Sutapa Sen and Aparna Dixit. Department of Physics, Christ Church P.G. College, Kanpur , India. Abstract

Transcription

1 SU(3) C SU(3) L U(1) X gauge symmetry from SU(4) PS SU(4) L+R Sutapa Sen and Aparna Dixit Department of Physics, Christ Church P.G. College, Kanpur , India Abstract We consider an extension of the standard model gauge symmetry to a local gauge group SU(3) C SU(3) L U(1) X which is a subgroup of SU(4) PS SU(4) L+R.The symmetry breaking pattern is SU(4) SU(3) U(1) for both weak SU(4) L+R and strong Pati-Salam SU(4) PS group. The SU(3) C U(1) B-L SU(3) L U(1) Y1 ( ) local gauge symmetry breaks to SU(3) C SU(3) L U(1) X and generates a model with threegeneration, anomaly-free fermions which transform as bifundamentals of ( ). The model is of Pleitez-Frampton type but SU(3) L gauge bosons (B-L = 0) do not include bilepton gauge boson.the neutral gauge bosons include γ, Z, Z and a fourth, heavy gauge boson Z which decouples from rest but can decay to ordinary fermions. An analysis for two -body decays of neutral Z gauge boson is presented.from Yukawa interactions, the masses of all exotic fermions are obtained in the TeV region.this restricts Z decays to exotic fermions The Z is also found to be leptophobic and decays mainly to quarks. PACS numbers: 1.60 Cn, Dg, Pw

2 1. Introduction One of the simplest extension of the Standard model is to enhance the SU() U(1) symmetry to SU(3) and SU(4) groups. This provides quark - lepton unification at TeV scale and the weak mixing angle θ W as[1] sin θ W = 0.5 at the unification scale. While SU(3) and SU(4) gauge symmetry work only for leptons, the symmetry has to be enhanced to SU(3) U(1) X to accommodate fractionally charged quarks as well [].The X charges are fixed by anomaly cancellations within three generations of fermions.the SU(3) C SU(3) L U(1) X symmetry include cases of subgroups of higher symmetry group as E 6 or SU(6) U(1) [3] with gauge bosons having ordinary electric charges. A second type of models include quarks with exotic electric charges 43 and 53 and doubly charged gauge bosons []. The electric charge operator Q is a linear combination of three generators of the SU(3) L group, Q = T 3L + a T 8L + XI 3, where T i L = 1 λ i L, e i = 1,,..8 ; λ i L are Gell-Mann matrices for SU(3) group with normalization Tr(λ i L λ j L) = δ ij and I 3 = Dg (1,1,1) unit matrix. For models with no doubly charged gauge bosons [3], a = -1 3 while a = + 3 for the class of models with doubly charged bosons [4]. An extension of local gauge group to SU(3) C SU(4) L U(1) X has been recently proposed for three-family models with gauge bosons without exotic charges [5]The Little Higgs models also deal with extended electroweak gauge symmetry and around TeV scale [6] A general expression for electric charge operator in the models is [5]

3 3 Q = T 3L + a T 8L + b T 15L + XI 4, (1) e where Ti L = 1 λ i L, i = 1,,..8 ; λ i L are Gell-Mann matrices for SU(4) group with normalization Tr(λ i L λ j L) = δij and I 4 = Dg (1,1,1,1) unit matrix. For models with gauge bosons with electric charges 0, + 1 only, the possibilities for simultaneous values of a, b are [5] a = b = + 1 3; a = 1 3, b = - 3 ; a = -1 3, b = 3 In this work we consider a version of model with doubly charged gauge boson and charged heavy leptons as derived from a gauge symmetry which is a subgroup of SU(4) PS SU(4) L+R. This group has been recently considered in 5D supersymmetric case [7] as a subgroup of SO(1) and E 7.The SU(4) PS strong gauge group as well as SU(4) L+R flavor group are decomposed as SU(4) SU(3) U(1), such that local gauge symmetry is G = SU(3) C SU(3) L U(1) B-L U(1) Y1 () The SU(4) generators B-L = Dg ( 16,16,16, - 1) = 3 T 15 PS ; Y 1 = Dg ( 1, 1, 1, -3) = 6 T 15 L+R The electric charge operator is Q = T 3-3 T T 15 + (B-L) I 4 (3) e where T α, α = 1,,.15 are diagonal generators of SU(4) L+R and I 4 is the 4 x 4 identity matrix. T 3 = 1 Dg (1,-1,0,0), T 8 = 1 Dg (1,1,-,0) and T 15 = 1 Dg(1,1,1,-3) 3 6 By extending the gauge symmetry to which is embedded in SU(4) PS SU(4) L+R gauge group, a bifundamental pattern is obtained for fermions and scalars. An important point of difference of our model from all other versions of 3-3-1

