New Topflavor Models with Seesaw Mechanism

New Topﬂavor Models with Seesaw Mechanism

Hong-Jian He 1, Tim M.P. Tait 2, C.–P. Yuan 1,3 1Michigan State University, East Lansing, Michigan 48824, USA 2Argonne National Laboratory, Argonne, Illinois 60439, USA 3CERN, CH-1211, Geneva, Switzerland A new class of models are constructed in which the third family quarks, but not leptons, ex- perience a new SU(2) or U(1) gauge force. Anomaly cancellation enforces the introduction of spectator quarks so that the top and bottom masses are naturally generated via a seesaw mechanism. We find the new contributions to the (S, T, U) parameters and Zb¯b vertex to be generically small. We further analyze how the reasonable flavor mixing pattern can be generated to ensure the top-seesaw mechanism and sufficiently suppress the flavor-changing effects for light quarks. Collider signatures for the light Higgs boson and top quark are also discussed. PACS number(s): 12.60.-i, 12.15.-y, 11.15.Ex hep-ph/9911266

The single Higgs doublet in the Standard Model (SM) tor fermions always carry weak-isospin so that they more generates the masses for weak gauge bosons (W ,Z0) actively participate in the EWSB dynamics than any sin- and all quarks and leptons by spontaneous Electroweak glet spectator. The topflavor seesaw scenario with dou- Symmetry Breaking (EWSB). However, the striking ex- blet spectator fermions thus provides a complementary perimental fact is that only the top quark mass (mt = prospect to the original topseesaw idea with extra sin- 174.3 5.1 GeV) lies at the same scale as the masses of glet quark [5]. As will be shown below, our new topfla- (W ,Z0), while all other SM fermions weigh no more vor seesaw models, besides theoretically well motivated than a few GeV. This strongly suggests that the top and defined, are fully compatible with low energy data quark sector may involve certain new gauge dynamics in and may further provide exciting collider signatures. An contrast to all light fermions, including the tau lepton. extension to the dynamical symmetry breaking (DSB) Following this guideline of model building, we are forced scenario is discussed. to introduce new spectator fermions associated with the top sector for gauge anomaly cancellation. We then find The Topflavor Seesaw Models that the seesaw mechanism is truely generic to the top We construct two types of models in which the top quark mass generation. sector, but not tau sector, experiences a new gauge in- The usual dynamical topcolor scenario [1] associates teraction of SU(2)t or U(1)t. The full gauge group is G ⊗ ⊗ ⊗ additional strong SU(3) with the top sector, while our I = SU(3)c SU(2)t SU(2)f U(1)y (called Type-I) G ⊗ ⊗ ⊗ topflavor seesaw models involve either extra SU(2) or or II = SU(3)c SU(2)w U(1)t U(1)f (called Type- U(1) and thus predict extra color-singlet heavy gauge II). The first two family fermions are singlets under new bosons such as W 0 and/or Z0. The old non-universality SU(2)t or U(1)t. For the third family, a doublet of spec- T B T [2] or topflavor [4] models assume the entire third fam- tator quarks S =( , ) is introduced to make the the- ily joins the same extra SU(2) gauge group, which fails ory free of anomaly (cf. Table 1). A complex Higgs scalar 0 · 0 0 to explain why the top mass is so much larger than the ΦI = u + σ + i~τ χ~ (ΦII = u + σ + iχ ), with a nonzero tau mass while tau is as light as charm in the second vacuum expectation value (VEV) of u, is introduced to