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1 NTHU March 27, 2008 TOP HYPERCHARGE MODEL Cheng-Wei Chiang ( ( ) National Central University & Academia Sinica Ref: JHEP 12 (2007) 001 ( [hep-ph[ hep-ph]) Enjoyable collaboration with Jing Jiang, Tianjun Li, and Yongrui Wang

2 Outline I. Motivations II. The model II. EW and flavor constraints III. Collider phenomenology + etc IV. Summary Top

3 Motivations

4 Theoretical Motivations for BSM Physics Fine-tuning problem: Tiny cosmological constant; Gauge hierarchy problem; Radiative corrections to Higgs boson mass; Strong CP problem; Flavor problem; Aesthetic appeal: Grand unification of couplings; Charge quantization; Reduce number of free parameters; Such considerations on the theory side call for more fundamental theories.

5 Experimental Motivations for BSM Physics Nonzero neutrino masses; Imperfect fitting in electroweak observables; Not sufficiently large CP violation or strong first-order phase transition for baryogenesis; Existence of dark matter & dark energy; These indirect evidences indicate the inadequacy of the SM to explain observed Universe.

6 Extra U(1) Symmetry Having one (or more) additional U(1) gauge factors provides one of the simplest extensions of the SM. Naively, it does not really solve any of the aesthetic problems. Moreover, its mass is not necessarily at the O(TeV) scale that can be probed at the LHC. Also, one needs to worry about the appropriate way to break the extra symmetry.

7 Extra U(1) Symmetry Detailed study of Z-pole observables shows both a small amount of missing invisible width in Z decays [N = ± , LEPEWWG (2005), ~ 2 below SM], and anomalous effective weak charge in atomic parity violation (6% accuracy, ~ 2.3 above SM). One simple solution: a U(1) model, e.g., Z from SO(10) SU(5) U(1). Fitting result even favors a family nonuniversal Z, as predicted by some superstring constructions. Four electroweak observables with significant deviations from experiments. PDG 2006 Erler and Langacker (2000)

8 Remarks It is more difficult to reduce the rank of an extended gauge group than it is to break the non-abelian factor. This can be seen by considering Higgs fields in the adjoint representation to break an SU(N) gauge group. In this case, the VEV of the Higgs fields can be made diagonal by an SU(N) transformation and thus commute with all the diagonal generators in SU(N). The rank is not reduced, but the original system is broken down to a smaller non-abelian group in tensor product with U(1) s.

9 Extra U(1) Symmetry In general, models with at least an extra U(1) symmetry is common in superstring constructions, 4D GUTs, higher-dim orbifold GUTs, as well as models with dynamical symmetry breaking. Existence of at least one additional Z gauge boson seems ubiquitous. The extra symmetry can forbid an elementary μ term in SUSY, while Cvetic and Langacker (1996); Kawamura (2000), Hall and Nomura (2001), Gogoladze, Mimura, Nandi (2003); Hill and Simons (2003). Suematsu and Yamagishi (1995); Langacker et al (1999). allowing effective μ and Bμ terms to be generated at the U(1) breaking scale (radiatively broken), providing a low-energy solution to the μ problem.

10 Extra U(1) Symmetry An extra low-energy U(1) symmetry in supersymmetric theories can also naturally solve the proton stability problem by forbidding all the baryon- and/or leptonviolating Yukawa couplings. Accompanying with the extra symmetry are some extra fermions to cancel the anomalies and at least one Higgs singlet for breaking the symmetry. Font, Ibanez and Quevedo (1989).

11 Model

12 The Model Gauge group: SU(3) C SU(2) L U(1) 1 U(1) 2 with couplings g s, g, g 1, and g 2, respectively, above the O(TeV) scale. Two-stage symmetry breaking: TeV-scale breaking down to U(1) Y by a Higgs singlet ~ (1, 1, 1/2, 1/2); EW-scale breaking down to U(1) EM by two Higgs doublets 1 ~ (1, 2, 1/2, 0) and 2 ~ (1, 2, 0, 1/2). The VEVs of these fields are rotation angle to Z and Z

13 Gauge Boson Spectrum After the symmetry breakings, we obtain the usual W boson mass M 2 W = g 2 (v v 22 )/4 = g 2 v 2 /4. Neutral gauge bosons in the gauge basis: small expansion paras The gauge basis is related to the mass basis by a rotation matrix R. The covariant derivative in the mass basis is then give rise to FCNC currents reduces to SM when B 2 decouples

14 Fermions Hinted by their heavier masses, we propose that the third-family fermions are charged differently from those in the first two families under the two U(1) s: first two families third family Quarks Leptons RH neutrinos We consider mainly v 2 >>v 1, i.e., large tan. The fermion spectrum is anomaly free by construction.