4 4 models [4 ] is that (B-L) baryon minus lepton number is conserved and is an operator of the strong SU(4) PS group. The gauge bosons of the model include singly and doubly charged vector bosons which are not bileptons and have B-L = 0.The doubly charged exotic gauge boson can couple only to exotic quarks and lepton.the neutral bosons include photon field γ, Z, Z and a fourth boson Z which decouples from the rest. The fourth gauge boson couples to ordinary fermions and has a large decay width and mass. The SU(3) C SU(3) L U(1) X gauge symmetry is obtained due to symmetry breaking U(1) Y1 U(1) B-L U(1) X at some scale M U by Higgs mechanism with a new neutral scalar Φ 0 with lepton number L = -3, which has vacuum expectation value aligned along < Φ 0 > = V. In section we present a general formalism of the model and consequences of SU(4) C SU(4) L+R symmetry breaking. Section 3 deals with the gauge boson sector with mixing and mass of neutral gauge bosons. Section 4 deals with the fermion content of the model and scalars needed for symmetry breaking. In section 5, the charged and neutral currents along with Yukawa couplings and fermion masses and mixing are discussed. The phenomenology of the Z, Z,Z gauge bosons and possible decays to quarks, leptons and scalars are presented in section 6. Section 7 is a brief discussion of results and conclusions.. General Formulation Recently, the SO(1) SU(4) C SU(4) L+R has been considered for grand unification group [7] in a 5D formalism. While SU(4) PS SU(3) C U(1) B-L breaking mechanism by (15,1) Higgs at a scale M U [11] gives leptoquark gauge bosons at high energies, we do not consider these bosons and assume a symmetry.

5 5 The decomposition of SU(4) L+R SU() L SU() R U(1) Y1 in the left-right symmetric model gives [7] 4 L+R = ( L, 1 R, 1 ) + ( 1 L, R, - 1) = ( x u, x d ) + ( y u, y d ) (4) where Y 1 is the SU(4) operator, Y 1 = 1 Dg ( 1,1,-1,-1) We consider the decomposition SU(4) L+R SU(3) L U(1) Y1 with 4 L+R = (3 L, 1 ) + ( 1 R, - 3 ) = ( x u, x d, y d y d y u ) + ( y d y d y d ) where the SU(4) operator Y 1 = 6 T 15 L+R (5) The gauge bosons belong to 15-plet representation of SU(4) and can be decomposed as 15 = (8, 0) + (3, ) + (3*, - ) + (1, 0) (6) The flavor SU(4) L+R decomposition gives 8 L SU(3) L gauge bosons, (3 + 3*) X bosons and a neutral singlet Y 1 µ associated with U(1) Y1. The strong SU(4) PS group is decomposed as SU(4) PS SU(3) C U(1) B-L where SU(3) C is the color QCD gauge group and operator (B-L) = Dg ( 1, 1 1, - 1 ) = T 15 PS PS = ( 3 C, 16) + ( 1, -1 ) = x C + x S (7) The gauge bosons include 8 gluons, 6 ( 3 + 3*) leptoquarks and a neutral singlet B µ (1,0) associated with U(1) B-L. The SU(4) L+R gauge bosons belong to the 15 plet adjoint representation W +µ Y -µ X ++ W -µ µ D Y - -µ X +µ D 1 µ λ m W µ m = Y +µ Y ++µ D 3 µ X +++µ X - -µ X -µ X - - -µ D 4 µ where m = 1,,.15 and D 1 µ = W 3µ + W 8 µ W 15 µ ; D µ = - W 3 µ + W 8 µ 3 + W 15 µ 6; D 3 µ = - 3 W 8 µ + W 15 µ 6 ; D 4 µ = -3 6 W 15 µ.

