetries of Bs→PP decays.
In the review part of this thesis, we firstly discussed the main problems of the standard model(SM) and introduced the motivation for building the new physics models. A brief summary of the theoretical frameworks of the standard model and the two-Higgs-doublet-models(2HDMs) were then given in the second chapter. In chapter three, we gave a mini-review about the theoretical framework of B Physics, presented the main points of the pQCD factorization approach to be used in this thesis.
Chapter four is the part of our own work. We evaluated the new physics contributions to the the Wilson coefficients Ci(mb) in the third type of 2HDM, and found that the NP corrections to Ci(i=3,…,10) are very small in magnitude and can be neglected safely, but the NP contributions to the Wilson coefficient C8g can be rather large.
Also in chapter four, we studied the NP contributions to the 13 Bs→P2P3 decays, and made some discussion about these channels. For the branching ratios of those chan-nels, only two of them have been measured experimentally. The NP contributions can be help in order to make the theoretical predictions becoming consistent with the cur-rent date. We found numerically that:(a) the NP contributions are very small for those channels without the contributions coming from the chromo-magnetic penguin diagrams. (b) for those O8g-dominated decay modes, the 2HDMⅢcontributions can provide an enhancement about 30%～190% to their branching ratios.
In chapter four, we also calculated the CP-violating asymmetries of the considered decays in the SM and the 2HDMⅢ. We found that (a) Compared with the SM pre-diction, in the four decay channels without chrorao-magnetic penguin diagrams, the NP contributions are also generally small. (b) In other decays, besides Bs→K+π-, the NP on direct CP-violations tend to make the SM predictions decreased. The largest correc-tion is about -57% for decay Bs→K+K-. (c) Only for Bs→K+π-, the NP correction can make an increase of 24% respect to the SM prediction.
Lastly, in chapter four, we also calculated the mixing-induced CP violation parameters Sf and Hf. For all decays, the 2HDMⅢcorrections to both the Sf and Hf are small or moderate.
In the last chapter, we gave a short summary of this thesis and some remarks on future developments of B physics in coining years.
在论文的综述部分,我们首先讨论了标准模型的局限性,介绍了建立新物理模型的动机。在第二章,我们对标准模型及双Higgs模型做了简要的介绍和讨论。在第三章中,我们首先对B物理研究的基本理论框架做了简单介绍,然后对B介子衰变过程强子矩阵元计算的各种因子化方法做了介绍和比较,最后重点介绍了pQCD因子化方案在Bs介子两体衰变中的运用。
第四章是论文的工作部分。我们首先对双Higgs模型III下的Wilson系数进行了计算,结果表明双Higgs模型III对于Wilson系数Ci(i=3～10)的修正非常小,可以忽略。主要的修正来自于色磁偶贡献C8g。
在第四章,我们采用pQCD因子化方案,计算了13个Bs→P2P3衰变道的衰变分枝比和CP破坏的新物理修正,并对其作了分析。目前Bs的衰变只有少数衰变道有实验测量值。对于部分衰变道的分枝比,只要在双Higgs模型下选择适合的参数,理论预言值和实验测量值就可以很好的符合。通过分析,我们发现：(a)对于没有色磁企鹅图贡献的四个衰变道,模型Ⅲ的修正非常小。(b)对于那些色磁企鹅图贡献为主的衰变道的衰变分枝比,模型Ⅲ可以给出30%～190%的增强。
第四章中,我们还在标准模型和双Higgs模型III的理论框架下计算了13个衰变道的直接CP破坏,并发现：(a)四个没有色磁企鹅图贡献的衰变道,双Higgs模型III的贡献依然很小。(b)在其他9个衰变道中,除了B8→K+π-,新物理修正都使直接CP破坏的模减小,衰变道Bs→K+K-的减幅最大,达到-57%。(c)只有Bs→K+π-衰变道,新物理修正使其直接CP破坏相比标准模型有24%的增强。
第四章的最后,我们还计算了时间相关的衰变道的混合CP破中可观测量Sf,Hf。对于所有13个衰变道,新物理修正对Sf,Hf的影响都不大。
最后一章中,我们对全文进行了总结,并对未来几年B物理研究做了讨论和展望。
As is well known, the theoretical studies and experimental measurements of the two-body charmless hadronic B and Bs meson decays provide a good opportunity for testing the standard model (SM), probing CP violation and searching for possible new physics(NP) beyond SM. Actually the comprehensive studies of the B meson system in the framework of the standard model have been undertaken frequently by using different factorization methods. In this paper, by employing the pQCD factorization, we calculated the new physics contributions, in the two-Higgs-doublet models, to the branching ratios and CP-violating asymmetries of Bs→PP decays.