G G G family. The non-commuting extended technicolor (ETC) break I ( II) down to the SM gauge group SM = SU(3)c ⊗ SU(2)w ⊗ U(1)y at the scale u( 246 GeV), model [3] has focused on generating a dynamical mt by √ T embeding an extra strong SU(2) into ETC gauge group and then a Higgs doublet H = π+, (v + h0 + iπ0)/ 2 with the anomaly issue ignored for simplicity. The recent breaks GSM to the electromagnetic U(1)em at the scale dynamical topcolor seesaw models [5,6] involve an ex- v ≈ 246 GeV. (Here, ~τ is the Pauli matrix.) tra singlet heavy quark which is not necessarily required The gauge sector of Type-I or -II models contain extra 0 0 0 by the anomaly cancellation since the SU(3) topcolor massive color-singlet weak gauge bosons (W ,Z )orZ . can be vector-like for SM quarks and an additional see- The basic parameters are a small gauge-mixing angle, saw condition usually needs to be imposed. Our con- sin φ, between heavy and light gauge bosons, and a large struction stresses that a rigorous realization of topflavor ratio of two VEVs, x = u2/v2 1, as often studied in the 0 gauge group of either SU(2) or U(1) in the top-sector literature [2–4,7]. In fact, the Z of extra U(1) is generic (but not tau-sector) enforces the introduction of specta- in grand unified models and string theories [7]. As long 0 tor fermions and uniquely leads to a seesaw mechanism as sin φ and 1/x are small enough, all the effects of W 0 for mt. The topflavor with SU(2) gauge group requires and/or Z to the low energy processes can be expressed spectators only in doublet while our topflavor U(1) allows in power expansions of sin φ and 1/x [2–4]. For Type- either doublet or singlet spectators. The doublet specta- I models, the true VEV vw of the EWSB is related to the VEV v of lighter Higgs boson h0 at tree level by

1 √ √ √ 4 φ − sin 1 where MS = ysu/ 2, mst = ystv/ 2, msb = ysbv/ 2. vw = v 1 2x + O( x2 ) , with the W -boson mass The parameter κ, allowed before spontaneous symmetry mw = gvw/2; while for Type-II models, we have vw = v. breaking, is expected to be of O(MS). Because of the Table. 1. Quantum number assignments for the third family doublet nature of (T , B) in our model, the same κ appears fermions and the Higgs sector in Type-I and -II models, where in both top- and bottom-seesaw, in contrast to the recent Q t ,b T L ν ,τ T S T , B T 3L =( L L) , 3 =( τL L) ,and =( ) . dynamical seesaw models with singlet χ and ω quarks S & st t Type-I SU(3)c SU(2)t SU(2)f U(1)y [5,6]. For the parameter space M κ m >m,the mass eigenvalues of (t, b)and(T , B) can be expanded as: Q3L 3211/3 2 4 (tR,bR) 311(4, −2)/3 mstκ (mst/MS) mt mt = √ 1 − + O( ) , 312 2 4 SL 1/3 MS 1+r 2(1 + r) MS 2 4 SR 3211/3 msbκ (msb/MS) mb mb = √ 1 − + O( ) , L 112−1 2 4 3 MS 1+r 2(1 + r) MS τR 111−2 √ 2 zt 4r +3 4 6 122 MT =MS 1+r 1+ + zt +O(zt ) , Φ 0 2(1 + r) 8(1 + r)2 112 H 1 √ 2 zb 4r +3 4 6 B S M =M 1+r 1+ + 2 zb +O(zb ) , Type-II SU(3)c SU(2)w U(1)t U(1)f 2(1 + r) 8(1 + r)

Q3L 321/30 (3) 31 − (tR,bR) 0(4, 2)/3 ≡ 2 ∼ ≡ 32 where r (κ/MS) O(1) and zt(b) mt(b)/κ with SL 01/3 32 zb zt 1. The mass splitting of the heavy quarks SR 1/30 T B − 12 − ( , ), ∆MTB = MT MB, is thus deduced as L3 0 1 " # τR 110 −2 p zt 3 Φ 11−1/31/3 ∆MTB = mt + O(zt ) mt . (4) 2 r(1 + r) H 1201 T B The main new feature of our models lies in the Yukawa The tiny mass-splitting of the ( , ) doublet is essen- and Higgs sector, which is the current focus. The scalar tial for satisfying the high precision bound of δρ or T parameter [8]. Φ breaks SU(2)t ⊗ SU(2)f (U(1)t ⊗ U(1)f ) to its diag- The seesaw mass matrices in (2) are diagonalized by onal SM group SU(2)w (U(1)y)inType-I(II)modelsat × j †Mj j Mj the scale u( v). Consequently, it generates the mass 2 2 bi-unitary transformations, KL KR = diag, 0 0 0 where the superscript j ∈ (t, b) specifies the up- and of W and/or Z as well as a physical neutral scalar σ . j j down-type rotations. The rotation angles (θ ,θ ) are Then, GSM breaks down to U(1)em by the doublet Higgs L R H at the scale v ≈ 246 GeV and a light neutral Higgs bo- j 0 j z r 2 5 son h is generated. Therefore, in contrast to the usual sin θR = √ 1+ zj +O(zj ) , 1+r 1+r two doublet Higgs model (2HDM), our models have no r " # 2 4 (5) charged Higgs bosons. There are a pair of neutral scalars j r zj 3rzj 6 sin θ = 1 − − +O(zj ) . (h0,σ0) with a mixing angle α. The value of α depends L 1+r 1+r 2(1 + r)2 on the details of the scalar potential V (h0,σ0) and will be treated as a free parameter below. As a result of the Since zb/zt = mb/mt ∼ 1/40 1, the seesaw rotation spontaneous symmetry breaking, the scalars are expected effects from the bottom sector are much smaller than that to obtain tree level masses of the order of their VEV’s, in the top sector. If we consider the typical situation . 2 i.e., mh ∼ v ∼ O(100 GeV) and Mσ ∼ u ∼ O(TeV). with zb O(zt ), the tiny contribution from the bottom Defining He = −iτ 2H∗, from Table 1, we find the fol- rotations to (S, T, U)andRb can be ignored. lowing Yukawa interactions of the third family quarks for With the above seesaw rotations and the α-rotation of 0 0 both Type-I and -II: (h ,σ ) from the Higgs potential, we derive from (1) the following Yukawa interactions of (h0,σ0)withtt¯ and b¯b ys e 3 2 −√ SLΦSR − ystSLHtR − ysbSLHbR − κQLSR +h.c. in the unitary gauge, up to O(zt ,zb), 2 (1) 2 −1/2 − mt zt x 1 r 2 0 − cα 1− −sα 1− z h tt¯ which generate top- and bottom-seesaw mass matrices: v 1+r 1+r 1+r t   2 −1/2 −  0 κ  tR mt zt x 1 r 2 0 − T   + sα 1− +cα 1− z σ tt¯ (6) (tL, L) T t  mst MS  R v 1+r 1+r 1+r (2) −1/2 −1/2  0 κ  bR mb x 0 mb x 0 −(bL, BL)  +h.c. − cα −sα h ¯bb + sα +cα σ ¯bb msb MS BR v 1+r v 1+r

2 where −π/2 ≤ α ≤ 0and(sα,cα) ≡ (sin α, cos α). There are also contributions to (S, T, U) from the Higgs Thus, the htt¯ coupling may be significantly different bosons. In the limit of 1/x 1, the heavy σ0 only from the SM value of mt/vw depending on the param- indirectly couples to W/Z via its α-mixing with the light 0 0 0 0 eter space of (α, x, MS,κ). This may provide, for in- h . The interactions of (h ,σ )with(W ,Z ) are stance, important non-SM signatures via the processes 2 2 0 ∗ ∗ 0 e 2 0 0 2 e 2 0 0 2 gg → h (→ W W → `ν`ν)attheTevatron,gg → h , α α α α 2 Wµ (c h +s σ ) + 2 2 Zµ(c h +s σ ) + gg → σ0 → h0h0 and WW → tt¯ at the LHC, and 2sw 2swcw (8) − + 0 emw 2 0 0 emz 2 0 0 e e → h tt,¯ ννt¯ t¯ at the high energy linear colliders. Wµ (cαh +sασ )+ Zµ(cαh +sασ ) . sw swcw Constraints from (S, T, U)andZb¯b Thus, the (h0,σ0) contribute to low energy observables in The three main new contributions to (S, T, U)andZb¯b 0 0 the same way as the SM Higgs, but with a scaling factor arise from (a) the small mixings of heavy W and/or Z of (c2 ,s2 ). From the SM Higgs correction to (S, T, U) T B α α with W (Z); (b) the -t and -b mixings from the seesaw [8], we derive the additional contributions from (h0,σ0): mechanismaswellas(T , B) doublet itself; (c) the mixing 2 2 sm 2 of the Higgs bosons. The type-(a) contribution