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Radiative fermion mass hierarchy in a nonsupersymmetric unified theory
Abstract
In nonsupersymmetric grand unified models a “radiative fermion mass hierarchy” can be achieved in which the spectrum of quark and lepton masses is determined entirely by physics at the unification scale, with many relations following from the unified gauge symmetry, and with the masses of the lightest family arising from loops. A simple, realistic, and predictive model of this kind is presented. A “doubly lopsided” structure, known to lead to bilarge neutrino mixing, plays a crucial role in the radiative hierarchy.
... 1. The result is similar to the many earlier attempts to calculate electron mass [20,222324 or fermion spectrum [25, 26]. The electron mass is estimated as ...
... . We should point out that the result depends sensitively on several parameters as in many previous works [20,22232425; however, a recent study in Refs. [26] indicates that the parameters could be reduced considerably. Note that the charged lepton are given masses by the VEV H ′ 4 which is not directly related to the neutrino masses, so we can calculate the mass eigenstates of charged leptons by using the biunitary transformations to diagonalize the mass matrix M l . ...
We study the lepton sector of a four generations model based on the discrete
flavor group (the even permutation of five objects). The best features of
the three family model survive, including the tribimaximal pattern of
three generation neutrino mixings. At leading order the three light neutrino
mass relations of and are predicted.
The splitting of the neutrino masses can be naturally obtained as a result of
the breaking of down to and a degenerate spectrum is preferred in
our model. In our model, the electron mass is zero at tree level, but
calculable through quantum corrections.
... The extended models for radiative fermion masses can mainly be categorized into two classes based on the nature of new particle(s) propagating in the fermion self-energy loops 1 (a) spin-0 (see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] for example) and (b) spin-1 [24][25][26][27][28][29]. In the case of the latter, SM gauge symmetry needs to be extended to include a gauged flavour symmetry group G F and the radiative correction can be determined in terms of the gauge couplings and masses of the new gauge bosons. ...
A bstract
We investigate a local SU(3) F flavour symmetry for its viability in generating the masses for the quarks and charged leptons of the first two families through radiative corrections. Only the third-generation fermions get tree-level masses due to specific choice of the field content and their gauge charges. Unprotected by symmetry, the remaining fermions acquire non-vanishing masses through the quantum corrections induced by the gauge bosons of broken SU(3) F . We show that inter-generational hierarchy between the masses of the first two families arises if the flavour symmetry is broken with an intermediate SU(2) leading to a specific ordering in the masses of the gauge bosons. Based on this scheme, we construct an explicit and predictive model and show its viability in reproducing the realistic charged fermion masses and quark mixing parameters in terms of not-so-hierarchical fundamental couplings. The model leads to the strange quark mass, m s ≈ 16 MeV at M Z , which is ~2 . 4 σ away from its current central value. Large flavour violations are a generic prediction of the scheme which pushes the masses of the new gauge bosons to 10 ³ TeV or higher.
... Some of the previous efforts in addressing the SM fermion masses in GUTs include Refs. [4][5][6][7][8][9][10][11][12][13][14]. In a seminal paper [15], Georgi suggested to extend the minimal into larger simple Lie groups (with ), and developed his three laws of GUTs. ...
We extend the unitary groups beyond the and to look for possible grand unified theories that give rise to three-generational Standard Model fermions without the simple repetition. By demanding asymptotic free theories at short distances, we find gauge groups of , and together with their anomaly-free irreducible representations are such candidates. Two additional gauge groups of and can also achieve the generational structure without asymptotic freedom. We also find these models can solve the Peccei-Quinn (PQ) quality problem which is intrinsic in the axion models, with the leading PQ-breaking operators determined from the symmetry requirement. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.
... Actually, the radiative corrections mediated by heavy scalars appear as a good candidate for an explanation of the observed mass pattern. Note for completeness, the attempts to calculate quark and lepton masses from the radiative corrections have long history [19][20][21][22][23][24][25]. ...
