Unification of Standard and Exotic Matter Through a $ Z 2 $ Symmetry

Unification of standard and exotic matter through a Z2 symmetry Ernesto A. Matute∗ Departamento de F´ısica, Universidad de Santiago de Chile, Casilla 307, Santiago 2, Chile We consider a scenario in which the discrete weak symmetry between quarks and leptons is extended to the weak force by introducing exotic partners. We conjecture that there exists a hidden discrete symmetry P,˜ defining a Z2 group, between standard and exotic quarks and leptons. The × × × × × ˜ unified model SU(3)q SU(3)q˜ SU(2)qℓ˜ SU(2)qℓ˜ U(1)Y P is discussed, where the unifying discrete symmetry extends over particles and forces. It is shown that the lighter neutral and charged weak bosons generated upon spontaneous symmetry breaking have the same properties as those of the standard model. Cabbibo-Kobayashi-Maskawa unitarity is used to set a mass of order 2.8 TeV for the nonstandard weak bosons, which do not exhibit quark-lepton universality. A grand unified × × ˜ theory of (GUT)qℓ˜ (GUT)qℓ˜ P type, with decay of exotic matter into standard matter and no decay of the ordinary nucleon, is put forward. PACS numbers: 12.60.Cn; 11.30.Hv; 12.10.Dm; 14.70.Pw The unification of quark and lepton properties under unified form G ˜ Gqℓ P,˜ whereq ˜ and ℓ˜ denote exotic qℓ × ˜ × strong and electroweak interactions through a continu- quarks and exotic leptons, respectively, and P,˜ hereafter ous or discrete symmetry has been one of the targets referred to as exotic symmetry, denotes the discrete sym- of research efforts over the last few decades [1]. Mainly metry which transforms standard quarks and leptons to the idea has been to assign similar degrees of freedom exotic ones and vice versa: q q˜, ℓ ℓ˜. This unifying to quarks and leptons, extending in a sense the color ↔ 2 ↔ symmetry defines a Z2 group as P˜ = 1. Moreover, this gauge group of quarks to include leptons. Nonstandard discrete exotic symmetry is extendible to strong interac- or exotic gauge bosons and fermions are commonly added tions. to the spectrum of the standard model (SM). The pur- Our aim in this paper is to discuss the unified gauge pose of this paper is to implement these developments ˜ Z group SU(3) SU(3) SU(2) ˜ SU(2) U(1) P, with the notion that there is a hidden 2 symmetry q × q˜ × qℓ × qℓ˜ × Y × in nature unifying the properties of standard and ex- assuming that each set of fermions is separately con- otic fermions. And that these interact with separate but served. It is a unified model in the sense that the du- symmetric gauge bosons, so duplicating the gauge group plicated gauge group factors have the same gauge coupling constant, and the standard and exotic quarks and SU(3)q SU(2)L U(1)Y of the SM and its unified ex- tensions.× In the scenario× of a duplicated grand unified leptons have similar quantum numbers. Symmetric stan- theory (GUT) with such a discrete symmetry, the decay dard and exotic quarks interact with symmetric gluons of exotic matter into standard matter and the stability of and weak bosons. The two SU(3) color groups are un- the ordinary nucleon are expected. This makes an inter- broken and exotic gluons confine exotic quarks into heavy esting point as nucleon decay is one of the pillars of GUTs exotic hadrons. Any explanation for the mass hierarchy and no ordinary proton decay has yet been observed. of standard quarks should be extended to include exotic quarks, since standard and exotic gluons confine at the In the strong interaction sector of the SM there are sub- same scale; in a sense, three new heavy generations of arXiv:hep-ph/0604274v1 28 Apr 2006 stantial differences between quarks and leptons as they quarks and leptons are added to the standard spectrum. come in triplets and singlets of the color gauge group We may say that the exotic symmetry P˜ has the incentive SU(3)q, respectively. However, in the electroweak sector of expanding the electroweak quark-lepton symmetry to their properties are so similar that it is conceivable an in- the strong interaction sector. We note here that the spon- teraction gauge symmetry completely or at least partially taneous breakdown of the discrete symmetry P˜ leads to duplicated in the form Gq Gℓ but unified through a dis- × well-known cosmological problems associated with topo- crete symmetry; the subscripts q and ℓ are to emphasize logical defects, namely, domain walls; they can be solved, that each G only acts on quarks or leptons. A trouble however, via interactions of domain walls with primordial with this picture is