is generic 1 2 mh − (mh)ref 2 Mσ ∆S = cα ln 2 ln 2 + sα ln 2 , to any extended gauge sector with a breaking pattern 12π mz mz mz (9) SU(2) ⊗ SU(2) → SU(2)w or U(1) ⊗ U(1) → U(1)y − 2 2 sm 2 1 2 1 2 3 2 mh − (mh)ref 2 Mσ ∆T = 2 cα ln 2 ln 2 + sα ln 2 , and can safely fit the data as long as the mixing an- 16πcw mz mz mz gle sin φ and the ratio 1/x are small enough [4,7]. Our ' sm real concern is the new type-(b) and -(c) corrections. and ∆U 0, where (mh)ref is the reference value of the sm h h The usual expectation is that only SU(2)w singlet heavy SM Higgs mass. For (m )ref = m = 100 GeV and − fermions are phenomenologically safe [5], but our analy- Mσ = 1 TeV, we find (∆S, ∆T )=(0.02, 0.07) with 2 sis shows that the contributions of the doublet fermions sα =0.2. The contributions of the Higgs and seesaw (T , B) in our seesaw mechanism are also generically small sectors to T can have opposite signs, which makes our enough to agree with the current data. For simplicity, we model easily accommodate the data with a small T for 4 reasonable (Mσ,MS). On the other hand, MS is bounded compute the type-(b) contributions up to O(zt ) in seesaw expansion while keeping leading orders in small sin φ and from above (since a larger MS lifts up S to positive side) 1/x expansions [4,7]. To the leading order in sin φ and and also from below (since a light MS pushes both S 1/x, the doublet (T , B) behaves essentially vector-like un- and T towards negative). Assuming 1/x 1andsum- der the SM gauge group, and thus their heavy masses are ming up dominant contributions in the Higgs and seesaw expected to respect the decoupling theorem [9]. Even sectors, we can derive constraints in the (Mσ,MS) plane though the masses MS and κ are invariant under G , from the precision fit of (S, T ) [10], as shown in Fig. 1. SM sm We have chosen (mh) = 100 GeV for the (S, T )fit, the other seesaw mass terms (mst and msb) are not. It ref is a nontrivial task to confirm that the spectator-fermion with the complete 1-loop SM corrections included (in ac- corrections to (S, T, U) can decouple sufficiently since the cord with the precision of our 1-loop new physics results). − fermion-loops involving heavy T /B do contribute dan- The fitted values of (S, T )=(0.13 0.11, 0.13 0.14) gerous O(M 2)andO(M 0) terms to the self-energies of deviate from (0, 0) at 1σ level. Fig. 1 shows that Mσ is S S 0 W/Z. always bounded from below since a too light σ drives The calculations of (S, T, U) are tedious, but the re- both (∆S, ∆T ) to zero. 2 sults to O(zt ,zb) can be compactly summarized, 2 10 2 4Nc MT 7 1 1 z S = ln − + − t , 2 (0.1, 0.8) (0.1, 0.2) 9π mt 8 16ht 560 ht 1+r 2 Ncht MB 4 z 10 − t (7) T = 2 2 8ln + 6 , 16πswcw mt 3r 1+r

(TeV) 2 S Nc 1 1 zt M (0.64, 0.2) U = 1+ + 2 , 6π 10ht 70ht 1+r 1 (0.64, 0.8)

2 3 where ht ≡ (mt/mz) and we have ignored tiny O(1/ht ) terms inside [···]. (sw ≡ sin θW and θW is the weak -1 10 mixing angle.) We see that these new contributions are -1 10 1 10 2 phenomenologically safe since zt 1. For instance, tak- Mσ (TeV) −3 ing MS =2κ =5TeV,wehave(S, T, U)=(4× 10 , Fig. 1. Constraints on (Mσ,MS )by(S, T )ﬁtat95%C.L., −4 2 0.13, 6 × 10 ), while choosing (MS,κ)=(5, 4) TeV, we for mh = 100 GeV and four sets of (r, sα) as shown. The al- get (S, T, U)=(1.4 × 10−3, 0.04, 2 × 10−4). So, the see- lowed regions (indicated by arrows) lie between two lines (or saw corrections to (S, U) are generally negligible. above one line) appropriate to each parameter set.

