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Three-Family Left-Right Symmetry with Low-Scale Seesaw Mechanism

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Three-Family Left-Right Symmetry with Low-Scale Seesaw Mechanism Published for SISSA by Springer Received: January 22, 2017 Revised: May 5, 2017 Accepted: May 12, 2017 Published: May 18, 2017 JHEP05(2017)100 Three-family left-right symmetry with low-scale seesaw mechanism Mario Reig, Jos´eW.F. Valle and C.A. Vaquera-Araujo AHEP Group, Institut de F´ısica Corpuscular | C.S.I.C., Universitat de Val`encia, Parc Cient´ıficde Paterna, C/ Catedr´atico Jos´eBeltr´an,2 E-46980 Paterna (Valencia), Spain E-mail: [email protected], [email protected], [email protected] Abstract: We suggest a new left-right symmetric model implementing a low-scale see- saw mechanism in which quantum consistency requires three families of fermions. The symmetry breaking route to the Standard Model determines the profile of the \next" ex- pected new physics, characterized either by the simplest left-right gauge symmetry or by the 3-3-1 scenario. The resulting Z0 gauge bosons can be probed at the LHC and provide a production portal for the right-handed neutrinos. On the other hand, its flavor changing interactions would affect the K, D and B neutral meson systems. Keywords: Beyond Standard Model, Gauge Symmetry, Neutrino Physics ArXiv ePrint: 1611.04571 Open Access, c The Authors. doi:10.1007/JHEP05(2017)100 Article funded by SCOAP3. Contents 1 Introduction1 2 The model2 3 Spontaneous symmetry breaking3 4 Phenomenological implications5 JHEP05(2017)100 5 Flavor-changing neutral currents6 6 Conclusion7 1 Introduction Both the great success as well as the shortcomings of the Standard Model (SM) in providing a full picture of reality are well publicized. Amongst the latter are the facts that it fails in giving a convincing explanation for small neutrino masses, the existence three families, and the dynamical origin of parity violation. Taking these as clues, we suggest a new Standard Model extension which provides a dynamical criterion for selecting the profile characterizing the \next step" towards physics Beyond the Standard Model. This would provide an answer to a current burning question, after the lack of convincing new signals in Run 2 of the LHC: what is the expected pattern of the upcoming new physics? By suggesting that these three features are deeply inter-connected we reconcile the idea of spontaneous parity violation with anomaly cancellation with, and only with, three families of fermions. The framework is based on a generalized left-right symmetric SU(3)c ⊗ SU(3)L ⊗ SU(3)R ⊗ U(1)X group structure, first proposed in [1] in a different context. In [2] we suggested a unique framework able to mimic either a usual left-right symmetric theory or a 331 model, incorporating spontaneous parity violation and small neutrino masses through the seesaw mechanism. In order to incorporate the cancellation of the Adler-Bell-Jackiw anomalies [3,4 ] the number of fermion families must chosen to match exactly the number of colors, with quarks assigned in a non-sequential way, in which one quark family differs from the other two [5], as in the early proposal of refs. [5,6 ] (see [7] for