Generations Of Chiral Fermions Research Articles

Dynamical symmetry breaking and fermion mass hierarchy in the scale-invariant 3-3-1 model

We propose an extension of the Standard Model (SM) based on the $SU(3)_C\otimes SU(3)_L\otimes U(1)_X$ (3-3-1) gauge symmetry and scale invariance. Maintaining the main features of the so-called 3-3-1 models, such as the cancellation of gauge anomalies related to the number of chiral fermion generations, this model exhibits a very compact scalar sector. Only two scalar triplets and one singlet are necessary and sufficient to break the symmetries dynamically via the Coleman-Weinberg mechanism. With the introduction of an Abelian discrete symmetry and assuming a natural hierarchy among the vacuum expectation values of the neutral scalar fields, we show that all particles in the model can get phenomenologically consistent masses. In particular, most of the standard fermion masses are generated via a seesaw mechanism involving some extra heavy fermions introduced for consistency. This mechanism provides a partial solution for the fermion mass hierarchy problem in the SM. Furthermore, the simplicity of the scalar sector allows us to analytically find the conditions for the potential stability up to one-loop level and show how they can be easily satisfied. Some of the new particles, such as the scalars $H$, $H^\pm$ and all the non-SM vector bosons, are predicted to get masses around the TeV scale and, therefore, could be produced at the high-luminosity LHC. Finally, we show that the model features a residual symmetry which leads to the stability of a heavy neutral particle; the latter is expected to show up in experiments as missing energy.

Totally asymptotically free trinification

Motivated by new ideas about the Higgs mass naturalness problem, we present realistic TeV-scale extensions of the Standard Model, into the gauge group SU(3) L ⊗ SU(3) R ⊗ SU(3) c , such that all gauge, Yukawa and quartic couplings can be extrapolated up to infinite energy. Three generations of chiral fermions and Higgses are needed, as well as some extra fermion.

Spinning squashed extra dimensions and chiral gauge theory from [formula omitted] SYM

New solutions of SU(N) N=4 SYM on R4 interpreted as spinning self-intersecting extra dimensions are discussed. Remarkably, these backgrounds lead to a low-energy sector with 3 generations of chiral fermions coupled to scalar and gauge fields, with standard Lorentz-invariant kinematics. This sector arises from zero modes localized on the rotation axes, which are oblivious to the background rotation. The remaining modes are not described by a Lorentz-invariant field theory and are mostly “heavy”, but there is one sextet of tachyonic excitations. Assuming that the latter get stabilized, e.g. by quantum effects, we argue that different rotation frequencies would induce a VEV for some of the low-energy scalar fields. We discuss configurations which may lead to a low-energy physics not far from the broken phase of the standard model.

Higgs properties in the fourth-generation MSSM: Boosted signals over the three-generation plan

The generalization of the MSSM to the case of four chiral fermion generations (4GMSSM) can lead to significant changes in the phenomenology of the otherwise familiar Higgs sector. In most of the 3GMSSM parameter space, the lighter CP-even $h$ is $\sim 115-125$ GeV and mostly Standard Model-like while $H,A,H^\pm$ are all relatively heavy. Furthermore, the ratio of Higgs vevs, $\tan \beta$, is relatively unconstrained. In contrast to this, in the 4GMSSM, heavy fourth generation fermion loops drive the masses of $h,H,H^\pm$ to large values while the CP-odd boson, $A$, can remain relatively light and $\tan \beta$ is restricted to the range $1/2 \lsim \tan \beta \lsim 2$ due to perturbativity requirements on Yukawa couplings. We explore this scenario in some detail, concentrating on the collider signatures of the light CP-odd Higgs at both the Tevatron and LHC. We find that while $gg \to A$ may lead to a potential signal in the $\tau^+\tau^-$ channel at the LHC, $A$ may first be observed in the $\gamma \gamma$ channel due to a highly loop-enhanced cross section that can be more than an order of magnitude greater than that of a SM Higgs for $A$ masses of $\sim 115-120$ and $\tan\beta<1$. We find that the CP-even states $h,H$ are highly mixed and can have atypical branching fractions. Precision electroweak constraints, particularly for the light $A$ parameter space region, are examined in detail.

