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Gauge Bosons and Fermions in SU(3)CSU(4)LU(1)X Model With

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Gauge Bosons and Fermions in SU(3)CSU(4)LU(1)X Model With 1 Gauge bosons and fermions in SU(3)CSU(4)LU(1)X model with SU(2)HU(1)AH symmetry Sutapa Sen Department of Physics ,Christ Church College ,Kanpur 208001,India Email:[email protected] Abstract We present a phenomenological study of neutral gauge bosons and fermions in an extended Standard model with SU(3)CSU(4)LU(1)X gauge symmetry .The model includes gauge bosons and fermions without exotic charges and is distinguished by the symmetry-breaking pattern SU(4)LSU(2)LSU(2)HU(1)AH This introduces an extended electroweak symmetry group SU(2)LSU(2)H at low energies We recover the fermion spectra of an anomaly-free three-family 3-4-1 model without exotic charges for U(1)X charge ,X = T3R+ (B-L)/2 The interaction of physical neutral gauge bosons ZZ, and exotic fermions are presented along with their masses and mixing angle The electroweak constraints from oblique corrections on the model are also calculated. PACS.12.60.Cn,12.15.Mm ,12.15Ff. 2 1.Introduction An important challenge of the LHC is to look for signals of new physics beyond the Standard Model (SM)[1] which has several extensions with predictions of exotic fermions, gauge bosons and scalar bosons[2]. Among these, the class of left-right symmetric [L-R] models [3] have interesting predictions for neutrino masses through the see-saw scenario. In this work, we consider an extension of the left-right symmetric model with additional SU(2)HU(1)AH SU 3 SU 4 U 1 symmetry which can be embedded in the C L X (3-4-1) gauge group. Recently, an extension of L-R symmetric model [4] has been proposed with additional global U(1)S symmetry with a generalized Lepton number [5] The SU(4)U(1)X flavor symmetry has been considered in literature for both exotic [6] and ordinary electric charges[7] for exotic fermions and gauge bosons. This extension can answer the question of family replication with the requirement of number of families equal to the number of colors for anomaly cancellations. The Little Higgs Model (LHM) [8] with SU(4)LU(1) gauge symmetry has been recently considered in literature In general, various 3-4-1 models can be classified by electric charge operator Q b c QT 3L T8L T15L XI4 1 3 6 where Tα , α = 3,8,15 denotes diagonal generators of SU(4)L and X is the hypercharge operator for U(1)X.I4 is a 4 x4 unit matrix. The values for X are fixed by anomaly cancellation of the fermion content of the three-family models. The condition of ordinary electric charges for 3 fermions and gauge bosons for 3-4-1 model restrict three-family models to only of four different types with possible choices for parameters b and c [7] as b = 1,c = -2; b = -1, c = 2 ; b = c = 1.and b = 1,c = -1 .The hypercharge of the SM embedded in SU(4)LU(1)X is Y b c T T XI .After symmetry breaking of 3-4-1 to SM, the gauge matching 2 3 8L 6 15L 4 conditions give [9] 2 2 c b sin m g 1 2 1 g X W x tanW ; ; 2 2 2 2 g g 3g g X g c 3 b2 2 2 1 sin W mx 3 (2) Here g, g are gauge coupling constants for SU(2)L and U(1)Y , gX is the coupling constant for U(1)X , g sin m In this work, we consider the b = -1, c = 2 case with X W x g 2 1 2sin W mx It is interesting to note that the U(1)X charges for the fermion spectrum obtained after anomaly cancellations ( X) satisfy (B -2X) = L – 2T3RV where B, L denote baryon and lepton numbers respectively.T3RV is the third component of isotopic spin ( T3R1+T3R2) for a diagonal SU 2 SU(2) SU(2) RV 1R 2R .Here SU(2)R1 is the right-handed group for L-R symmetric model. SU(2)R2 is an additional right handed group for exotic fermions. The values for X are obtained with distinct Baryon and Lepton numbers which is a special feature of this model, 4 B L X T3R 1 T3 R 2 2 (3) The symmetry-breaking pattern is considered as in [9] with three stages .The first stage of SU 4 SU 2 SU 2 U 1 symmetry-breaking L L HL AH is achieved by a 15-plet Higgs