3 We finally discuss the ratio of Z-decay width Rb = where Λf is the cutoff scale√ of the flavor symmetry break- Γ(Z → b¯b)/Γ(Z → hadrons) and the Zb¯b coupling asym- ing. Defining mij = yij v/ 2, we find that the resulting 2 2 2 2 metry Ab =(gbL − gbR)/(gbL + gbR). The current ex- mass matrix for (u, c, t, T ) poses a natural hierarchy, perimental data from Rb and Ab can be translated into   2 ¯ m11 m12 m13 m14δ the bounds on the allowed deviation of the Zbb-couplings   (gbL,gbR) from their SM values, 0.002 ≤ δgbL ≤ 0.009  m m m 2 m δ  M  21 22 23 24  and 0.004 ≤ δgbR ≤ 0.036, at 2σ level [11]. It is straight- u =   (13)  m 3 m 3 m κ forward to compute the corrections to Zb¯b couplings from 31 33 33 2 2 the seesaw sector of our model. The correction associated m41 m42 mst MS 2 with the top sector only comes from loop and is of O(zt ) 2 so that it is generally small, but the bottom-seesaw in- in which = u/Λf and δ = (u/v) are small parameters. new The down-type quarks exhibit a similar pattern in Md. duces a tree level correction δgbR to the right-handed Zb¯b coupling, A proper bi-unitary field transformation, containing the dominating 2×2 seesaw-rotations in the t-T (b-B) sector, new e b 2 δgbR = − (sin θR) . (10) can first rotate away the small mixings of T (B) with all 2swcw light quarks so that the 4×4 mass matrix reduces to 3×3 b 2 This negative correction is at the order of (sin θR) ' for the three-family quarks of the SM, i.e., 2 −6 −8 b . − − (m /κ) /(1+r) O(10 10 )forκ = O(1 10) TeV  0  and thus essentially negligible. This feature is different m11 m12 m13δ   Mc 0 from the recent dynamical seesaw models with singlets χ u =  m21 m22 m23δ  (14) and ω in which the left-handed (instead of right-handed) 0 0 0 m 2 m 2 m b-ω mixings contribute to Zb¯b vertex [6]. Another nice 31 32 t 0 feature is that our models contain no charged Higgs and where mt . mt. A similar analysis applies to Type-II are thus free of their undesirable negative correction to models. Following the procedure of Ref. [12], realistic Rb and also their enhancement to b → sγ decay rate in CKM mixings of SM fermions can be generated with a the usual 2HDM [11]. proper construction of left-handed rotations for the up- Quark Mass Matrices and Flavor Mixings and down-type quarks. The flavor changing effects asso- To establish realistic flavor mixings among all three ciated with light quarks were found to be reasonably sup- families with the well constrained Cabibbo-Kobayashi- pressed [12] in consistency with low energy data, while Maskawa (CKM) matrix generated is a more challenging right-handed mixings are constrained by the mass pat- task. We do not want to spoil the seesaw pattern of the tern (14). Sizable flavor mixings between right-handed mass matrices in (2) after the mixings with the first two cR and tR are allowed [12]: p family fermions are included, and we also need to prop- tc 0 K . 