6 6 The SU(4) L+R SU(3) L U(1) Y1 breaking by 15-plet Higgs scalar [11] is assumed so that the local gauge symmetry group G = SU(3) C U(1) B-L SU(3) L U(1) Y1 = G C G L This is broken at unification scale as U(1) Y1 U(1) B-L U(1) X, where X = Y 1 + (B-L) = 6 T 15 + (B-L) I 4 (8) A neutral gauge boson V µ is associated with U(1) X. We consider a neutral scalar Φ 0 = ( 1 C, 1 L, - 3, 3) = ( y d y d y d x S x S x S ) = (1 C, 1 L, 0) aligned with vacuum expectation value [VEV} < Φ 0 > = V I 4 The physical gauge fields V µ and a fourth neutral boson Z µ are defined as B µ = cosθ V µ - sinθ Z µ ; Y µ 1 = sin θ V µ + cosθ Z µ (9) The unification condition gives! = ; tan θ = g B-L g 15 ; g X g 15 = sinθ g X g B-L g 15 The covariant derivative D µ = µ - i g T a W a µ - i g X X V µ - i g T b W µ b - ig X.( 6 T 15 X sin θ )Z µ sinθ cosθ where a = 1,,..8 and b = 9,10,.14. (10) The neutral gauge boson Z µ decouples from the rest and acquires a large mass, M Z = 9 g X V sin θ cos θ The pattern of symmetry breaking in the present case is SU(3) C x SU(3) L x U(1) Y1 x U(1) B-L SU(3) C x SU(3) L x U(1) X M U SU(3) L U(1) X SU() L U(1) X U(1) X SU() L U(1) Y U(1) em M χ M χ M η,m ρ Further breaking of SU(3) L U(1) X symmetry requires three scalar triplets χ, ρ, η with VEV aligned in the directions

7 7 < χ 0 > = [0, 0, V ] T ; < ρ 0 > = [0, u, 0 ] T ; < η 0 > = [ v, 0, 0 ] T (1) η (1,3,0) = (η 0,η 1 -, η + ) T ; ρ(1,3,1) = ( ρ +, ρ 0, ρ ++ ) T ; χ (1,3,-1) = (χ -, χ - -, χ 0 ) T (13) The sextet scalar is not required for charged lepton masses in this case. We consider [1] spontaneous symmetry breaking U(1) X U(1) X U(1) Y by Higgs scalar χ,where X = 3 T 8L, and g X = g 3. The unification condition gives 1 = ; g Y = g g X ; tan θ W = g Y = g X. g Y g X g X (3g X + g ) g (3g X + g ) g X = sin θ W (14) g ( 1-4 sin θ W ) The weak mixing angle sin θ W < 0.5 at unification scale. An important difference from model with orbifold breaking [1] lies in the hypercharge operator Y defined as Y = ( X X ). Case (1): a = - 3, b = 6 From eqn (8) the electric charge operator Q = T 3 L + Y = T 3L - 3 T 8L + 6T 15 + (B-L)I 4. (15) e In terms of SU(4) operator T 3R = 1 Dg ( 0,0, 1, - 1) = 3 T 8L - 6T 15 Q = T 3L - T 3R + (B-L) I 4 which corresponds to the flipped model [10] Case () a = 3, b = - 6 A second type of model with a = 3 exists in literature [4,13] with mathematically equivalent formalism.this is obtained in the model by choosing an Orthogonal combination for vector boson for V µ associated with U(1) X and Redefining hypercharge Y.

