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3-3-1 Models Vicente Pleitez Instituto De Física Teórica-UNESP-BRAZIL Newphysics at the Junction of Flavor and Collider Phenomenology – Portoroz-April -- 2017

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3-3-1 Models Vicente Pleitez Instituto De Física Teórica-UNESP-BRAZIL Newphysics at the Junction of Flavor and Collider Phenomenology – Portoroz-April -- 2017 Aspects of 3-3-1 models Vicente Pleitez Instituto de Física Teórica-UNESP-BRAZIL NewPhysics at the junction of flavor and collider phenomenology – Portoroz-April -- 2017 The authot woul like to FAPESP, CNPq and Josez Stefan Institut for partial financial support Outline 1.Introduction: 3-3-1 models 2.Type of 3-3-1 models 3.The Landau pole in 3-3-1 models 4.Phenomenology:proposals 5.Conclusions 3-3-1 MODELS: 푆푈(3)퐶푆푈(2)퐿푈(1)푌 푆푈(3)퐶푆푈(3)퐿푈(1)푋 + REPRESENTATION CONTENT 3, 3∗, 6,10, … (anti)triplet of SU(3): 3=2 1 SU(3) (anti)DUBLETO DE SU(2) SINGLET OF SU(2) SU(3): 6=1 2 3 SU(3) TRIPLET OF SU(2) 6 = 3-3-1 MODELS ELECTRIC CHARGE OPERATOR 3 푄αβ(푋) = λ3 α + λ8 β + 푋 Hereafter α=1 ∗ 3 푄αβ(푋) = −λ3 α − λ8 β + 푋 푋 0 0 1 + 푋 0 0 푄 − 3(X)= 0 −1 + 푋 0 푄 3(X)= 0 0 0 0 0 1 + 푋 0 0 −1 + 푋 1 2 + 푋 0 0 + 푋 0 0 3 3 2 1 푄 (X)= 0 − + 푋 0 푄 (X)= 0 − + 푋 0 −1/ 3 3 1/ 3 3 1 1 0 0 + 푋 0 0 − + 푋 3 3 MODELS, IN GENERAL, HAVE TWO INGREDIENTS 1. GAUGE SYMMETRY 2. PARTICLE CONTENT (DEGREES OF FREEDOM) Although the 3-3-1 models can be classified by the β parameter in the electric charge operator Q, this is not enough to distinguishes all the models: the particle content, matter. Models with the same β have different phenomenology We will consider below two examples, two with β=− 3 and two with β = −1/ 3. = − 3 The minimal 3-3-1 model (m331) 푐 푇 푙 = (푙 푙 푙 )퐿 (1,3,0), 푙 = 푒, , only the known leptons 2 푄 = (푑 , −푢 , 푗 )푇 3, 3∗, ; 푚 = 1,2 푚 푚 푚 푚 퐿 3 2 푄 = (푢 , 푑 , 퐽)푇 3,3, 3 3 3 퐿 3 2 1 5 4 푢 3,1, , 푑 (3,1, − ) 퐽 3,1, , 푗 (3,1, − ) 푅 3 푅 3 푅 3 푚푅 3 Scalar sector: 0 η ρ+ χ− η− −− η = 1 ~(3,0), ρ0 χ = χ + ρ = ~(3,+1), 0 ~(3,-1) η 2 ρ++ χ 푆푈(3)퐶 푆푈(3)퐿 푈(1)푋 푆푈(3) 푆푈(2) 푈(1) 퐶 퐿 푌 푆푈 3 퐶 푈(1)푄 푣χ 푣η, 푣휌, 푣푠 The VEVs of η,ρ and χ are enough to break the symmetries espontaneously and giving at the same time the quark masses. But no for leptons. For the later ones it is necessary to add 푇 퐷 The sextet: 푆 = ~(6,0) 퐷푇 퐻−− Under SU(2): doublet, triplet, and singlet + 푠 , 푡0 푡+ D= 0 T= , , −− 푠 푡+ 푡++ 퐻 Several options for neutrino mass generation Leptons in the minimal 331 model 푒퐿 푙 = 퐿 ~(3,0) 푙푅~(1,0) Optional as in the SM 푐 푙퐿 푒 푒 NEUTRAL CURRENTS: 푔푉 , 푔퐴 , 푔푉, 푔퐴 with Z 푒 푒 ′ 푓푉 , 푓퐴 , 푓푉 , 푓퐴 with 푍 There is Lepton