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FCNC Z 0 Model and Effects in B Physics Cheng-Wei Chiang National Central University & Academia Sinica Cheng-Wei Chiang National Central University & Academia Sinica Enjoyable collaborations with: V. Barger, J. Jiang, H.-S. Lee, and P. Langacker PLB 580, 186 (2004); 596, 229 (2004); 598, 218 (2004). July 21- 22, 2005 Taipei Summer Institute

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C.W. ChiangFCNC Z' Boson (7/21/2005)2 Outline Introduction to a FCNC Z 0 boson Collider constraints Effects in low-energy effective Hamiltonian Some hintsnew physics in charmless | S| = 1 transitions Some hints of new physics in charmless | S| = 1 transitions B s mixing Summary

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C.W. ChiangFCNC Z' Boson (7/21/2005)3 Extra heavy neutral Z 0 gauge bosons exist in most extensions of the Standard Model and their supersymmetric versions. Examples include GUT’s, extra-dimensional models, string models, little Higgs, etc. The extra symmetry can forbid an elementary term in SUSY, while allowing effective and B terms to be generated at the U(1) 0 breaking scale, providing a solution to the problem. Accompanying with the extra symmetry are some exotic fermions to cancel the anomaly and at least a Higgs singlet to break the symmetry. Conclusion: for physics beyond the SM, the existence of a Z 0 gauge boson is almost model-independent; only the details, such as the mass and couplings, are model specific. Need for a Z 0 Boson

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C.W. ChiangFCNC Z' Boson (7/21/2005)4 The Fifth Force

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C.W. ChiangFCNC Z' Boson (7/21/2005)5 In the gauge eigenbasis, the Z 0 neutral current Lagrangian is given by In string models, it is possible to have family-nonuniversal Z 0 couplings to fermion fields due to different constructions of the different families. [Chaudhuri et al, NPB 456, 89 (1995)] After flavor mixing, one obtains FCNC Z 0 interactions (non-diagonal) in the fermion mass eigenstates, which may lead to new CP-violating effects: This may also imply flavor-violating Z couplings if there is Z-Z 0 mixing. FCNC Z 0 Boson

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C.W. ChiangFCNC Z' Boson (7/21/2005)6 The mass of an extra Z 0 from the non-observation of direct production (p anti-p → Z 0 → l l) at CDF (√s = 1.96 TeV) is found to be ≥ 670 GeV (95% CL). [http://www-cdf.fnal.gov/physics/exotic/r2a/20040916.dilepton_zprime/] The mass of an extra Z 0 from the non-observation of direct production (p anti-p → Z 0 → l l ) at CDF (√s = 1.96 TeV ) is found to be ≥ 670 GeV (95% CL). [http://www-cdf.fnal.gov/physics/exotic/r2a/20040916.dilepton_zprime/] Direct Search at CDF Run II The initial LHC reach will be 2 TeV (with power to discriminate among models) and can go up to 5 TeV.

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C.W. ChiangFCNC Z' Boson (7/21/2005)7 Precision data also provide stringent constraints. [Erler and Langacker, Review of Particle Physics 2004] More Constraints

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C.W. ChiangFCNC Z' Boson (7/21/2005)8 The Z-Z 0 mixing is given as Z 1 = Z SM cos + Z 0 sin Z 2 = – Z SM sin + Z 0 cos The mixing angle between Z and Z 0 satisfies LEP precision measurement of coupling constants at the Z-pole gives | | < (a few) £ 10 -3. [Erler and Langacker, PLB 456, 68 (1999)] This also implies a heavy Z 0 boson. Z-Z 0 Mixing

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C.W. ChiangFCNC Z' Boson (7/21/2005)9 The sin2 measurements from various | S| = 1 B meson decays do not completely agree with the measurements from the charmonium modes. These inconsistencies may have the same new physics origin. Studies of the K S mode, which has a simpler amplitude structure, indicates that it is likely to be polluted with a new EW penguin amplitude. Anomalies in Hadronic b → s q q Transitions

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C.W. ChiangFCNC Z' Boson (7/21/2005)10 Consider the following ratios of the BR’s of K modes: R c and R n should be the same in the SM. Possible explanations: underestimate of 0 detection efficiency, thus overestimating the BR’s of those corresponding modes; [Gronau and Rosner, PLB 572, 43 (2003)] Isospin-violating new physics contribution to color-allowed EW penguin amplitude. [Buras et al, PRL 92, 101804 (2004); NPB 697, 133 (2004), hep-ph/0410407] K Anomaly 2.4