8 8 We consider U (1) Y1 U(1) B-L U(1) X breaking with charge X defined as the orthogonal combination X = - Y 1 + (B-L) = - 6 T 15 + (B-L) I 4 The hyper charge operator is defined as Y = X + X [1] while the charge operator Q = T 3L + 3 T 8L - 6 T 15 + ( B- L) I 4 e In terms of SU(4) operator T 3R, Q = T 3L + T 3R + (B-L ), which corresponds to Georgi-Glashow model [9].The orthogonal combination for Z µ is changed in this case while 3 L 3 L * adjoint representation for quarks and leptons. This requires a conjugate adjoint representation for gauge bosons.this case has been considered in literature [13]. We shall consider only case (1) in this work. 3. Gauge boson sector and masses in model. The charged gauge bosons acquires masses as given below M ( Y + ) = ½ g (V + v ), M ( Y + + ) = ½g (V + u ); M (W + ) = ½ g ( v + u ) (16) The neutral gauge bosons include the photon field A µ, massive physical fields Z µ, Z µ and a fourth heavy gauge boson Z µ so that the covariant derivative D µ = µ - i e QA µ - i e ( T 3L Q s W ) Z µ + ig ( (1 4 s W ) [T 8L + 3 s W X ]Z µ s W c W c W (1-4 s W ) _ i g X [ 6T 15 - sin θ X]Z µ - i g [ λ 1 W µ + +λ 45 Y µ - + λ 67 Y µ H.c] (17) sinθ cosθ where λ a b = ½ (λ a + iλ b ) = T a + it b and sinθ W = s W (eqn.14) The photon field A µ and the fields Z µ and Z µ are given by A µ = s W W 3 µ + c W [ 3 t W W 8 - (1-3 t W ) V µ ] Z µ = c W W 3 µ - s W [ 3 t W W 8 µ - (1-3 t W ) V µ ] Z µ = (1-3 t W ) W 8 µ + 3 t W V µ (18) The Y hypercharge associated with SM abelian gauge boson is

9 9 Y µ = [ 3 t W W 8 µ - (1-3 t W ) V µ ] (19) For the mass spectrum of neutral gauge bosons, we obtain M = g 4 [V {W 8 µ 3 + g X g V µ } + u { (- W 3 µ + W 8 µ 3) + g X g V µ } where g X g = s W (1-4 s W ) + v { W 3 µ + W 8 µ 3 } ] (0) This gives zero mass for photon while masses for Z µ, Z µ are obtained from M Z =g ( v + u ) (1) c W M Z = g [ V c W + (1-4 s W ) (v + u ) + 3u s W ] () 3 (1-4s W ) 4c W (1-4s W ) M ZZ = g (1-4s W ) [ v - u ( 1+ s W ) ] (3) 4 3c W ( 1-4 s W ) From the mixing of Z µ, Z µ through angle ϕ, tan ϕ = M ZZ (M Z - M Z) ϕ = M ZZ M Z. The mixing between Z, Z can be considered by defining Z 1 µ = cosϕz µ - sinϕ Z µ ; Z µ = sinϕ Z µ + cos ϕ Z µ (4) M Z1, Z = 1 [M Z + M Z + { (M Z + M Z ) - 4( M Z M Z - ϕ M Z 4 ) }] (5) 4. Fermions and Scalars. In the present model, bifundamental structures are obtained for fermions and scalars with six basic fundamentals G C = SU(3) C U(1) B-L : M = x C = (3 C, 16 ), N = x S = (1 C, -1), N =(1 C,-3) G L = SU(3) L U(1) Y1 : a = (3 L, 1); b = y d y d y d = (1 R, -3) ; c= y d = (1 R, -1) The X- charges are defined by X = Y 1 + ( B-L) Table 1 lists three generation, anomaly-free fermion representation in which