Pseudoscalar Higgs bosons at the LHC: production and decays into electroweak gauge bosons revisited

We analyse and compute, within a number of standard model (SM) extensions, the cross sections σ A→VV′ for the production of a heavy neutral pseudoscalar Higgs-boson/spin-zero resonance at the LHC and its subsequent decays into electroweak gauge bosons. For comparison we calculate also the corresponding cross sections for a heavy scalar. The SM extensions we consider include a type-II two-Higgs doublet model (2HDM), a 2HDM with four chiral fermion generations, the minimal supersymmetric extension of the SM (MSSM), and top-colour assisted technicolour models. Presently available phenomenological constraints on the parameters of these models are taken into account. We find that, with the exception of the MSSM, these models permit the LHC cross sections σ A→VV′ to be of observable size. That is, a pseudoscalar resonance may be observable, if it exists, at the LHC in its decays into electroweak gauge bosons, in particular in WW and γ γ final states.

Invariant bundles on B-fibered Calabi-Yau spaces and the Standard Model

We derive the Standard model gauge group together with chiral fermion generations from the heterotic string by turning on a Wilson line on a non-simply connected Calabi-Yau threefold with an SU(5) gauge group. For this we construct stable ${\bf Z_2}$-invariant $SU(4)\times U(1)$ bundles on an elliptically fibered cover Calabi-Yau threefold of special fibration type (the $B$-fibration). The construction makes use of a modified spectral cover approach giving just invariant bundles.

The landscape of intersecting brane models

We develop tools for analyzing the space of intersecting brane models. We apply these tools to a particular T^6/Z_2^2 orientifold which has been used for model building. We prove that there are a finite number of intersecting brane models on this orientifold which satisfy the Diophantine equations coming from supersymmetry. We give estimates for numbers of models with specific gauge groups, which we confirm numerically. We analyze the distributions and correlations of intersection numbers which characterize the numbers of generations of chiral fermions, and show that intersection numbers are roughly independent, with a characteristic distribution which is peaked around 0 and in which integers with fewer divisors are mildly suppressed. As an application, the number of models containing a gauge group SU(3) x SU(2) x U(1) or SU(4) x SU(2) x SU(2) and 3 generations of appropriate types of chiral matter is estimated to be order O (10), in accord with previous explicit constructions. As another application of the methods developed in the paper, we construct a new pair of 3-generation SU(4) x SU(2) x SU(2) Pati-Salam models using intersecting branes. We conclude with a description of how this analysis can be generalized to a broader class of Calabi-Yau orientifolds, and a discussion of how the numbers of IBM's are related to numbers of stabilized vacua.

Yukawa couplings in SO(10) heterotic M-theory vacua

We demonstrate the existence of a class of N=1 supersymmetric nonperturbative vacua of Hořava–Witten M-theory compactified on a torus fibered Calabi–Yau 3-fold Z with first homotopy group π 1(Z)= Z 2 , having the following properties: (1) SO(10) grand unification group, (2) net number of three generations of chiral fermions in the observable sector, and (3) potentially viable matter Yukawa couplings. These vacua correspond to semistable holomorphic vector bundles V Z over Z having structure group SU(4) C , and generically contain M5-branes in the bulk space. The nontrivial first homotopy group allows Wilson line breaking of the SO(10) symmetry. Additionally, we propose how the 11-dimensional Hořava–Witten M-theory framework may be used to extend the perturbative calculation of the top quark Yukawa coupling in the realistic free-fermionic models to the nonperturbative regime. The basic argument being that the relevant coupling couples twisted–twisted–untwisted states and can be calculated at the level of the Z 2× Z 2 orbifold without resorting to the full three generation models.