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C.W. ChiangFCNC Z' Boson (7/21/2005)11 The effective Hamiltonian of the anti-b → anti-s q anti-q transitions mediated by the Z ' is Even though the operator is suppressed by the heavy Z 0 mass, they can compete with SM loop processes because of their tree-level nature. Low-Energy Effective Hamiltonian s s Z 0Z 0 Z 0Z 0 [Barger, CWC, Langacker and Lee, PLB 580, 186 (2004); 598, 218 (2004)]

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C.W. ChiangFCNC Z' Boson (7/21/2005)12 In general, one will receive new contributions in both QCD and EW penguin operators. In view of the fact that the K data can be explained with a new EW penguin amplitude, we assume that the Z 0 mainly contributes to these operators and obtain This is possible through an O(10 -3 ) mixing angle between Z and Z 0. Note also that here we only include the LH coupling for the Z 0 -b-s coupling. The RH coupling can in principle be included, at the price of more free parameters to play with. Low-Energy Effective Hamiltonian

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C.W. ChiangFCNC Z' Boson (7/21/2005)13 To study the K anomaly Buras et al introduce the ratio [PRL 92, 101804 (2004] [PRL 92, 101804 (2004)] One should note that although c 7,8 play a less important role compared with c 9,10 in the SM, they can receive contributions from the Z ' such that we cannot neglect them. In the analysis of Buras et al, it was implicitly assumed that new physics contributes dominantly to the (V-A) (V-A) EW penguins. As one of their conclusions under this assumption, S K S will be greater than S K S or even close to unity if one wants to explain the K anomaly. Some Notations

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C.W. ChiangFCNC Z' Boson (7/21/2005)14 Using the same hadronic inputs from modes as given by Buras et al, we get two sets of solutions: (q, ) = (1.61,–84 。 ) and (3.04,–83 。 ), whereas they only take the small q solution. Solutions

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C.W. ChiangFCNC Z' Boson (7/21/2005)15 Use the following variables to parameterize our model: We obtain the solutions (RH couplings included for illustration purposes only): We were able to find solutions (except for (A L )) to account for both the K and S K S data because the contributions from the O 7,8 (from RH couplings at the Z 0 -q-qbar vertices) and O 9,10 operators interfered differently in these two sets of decay modes. Fitting with S K S Too

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C.W. ChiangFCNC Z' Boson (7/21/2005)16 In the SM M B s is expected to be about 18 ps -1 and its mixing phase s is only a couple of degrees. In contrast to the B d system, the more than 25 times larger oscillation frequency and a factor of four lower hadronization rate from b quarks pose the primary challenges in the study of B s oscillation and CP asymmetries. Although new physics contributions may not compete with the SM processes in most of the b → c decays ( s less modified), they can play an important role in B s mixing because of its loop nature in the SM. In the following, we quote the SM values: M s SM = (1.19 ±0.24) £ 10 -11 GeV = 18.0 ±3.7 ps -1, and M s SM = (1.19 ± 0.24) £ 10 -11 GeV = 18.0 ± 3.7 ps -1, and x s SM ≡ ( M s / s ) SM = 26.3 ± 5.5. Testable at Tevatron and LHC for x s up to ~75 with error at a few % level and s / s ~0.15 with error ~0.02. Precision on sin(2 s ) depends upon x s. B s Mixing

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C.W. ChiangFCNC Z' Boson (7/21/2005)17 The mixing is induced by a tree-level Z 0 exchange (LH current only): In the particular case of a left- chiral (right-chiral) Z ' model, one can combine the measurements of M s (or x s ) and sin 2 s to determine the coupling strength L ( R ) and the weak phase L ( R ) up to discrete ambiguities. Once RH currents are introduced, L-R interference dominates over purely LH or RH interactions. B s Mixing with a FCNC Z 0 Barger, CWC, Jiang and Langacker, PLB 596, 229 (2004)

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C.W. ChiangFCNC Z' Boson (7/21/2005)18 Extra U(1) gauge bosons are common in many extensions of the SM. FCNC can be induced in models where the U(1) 0 charges are non- diagonal or family-nonuniversal. Such models provide new CP-violating sources that may have significant effects on low-energy physics. BR’s and CPA’s of K and K S modes can be readily accounted for. Implications in B s mixing are analyzed. Analysis of EDM, updated results of hadronic Bdecays along with analyses of semileptonic Bdecays are in progress. Analysis of EDM, updated results of hadronic B decays along with analyses of semileptonic B decays are in progress. Summary and Outlook