10 10 the SU(3) L triplet (3 L, 1 ) is considered for both quarks and leptons.the (8,0) gauge bosons have B-L = 0 and are not bileptons. TABLE 1 Three generations of anomaly-free fermions as bifundamentals of 3 C - 3 L 1 Y1 1 B-L Fermion content Q i ( d Li, u Li, D Li ) a*m (3 C,3 L *, -13) Q 3 ( t L, b L, T L ) am (3 C,3 L, 3) u Rα c d Rα c cm* (3 C *,1 R,-3) c*m* (3 C *,1 R, 13) D Ri c (D R1 c, D R c ) b* M* (3 C *,1 R, 43) T R c bm* (3 C *, 1 R, -53) L α (ν α, e α,p α + ) an (1 C, 3 L, 0) e Rα c P Rα c c* N* (1 C,1 R, 1) bn* (1 C, 1 R,-1) Here i = 1, and α = 1,,3 denote family indices. The scalars are also bifundamentals and include η (η 0,η - 1, η + ) T a c (1 C, 3 L, 0) ρ ( ρ +, ρ 0, ρ ++ ) T a c* ( 1 C, 3 L, 1) χ (χ -, χ - -,χ 0 ) T a b ( 1 C, 3 L,-1) Φ 0 b N * ( 1 C, 1 L, 0) The above particles correspond to an anomaly-free, three generation Pleitez- Frampton model with heavy leptons and exotic quarks. The special assumption of the

11 11 present model is that in 3 L the third flavor is T 3R = + 3.The leptonsψ L (ν,e -,P + ) are obtained as a result of the triplet 3 L structure and symmetry breaking pattern for the c model. The positron e Rα ( 1,1,1) and heavy lepton P c Rα (1,1,-1) have to be added in this case. The scalar sector also do not require a sextet scalar field and consists of three triplet scalars and one new scalar Φ 0 with L = - 3. The mass of Φ 0 is obtained from symmetry breaking as m Φ0 V where <Φ 0 > = V >>V. There is no further difference for scalar sector from detailed work by several authors [13,14] We consider the relations between ordinary and physical scalars in eqn. (1),(13) ρ ++ = 1 [u G ++ + V H ++ ] ; χ ++ = 1 [ VG ++ + u H ++ ] (u + V ) (u + V ) η 1 + = 1 [ -v G uh 1 + ] ; ρ + = 1 [ u G v H 1 + ] (u + v ) (u + v ) η + = 1 [ -v G + + uh + ] ; χ + = 1 [ V G + + vh + ] (V + v ) (V + v ) (6) For neutral scalars, the vacuum expansion of η 0, ρ 0, χ 0 are η 0 = v + ξ η + iζ η ; ρ 0 = u + ξ ρ + iζ ρ ; χ 0 = V + ξ χ + iζ χ ξ η = 1 (v H u H 0 ) ; ξ ρ = 1 ( u H vh 0 ) ; ξ χ = H 3 0 ; ζ χ = h 0. (u + v ) (u + v ) (7) 5.(a) Neutral Currents The neutral current Lagrangian contains an additional gauge boson Z L NC = -e J em µ A µ - g J(Z) µ Z µ - g J(Z ) µ Z µ - g s W J ( Z ) µ Z µ c W c W sinθ (1-4s W ) (8) The Lagrangian for Z, Z couplings to fermions L(Z) = g Σ f f γ µ [( g L P L + g R P R )] f Z µ ; g L = T 3L - Qs W ; g R = -Qs W c W

12 1 = g Σ f f γ µ ( v f Z + a Z f γ 5 )f Z µ f ; v Z = T 3L - Qs W, f a Z c W L(Z ) = g Σ f f γ µ [( g L P L + g RP R )] f Z µ c W = - T 3L (9) where g L = (1-4s W ) T 8L + 3 s W X ; g R = + 3 s W X ; (1-4s W ) (1-4s W ) (30) L(Z ) = g Σ f f γ µ ( v Z f + a Z f γ 5 ) f Z µ, c W where v Z = g L + g R ; a Z = - g L + g R (31) v Z f = (1-4s W ) T 8L + 3 s W X ; a Z f = - (1-4s W ) T 8L (1-4s W ) TABLE Z f f and Z f f couplings Fermion ChargeQ v Z f a Z f v Z f a Z f d i U i + 3 D i - 43 t s W s W s W s W 3 B s W 3 T s W s W 3(1-4 s W ) 1-8s W 3(1-4 s W ) -1+ s W 3(1-4 s W ) 1+4Sw 3(1-4 s W ) 1+4Sw 3(1-4 s W ) -1+8s W 3(1-4 s W ) - (1-4 s W ) 3 - (1-4 s W ) 3 (1-4 s W ) 3 - (1-4 s W ) 3 - (1-4 s W ) 3 (1-4 s W ) 3 ν (1-4 s W ) 3 - (1-4 s W ) 3 e s W P s W 1 0 (1-4 s W ) 3 - (1-4 s W ) 3 - (1-4 s W ) 3 (1-4 s W ) 3

