Fermion Mass Spectrum Research Articles

STRING-MOTIVATED GRAND UNIFIED THEORIES WITH HORIZONTAL GAUGE SYMMETRY

In the framework of four-dimensional heterotic superstring with free fermions, we investigate the rank 8 grand unified string theories (GUST’s) which contain the SU(3) H gauge family symmetry. GUST’s of this type accommodate naturally the three fermion families presently observed and, moreover, can describe the fermion mass spectrum without high-dimensional representations of conventional unification groups. We explicitly construct GUST’s with gauge symmetry G= SU(5) × U(1) ×[ SU(3) × U(1) ]H ⊂ SO (16) in free complex fermion formulation. As the GUST’s originating from Kac-Moody algebras (KMA’s) contain only low-dimensional representations, it is usually difficult to break the gauge symmetry. We solve this problem by taking for the observable gauge symmetry the diagonal subgroup G sym of the rank 16 group G×G ⊂ SO(16) × SO(16) ⊂ E(8)×E(8). Such a construction effectively corresponds to a level 2 KMA, and therefore some higher-dimensional representations of the diagonal subgroup appear. This (due to G×G tensor Higgs fields) allows one to break GUST symmetry down to SU (3c)× U(1) em . In this approach the observed electromagnetic charge Q em can be viewed as a sum of two Q I and Q II charges of each G group. In this case, below the scale where G×G breaks down to G sym the spectrum does not contain particles with exotic fractional charges.

Generation permutation symmetry and the quark mixing matrix

We propose a new discrete symmetry in the generation space of the fundamental fermions, consistent with the observed fermion mass spectrum. In the case of the quarks, the symmetry leads to the unique prediction of a flat CKM matrix at high energy. We explore the possibility that evolution due to quantum corrections leads to the observed hierarchical form of the CKM matrix at low energies.

Effective Lagrangian approach to the fermion mass problem.

An effective theory is proposed, combining the standard gauge group ${\mathrm{SU}(3)}_{C}\ensuremath{\bigotimes}{\mathrm{SU}(2)}_{L}\ensuremath{\bigotimes}{\mathrm{U}(1)}_{Y}$ with a horizontal discrete symmetry. By assigning appropriate charges under this discrete symmetry to the various fermion fields and to (at least) two Higgs doublets, the broad spread of the fermion mass and mixing angle spectrum can be explained as a result of suppressed, nonrenormalizable terms. A particular model is constructed which achieves the above while simultaneously suppressing neutral Higgs-induced flavor-changing processes.

Natural doublet-triplet splitting in supersymmetric SO(10) models

We construct a supersymmetric SO(10) model, where the Dimopoulos-Wilczek mechanism for doublet-triplet splitting is stable under the addition of Higgs superfields belonging to 126 + 126 often used to implement the see-saw mechanism for neutrino masses and where the charged fermion and neutrino mass spectra arise from a single set of 10 and 126 Higgs representations.

Quark mass hierarchies from the universal seesaw mechanism.

The paper is an extension of the previous work based on the idea of a universal seesaw mechanism to explain the hierarchies in the fermion mass spectrum. A model is proposed within the framework of left-right symmetry with a minimal Higgs system and an axial U(1) symmetry imposed to distinguish the generations. Previous work was confined, for mathematical simplifications, to the case of nonsingular mass matrices. In the present paper, singular matrices are considered. A systematic perturbative technique is developed to display the mass eigenvalues in terms of the vacuum expectation values of the assumed Higgs multiplets. The model successfully correlates the mass hierarchies among the quarks to the assumed hierarchies in the vacuum expectation values without appealing to a hierarchy in the Yukawa-type fermion-Higgs-boson couplings. By considering a general Higgs potential appropriate to the model, we study its minimization and prove that there exists an open subdomain in the parameter space where the orbit of the lowest minima of the potential corresponds to the kind of hierarchy in the vacuum expectation values needed for the success of the model.

Ward-Takahashi identities at finite temperature and phase structure in (2+1)-dimensional chiral Gross-Neveu model.