15 Yukawa Couplings Explicitly, the Yukawa terms in the Lagrangian are In the presence of 1 and 2, only mixing between first two families (quarks and leptons) exists. Bi-maximal neutrino mixing can be achieved via the mixing in the RH Majorana neutrino mass matrix M N kl through the usual seesaw mechanism.

16 Models With Similar Ideas Top-flavor model: SU(2) 1 SU(2) 2 U(1) Y SU(2) L U(1) Y. symmetry breaking achieved using one Higgs field transforming as a bidoublet under the two SU(2) s; needs two Higgs doublets to give masses to third-family and first-twofamily fermions, respectively; and contains heavy W and Z bosons. Top hypercharge-like model: also SU(2) L U(1) 1 U(1) 2 SU(2) L U(1) Y. only third-family quarks charged under U(1) 2 ; symmetry breaking achieved using one Higgs field transforming under the two U(1) s; needs only one Higgs doublet for EWSB, as in the SM; introduces spectator quarks for anomaly cancellation and top-seesaw mechanism; and contains only a heavy Z boson and no charged Higgs boson. Muller and Nandi (1996) He, Tait, and Yuan (2000)

17 Electroweak and Flavor Constraints

18 Z-pole Observables Predicted values of the EW observables are computed in the MS-bar scheme. PDG 2006 Experimental inputs: sin , -hat(m Z ) -1 = , and v=246.3 GeV. Concentrate on larger tan cases. Restrict to M Z 1 TeV to satisfy the requirement of small mixing (<~ 10-3 ) with the regular Z boson.

19 24 observables. 2 new paras. EW Observable Fitting tan SM min

20 Allowed Parameter Space Illustrate tan = 2 and 50 as two examples. No mixing between Z and Z when tan = tan, thus larger 2 -favored region for low tan. In general, M Z 2 TeV by EW constraints.

21 Fermion Mixing No mixing between first two and third families yet. Introduce, for example, additional Higgs doublet fields 3 ~ (1, 2, -1/6, -1/3) and 4 ~ (1, 2, -1/3, -1/6), the down-type quark mixing is induced from the Yukawa terms: Similar arrangement can be done to the up sector as well. The mismatch between the flavor eigenstates and mass eigenstates of the quarks will result in tree-level flavorchanging Z couplings because the U(1) charges of the third-generation quarks are different from those of the first two generations.

22 FCNC in Down Sector Reduce uncertainties from the up sector by assuming no difference between the flavor and mass eigenstates for the up-type quarks, corresponding to the case where only the 3 and 4 Higgs fields are introduced. Universal Z charge for RH fermions for simplicity. Z charges in flavor basis 180 o phase FCNC coupling hierarchy: B L sb > B L db > B L ds.

23 FCNC in Down Sector Dominant off-diagonal Z coupling is between the LH bottom and strange quarks due to the hierarchical structure in the CKM matrix B sb L = L Q dl V tb V * ts, where L Q dl = e/(3 sin2 cos ). No tan dependence in the FCNC coupling B sb L. Such a coupling can contribute to processes involving b s transitions, e.g., B = S = 2 operators that affect B S mixing: Barger, CWC, Jiang, Langacker (2004) same op as in SM

24 Remark In principle, one can also introduce FCNC in the RH sector. This generally introduces more independent parameters into the game.

25 B Constraints Use both M s and BR(B X s l l) constraints: M s exp = ± 0.10 ± 0.07 ps -1, M s SM = ± 5.28 ps -1, M s exp / M s SM = 0.89 ± 0.24 ; BR(B X s l l) = (4.50 ± 1.02) CDF (2006) Cheung, CWC, Deshpande, Jiang (2007) BABAR (2004) Belle (2005) LH LH+RH B X s l l M s

26 Z Production at LHC, Dark Matter and Higgs

27 Direct Searches at CFD Run II (2006) Recent data based on integrated luminosity of 819 pb -1 of the Drell-Yan process at CDF ( = 1.96 TeV ): The initial LHC reach will be 2 TeV (with power to discriminate among models) and can go up to 5 TeV.