13 13 v Z f = g L + g R ; a Z f = - g L + g R v Z f = g L + g R ; a Z f = - g L + g R The Lagrangian for the fourth neutral gauge boson is given by L (Z ) = g s W Z µ Σ f f γ µ [( 6T 15 - sin θ X )P L + ( - sin θ X )P R ] f sin θ (1-4s W ) = g s W Z µ Σ f f γ µ (g L P L + g R P R ) f sin θ (1-4s W ) = g s W Z µ f Σ f f γ µ ( v Z sinθ (1-4s W ) + a Z f γ 5 ) f (3) where v Z f = g L + g R = 6T 15 - sin θ X ; a Z f = -g L + g R = - 6T 15 5(b) Charged currents The Charged Current Lagrangian is given by L CC lepton = g [ ν α γ µ (e α - W +µ + P + α Y - µ ) + e α - γ µ (ν α W - µ + P + α Y - - µ ) + P + α γ µ (ν α Y + µ + e α Y µ ++ )] + Η.c. (33) L CC quark = - g [ d i γ µ ( u i W - µ + D j Y + µ ) + u i γ µ ( W + µ d i + Y ++ µ D j ) + D j γ µ (d i Y - µ + u i Y - - µ ) + t γ µ ( b W + µ +Τ Y - µ ) + b γ µ ( t W - µ + Τ Y - - µ ) + Τ γ µ (ty + µ + by ++ µ )] + H.c. where α = 1,,3 ; i = 1,,3 and j = 1, generation indices. (34) 5(c) Flavour changing Neutral Currents (FCNC) The FCNC processes in models have been analysed recently[15] for several cases.we consider the coupling to fermions as mediated only by Z gauge boson for a small mixing angle for Z, Z.The FCNC Lagrangian mediated by Z, Z contribute in left-

14 14 handed sector only and are a result of different X quantum numbers for the third and first two generations. L FCNC = -g J µ (Z )Z µ - g s W J µ (Z ) Z µ (35) C W sinθ (1-4s W ) J µ (Z ) = Σ i,j f i γ µ (g L ) ij P L f j ; J µ (Z ) = Σ i,j f i γ µ (g L ) ij P L f j g L = 3 s W X. ; g L = - sin θ X (36) (1-4s W ) The mass eigenstates f i can be related to gauge states [16] Ui ( i = u, c,t ), D i (i = d, s, b) for up and down sectors by unitary matrices V i j, W i j f i u = V i j U j ; f i d = W ij D j For up-sector FCNC, J µ u (Z ) = Σ i,j V 3i * U i γ µ (g L ) i j P L V 3 j U j = Σ i,j U i γ µ (B u ) i j P L U j where B u i j = V 3 i * (g L ) i jv 3 j. (37) For down sector FCNC J µ (Z ) = Σ i,j W 3i * D i γ µ (g L ) i j P L W 3 j D j = Σ i,j D i γ µ ( B d ) i j P L D j B d i j = W 3 i * (g L ) i j W 3 j. (38) The FCNC Lagrangian for Z transitions L FCNC = - g ( sin ϕ Z 1 µ + cosϕz µ ) Σ [ U i B u i j γ µ P L U j + D i γ µ B d i j P L D j ] (39) c W i,j 5(c) Fermion Masses and mixing The Yukawa interactions in model include additional terms for new charged quarks and Higgs scalars. From Table 1 we obtain Yukawa couplings and Lagrangian L Y = [ h k t (a*m*) (ac)( c*m) k + h b k ( a*m*)( ac*)( cm) k ]+ h T ( a* M*)( ab)(b*m) k + (a M*) i [ { h u i k (a*c)( c*m) k + h d i k (a*c*)( cm) i } + (a*b*) h D i j (bm) j ] i k j