number violation OTHE MODEL WITH = − 3 331HL (ONE HEAVY LEPTON PER FAMILY) 푒퐿 푙 = 퐿 ~(3,0) 푙푅 1, −1 , 퐸푅(1, +1) + 퐸퐿 푙푅~ 1,0 are again optional Only the three scalar triplets (3,0), (3,+1), (3,-1) 푒 푒 퐸 퐸 NEUTRAL CURRENTS: 푔푉 , 푔퐴 , 푔푉, 푔퐴, 푔푉 , 푔퐴 with Z 푒 푒 퐸 퐸 ′ 푓푉 , 푓퐴 , 푓푉 , 푓퐴 , 푓푉 , 푓퐴 with 푍 Then in models with = − 3 and heavy leptons 1. Lepton number is not violated if the heavy leptons E´s are particles not anti-particles (Konopinski-Mahmoud scheme) 2. The heavy leptons, E’s, do not mix with the known leptons e,,, they may be stable because an acidental 푍2 symmetry unless interactions in the scalar sector allow them to decay into the known leptons. + + In fact, the term 푎10( )( ) in the escalar potential breaks the 푍2 symmetry alowing the decay 퐸푙 + + MODELS WITH β = −1/ 3 푒퐿 = 푙퐿 ~(3,-1), 푙푅(1,-1) 푐 퐿 푒 푒 NEUTRAL CURRENTS: 푔푉 , 푔퐴 , 푔푉, 푔퐴 with Z 푒 푒 ′ 푓푉 , 푓퐴 , 푓푉 , 푓퐴 with 푍 AS IN THE m331 MODEL, THERE IS THE LEPTON NUMBER VIOLATION The neutral férmions (neutrinos) mass matrix is 6x6 or 푒퐿 = 푙퐿 ~(3,-1), 푙푅(1,-1), 푁푅 1,0 , 푅(1,0) 푁퐿 푒 푒 푁 푁 NEUTRAL CURRENTS: 푔푉 , 푔퐴 , 푔푉, 푔퐴, 푔푉 , 푔퐴 with Z 푒 푒 푁 푁 ′ 푓푉 , 푓퐴 , 푓푉 , 푓퐴 , 푓푉 , 푓퐴 with 푍 THE LEPTON NUMBER IS CONSERVED IF N ARE IS CONSIDER PARTICLES. N MAY BE STABLE AND THE LIGHTEST ONE CAN BE CANDIDATE TO DARK MATTER The neutral férmions mass matrix is 12x12 LANDAU POLE IN 3-3-1MODELS Gauge couplings in 3-3-1 models: 푔푠, 푔푆푈(3) = 푔, 푔푋 푔 DEFINING tan θ = 푋 푋 푔 푠푋 푠푋 e=g e=푔푋 2 2 1+3푠푋 1+3푠푋 Matching condition with the SM = 3 (m331) 2 푠푋 2 2 = 푠푊 1 + 3푠푋 2 2 푠푊 2 푡푎푛 θ푋 = 2 푠푊 < 0.25 1−4푠푊 =1/ 3 =0.25 at 4-8 TeV 2 2 푠푊 2 푡푎푛 θ푋 = 4 푠푊 < 0.75 1− 푠2 3 푊 It seems as if the existence of the pole is just due to the introduction of an angle that do not exist in the model. PHENOMENOLOGY: PROPOSALS 1. Better calculation of the Landau pole (lattice gauge theories) 2. Flavor physics, 푍′ but scalars has to be consider too 2. Low energy processes. For example QMeV-GeV N scattering 3. Colliders phenomenology, see Cao and Zhang arXiv:1611.09337 4. High energy neutrino processes TRILEPTON EVENTS − − + + 퐿 + 푒퐿 푙1퐿+푙2퐿+푙2푅 + 푙퐿 − + + 휇퐿 + 푁푙1퐿+푙2퐿+푙2푅 +N TRIDENT NEUTRINO PRODUCTION − + 퐿 + 푁퐿 + 푙 + 푙 + 푁 PINGU AND ROCA EXPERIMENTS Ge et al arXiv:1702.02617 FINALLY If right-handed neutrinos do really exist: the electroweak symmetry may be 푆푈(4)퐿푈(1)푋 푒 Pisano and Pleitez PRD 1994 푐 푒 e 푙푐 CONCLUSIONS 1. 331 models are three families models 2. All models have Landau-like pole implying an upper bound on 2 푠푊 < 0.25 in some models 3. They give rationale for the multi-Higgs extensions of the SM 4. The electric charge is quantized independently of the neutrino masses (massless or massive Dirac or Majorana). 