an alternative formulation).1 We choose the simplest scalar sector for which light neutrino masses are proportional to a small parameter, implementing a genuine low-scale realization of the see- saw mechanism, such as the inverse [10{15] or linear seesaw mechanism [12{14], instead 1The model is unique up to exotic fermion charge assignments. Unfortunately, the interesting choice made in [8,9 ] is inconsistent with our construction, due to the perturbativity requirement of the gauge couplings [1]. { 1 { a a α α 3 3 a L R QL QR QL QR SL Φ ρ χL χR SU(3)c 1 1 3 3 3 3 1 1 1 1 1 ∗ SU(3)L 3 1 3 1 3 1 1 3 3 3 1 ∗ ∗ SU(3)R 1 3 1 3 1 3 1 3 3 1 3 1 1 1 1 1 1 1 U(1)X − 3 − 3 0 0 3 3 0 0 3 − 3 − 3 Table 1. Particle content of the model, with a = 1; 2; 3 and α = 1; 2. of the more conventional high-scale seesaw [16{20]. Moreover the model suggests that the JHEP05(2017)100 CKM matrix characterizing quark weak interactions may have a dynamical origin through a new \leptophobic" vacuum expectation value. The scheme has potentially accessible new neutral gauge bosons coupling non-diagonally to the quark flavors, inducing flavor changing neutral currents in the K, D and B neutral meson systems [21]. On the other hand such Z0's can also be searched directly in Dilepton studies at the LHC [22] This paper is organized as follows. First we sketch our framework reconciling the existence of parity at a fundamental level with a gauge structure consistent only for the case of three families of fermions. We then show how different patterns of symmetry breaking determine alternative profiles for the \next" expected physics beyond the Standard Model. Finally we briefly discuss generic features of fermion masses and mixings, as well as their interactions and phenomenological implications for the LHC and K, D and B meson mixing. 2 The model The gauge group is SU(3)c ⊗ SU(3)L ⊗ SU(3)R ⊗ U(1)X with the three families of fermion fields assigned as, 0 1a 0 1α 0 13 ν d u a B − C α B C 3 B C L;R = @ ` A ;QL;R = @ −u A ;QL;R = @ d A ; (2.1) N D U L;R L;R L;R a a α α 3 3 where parity acts as: L $ R, QL $ QR, QL $ QR. The particle content of the model is summarized in table1 . We also introduce the a fermion fields SL, transforming as singlets under the SU(3)c ⊗ SU(3)L ⊗ SU(3)R ⊗ U(1)X gauge symmetry and crucial ingredients of low-scale seesaw schemes [10] as well as a set of scalar multiplets including a bi-triplet scalar Φ involved in the generation of charged fermion masses, as well as χL and χR triggering neutrino masses, see below. Notice that, following the procedure used in refs. [12{14], in the current model we replace the sextets ∆L and ∆R present in the construction of refs. [2, 23], by the fields χL and χR 1 1 χL ∼ 1; 3; 1; − ; χR ∼ 1; 1; 3; − : (2.2) 3 3 { 2 { In the presence of the gauge singlet fermions, the Yukawa interactions for leptons are given by X h ab a b ab a b c ab a b µab a c b i − L = y χRS + y χL(S ) + y Φ + (S ) S + h.c. (2.3) leptons R R L L L L L R 2 L L a;b c y Parity acts on singlet fermions as SL $ (SL) and the scalar fields transform as Φ $ Φ , y χL $ χR, which implies that yR = yL and y = y . Spontaneous symmetry breaking is driven by the following structure of vacuum expectation values (VEVs):2 0 1 0 k3 0 1 1 