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Other slides

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C.W. ChiangFCNC Z' Boson (7/21/2005)20 If the H 1 H 2 term is missing from the superpotential ( = 0), then the theory presents an additional Peccei-Quinn symmetry. Under this symmetry, the Higgs superfield H 1 undergoes a phase transition. When the bosonic component of H 1 gets a non-zero vev, the PQ symmetry is broken, leading to an experimentally unacceptable Weinberg-Wilczek axion. Thus, a non-vanishing is required to render a physically acceptable theory. At least a Higgs singlet is required to break the U(1)’ symmetry. This may lead to mixing between the standard Higgs doublet and the new singlet. The LEP limit of SM-like Higgs mass (m h >= 115 GeV) does not apply and a lighter Higgs is allowed. The neutralino sector is extended to have 6 components [MSSM: 4 and NMSSM: 5]. This may have significant effects on CDM. Neutrinos may carry U(1)’ charges. They are Dirac fermions if they carry such charges; otherwise, they are still Majorana. Some Notes

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C.W. ChiangFCNC Z' Boson (7/21/2005)21 Accompanying with the extra symmetry are some exotic fermions to cancel the anomaly, or the anomalies are canceled by a Green-Schwarz mechanism and at least a Higgs singlet to break the symmetry. In perturbative heterotic string models with supergravity mediated symmetry breaking, the U(1)’ and EW breaking are both driven by a radiative mechanism, with their scales set by the soft SUSY breaking parameters, implying that the Z’ mass should be around 1 TeV. [Cvetic et al, PRD 56, 2861 (1997)] Radiative breaking of EW symmetry (SUGRA or GMSB) often yields EW/TeV-scale Z’. In contrast to the B d system, the more than 25 times larger oscillation frequency and a factor of four lower hadronization rate from b quarks pose the primary challenges in the study of B s oscillation and CP asymmetries. World average s / s = 0.24 +0.28+0.03 –0.38–0.04. [hep-ex/0507084] Some Notes

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C.W. ChiangFCNC Z' Boson (7/21/2005)22 B d K s and 0 K s (I) CWC and Rosner, PRD 68, 014007 (2003); Barger, CWC, Langacker, and Lee, PLB 580, 186 (2004) The K s mode is a loop-dominated process in SM (susceptible to new physics): A( K s ) = p e i ( SM + p ) + s e i ( SM + s ), SM ~ arg[V cb V cs * ]. Assume new physics contributes to one of the decay amplitudes. |p| can be normalized by BR(K *0 + ), consistent with SM prediction. s contains EWP, assumed to be modified by new interactions. The 0 K s mode is slightly more complicated and involves color-suppressed tree amplitude. 1.3 / 2.7 discrepancy 2.2

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C.W. ChiangFCNC Z' Boson (7/21/2005)23 B d K s and 0 K s (II) Assume new isospin-violating 4-quark interactions induced by flavor-changing Z’ couplings. Involve the parameters: and the weak phase L. BR’s subject to hadronic uncertainties, which are cancelled in CPA’s. CPA’s seem to favor a new weak phase of L ' 100 ± and | | ' 10 -3 ~10 -2. Z’ changes the CPA’s for both modes in the same direction. K s 0 K s

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C.W. ChiangFCNC Z' Boson (7/21/2005)24 Basics of B Factories SLAC PEPII collider using BaBar detector: 9.0GeV(e - ) £ 3.0GeV(e + ); L=6.5 £ 10 33 /cm 2 /sec s L dt = 131 fb -1 ; on resonance: 113 fb -1 ; 123M B anti-B pairs (2003 summer) KEKB collider using Belle detector: 8.0GeV(e - ) £ 3.5GeV(e + ); L=1.0 £ 10 34 /cm 2 /sec s L dt = 158 fb -1 ; on resonance: 140 fb -1 ; 152M B anti-B pairs (2003 summer) s L dt = 219 fb -1 (3/30/2004).

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C.W. ChiangFCNC Z' Boson (7/21/2005)25 V. Barger, J. Jiang, P. Langacker, hep-ph/0405108, submitted to PLB.

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