Type I strings with F- and B-flux

We present non-supersymmetric toroidal compactifications of type-I string theory with both constant background NSNS two-form flux and non-trivial magnetic flux on the various D9-branes. The non-vanishing B-flux admits four-dimensional models with three generations of chiral fermions in standard model like gauge groups. Additionally, we consider the orbifold 4/2, again with both kinds of background flux present, leading to non-supersymmetric as well as supersymmetric models in six dimensions. All models have T-dual descriptions as intersecting brane worlds.

On vector bundles and chiral matter in N = 1 heterotic compactifications

In this note we derive the net number of generations of chiral fermions in heterotic string compactifications on Calabi-Yau threefolds with certain SU(n) vector bundles, for n odd, using the parabolic approach for bundles. We compare our results with the spectral cover construction for bundles and make a comment on the net number interpretation in F-theory.

Non-tachyonic open descendants of the 0B string theory

We use the crosscap constraint to construct open descendants of the 0B string compactified on T 6/ Z 3 and on T 4/ Z 2 free of tachyons both in the closed and in the open unoriented sectors. In four dimensions the construction results in a Chan-Paton gauge group U(8)⊗U(12)⊗U(12) with three generations of chiral fermions in the representations ( 8,1, 12)⊕(8,12,1)⊕(1, 66,1)⊕(1,1,66) .

Three-Generation Distler-Kachru Models

Distler-Kachru models which yield three generations of chiral fermions with gauge group SO(10) are found. These models have mirror partners.

Construction of realistic standard-like models in the free fermionic superstring formulation

I discuss in detail the construction of realistic superstring standard-like models in the four dimensional free fermionic formulation. The analysis results in a restricted class of models with unique characteristics: (i) Three and only three generations of chiral fermions with their superpartners and the correct standard model quantum numbers. (ii) Proton decay from dimension four and dimension five operators is suppressed due to gauged U(1) symmetries. (iii) There exist Higgs doublets from two distinct sectors, which can generate realistic symmetry breaking. (iv) These models explain the top-bottom mass hierarchy. At the trilinear level of the superpotential only the top quark gets a nonvanishing mass term. The bottom quark and the lighter quarks and leptons get their mass terms from nonrenormalizable terms. This result is correlated with the requirement of a supersymmetric vacuum at the Planck scale. (v) The models predict the existence of small hidden gauge groups, like SU(3), with matter spectrum in vector representations.

FLUX-BREAKING OF SECOND E8 IN THREE-GENERATION SUPERSTRING MODELS

Some Calabi-Yau manifolds leading to three generations of chiral fermions in the heterotic E8×E8 some superstring theory are endowed with a freely acting discrete symmetry Z3, which when mapped homomorphically into the E6 subgroup of the first E8 causes it to break to ( SU (3))3 or SU(6)×U(1). The same discrete group can be mapped homomorphically into the second E8 and can result in its breaking. We obtain some of the maximal subgroups of E8 and present the breaking directions in weight space for some breakings. Flux-tubes arise in these theories and their significance in cosmology is briefly discussed.

A standard-like model in the four-dimensional free fermionic string formulation

We show how the Standard Model may be derived from the heterotic string with no intermediate energy scale by using the free fermionic formulation. An explicit model is presented, with the following properties: (i) The observable gauge group is SU(3) C × SU(2) L × U(1) n where n = 1 or 2, after a possible symmetry breaking at the string level. (ii) The complete massless spectrum is derived and is shown to be anomaly free apart from a single “anomalous” U(1). In the observable sector there are only three generations of chiral fermions with their superpartners. (iii) There are enough scalar doublets and singlets to break the gauge symmetry in a realistic way. (iv) All trilinear superpotential couplings have been calculated. (v) The weak hypercharge is uniquely defined, including a possible new, generation independent, U(1) symmetry, which may remain unbroken down to low energies, and prevents fast proton decay.

