JID:PLB AID:32515 /SCO Doctopic: Phenomenology [m5Gv1.3; v1.194; Prn:28/12/2016; 9:09] P.1(1-6) Physics Letters B ••• (••••) •••–••• 1 Contents lists available at ScienceDirect 66 2 67 3 68 4 Physics Letters B 69 5 70 6 71 7 www.elsevier.com/locate/physletb 72 8 73 9 74 10 75 11 76 12 Unifying left–right symmetry and 331 electroweak theories 77 13 78 14 Mario Reig, José W.F. Valle, C.A. Vaquera-Araujo 79 15 80 AHEP Group, Institut de Física Corpuscular – C.S.I.C./Universitat de València, Parc Científic de Paterna, C/Catedrático José Beltrán, 2, E-46980 Paterna (Valencia), 16 81 Spain 17 82 18 83 19 84 a r t i c l e i n f o a b s t r a c t 20 85 21 86 Article history: We propose a realistic theory based on the SU(3)c ⊗ SU(3)L ⊗ SU(3)R ⊗ U(1)X gauge group which requires 22 Received 8 November 2016 the number of families to match the number of colors. In the simplest realization neutrino masses arise 87 Received in revised form 19 December 2016 23 from the canonical seesaw mechanism and their smallness correlates with the observed V-A nature of 88 Accepted 22 December 2016 24 the weak force. Depending on the symmetry breaking path to the Standard Model one recovers either 89 Available online xxxx a left–right symmetric theory or one based on the SU(3) ⊗ SU(3) ⊗ U(1) symmetry as the “next” step 25 Editor: A. Ringwald c L 90 26 towards new physics. 91 © 27 2016 Published by Elsevier B.V. This is an open access article under the CC BY license 92 3 (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP . 28 93 29 94 30 95 31 96 1. Introduction the seesaw mechanism [13–17], their explicit chiral structure pre- 32 97 vents a dynamical understanding of parity and its possible relation 33 98 to the smallness of neutrino mass, precluding a deeper under- 34 Despite its great success, the Standard Model (SM) is an in- 99 standing of the meaning of the hypercharge quantum number. 35 complete theory, since it fails to account for some fundamental 100 In this paper we will address some of these issues jointly, 36 phenomena such as the existence of neutrino masses, the under- 101 suggesting that they are deeply related. Our framework will be 37 lying dynamics responsible for their smallness, the existence three 102 an extended left–right symmetric model which implies the ex- 38 families, the role of parity as a fundamental symmetry, as well 103 istence of mirror gauge bosons, i.e. in addition to weak gauge 39 as many other issues associated to cosmology and the inclusion 104 bosons we have right-handed gauge bosons so as to restore par- 40 of gravity. Here we take the first three of these shortcomings as 105 ity at high energies. We propose a unified description of left– 41 valuable clues in determining the next step in the route towards 106 physics Beyond the Standard Model. right symmetry and 331 electroweak theories in terms of the 42 ⊗ ⊗ ⊗ 107 43 One unaesthetic feature of the Standard Model is that the chiral extended SU(3)c SU(3)L SU(3)R U(1)X gauge group as a com- 108 44 nature of the weak interactions is put in by hand, through ex- mon ancestor: Depending on the spontaneous symmetry break- 109 45 plicit violation of parity at the fundamental level. Moreover the ing path towards the Standard Model one recovers either con- 110 ⊗ ⊗ ⊗ 46 Adler–Bell–Jackiw anomalies [1,2] are canceled miraculously and ventional SU(3)c SU(2)L SU(2)R U(1)B−L symmetry or the 111 ⊗ ⊗ 47 thanks to the ad-hoc choice of hypercharge assignments. Left–right SU(3)c SU(3)L U(1) symmetry as the missing link on the road to 112 48 symmetric schemes such as Pati–Salam [3] or the left–right sym- physics beyond the Standard Model. Other constructions adopting 113 49 metric models can be made to include parity and offer a solution these symmetries have been already mentioned in the literature. 114 50 to neutrino masses through seesaw mechanism [4–8] and a way to In [18,19] a model for neutrino mass generation through dimen- 115 51 “understand” hypercharge [6]. However in this case the number of sion 5 operators is studied, and in [20,21] models for the diphoton 116 52 fermion families is a free parameter. anomaly and dark matter were presented. 