In the review part of this thesis, we firstly discussed the main problems of the standard model(SM) and introduced the motivation for building the new physics models. A brief summary of the theoretical frameworks of the standard model and the two-Higgs-doublet-models(2HDMs) were then given in the second chapter. In chapter three, we gave a mini-review about the theoretical framework of B Physics, presented the main points of the pQCD factorization approach to be used in this thesis.
Chapter four is the part of our own work. We evaluated the new physics contributions to the the Wilson coefficients Ci(mb) in the third type of 2HDM, and found that the NP corrections to Ci(i=3,…,10) are very small in magnitude and can be neglected safely, but the NP contributions to the Wilson coefficient C8g can be rather large.
Also in chapter four, we studied the NP contributions to the 13 Bs→P2P3 decays, and made some discussion about these channels. For the branching ratios of those chan-nels, only two of them have been measured experimentally. The NP contributions can be help in order to make the theoretical predictions becoming consistent with the cur-rent date. We found numerically that:(a) the NP contributions are very small for those channels without the contributions coming from the chromo-magnetic penguin diagrams. (b) for those O8g-dominated decay modes, the 2HDMⅢcontributions can provide an enhancement about 30%～190% to their branching ratios.
In chapter four, we also calculated the CP-violating asymmetries of the considered decays in the SM and the 2HDMⅢ. We found that (a) Compared with the SM pre-diction, in the four decay channels without chrorao-magnetic penguin diagrams, the NP contributions are also generally small. (b) In other decays, besides Bs→K+π-, the NP on direct CP-violations tend to make the SM predictions decreased. The largest correc-tion is about -57% for decay Bs→K+K-. (c) Only for Bs→K+π-, the NP correction can make an increase of 24% respect to the SM prediction.
Lastly, in chapter four, we also calculated the mixing-induced CP violation parameters Sf and Hf. For all decays, the 2HDMⅢcorrections to both the Sf and Hf are small or moderate.
In the last chapter, we gave a short summary of this thesis and some remarks on future developments of B physics in coining years.
引文
[1]A. Ali, G. Kramer, Y. Li, CD. Lu, Y.L. Shen, W. Wang, and Y.M. Wang, Charmless nonleptonic Bs decays to PP, PV, and PV final states in the perturbative QCD approach, Phys. Rev. D 76, 074018 (2007).
[2]Z.J. Xiao, C.S. Li and K.T. Chao, Charmless hadronic decays B→PP,PV,VV and new physics effects in the general two-Higgs-doublet models, Phys. Rev, D 63,074005(2001).
[3]S.L. Glashow, Partical symmetries of weak interactions, Nucl. Phys. 22 (1961)579; S. Weinberg, A model of leptons, Phys. Rev. Lett. 19(1967) 1264.
[4]M. Beneke, G. Buchalla, M. Neubert, and C.T. Sachrajda, QCD Factorization for B→π π Decays: Strong Phases and CP Violation in the Heavy Quark Limit, Phys Rev. Lett. 83, 1914(1999).
[5]M. Beneke and M. Neubert, QCD factorization for BPP and B→PV decays, Nucl. Phys. B 675, 333(2003).
[6]S. Glashow and S. Weinberg, Natural conservation laws for neutral currents, Phys Rev. D 15, 1958(1997).
[7]F.M. Borzumati and C. Greub, Two Higgs doublet model predictions for B → Xs in NLO QCD, Phys. Rev. D 58, 074004(1998); Addendum, to "Two Higgs doublet model predictions for B → Xsγ in NLO QCD" , Phys. Rev. D 59, 057501(1999).
[8]M. Misiak, S. Pokorski and J. Rosick, in Heavy Flavor Ⅱ edited by A.J. Buras and M. Linder(World Scientific, Singapore, 1998).