1 − (m /mt)2 ' 0.11 − 0.33 , (15) erly suppress flavor-changing effects associated with the UR t 0 light quarks. The quantum number assignments in Ta- for reasonable values of δmt = mt −mt = O(1−10) GeV. ble 1 do not automatically suppress the mixings of (T , B) Hence, the charm-gluon fusion process gc → h0t [13] pro- and (t, b) with light fermions. We impose a simple dis- vides an important Higgs discovery channel at the LHC. crete Z4 symmetry to ensure the desired pattern of the 4 × 4 mass matrices for up- and down-type quarks. Un- Extension to Dynamical Symmetry Breaking Scenario der Z4 =exp(inπ/2) with n ∈ (0, 1, 2, 3), we define the While the above topflavor seesaw models have provided following field transformations: the crucial ingredients on how a large top mass is gen- → → → erated together with the EWSB, it is desirable to invoke Q3L iQ3L,SR iSR, Φ iΦ, dynamical symmetry breaking at the TeV scale without →− →− (11) (tR,bR) (tR,bR),SL SL, introducing fundamental Higgs. Here, we only consider and other fields are unchanged by Z4. Then, we can the simplest DSB realization of our seesaw mechanism of write down all relevant effective operators in the quark Type-II models, which is called Type-IID below. Yukawa sector, invariant under GI (GII). For instance, in To replace the fundamental VEV hHi by a dynami- the Type-I models, the Yukawa Lagrangian −LY (U) of cal condensate, we may introduce a strong SU(3)t gauge the up-type quarks becomes interaction for (tR,bR)andSL while all other quarks X2 join the weaker SU(3)f group. (The strong SU(3)t is e e det Φ yi4 det Φ yij QiLHujR+ yi QiLHtR + √ QiLΦSR traditionally called topcolor [1].) Thus, our Type-IID 3 Λ2 Λ2 i,j=1 f 2 f models, as an extension of the above Type-II scenario, † G ⊗ ⊗ † e det Φ Φ e have the gauge structure IID = SU(3)t SU(3)f +y jQ LΦ HujR + y Q L HtR +κQ LSR 3 3 3 33 3 3 SU(2)w ⊗ U(1)t ⊗ U(1)f , which turns out to match the Λf Λf gauge group of the original non-seesaw topcolor models e det Φ e √yS +y4jSLHujR 2 + ytsSLHtR + SLΦSR (12) [1]. But our Type-IID models differ in that they contain Λf 2

4 new doublet spectator fermions for generating the seesaw where, for example, (κ, MS,Mc) ∼ (2, 5, 50) TeV and t mechanism and have very different quantum number ar- mt/ sin θL ∼ 600 GeV. Note that (19) involves the left- rangement enforced by the anomaly cancellation (cf. Ta- handed (instead of right-handed) seesaw rotation angle t ble. 2). The first two family fermions are charged under θL, unlike the situation in Refs. [5,6]. weaker SU(3)f and U(1)f as in the SM. The strong U(1)t As a final remark, the small masses of b, τ and the is now designed to tilt the vacuum such that only top but first two family fermions have to be generated by differ- not bottom gets a large seesaw mass, cf. (17)-(18). ent mechanisms, which are much more model-dependent The gauge group GIID first breaks down to GSM at the [14]. For instance, they can come from higher dimen- scale u and then breaks down to U(1)em at the scale v. sional effective operators [6], composite Higgs doublet The first step breaking may be effectively parametrized (formed at higher scale) with a small VEV vf & O(1− by a scalar Φ with VEV u, from which the massive octet 10) GeV [15], or extended technicolor interactions [16]. 0a 0 colorons (Gµ )andU(1) gauge boson (Zµ) are generated Table 2. Quantum number assignments for the third family at the scale Mc ∼ My . 4πu.(Mc and My are the masses fermions and the effective Higgs scalar Φ in Type-IID models. 