scalar boson S [9] The second and third stages are considered by introducing four Higgs scalar 1 1 1 1 bosons, 1,4, , 1,4, , 1,4, , 1,4, 2 2 2 2 SU 4 U 1 SU 2 SU 2 U 1 U 1 L X S 1L 2HL AH X SU 2 SU 2 U 1 U 1 SU 2 U 1 U (1) 1L 2HL AH X , L Y AH U 1 U (1) , em AH (4) The diagonal generators of SU(4)L include T3L, T8L and T15L which allow the combinations 2 1 1 2 1 1 AH 8 Diag 1,1, 1, 1 = T8 T15 ; T3H T8 T15 = Diag 0,0,1, 1 3 3 3 3 2 (5) The charge operator Q is similar to that for the left-right symmetric model [3,4] with additional SU(2)HL left-handed group for exotic fermions instead of SU(2)R QT 3L T3H XI4 . (6) The anomaly-free three families of fermions are listed in Table I along with (B-2X) for the 5 fermion spectrum. The leptons ,,,e N E , 1,2,3 are assigned to the SU(4)LU(1)X e 1 multiplet Lα ~ 1,4, which restrict these to only leptons (L = 1). The sterile neutrino is thus 2 obtained in three generations along with a heavy lepton E .The model predicts a rich phenomenology for these leptons through interaction with new gauge bosons and four scalar bosons corresponding to SU(2)H U(1)AH gauge symmetry Table I: The fermion content ,(B – 2X) and X charges for anomaly-free 3-4-1 model. Fermion Content Representation (B -2X) X Q , i = 1,2 ( d , -u , D ,U ) (3,4) 0 1 i L i i i i L 6 Q (t, b, U,D ) (3,4*) 0 1 3L L 6 (3*,1) 1 2 uR , 1,2,3 u,, c t R 3 d , 1,2,3 (3*,1) -1 1 R d,, s b R 3 U , 1,2,3 U ,U ,U (3*,1) 1 2 R R1 R2 R3 3 D , 1,2,3 D , D , D (3*,1) -1 1 R R1 R2 R3 3 l , 1,2,3 ,e, N, E (1,4) 1 1 L - 2 (1,1) -2 1 e , E , 1,2,3 e , , R R EEE , , (1,1) -2 1 1 2 3 R 6 The work is organized as follows. In Section 2 we present the main features of the model and discuss its SU(3)L limit .Section 3 deals with the gauge boson sector with charged and neutral gauge bosons .We consider neutral currents and their mixing and obtain the electroweak constraints on the parameters of the model from oblique corrections. Section 4 is a short discussion on results and conclusions. 2. The 3-4-1 model without exotic charges The 3-4-1 model without exotic charged particles [7] has been considered in literature for ( b=1,c = -2;b = -1,c = 2) [10] .For the second case , the electric charge operator 1 2 Q= T T T XI . The application of renormalization group equations discussed 3L 3 8L 6 15L 4 2 2 in [9] leads to ( sin θW= sin θW(mZ)) 1 m m 44 m 1 2sin2 X Z Z ln X W 1 m 4 3 m Z Z (7) 2 -1 where mX is the unification scale, sin θW(mZ) = 0.2226 and α(mZ) = 128.91 The anomaly-free three families of fermions are listed in Table I. The X charges satisfy the condition of assumption (1) which relates (B-2X) to (2T3RV – L) for the fermion spectrum. 1 1 1 The model includes four Higgs scalars with X , (,; T ) ; (, ;T ) 2 3R 1 2 3R 2 2 7 i 1 1 2 1 i ~ 1,4, 0 ; ~ 1,4, 2 2 3 3 0 4 4 0 1 1 0 1 1 2 2 ~ 1,4, , ~ 1,4, 2 i 2 3 i 4 (8) 0 0 0 0 The neutral fields 3 , 1 ,2 and 4 are real while the remaining neutral fields are complex. The vacuum expectation values (VEV’s) are aligned as T T T T v u V V 0, ,0,0 , ,0,0,0 ; 0,0,0, , 0,0, ,0 2 2 2 2 (9) In addition, we consider a 15-plet Higgs scalar boson S transforming as (1,1,0) for first stage of SU 4 SU 2 SU 2 U 1 symmetry-breaking L S L H AH w S diag 1,1, 1, 1 2 2 (10) 2.1 The SU(3)L electroweak symmetry limit of 3-4-1 model: The model , in the SU(3)L limit , corresponds to the anomaly-free three-family 3-3-1 model [11] recently 8 considered for phenomenology of exotic 2/3 charge quarks[12]. In this case, the electric charge operator 1 2 BL QT 3L T8L XX; T15L XI4 ; X T3R 3 6 2 (11) The Weinberg angle is now defined by 2 2 g 1 1 1 g sin m tan = Y , ; W X W 2 2 2 2 4 g gY 3g g g 2 1 sin W mX 3 (12) where g, g are now the coupling constants of SU(3)L and U (1)X The scalar sector consists of three scalar triplets (1, 3, 2/3 ), (1,3,-1/3), (1,3,-1/3) which can be associated with (1,4,1/2), (1,4,-1/2) and (1.4.-1/2) scalar bosons in the 3-4-1 model .The + study of the scalar sector in 3-3-1 case show that , give mass to W and Z bosons.
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