[9]Z.J. Xiao, L.X. Lu, H.K. Guo, and G.R. Lu, Rare Decays B→ Xs,d, VV and Bs,d→ 1+1- in the Multiscale Walking Technicolor Model, Chin. Phys. Lett. 16, 88(1999); Z.J. Xiao, L.X. Lu, H.K. Guo, and G.R. Lu, The rare K-decays in the Multiscale Walking Technicolor Model, Eur. Phys. J. C 7. 487(1999).
[10]P.W. Higgs,Broken symmetries, massless particles and gauge fields., Phys. Lett. 12(1964) 132; Spontaneous Symmetry Breakdown without Massless Bosons, Phy. Rev.145(1966) 1156.
[11]S.L. Glashow, J. Iliopoulos and L. Maiani, Weak Interacttions With Lepton-Hadron Symmetry, Phys. Rev. D 2(1970)1285.
[12]N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett.10(1963) 531; M. Kobayashi and T. Maskawa. CP-Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor Phys.49(1973)652.
[13]L. Wolfenstein, Parametrization of the Kobayashi-Maskawa Matrix, Phys. Rev. Lett. 51(1983)1945.
[14]J.F. Guinion, H.E. Haber, G. Kane, and S. Dawson, The Higgs Hunter's Guide, Addison-Wesley Publishing Company.1990.
[15]T.D. Lee, A Theory of Spontaneous T Violation, Phys. Rev. D 8,1226(1973).
[16]G.C. Branco and M.N. Rebelo, The Higgs mass in a model with two scalar doublets and spontaneous CP violation, Phys. Lett. B 160,117(1985).
[17]T.P. Cheng and M. Sher, Mass-matrix ansatz and flavor nonconservation in models with multiple Higgs doublets, Phys. Rev. D 35,3484(1987).
[18]D. Atwood, L. Reina. and A. Soni, Phenomenology of two Higgs doublet models with flavor-changing neutral currents, Phys. R.ev. D 55.3156(1997).
[19]Z.J. Xiao, C.S. Li and K.T. Chao, Charm multiplicity and the branching ratios of inclusive charmless b quark decays in the general two-Higgs-doublet models, Phys. Rev. D 62,094008(2000).
[20]Z.J. Xiao, C.S. Li and K.T. Chao, Gluon penguin enhancements to inclusive charm-less decays of b quark in the 2HDM with flavor changing couplings, Phys. Lett. B 473(2000)148.
[21]C.D. Lu, K. Ukai, and M.Z. Yang, Branching ratio and CP violation of B? π π decays in the perturbative QCD approach, Phys. Rev. D 63,074009(2001).
[22]J.C. Collins and D.E. Soper, Back-to-back jets in QCD, Nucl. Phys. B 193, 381(1981).
[23]H.N. Li, Unification of the κT and threshold re summations, Phys. Lett. B 454,328(1999).
[24]H.N. Li, Threshold resummation for exclusive B meson decays, Phys. Rev. D 66, 094010(2002).
[25]P. Ball, B →π and B→K transitions from QCD sum rules on te light-cone, JHEP 9809,005(1998). Theoretical update of pseudoscalar mesons DAs of high twist: the non-singlet case, JHEP 9901,010(1999).
[26]P. Ball and R. Zwicky, New reults on B →π, K,η decay form factors from light-cone sum rules, Phys. Rev. D 71,014015(2005).
[27]P. Ball, V.M. Braun, A. Lenz, High-Twist DAs of the K meson in QCD,JEEP 0605(2006)004;hep-ph/0603063.
[28]T. Feldmann, P. Kroll, and B. Stech, Mixing and decay constants of pseudo-scalar mesons, Phys. Rev. D 58,114006(1998); Mixing and decay constants of pseudoscalar mesons: the sequel. Phys. Lett, B 449,339(1999).
[29]A,J. Buras, in Probing the Standard model of Particle Interactions, ed. F. David and R. Gupta. 1998 Elsevier Science B.V., hep-ph/9806471.
[30]S. Mishima and A.I. Sanda, Calculation of Magnetic Penguin Amplitudes in B→ φ K Decays Using PQCD Approach, Prof. Theor. Phys. 110,549(2003).
[31]H.N li, S. Mishima, and A.I. Sanda, Resolution to the B→π K puzzle, Phys. Rev. D72 114005(2005)
[32]Particle Data Group, D.E. Groom et al., Eur. Phys. J. Cl5(2000)l.