5. Many mechanism for netrino mass generation 6. They have an almost automatic Peccei-Quinn symmetry ++ 7. They predict the existence of doubly charged vector bóson 푈 or 0 complex neutral ones, 푋. 8. Dark matter candidates 9. The models predict FCNC effects, in particular it can explains the anomaly in 퐵푠 decay (added after the presentation) Some references 1. Machado et al Lepton flavor violating processes in the minimal 3-3-1 model with singlet sterile neutrinos, arXiv:1604.08539 2. Machado et al Flavor-changing neutral currents in the minimal 3-3-1 model revisited, Phys. Rev. D 88, 113002 (2013) 3. A. J. Buras et al 331 models Facing the tension in F=2 processes ´′ + − ∗ + − with the impact on , 퐵푠 → 휇 휇 , 퐵 → 퐾 휇 휇 , JHEP 1608 (2016) 115 ´′ 4. A. J. Buras et al, in 331 models, JHEP 1603 (2016) 010 and references therein thanks! Triangle anomalies (only the nontrivial ones) 2 푎 푏 1) [푆푈(3)퐶] 푈(1)푋 : Tr({푇푐 , 푇푐 }X)=0 Sum only over the quark degrees of freedom: 1 2 2 1 5 4 Tr({푇푎, 푇푏}X)= 푎푏푇푟 푋=6(− )+3( )+3( − )+ + 2 − = 0 푐 푐 3 3 3 3 3 3 3 푎 푏 푐 2) [푆푈(3)퐶] : Tr({푇 , 푇 }푇 )=0 Since 푇푎 = −푇푎∗ This trace cancel out if the number of triplets is equal to the number of antitriplets 2 푎 푏 3) [푆푈(3)퐿] 푈(1)푋 : Tr({푇 , 푇 }X)=0 sum is over all fermions in triplets 1 2 푇푟 푇푎, 푇푏 푋 = 푎푏푇푟 푋 = 6 − + 3 + 3 0 = 0 3 3 3 3 4) [푈 1 ]3 : Tr({푋, 푋}X)= Tr({X,X}X)=Tr푋퐿 − Tr푋푅 1 2 2 3 1 3 5 3 4 3 =18( − )3 + 9( )3 − 3 3 + 3 − + + 2 − = 0 3 3 3 3 3 3 Scalar sector in both: 0 + 1 1 0 η− 0 1 η = ~(3,-1/3), ρ = ρ ~(3,+2/3), χ = χ− ~(3,-1/3) η0 + 0 2 2 2 Depending of the model 푐 or N in the third components, the vacuum aligment may be Different and also a sextet coul be added. + − 푙퐿 + 푁 → 퐿 + 푋푗 (푗푢푑) THE STANDARD MODEL FERMIONS (three generations) 푙 No right-handed (sterile) neutrinos 푙푅 9 degrees of freedom 푙 퐿 푢 푢 푢 푢 푢푅→푢푅 푢푅 푢푅 → 36 degrees of freedom 푑 퐿 푑 퐿 푑 퐿 푑 퐿 푑푅→푑푅 푑푅 푑푅 BOSONS ± 0 푎 0 GAUGE: ϒ, 푊 , 푍 , 퐺 , 푎 = 1, … 8 HIGGS: 퐻 12 degrees of freedom TOTAL 57 degrees of freedom ALL THESE PARTICLES AND ITS PROPERTIES HAVE BEEN OBSERVED AND MEASURED IN LABORATORY (FERMILAB,LEP,LHC,...) (퐶) − + + 푙퐿 + 푁푙1퐿+푙2퐿+푙2푅+hadrons − + + 퐿 + 푁푙1퐿+푙2퐿+푙2푅 + 푙퐿 MODELS WITH THE SAME GAUGE SYMMETRY BUT DIFFERENT REPRESENTATION CONTENT HAVE TO BE CONSIDRED DIFFERENT BECAUSE THEY HAVE DIFFERENT PHENOMENOLOGY IN THE CASE OF 3-3-1 MODELS THERE IS A PARAMETER 훽 WHICH DISTINGUISH THE MODELS. HOWEVER, EVEN MODELS WITH THE SAME CAN HAVE DIFFERENT REPRESENTATION CONTENT AND THUS, DIFFERENT PHENOMENOLOGY. THE STANDARD MODEL LEP:LEP+SLD COLL. Phys.
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