Chiral Ward-Takahashi identities with composite fields are generalized to finite temperature and applied to investigate the chiral phase transition and phase structure in the (2+1)-dimensional chiral Gross-Neveu model. In terms of these identities, the mass spectra of fermions and bound states and the Goldberger-Treiman relation at finite temperature are obtained. The vertex correction between the fermion and bound states [sigma] is evaluated beyond the leading order in the 1/[ital N] expansion at zero and finite temperatures. With the aid of the gap equation derived from Ward-Takahashi identities, the phase structure is discussed at zero and finite temperatures. It turns out that (i) at zero temperature, the vertex correction is very small and its influence on the phase structure can be neglected and (ii) at nonzero temperature, the infrared divergence in the vertex correction will make the results of the chiral phase transition obtained at the leading order invalid in next to the leading order and the phase structure is in agreement with Coleman's theorem.

Aspects of non-renormalizable terms in a superstring derived standard-like model

I investigate the role of non-renormalizable terms, up to order N = 8, in a superstring derived standard-like model. I argue that non-renormalizable terms restrict the gauge symmetry, at the Planck scale, to be SU(3)×SU(2)×U(1) B ×U(1) T 3 R rather than SU(3)×SU(2)×U(1) Y . I show that breaking the gauge symmetry directly to the Standard Model leads to breaking of supersymmetry at the Planck scale, or to dimension four, baryon and lepton violating, operators. I show that if the gauge symmetry is broken directly to the Standard Model the cubic-level solution to the F and D flatness constraints is violated by higher-order terms, while if U(1) Z' remains unbroken at the Planck scale, the cubic-level solution is valid to all orders of non-renormalizable terms. I discuss the Higgs and fermion mass spectrum. I demonstrate that realistic, hierarchical, fermion mass spectrum can be generated in this model.

Fermion-Higgs model with strong Wilson-Yukawa coupling in two dimensions

The fermion mass spectrum is studied in the quenched approximation in the strong-coupling vortex phase (VXS) of a globally U(1) L⊗U(1) R symmetric scalar-fermion model in two dimensions. In this phase fermion doublers can be completely removed from the physical spectrum by means of a strong Wilson-Yukawa coupling. The lowest lying fermion spectrum in this phase consists most probably only of a massive Dirac fermion which has charge zero with respect to the U(1) L group. We give evidence that the fermion which is charged with respect to that subgroup is absent in the VXS phase. When the U(1) L gauge fields are turned on, the neutral fermion may couple chirally to the massive vector boson state in the confinement phase. The outcome is very similar to our findings in the strong-coupling symmetric phase (PMS) of fermion-Higgs models with Wilson-Yukawa coupling in four dimensions, with the exception that in four dimensions the neutral fermion does most probably decouple from the bosonic bound states.

Universal seesaw mechanisms for quark-lepton mass spectrum.

Problems of fermion mass hierarchies and generation mixings are investigated through universal seesaw mechanisms (USM's) in an extension of the standard model with a left-right-symmetric gauge group $\mathrm{SU}{(3)}_{c}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{y}$. Electroweak Higgs doublets and singlets induce USM's between ordinary fermion multiplets and exotic electroweak singlets of fermions. The USM's work singly in the charged-fermion sectors to suppress their masses below the electroweak mass scale, and doubly in the neutral-fermion sector to make neutrinos superlight. The wide gap between vanishingly small neutrino masses and the 100 GeV scale of the top-quark mass is explained by multiple USM suppressions without presuming a huge Majorana mass. A global chiral $\mathrm{U}{(1)}_{A}$ symmetry is introduced so as to circumvent the strong $\mathrm{CP}$ violation, to distinguish generations, and to restrict the pattern of the Yukawa interactions. Three kinds of electroweak Higgs singlets bring about USM's and cause the generation mixing leading to a realistic variety in each charge sector of the fermion mass spectrum. A fourth Higgs singlet with the largest vacuum expectation value is introduced to make the neutrino masses tiny and to make the axion invisible. By assigning chiral charges to make effective mass matrices of all fermion sectors of the extended Fritzsch type, characteristics of the mass spectra of charged fermions and the quark mixing matrix are described without introducing unnatural hierarchies in the Yukawa coupling constants. Neutrinos have a spectrum comprising doubly degenerate states with a smaller mass and a singlet state with a larger mass. The vacuum mixing angle takes a small value which is favorable for explaining both the new results of the GALLEX Collaboration and the data of the Homestake and Kamiokande experiments.