[33]D.B. Chao, K. Cheung, and W.Y. Keung, Phace effect of a general two- Higgs-doublet model in b → sγ, Phys. Rev. D59,115006(1999).
[34]肖振军,B介子非粲衰变过程与新物理量子修正研究,北京大学博士研究生学位论文,2000。
[35]T.M. Aliev and E.O. Iltan. B→sγ decay in the two-Higgs-doublet model with flavor changing neutral current J. Phys. G25,989(1999).
[36]V.L. Chernyak and A.R. Zhitnitsky, Asymptotic behaviour of exclusive processes in QCD, Phys. Rep.112,173(1984);V.M. Braun and I.E. Filyanov, QCD sum rules in exclusive kinematics and pion wave function. Z. Phys.C44.157(1989); P. Ball, B→π and B→K transitions from QCD sum rules on the light-cone, J. High Energy Phys.09(1998)005; V.M. Braun and I.E. Filyanov, Conformal invariance and pion wave functions of nonleading twist, Z.Phys. C48,239(1990):A.R. Zhitnisky, I.R. Zhitnisky, and V.L. Chernyak, Yad. Fiz.41,445(1985).
[37]K. Nakamura et al (Particle Data Group), J. Phys. G 37,075021 (2010).
[2]Z.J. Xiao, C.S. Li and K.T. Chao, Charmless hadronic decays B→PP,PV,VV and new physics effects in the general two-Higgs-doublet models, Phys. Rev, D 63,074005(2001).
[3]S.L. Glashow, Partical symmetries of weak interactions, Nucl. Phys. 22 (1961)579; S. Weinberg, A model of leptons, Phys. Rev. Lett. 19(1967) 1264.
[4]M. Beneke, G. Buchalla, M. Neubert, and C.T. Sachrajda, QCD Factorization for B→π π Decays: Strong Phases and CP Violation in the Heavy Quark Limit, Phys Rev. Lett. 83, 1914(1999).
[5]M. Beneke and M. Neubert, QCD factorization for BPP and B→PV decays, Nucl. Phys. B 675, 333(2003).
[6]S. Glashow and S. Weinberg, Natural conservation laws for neutral currents, Phys Rev. D 15, 1958(1997).
[7]F.M. Borzumati and C. Greub, Two Higgs doublet model predictions for B → Xs in NLO QCD, Phys. Rev. D 58, 074004(1998); Addendum, to "Two Higgs doublet model predictions for B → Xsγ in NLO QCD" , Phys. Rev. D 59, 057501(1999).
[8]M. Misiak, S. Pokorski and J. Rosick, in Heavy Flavor Ⅱ edited by A.J. Buras and M. Linder(World Scientific, Singapore, 1998).
[9]Z.J. Xiao, L.X. Lu, H.K. Guo, and G.R. Lu, Rare Decays B→ Xs,d, VV and Bs,d→ 1+1- in the Multiscale Walking Technicolor Model, Chin. Phys. Lett. 16, 88(1999); Z.J. Xiao, L.X. Lu, H.K. Guo, and G.R. Lu, The rare K-decays in the Multiscale Walking Technicolor Model, Eur. Phys. J. C 7. 487(1999).
[10]P.W. Higgs,Broken symmetries, massless particles and gauge fields., Phys. Lett. 12(1964) 132; Spontaneous Symmetry Breakdown without Massless Bosons, Phy. Rev.145(1966) 1156.
[11]S.L. Glashow, J. Iliopoulos and L. Maiani, Weak Interacttions With Lepton-Hadron Symmetry, Phys. Rev. D 2(1970)1285.
[12]N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett.10(1963) 531; M. Kobayashi and T. Maskawa. CP-Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor Phys.49(1973)652.
[13]L. Wolfenstein, Parametrization of the Kobayashi-Maskawa Matrix, Phys. Rev. Lett. 51(1983)1945.
[14]J.F. Guinion, H.E. Haber, G. Kane, and S. Dawson, The Higgs Hunter's Guide, Addison-Wesley Publishing Company.1990.
[15]T.D. Lee, A Theory of Spontaneous T Violation, Phys. Rev. D 8,1226(1973).