Three-generation four-dimensional SU(3)×SU(2)×U(1) 5 string models

We generalize the string construction which possesses four-dimensional space-time symmetry to allow for the removal of the fixed-point degeneracy of the partition function in the twisted sectors. We present two examples, one supersymmetric and the other non-supersymmetric, based on Z 6 discrete symmetry. Both have a rank-8 gauge group SU(3)×SU(2)×U(1) 5 (no hidden sector), three generations of chiral fermions, Higgs doublets and no Higgs color triplets.

Non-supersymmetric four-dimensional strings

The general formalism of non-supersymmetric four-dimensional strings is worked out in the Green-Schwarz formalism. The conditions on twisting parameters from world-sheet supersymmetry and Lorentz invariance in the light-cone gauge are shown to be identical. Tachyonic states can be projected out in many models by the modular invariance conditions. Tachyon-free models based on twisting parameters with Z 2, Z 3, Z 4 and Z 6 discrete symmetries are discussed. In particular, the four-dimensional analogue of the tachyon-free ten-dimensional O(16) × O(16) model is obtained. Two specific models with Z 4 and Z 6 symmetry are presented. The Z 6 model has E 6 × U(1) 2 as gauge group, 18 generations of chiral fermions and 17 multiplets of complex scalars in the 27 of E 6 . The Z 4 model has a gauge group SO(10) × SU(2) × U(1) 4, the matter in 4 · ( 16) + 2 · ( 16 + 16) of SO(10) chiral fermions and complex scalars, and a Higgs scalar in the adjoint representation of the gauge group.

COSET SPACES AS ALTERNATIVES TO CALABI-YAU SPACES IN THE PRESENCE OF GAUGINO CONDENSATION

Compactification of the field-theory limit of the E8 × E′8 heterotic string on six-dimensional coset manifolds is discussed, with specific reference to maintaining four-dimensional super-symmetry. By choosing a torsion proportional to the background value of the three-index field Hmnp occurring in the theory it is possible to satisfy the condition of SU(3) holonomy necessary for supersymmetry. However, in all cases considered, it is found impossible to satisfy all the remaining conditions for supersymmetry. If gaugino condensation is assumed to occur, it is possible to preserve supersymmetry satisfying all the modified requirements of supersymmetry for the spaces SU (3)/ U (1) × U (1), G 2/ SU (3) and SO (5)/ SU (2) × U (1). The question of chiral fermions is examined in these cases using the Atiyah-Singer index theorem. Background gauge fields, which correspond to different numbers of generations of chiral fermions, are constructed explicitly. In all these cases the low-energy symmetry group is E6 × E′8.

Alternative superstring compactifications will not give new low-energy models

Alternatives to Calabi-Yau and related compactifications, such as orbifolds with nonabelian space groups, could in principle yield low-energy models based on a GUT group different from E 6, SO(10) or SU(5). Such models with chiral fermion generations, trilinear superpotential terms yielding quark and lepton masses as well as Higgs mixing, pertubative gauge couplings, and at least one extra U(1) beyond the standard model are looked for. The only viable model based on an SU(6) GUT group is equivalent to the minimal rank-5 E 6 model studied previously. There are no acceptable models based on the GUT groups SU( N⩾7) or SO(14). When combined with previous arguments disfavouring SU(5) and SO(10) GUT groups, as well aṡ rank-6 E 6 models, the present results point to a unique low-energy SU(3) c×SU(2) L×U(1) Y×U(1) E model inspired by the superstring.

Supersymmetric compactification of the heterotic string on coset spaces.

Compactification of ten-dimensional ${E}_{8}\ensuremath{\bigotimes}{E}_{8}^{\ensuremath{'}}$ heterotic string theory on coset manifolds is discussed. It is pointed out that $N=1$ supersymmetry can be preserved on $\frac{{G}_{2}}{\mathrm{SU}(3)}$, SO(5)/SU(2)\ensuremath{\bigotimes}U(1), and SU(3)/U(1)\ensuremath{\bigotimes}U(1) if gauge-fermion condensation occurs and the third-rank antisymmetric field strength is nonzero. In particular, three generations of chiral fermions can be obtained.