Mass spectrum and bounds on the couplings in Yukawa models with mirror-fermions

The SU(2) L ⊗SU(2) R symmetric Yukawa model with mirror-fermions in the limit where the mirror-fermion is decoupled is studied both analytically and numerically. The bare scalar self-coupling λ is fixed at zero and infinity. The phase structure is explored and the relevant phase transition is found to be consistent with a second order one. The fermionic mass spectrum close to that transition is discussed and a first non-perturbative estimate of the influence of fermions on the upper and lower bounds on the renormalized scalar self-coupling is given. Numerical results are confronted with perturbative predictions.

Fermion masses at strong Wilson-Yukawa coupling in the symmetric phase

The fermion mass spectrum is studied in the strong-coupling symmetric (PMS) phase of a scalar-fermion model derived from a lattice proposal of the standard model with Wilson-Yukuwa coupling. We find that the fermions are massive and argue for the following interpretation of our numerical results in this PMS phase. The lowest lying fermion spectrum in this phase consists only of a Dirac fermion which is a singlet with respect to the SU(2) L group (the “neutral” fermion). We give evidence that the SU(2) L doublet fermion (the “charged” fermion), in terms of which the model is originally formulated and which is present in the weak-coupling symmetric phase, is absent in the PMS phase. The neutral fermion is only weakly coupled to the scalar particles and appears to become non-interacting in the scaling region. If this interpretation is correct, the Wilson-Yukawa approach does not lead to a satisfactory lattice formulation of the standard model.

On the origin of fermion masses

We review some recent work on nonperturbative properties of fermions and connections with chiral gauge theories. In particular, we consider one of the ultimate goals of this program: the understanding of the actual fermion mass spectrum. It is pointed out that if quarks and leptons are composite, their masses may be set by the physics of the preons and their interactions in such a manner as to differ considerably from the Yukawa form m f α ν (where ν is the electroweak symmetry breaking scale) or analogous forms involving ν. Some ideas of how this might work are given, and some implications are discussed.

RADIATIVE CORRECTIONS TO HIGGS MASSES IN THE SUPERSYMMETRIC MODEL WITH AN EXTRA FAMILY AND ANTI-FAMILY

Radiative corrections to Higgs masses are calculated in a supersymmetric standard model with an extra family and its mirror partners. These corrections, in general, depend on the mass spectrum of fermions, bosons and the strength of Yukawa couplings of the extra families. If we assume that the Yukawa couplings do not blow up below the GUT scale, the upper bound of the lightest Higgs mass increases about 12 GeV. We also notice that, in some cases, the charged Higgs mass becomes lighter than that of the tree level prediction.

Investigation of the fermion spectrum at strong Wilson-Yukawa coupling in the symmetric phase

The fermion mass spectrum is investigated in the strong coupling symmetric phase of a globally SU(2) L ⊗SU(2) R symmetric scalar-fermion model with Wilson-Yukawa coupling. The fermion spectrum consists only of a Dirac fermion which is ‘neutral’ with respect to the SU(2) L group (which is gauged when the gauge interactions are turned on). We give strong evidence that the fermion which is charged with respect to the SU(2) L group is absent in the strong coupling symmetric phase. If this result is valid the neutral fermion become almost non-interacting in the scaling region since its couplings to the scalar and gauge fields would vanish as a power of the lattice spacing a .

Universal Seesaw Mechanism for Quarks and Leptons

Universal seesaw mechanism (USM) is implemented in a left-right symmetric unified theory of extended color and electroweak interactions to solve the problems of fermion mass hierarchies and generation mixings. The gauge group has the structure SU(4)cL ×SU(4)cR ×SU(2)L ×SU(2)R ×U(1)X in which the lepton number is treated as the fourth color and the U(1)X group is generated by a new charge X. Colored and non-colored Higgs fields induce USM between ordinary fermion multiplets and exotic electroweak singlets. USM is singly applied to the charged fermion sectors to suppress their average mass below the electroweak mass scale. On the other hand, USM applied doubly to the neutral fermion sector works to make neutrinos superlight. Prodigious gap between vanishingly small neutrino masses and the 102 GeV scale of the yet-undiscovered top quark is explained without presuming unnaturally huge mass scales. A global horizontal U(1)A symmetry is introduced so as to circumvent the strong CP violation and to restrict the Yukawa coupling constants. Colored Higgs quartets break the extended color symmetry SU(4)cL ×SU(4)cR down to SU(3)cL ×SU(3)cR by making the color interaction of lepton to be superweak. It is three kinds of colored Higgs bi-quartets which degrade the left-right symmetric color interaction into the conventional color interaction of vector type and play at the same time the roles to cause the USM and the generation mixing leading to a realistic variety in each sector of the fermion mass spectrum. Characteristics of mass spectra of charged fermions and the quark mixing matrix are described by adjusting the Yukawa coupling constants over a reasonable range of values.