0a 0 of Gµ and Zµ, respectively.) Thus, integrating out the 0a 0 heavy Gµ and Zµ results in the effective interaction for Type-IID SU(3)t SU(3)f SU(2)w U(1)t U(1)f the third family quarks: Q L 13 2 01/3 a a a 2 3 4πκc µ λ µ λ µ λ (tR,bR) 31 1(4, −2)/30 − L L R R R R 2 S γ S + t γ t + b γ b Mc 2 2 2 SL 31 21/30 2 (16) 4πκy 1 µ 2 µ 1 µ SR 13 2 01/3 − L L R R − R R 2 S γ S + t γ t b γ b . 11 2− My 6 3 3 L3 10 τR 11 1−20 2 2 02 2 0 0 Here, (κc,κy)=(g cot θ, g cot θ )/8π,withg (g )the 3 3 3 31 − gauge coupling of the SM color (hypercharge) force and Φ 1/3 1/3 θ(θ0) the mixing angle of the two SU(3)’s (U(1)’s) [1]. Applying Fierz transformation to (16) leads to Nambu- We thank B. A. Dobrescu, J. Erler, A. Grant, C.T. Hill, and M. E. Peskin for valuable discussions, and E. H. Jona-Lasinio (NJL) type interactions, for My ' Mc, Simmons for helpful comments on the manuscript. This 8π 2κy κy work is supported by the U.S. NSF (PHY-9802564) and c L R R L c− L R R L 2 (¯κ + )(S t )(t S )+(¯κ )(S b )(b S ) Mc 9Nc 9Nc DOE (HEP Division, Contract W-31-109-Eng-38). (17) [1] For reviews, C.T. Hill, hep-ph/9702320, hep-ph/9802216; 2 whereκ ¯c = κc(1 − 1/Nc ). In the large-Nc expansion, G. Cvetic, Rev. Mod. Phys. 71, 513 (1999). −2 a generic NJL-type vertex, κbΛ XLYR YRXL ,hasa [2] X. Li and E. Ma, Phys. Rev. Lett. 47, 1788 (1981). 2 critical coupling κbcrit ' 8π /Nc for the dynamical con- [3] R.S. Chivukula, E.H. Simmons, and J. Terning, Phys. B densation. With the U(1)t-tilting in (17), we thus have Lett. 331, 383 (1994). 385 hTLtRi6=0andhBLbRi = 0, provided [4] E. Malkawi, T. Tait, C.-P. Yuan, Phys. Lett. B , 304 (1996). D. Muller and S. Nandi, ibid. B383, 345 (1996). 3π κy 3π κy [5] B.A. Dobrescu and C.T. Hill, Phys. Rev. Lett. 81, 2634 − ≤ κc ≤ + . (18) 8 12 8 24 (1998); R.S. Chivukula, B.A. Dobrescu, H. Georgi and C.T. Hill, Phys. Rev. D59, 075003(1999). An essential feature of our scenario is that the spectator [6] H. Collins, A. Grant, and H. Georgi, hep-ph/9908330. T L, but not the SM tL, plays the key role in the dynam- [7] J. Erler and P. Langacker, Phys. Rev. Lett. 84, 212 ical condensate which generates the EWSB and seesaw (2000); and references therein. top-mass, in contrast to the recent topseesaw models in- [8] M.E. Peskin, and T. Takeuchi, Phys. Rev. Lett. 65, 964 volving extra singlet heavy quark [5,6]. Consequently, (1990); Phys. Rev. D46, 381 (1992). two composite Higgs doublets Hst and Hsb are gener- [9] N. Maekawa, Phys. Rev. D52, 1684 (1995). ated, which are made of (SLtR)and(SLbR), respec- [10] J. Erler and P. Langacker, review at http://pdg.lbl.gov. tively. The U(1)-tilting in (18) ensures that hHsti6=0 [11] H. E. Haber and H. E. Logan, hep-ph/9909335; M. L. Swartz, hep-ex/9912026. and hHsbi = 0. Thus, the Higgs spectrum contains a 0 0 [12] H.-J. He and C.-P. Yuan, Phys. Rev. Lett. 83, 28 (1999). top-condensate Higgs hst,ab-Higgs hsb and three b- 0 T B [13] W.-S. Hou, G.-L. Lin, C.-Y. Ma, and C.-P. Yuan, Phys. pions (πsb,πsb), as hybirds between ( L, L)and(tR,bR). 409 . Lett. B , 344 (1997). With the coloron mass Mc 4πu as a cut-off, we can now [14] H.-J. He, C.T. Hill, T. Tait, C.-P. Yuan, in preparation. re-derive Pagels-Stokar formula for generating both the [15] B.A. Dobrescu and E.H. Simmons, Phys. Rev. D 59, dynamical top mass and EWSB with v ≈ 246 GeV, i.e., 015014 (1999). 2 2 [16] For recent reviews, K. Lane, hep-ph/9501249; R. S. 2 Nc mt Mc 2 Chivukula, hep-ph/9701322, 9803219. v = 2 2 t ln 2 + O(zt ) , (19) 8π sin θL MS(1 + r)