JHEP05(2017)100 hΦi = p diag(k1; k2; n) ; hρi = p B k4 0 0 C ; 2 2 @ A 0 0 0 0 1 0 1 (2.4) v v 1 R 1 L hχRi = p B 0 C ; hχLi = p B 0 C : 2 @ A 2 @ A ΛR ΛL In this work, we assume for simplicity k4; ΛL = 0 and the hierarchy n ; vR ; ΛR ki ; vL, i = 1;:::; 3. After symmetry breaking the electric charge is identified as the unbroken combination 3 3 8 8 Q = TL + TR + β(TL + TR) + X; (2.5) and the parameter β is given, in our construction, by p β = −1= 3 ; (2.6) which corresponds to the SVS case [5]. 3 Spontaneous symmetry breaking The most general scalar potential characterizing symmetry breaking in our model can be written as V = Vχ + VΦ + Vρ + VΦχ + VΦρ + Vχρ + VΦρχ ; (3.1) 2 y y y 2 y 2 y y Vχ = µχ(χLχL + χRχR) + λ1[(χLχL) + (χRχR) ] + λ2χLχLχRχR ; V = µ2 Tr(ΦΦy) + f [l1l2l3 Φr1 Φr2 Φr3 + h:c:] + λ Tr(ΦΦy)2 + λ Tr(ΦΦyΦΦy) ; Φ Φ Φ r1r2r3 l1 l2 l3 3 4 2 y y 2 y y Vρ = µρTr(ρρ ) + λ5Tr(ρρ ) + λ6Tr(ρρ ρρ ) ; y y y y y y y y VΦχ = fχ(χLΦχR + h:c:) + λ7(χLχL + χRχR)Tr(ΦΦ ) + λ8 χLΦΦ χL + χRΦ ΦχR ; y y y y y T ∗ VΦρ = λ9Tr(ρρ )Tr(ΦΦ ) + λ10 Tr(ΦΦ ρρ ) + Tr(Φ Φρ ρ ) y T ∗ T ∗ y + λ11 Tr(Φ ρΦ ρ ) + Tr(Φρ Φ ρ ) ; y y y y y y T ∗ Vχρ = λ12Tr(ρρ )(χLχL + χRχR) + λ13(χLρρ χL + χRρ ρ χR) ; l1l2l3 T y r1r2 r3 VΦρχ = fρ[ (Φρ )l1l2 (χL)l3 + r1r2r3 (Φ ρ) (χR) + h:c:] T y y + λ14(Φρ ΦχR + Φ ρΦ χL + h:c:) ; 2We restrict our analysis to the case in which there is no mixing at tree level between exotic and SM fermions. Note that, for the most general VEV structure a small mixing between Standard Model and exotic fermions is induced, but it will be controlled by the ratio ki=n which is expected to be small. { 3 { Minimization leads to the following tadpole equations: " 2 2 2 2 # 2 2 2 2 2 2 1 2 k2k3 n ΛR 2 2 2 µΦ = − n +k1 +k2 λ3 −(n +k2)λ4 − k3λ9 − 2 2 λ10 + 2 2 λ8 +(vL +vR +ΛR)λ7 ; 2 n −k2 n −k2 " 2 2 2 2 2 2 2 2 2 1 vLΛR(vL −vR −ΛR) 2 (n −k1)ΛR 2 2 2 µρ = − 2 2 2 (2λ1 −λ2)+k3(λ5 +λ6)+ 2 λ8 +(k1 +k2 +n )λ9 2 k3(vL −vR) k3 2 # 2 2 2 2 2 2 ΛR + (k1 + k2)λ10 + (vL + vR + ΛR)λ12 + vL 1 + 2 2 λ13 ; JHEP05(2017)100 vL − vR 2 2 " 2 2 2 2 2 vRΛR 1 ΛRvL 2 2 2 2 2 µχ = − vL + vR + 2 2 λ1 − 2 2 λ2 + (k1 + k2 + n )λ7 + k1λ8 + k3λ12 vR − vL 2 (vL − vR) 2 2 # k3vL + 2 2 λ13 ; (vL − vR) 2(n2 − k2)nk λ − nk k2λ + k Λ (n2 − k2)λ + nk Λ2 λ 2 2 4 2 p3 10 3 R 2 14 2 R 8 fΦ = 2 2 ; 2k1(vL − vR) ( 2 2 2 ) 1 ΛR(k1 −n ) vLΛR 2 2 2 2 fρ = p nk2λ14 + λ8 + 2 2 [k3λ13 +(vL −vR −ΛR)(2λ1 −λ2)] ; 2k1 k3 k3(vL −vR) v v (2λ − λ )(v2 + Λ2 − v2 ) − k2λ L R 1 p2 R R L 3 13 fχ = 2 2 ; (3.2) 2(vR − vL)k1 together with the relations 2 2 2 2 2 2 2 2 2 2k1k2k3(vL − vR)λ11 − nvLvRΛR[k3λ13 + (2λ1 − λ2)(vL − vR − ΛR)] = 0 2 2 2 2 2 k3vL(nvR − k2vL)ΛR nk3(k1 − k2)λ14 + (n − k1)k2ΛRλ8 + 2 2 λ13 vL − vR 2 2 2 vL(k2vL − nvR)ΛR(vL − vR − ΛR) + 2 2 (λ2 − 2λ1) = 0 ; vL − vR 2 2 4 2 2 2 2 2 2 2 2 n k3 λ8 2 2 2 [n + (k1 − 2n )k2]ΛR (k1 − k2) (k1 − n )λ4 + 2 2 λ10 + k1(vL + vR) − 2 2 (n − k2) 2 n − k2 2 2 vR + ΛR 2 2 2 2 2 2 + nk2k3ΛRλ14 + 2 2 k3vLλ13 + vL(vL − vR − ΛR)(2λ1 − λ2) = 0 : (3.3) 2(vL − vR) Different patterns of symmetry breaking associated to different hierarchies of the above vacuum expectation values will thus translate into a different nature for the physics beyond the Standard Model expected above current LHC energies.
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