Universal Seesaw Mechanism for Quarks and Leptons

2GeV scale of the yet-undiscovered top quark is explained without presuming unnaturally huge mass scales. A global horizontal U(I)A symmetry is introduced so as to circumvent the strong CP violation and to restrict the Yukawa coupling con­ stants. Colored Higgs quartets break the extended color symmetry SU(4)CL X SU(4)CR down to SU(3)CL X SU(3)CR by making the color interaction of lepton to be superweak. It is three kinds of colored Higgs bi-quartets which degrade the left-right symmetric color interaction into the conven­ tional color interaction of vector type and play at the same time the roles to cause the USM and the generation mixing leading to a realistic variety in each sector of the fermion mass spectrum. Characteristics of mass spectra of charged fermions and the quark mixing matrix are described by adjusting the Yukawa coupling constants over a reasonable range of values.

Decisive role of nonrenormalizable terms in the flipped string

We study the phenomenology of the flipped SU (5) × U (1) superstring model emphasizing the Higgs and fermion mass spectra. Our calculations take into account up to quintic, rigorously derived, nonrenormalizable terms in the superpotential. We also consider the role of the hidden sector on observable sector physics, and find it to be manifold and decisive. We conclude that at low energies a realistic model will only have one pair of Higgs doublets with adequate electroweak mixing, and no exotic particles besides the ones in the supersymmetric standard model. These two results are a direct consequence of the inclusion in the analysis of nonrenormalizable terms, and have been obtained here for the first time. We also deduce an upper bound on the top quark mass of m t≲180 GeV, and find that the hierarchichal fermion mass spectrum follows naturally in this model.

Issues in technicolor model building

We consider three striking features of the fermion mass spectrum and their possible connection to the pattern of symmetry breaking in extended technicolor models. Why are the neutrino masses so small, why is the top quark mass so large, and why is there CKM mixing among all three families?

Can an anomalous U (1) solve the strong CP problem?

Abstract Many low-energy superstring models contain a pseudo-anomalous U (1) as a global symmetry. We investigate the possibility of having the ensuing axion solve the strong CP problem. We conclude that in heterotic strings with non-abelian hidden gauge groups, this axion cannot solve the strong CP problem. We also comment on alternative solutions to the strong CP puzzle in strings, based on approximate global symmetries of the low-energy lagrangian. We point out potential problems this mechanism would face when applied to realistic models. We find the massless up quark solution to the strong CP problem quite satisfactory. As an example, we work out all the details behind our general remarks for the flipped SU (5) × U (1) model. Previous studies of the hierarchical fermion mass spectrum in this model offer substantial support to our proposed solution to the puzzle.

Calculability of the Flavor‐Mixing Parametersa

Despite the impressive success of the standard model, the repetition of the family‐generation of leptons and quarks persists as one of the most challenging unresolved problems in particle physics. The fermion family problem is to understand the fermion mass hierarchy of the leptons and quarks as observed in family‐generations. Any consistent solution to this problem should also describe the flavor mixings in the charged‐current sector including the CP‐invariance violation as well as the empirical flavor‐conservation up to the αGf order in the neutral weak interaction sector. In the standard model the fermion masses are generated by spontaneous breaking of the electroweak symmetry via the Higgs mechanism, but they are arbitrary free parameters. In other words, the standard model can be adjusted to accommodate the fermion family‐generations but lacks calculability for the fermion mass spectrum. Because there are several fermion generations, the weak interaction eigenstates are not necessarily the mass eigenstates and therefore there will inevitably be mixings between different flavor states in the charged current sector thus introducing further arbitrary parameters to the standard model. However, the neutral‐current sector is flavor diagonal up to αGf order in the standard model because the fermions in each generation are assigned in the same dimensional representations.