[16]G.C. Branco and M.N. Rebelo, The Higgs mass in a model with two scalar doublets and spontaneous CP violation, Phys. Lett. B 160,117(1985).
[17]T.P. Cheng and M. Sher, Mass-matrix ansatz and flavor nonconservation in models with multiple Higgs doublets, Phys. Rev. D 35,3484(1987).
[18]D. Atwood, L. Reina. and A. Soni, Phenomenology of two Higgs doublet models with flavor-changing neutral currents, Phys. R.ev. D 55.3156(1997).
[19]Z.J. Xiao, C.S. Li and K.T. Chao, Charm multiplicity and the branching ratios of inclusive charmless b quark decays in the general two-Higgs-doublet models, Phys. Rev. D 62,094008(2000).
[20]Z.J. Xiao, C.S. Li and K.T. Chao, Gluon penguin enhancements to inclusive charm-less decays of b quark in the 2HDM with flavor changing couplings, Phys. Lett. B 473(2000)148.
[21]C.D. Lu, K. Ukai, and M.Z. Yang, Branching ratio and CP violation of B? π π decays in the perturbative QCD approach, Phys. Rev. D 63,074009(2001).
[22]J.C. Collins and D.E. Soper, Back-to-back jets in QCD, Nucl. Phys. B 193, 381(1981).
[23]H.N. Li, Unification of the κT and threshold re summations, Phys. Lett. B 454,328(1999).
[24]H.N. Li, Threshold resummation for exclusive B meson decays, Phys. Rev. D 66, 094010(2002).
[25]P. Ball, B →π and B→K transitions from QCD sum rules on te light-cone, JHEP 9809,005(1998). Theoretical update of pseudoscalar mesons DAs of high twist: the non-singlet case, JHEP 9901,010(1999).
[26]P. Ball and R. Zwicky, New reults on B →π, K,η decay form factors from light-cone sum rules, Phys. Rev. D 71,014015(2005).
[27]P. Ball, V.M. Braun, A. Lenz, High-Twist DAs of the K meson in QCD,JEEP 0605(2006)004;hep-ph/0603063.
[28]T. Feldmann, P. Kroll, and B. Stech, Mixing and decay constants of pseudo-scalar mesons, Phys. Rev. D 58,114006(1998); Mixing and decay constants of pseudoscalar mesons: the sequel. Phys. Lett, B 449,339(1999).
[29]A,J. Buras, in Probing the Standard model of Particle Interactions, ed. F. David and R. Gupta. 1998 Elsevier Science B.V., hep-ph/9806471.
[30]S. Mishima and A.I. Sanda, Calculation of Magnetic Penguin Amplitudes in B→ φ K Decays Using PQCD Approach, Prof. Theor. Phys. 110,549(2003).
[31]H.N li, S. Mishima, and A.I. Sanda, Resolution to the B→π K puzzle, Phys. Rev. D72 114005(2005)
[32]Particle Data Group, D.E. Groom et al., Eur. Phys. J. Cl5(2000)l.
[33]D.B. Chao, K. Cheung, and W.Y. Keung, Phace effect of a general two- Higgs-doublet model in b → sγ, Phys. Rev. D59,115006(1999).
[34]肖振军,B介子非粲衰变过程与新物理量子修正研究,北京大学博士研究生学位论文,2000。
[35]T.M. Aliev and E.O. Iltan. B→sγ decay in the two-Higgs-doublet model with flavor changing neutral current J. Phys. G25,989(1999).
[36]V.L. Chernyak and A.R. Zhitnitsky, Asymptotic behaviour of exclusive processes in QCD, Phys. Rep.112,173(1984);V.M. Braun and I.E. Filyanov, QCD sum rules in exclusive kinematics and pion wave function. Z. Phys.C44.157(1989); P. Ball, B→π and B→K transitions from QCD sum rules on the light-cone, J. High Energy Phys.09(1998)005; V.M. Braun and I.E. Filyanov, Conformal invariance and pion wave functions of nonleading twist, Z.Phys. C48,239(1990):A.R. Zhitnisky, I.R. Zhitnisky, and V.L. Chernyak, Yad. Fiz.41,445(1985).
[37]K. Nakamura et al (Particle Data Group), J. Phys. G 37,075021 (2010).