15 15 where k = 1,,3 and i,j = 1,. (40) The Yukawa Lagrangian for quarks Q L Y = Q 3L k [ η h t k u k R + ρ h b k d k R ] + Q 3 L χ h T T R + Q il [ {ρ* h u i k u k R + η* h d i k d kr } + χ* Σ h D i j D j R ] (41) i k j where h s are Yukawa coupling constants with k = 1,,3 and i,j =.1, From above we get the mass matrix for 3 and 13 charged quarks of the form h u 11 u h u 1 u h u 13 u M u = h u 1 u h u u h u 3 u h t 1 v h t v h t 3 v (4 ) h 11 d v h 1 d v h 13 d v M d = h 1 d v h d v 3 h d v 1 h b u h b u h 3 b u (43) For exotic charged quark T, the mass m T = h T V while for D i ( i = 1, ) M D = h D 11 V h D 1] V h D 1 V h D V (44) The D 1, D quarks also acquire masses proportional to V. The lepton Yukawa couplings are L Y l = ( a c *) h k m (a *N*) k (c N) m + (a b) h k m ( a* N*) k (b*n) m (45) k,m k,m where k,m = 1,,3. The mass terms for lepton are

16 16 L M l = - [ h l k m ψ L k ψ R m ρ + h P k m P L k P R m χ ] (46) k,m where k, m = 1,,3 family indices.the lepton field ψ Lk = ( e, µ,τ ) L while the right- handed Ψ Rm = (e R,µ R,τ R ) The heavy leptons include P Lk = ( P 1,P,P 3 ) L and right-handed P Rm = ( P 1,P,P 3 ) R The interaction terms are L l int = - [ h k m ψ L k P R m χ + h k m P L k ψ R m ρ ] (47) k,m The right-handed neutrino is a singlet (1,1,0) in the model and optional since it does not affect anomaly cancellations Quark Masses : To obtain quark masses we consider mass states f i to be related to gauge states by U i, Di by unitary matrices V L, R and W L,R u 1 u d 1 d u = V L, R c d = W L,R s u 3 t d 3 b L,R L,R L,R L,R We consider the following conditions for Yukawa couplings h u, h d << h t, h b h t ~ h b = h = Σ i ( h i t ) ; i = 1,,3 After transforming M q M q to diagonal form, we obtain masses for quarks at tree level as m t m b = vu ; m u = m b = 0, M D = h D V,M T = h T V (48) Lepton Masses: Leptons include three generations of heavy leptons (P 1, P,P 3 ) with masses M P = h P V. At tree level the charged fermions ( e -, µ -,τ - ) obtain masses m e = Γ u where

17 17 h l e h 1 h 13 Γ = h 1 h µ h 3 h 31 h 3 h τ (49) We consider h i j = 0 for i j so that only diagonal terms contribute to charged lepton masses.the exotic fermion masses are all proportional to V.For neutrinoes, one-loop diagrams have been suggested for no right-handed ν R c neutrino case [15] 6.Phenomenology of neutral gauge bosons and Z, Z decays The invariant amplitudes for various decay channels for the neutral gauge bosons can be considered to calculate the decay rates. The decay modes include Z f f flavor-conserving and flavor changing cases and Z ZH where H is a Higgs scalar.the Z decay channels have been considered in model without charged heavy leptons and for a = 3case [13].We consider these cases in the present formalism. 6.1 Z f i f i decays(flavor conserving case) From eqn.(31)the lagrangian L = - ig Z µ { f γ µ (v f f Z + a Z γ 5 ) f } c W f where v Z f and a Z f are vector and axial currents as in Table. The amplitude for fermion f (quarks and leptons) is M = - g ε µ (p) u (l) γ µ ( v Z f + a Z f γ 5 ) v(k) (50) c W From Feynman rules, the decay rate f Г = α M Z N c [ v Z { 1 + m f } + a f Z {1-4 m f }] (1-4 m f 3 s W M Z M Z M Z ) 1 (51)