117 This work is organized as follows. We first construct a new left– 53 Conversely, SU(3)c ⊗ SU(3)L ⊗ U(1)X schemes provide an ex- 118 54 planation to the family number as a consequence of the quantum right symmetric theory showing how the gauge structure is deeply 119 55 consistency of the theory [9,10], but are manifestly chiral, giving related both to anomaly cancellation as well as the presence of 120 56 no dynamical meaning to parity. Even if these models allow for parity at the fundamental level. In the next sections we build 121 57 many ways to understand the smallness of neutrino mass either a minimal model where neutrino masses naturally emerge from 122 58 through radiative corrections [11,12] or through various variants of the seesaw mechanism. Finally we study the symmetry breaking 123 59 sector, identifying different patterns of symmetry breaking and 124 60 showing how they are realized by different hierarchies of the rel- 125 61 E-mail addresses: [email protected] (M. Reig), valle@ific.uv.es (J.W.F. Valle), evant vacuum expectation values. In the appendix we outline the 126 62 vaquera@ific.uv.es (C.A. Vaquera-Araujo). anomaly cancellation in the model. 127 63 128 http://dx.doi.org/10.1016/j.physletb.2016.12.049 64 129 0370-2693/© 2016 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 65 130 JID:PLB AID:32515 /SCO Doctopic: Phenomenology [m5Gv1.3; v1.194; Prn:28/12/2016; 9:09] P.2(1-6) 2 M. Reig et al. / Physics Letters B ••• (••••) •••–••• 1 Table 1 66 2 Particle content of the model, with a = 1, 2, 3and α = 1, 2. See text for the definition of q. 67 3 α α 3 3 68 ψaL ψaR Q L Q R Q L Q R φ ρ L R 4 69 SU(3)c 113333111 1 5 ∗ 70 SU(3)L 313131336 1 ∗ ∗ 6 SU(3)R 131313331 6 71 q−1 q−1 − q − q q+1 q+1 2q+1 2(q−1) 2(q−1) 7 U(1)X 3 3 3 3 3 3 0 3 3 3 72 8 73 9 74 2. The model In this setup, the mechanism behind anomaly cancellation is anal- 10 75 ogous to the one characterizing 331 models, as detailed in Ap- 11 76 In this paper we propose a class of manifest left–right sym- pendix A. Thus the first interesting result in this framework is the 12 77 metric models based on the extended electroweak gauge group fact that quantum consistency requires that the number of triplets 13 78 SU 3 ⊗ SU 3 ⊗ SU 3 ⊗ U 1 in which the electric charge gen- must be equal to the number of antitriplets. This can be achieved 14 ( )c ( )L ( )R ( )X 79 erator is written in terms of the diagonal generators of SU 3 if two quark multiplets transform as triplets whereas the third one 15 ( )L,R 80 transforms as an antitriplet, which in turn implies that the num- 16 and the U(1)X charge as 81 ber of generations must coincide with the number of colors, an 17 82 Q = T 3 + T 3 + β(T 8 + T 8 ) + X, (1) appealing property of 331 models [9]. 18 L R L R 83 The scalar sector needed for spontaneous symmetry breaking 19 where β is a free parameter that determines the electric charge of 84 and fermion mass generation contains a bitriplet 20 the exotic fields of the model [22–24], and its value is restricted 85 21 by the SU(3) and U(1) coupling constants g = g = g and g ⎛ + − ⎞ 86 L,R X L R X φ0 φ φ q 22 to comply with the relation 11 12 13 87 ⎜ − − ⎟ 23 = − 0 q 1 ∼ ∗ 88 φ ⎝ φ φ φ ⎠ (3L, 3R), (5) 2 2 21 22 23 24 g sin θ q q+1 89 X = W 0 25 , (2) φ31 φ32 φ33 90 g2 1 − 2(1 + β2) sin2 θ 26 W 91 a bi-fundamental field 27 92 with θW as the electroweak mixing angle [18]. This relation im- 28 2 − + 2 ⎛ ⎞ 93 plies that β < 1 1/(2 sin θW ), consistent with the original + 0 q+1 1 ρ ρ ρ 29 models [9,10] Notice that special features may arise for specific 11 12 13 94 ⎜ − q ⎟ 30 = ⎝ 0 ⎠ ∼ 95 choices, such as β = 0, which contains fractionally charged lep- ρ ρ21 ρ22 ρ23 (3L, 3R), (6) 31 q+1 q 2q+1 96 tons [25]. In a general SU(N)L ⊗ SU(M)R ⊗ U(1)X theory β = 0 ρ31 ρ32 ρ33 32 always implies that the charge X becomes proportional to B − L.