that the U(1)Y charges of quarks and black holes [2]. The model provides a framework for un- leptons are different. Nonetheless, the symmetric dupli- derstanding possible deviations from the SM predictions. cation of the electroweak gauge group produces triangle We use the reported quark-lepton universality violation anomalies which can be cancelled by introducing exotic of weak interactions at low energies to fix the scale of the quarks and leptons, related to the standard ones through new weak physics. the same discrete symmetry. This pattern then allows Specifically, the transformation properties of standard to expand the standard electroweak gauge group to the quarks and leptons are i 1 q (3, 1, 2, 1, ), ℓnL (1, 1, 1, 2, 1), nL ∼ 3 ∼ − ∗ i 4 Electronic address: [email protected] (E.A. Matute). u (3, 1, 1, 1, ), νnR (1, 1, 1, 1, 0), nR ∼ 3 ∼ 2 i 2 dnR (3, 1, 1, 1, 3 ), enR (1, 1, 1, 1, 2), (1) after spontaneous symmetry breaking Σ splits into a sin- ∼ − ∼ − glet and a triplet. Each row and each column of Σ is a where n denotes the three generations, qnL = (unL, dnL) doublet under SU(2)qℓ˜ and SU(2)qℓ, respectively. Under and ℓ = (ν ,e ) are the SU(2) doublets, i denotes ˜ nL nL nL P˜ symmetry φ φ and Σ Σ. The equality of the the color degree of freedom, and the numbers in brackets q q˜ bare VEVs of φ ↔and φ is broken↔ by radiative corrections describe the transformation properties under the unified q q˜ due to the hierarchy of Yukawa couplings responsible for gauge group. The ν ’s are introduced because of the R fermion masses, so that the renormalized quantities are experimental signatures for neutrino masses [3]. actually equal up to finite radiative corrections. We re- The quark and lepton assignments in Eq. (1), however, mark that this type of Higgs multiplets is also present introduce axial anomalies of the U(1) [SU(2)]2 type. Y in ununified models, but without any restriction on the They are associated with the nonvanishing trace of Y VEVs of Higgs doublets. for quarks and for leptons due to the separation of the The gauge symmetry breaking follows the pattern weak gauge group. To achieve their cancellation we include exotic fermions as done in the so-called ununified SU(2) ˜ SU(2) U(1) P˜ models [4]. We consider the exotic quarks and leptons qℓ × qℓ˜ × Y × i 1 ↓ q˜ (1, 3, 1, 2, ), ℓñL (1, 1, 2, 1, 1), SU(2) U(1) nL ∼ 3 ∼ − L × Y i 4 u˜ (1, 3, 1, 1, ), νñR (1, 1, 1, 1, 0), nR ∼ 3 ∼ ↓ i 2 U(1) . (6) d˜ (1, 3, 1, 1, ), eñR (1, 1, 1, 1, 2). (2) em nR ∼ − 3 ∼ − The unbroken electric charge generator is given by Under the exotic symmetry P,˜ ordinary and exotic fermions are transformed as follows: 1 1 Q = I3L + Y = I3q + I3˜q + Y, (7) i i i i i ˜i 2 2 qnL qñL, unR uñR, dnR dnR, ↔ ↔ ↔ and the electroweak couplings of the model, in terms ℓñL ℓnL, νñR νnR, eñR enR, (3) ↔ ↔ ↔ of the standard electromagnetic coupling constant and a a b b a a Weinberg angle, take the form and Wq Wq˜ , Gq Gq˜, where Wq , Wq˜ are the weak ↔ ↔ b b gauge bosons of SU(2) ˜, SU(2) , and Gq, Gq are the qℓ qℓ˜ ˜ √2e ′ e gluons of SU(3) , SU(3) , respectively. Besides, the cor- g = gq = gq˜ = , g = . (8) q q˜ sin θ cos θ responding bare gauge couplings are required to be equal. W W Thus the whole Lagrangian of electroweak and strong in- The two physical sets of left-handed weak bosons and teractions, with the Higgs fields defined below, becomes the photon get the following linear combinations of the ˜ invariant under P symmetry. This leads to a great sim- electroweak gauge bosons Wq, Wq˜ and A: plification of many results which cannot be achieved for ± 1 ± ununified models due to current structures; phenomeno- W = (W ± + W ), logical implications are therefore different. 1 √2 q q˜ In this work we assume that the weak gauge sym- 1 3 3 ˜ Z1 = cos θW (Wq + Wq ) sin θW A, metry and exotic symmetry P are spontaneously bro- √2 ˜ − ken at one stage, which happens with our choice of 1 3 3 Higgs multiplets. The minimal set of colorless scalar Aem = sin θW (W + W )+cos θW A, √ q q˜ multiplets that breaks the electroweak gauge symmetry 2 ± 1 ± ± SU(2) ˜ SU(2) U(1) P˜ down to U(1) and gives qℓ qℓ˜ Y em W2 = (Wq Wq ), mass to× all fermions× of the× model includes √2 − ˜ 1 3 3 φq (2, 1, +1), φq (1, 2, +1), Z2 = (Wq Wq˜ ). (9) ∼ ˜ ∼ √2 − Σ= σ + iτ π (2, 2, 0), (4) · ∼ They pick up the mass with vacuum expectation values (VEVs) 2 2 1 2 2 2 1 2 ′2 2 mW1 0 0 mW1 = g v , mZ1 = (g +2g )v = 2 , 4 4 cos θW φq = , φq˜ = , h i h i 2 1 2 2 2 v/√2 v/√2 mAem =0, mW2 = g (v +2u ), 4 u 0 mZ2 = mW2 .

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