1. 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

2. 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

3. 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

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

5. 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

6. 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.

7. 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

8. 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

9. 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

10. 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 

11. 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)]

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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)

18. 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

19. Other slides

20. 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

21. 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

22. 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 

23. 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

24. 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).

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