18 18 where α is fine structure constant. α = e. For quarks (lepton), N c = 3 (1) 4π From Table, the Z e + e -, ν ν, P + P - decays are proportional to (1-4s W ) and suppressed giving a leptophobic nature to Z. For Z t t, b b decays, only vector current v Z f contributes significantly. Γ ( Z f t t ) = α M Z N c v Z (1 + m t ) (1-4 m t ) 1 (5) 3 s W M Z M Z For s t W = 0.3, v Z = 1 + 4s W = ; <v> = 4GeV 3(1-4s W ) < V> = 1 TeV, M Z = 1.13 TeV; Γ( Z t t ) = TeV. <V> = TeV, M Z =.6 TeV; Γ( Z t t ) = TeV Since M D, M T exotic quark masses are proportional to <V>, M Z < M D,T so that Z cannot decay to DD, T T exotic quarks. This also applies to the decay of Z to PP + charged heavy leptons. 6. Z f i f j flavor changing decays. The amplitude for Z decay to t and q (c or u) M (Z U i U j ) = - gε µ (Z ) U i γ µ B u i j P L U j (5) C W For Z q t, B u t c = - V * t q V t t 3s W, (1 4 s W ) Γ( Z q t ) =4α M Z s 4 W N c V * t q V t t [1 - {( m t + m q )+ (m t - m q ) }] s W ( 1 4s W ) M Z 4 M Z.. {1 + ( m t - m q ) - ( m t + m q ) } (53) 4 M Z M Z The V * t q V t t factor obtained from Z t c couplings are proportional to products of Kobayashi Masakawa matrix elements and V * t q V t t = 1.9 x 10-3 ; For the decay Z c t [13]

19 19 At <V> = 1 TeV, M Z = 1.13 TeV, Γ( Z c t ) = x 10-3 TeV. 6.3 Z Z H 1 0 decay mode The decay of Z Z 1 H 0 can be considered for small Z-Z mixing as Z to ZH mode, M = ε µ (k ) ( - g v) g µν ε ν * ( k) (54) (u + v ) Γ (Z ZH 0 ) = πα v sin β [ { 1+ 1 (M Z M H ) }][ 1 (M H + M Z ) 3s 4 W M Z 4M Z M 4 Z M Z + 1 (M H -M Z ) ] 1 (55) M Z 4 These decay modes can contribute to single Higgs production in Z t t H 0 decays.

20 0 7.Results and Conclusions The basic motivation of this work is to extend the gauge symmetry to which can be embedded in SU(4) C SU(4) L+R gauge group. The special feature of the model is that B-L number is well defined so that the gauge bosons are not bileptons.the charged heavy lepton version of model with two possible electric charge assignments is obtained[8].an interesting bifundamental picture emerges for fermions and scalars as a consequence of both (3,4,1) and (3,4 *,1) representations for three generation anomally free fermions of the model. The gauge boson sector is extended by an additional Z which decouples from the other three neutral gauge fields. However, the Z couples to ordinary fermions.we consider a pattern of symmetry breaking with SU(3) L SU() L U(1) X where X = 3T 8L and hypercharge Y = (X X ). The masses for exotic charged ( D,T) quarks and heavy leptons P are proportional to VEV of the scalar χ, < χ > = V ~ 1 TeV. Only top and bottom quarks get masses at tree level while the masses of ordinary fermions cannot be obtained at tree level. These have been generated by one-loop diagrams in a SUSY formalism for a = model [17,18] We present some phenomenological consequences of the model for neutral gauge boson decays. The Z decays are obtained at tree level with quark, lepton pairs and single Higgs in the final states. The masses of Z, P +, D 1,, T exotics depend on VEV of scalar χ 0, (<V>) and exotic decay modes are restricted ( M Z > M f ) for Z gauge boson in the present model. The leptonic modes are suppressed due to a factor (1-4s W ) where s W = 0.3 thus predicting a leptophobic nature for Z.The model is a straightforward

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