28 Discovery Reach of Z at LHC The LHC can readily discover an extra neutral gauge boson with a mass of about 1 TeV cleanly from the Drell- Yan process. Dittmar, Nicollerat, Djouadi (2004) ; Rizzo (2006)

29 Discovery Reach of Z at ILC At the ILC (500 GeV and 50 fb 1 ), observations of: leptonic cross sections, leptonic FB asym., hadronic FB asym., ratio of hadronic to QED x-sec., should be able to probe a Z up to ~ 1-3 TeV through virtual exchanges. Cvetic and Godfrey (1995)

30 Further Determinations If one Z gauge boson is really found at the LHC, the next job would be to determine its couplings to chiral fermions in order to pin down its origin (e.g., which model it belongs to). A combination of forward-backward asymmetries as a function of rapidity, rapidity distributions, rare decays (Z W l ), and associated production of Z Z, Z W, Z should provide significant diagnostic ability up to 1-2 TeV.

31 Drell-Yan Process As in other Z models, the Z in our model can be searched for through the Drell-Yan processes. For the mass range we consider, the decay width of the Z is typically a few tens of GeV. Apply simple cuts of requiring: p T of the outgoing leptons be larger than 20 GeV, absolute value of rapidities of the leptons be less than 2.5, and invariant mass of the lepton pair be between M Z Z /2 and M Z + Z /2. After these cuts, SM background becomes negligible compared to the signal.

32 Drell-Yan Process Total luminosities required for a 5 discovery for different cos and M Z in the model. With 100 fb -1, the discovery reaches for cos = 0.8, 0.6, 0.4 and 0.2 are about 4.1, 5.0, 5.8 and 6.9 TeV. Production cross section is strongly dependent of cos.

33 Dark Matter Candidate Stability of dark matter is usually achieved using a discrete global symmetry (e.g., a Z 2 symmetry such as the R parity in SUSY LSP). However, the global symmetry can be broken by nonrenormalizable higher-dim operators due to quantum gravity effects if it is not gauged. A possible solution: a gauged Z 2 symmetry derived from a continuous local symmetry that is broken at the TeV scale stable particle with mass ~ O(TeV). Krauss and Wilczek (1989)

34 Dark Matter Candidate Introduce a singlet scalar field ~ (1, 1, -1/4, 1/4). Relevant Lagrangian for and its couplings to (both carrying U(1) charges) is After the U(1) 1 U(1) 2 U(1) Y breaking, becomes a stable particle due to the gauged Z 2 symmetry under which goes to and the other fields are invariant. Interaction with the flavor sector depends on its mixing with 1 and 2.

35 Higgs Potential Most general CP-conserving, renormalizable Higgs potential (without yet): A m is dim-1 and chosen to be real, i are dimensionless. Two global SU(2) symmetries if we neglect the terms [A m h.c.] and 4 ( 1 2 )( 2 1 ). In this case, it is always possible to make an SU(2) 1 SU(2) 2 rotation so that the left-over U(1) EM gauge symmetry is unbroken.

36 Alignment Issue After introducing the two terms into the Higgs potential, the SU(2) 1 SU(2) 2 global symmetries is broken down to the SU(2) global symmetry identified as the SU(2) L. For simplicity and without loss of generality, assume that no CP violation and positive v 1, v 2 and A m. One can make an SU(2) L rotation so that 2 does not break the U(1) EM gauge symmetry. If A m is around the EW scale and 4 ~ O(1), the magnitude of the -[A m h.c.] terms is much larger than that of 4 ( 1 2 )( 2 1 ) because u is much larger than v 1 and v 2. Therefore, the Higgs potential naturally leads to an alignment that U(1) EM is not broken.

37 Higgs Spectrum There are 10 degrees of freedom in the three Higgs fields. After SU(2) L U(1) 1 U(1) 2 U(1) EM, there will be left with 6 physical Higgs fields: three CP-even ones (H 1, H 2 and H 3 ), one CP-odd one (A), and one charged pair (H ± ). The squared mass of the CP-odd Higgs is proportional to A m u and tan enhanced. The charged Higgses have the squared mass

38 Summary We construct a model based upon the gauge group of SU(3) C SU(2) L U(1) 1 U(1) 2, where an extra heavy Z possibly exists at the TeV scale. Fermions in the third family are charged differently from the first two families under U(1) 1 U(1) 2, thereby inducing tree-level FCNC currents. Some constraints are imposed on its parameters from electroweak precision observables and B physics data, with the former being stronger and more solid. We compute its production rate at the LHC. We discuss a possible dark matter can didate by gauging a discrete Z 2 symmetry. Future project: Higgs sector phenomenology.

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