We study a hybrid model in which the Technicolor and fundamental heavy
scalars live together. We concern extreme case, where electroweak symmetry
breaking (EWSB) comes almost entirely from the strong dynamics of Technicolor,
but the masses of the light fermions, e.g. leptons arises due to the weakly
interacting scalars with one universal Yukawa interaction. We have found that
SU(2) scalar two doublets, which are private but universal for each generation,
offer a natural explanation of the vertical mass hierarchy. There is no large
Yukawa coupling in the theory and the scalar masses are expected to be quite
universal and large. The lepton mass hierarchy arises radiatively from the
quark mass hierarchy, which is affected by the scalar sector as well. Lepton
and down quark masses are calculated in a simplified case of neglected mixing.
... Ref. [60]. More realistic models came along somewhat later [61, 62, 63, 64, 65]. There is a resurgence of interest in this idea as the LHC turns on, since new particles with specific properties which may be seen at the LHC are predicted. ...
This review is based on lectures on flavor physics given at TASI 2008. First I summarize our present knowledge on the fundamental parameters of the flavor sector. Then I discuss various scenarios going beyond the standard model which attempt to explain aspects of the "flavor puzzle". Relating quark masses and mixing angles via flavor symmetry is explored. Explaining the mass hierarchy via the Froggatt-Nielsen mechanism is reviewed and illustrated. Grand unification ideas are pursued to seek a pattern in the observed masses and mixings of quarks and leptons. Generating light fermion masses as radiative corrections is explained and illustrated. The popular solutions to the strong CP problem are summarized. Finally, specific processes in B meson system where significant new flavor contributions can arise are discussed. Comment: 74 pages LaTeX, 24 figures
... Radiative models of flavor have a long history192021222324. Several of the models have some similarities to the flavor structure of our model252627, and especially [1], including some with supersymmetry (SUSY)28293031 or in a GUT [28,32333435. Many of these models only generate some but not all of the Yukawa couplings or require complicated new sectors. ...
We argue that the fermion masses and mixings are organized in a specific
pattern. The approximately equal hierarchies between successive generations,
the sizes of the mixing angles, the heaviness of just the top quark, and the
approximate down-lepton equality can all be accommodated by many flavor models
but can appear ad hoc. We present a simple, predictive mechanism to explain
these patterns. All generations are treated democratically and the flavor
symmetries are broken collectively by only two allowed couplings in
flavor-space, a vector and matrix, with arbitrary O(1) entries. Repeated use of
these flavor symmetry breaking spurions radiatively generates the Yukawa
couplings with a natural hierarchy. We demonstrate this idea with two models in
a split supersymmetric grand unified framework, with minimal additional
particle content at the unification scale. Although flavor is generated at the
GUT scale, there are several potentially testable predictions. In our minimal
model the usual prediction of exact b-tau unification is replaced by the SU(5)
breaking relation m_tau / m_b = 3 / 2, in better agreement with observations.
Other SU(5) breaking effects in the fermion masses can easily arise directly
from the flavor model itself. The symmetry breaking that triggers the
generation of flavor necessarily gives rise to an axion, solving the strong CP
problem. These theories contain long-lived particles whose decays could give
striking signatures at the LHC and may solve the primordial Lithium problems.
These models also give novel proton decay signatures which can be probed by the
next generation of experiments. Measurement of the various proton decay
channels directly probes the flavor symmetry breaking couplings. In this
scenario the Higgs mass is predicted to lie in a range near 150 GeV.
... This procedure guarantees a self-consistent check of the viability of the theory. (A similar line of approach has been taken in an SO(10) model with radiatively induced fermion mass hierarchy [46] very recently [47].) ...
A good fit of the fermion masses and mixings has been found in the minimal renormalizable supersymmetric SO(10). This solution needs a strongly split supersymmetry breaking scenario with gauginos and higgsinos around 100 TeV, sfermions close to 10^14 GeV and a low GUT scale of around 6 10^15 GeV. We predict fast proton decays through SO(10) type of d=6 operators and the leptonic mixing angle theta_13 approximately 0.1.
A bstract
A mechanism for the masses of third, second, and first generation charged fermions at the tree, 1-loop, and 2-loop levels, respectively, is proposed. The fermionic self-energy corrections that lead to this arrangement are induced through heavy vector bosons of a new gauged flavour symmetry group G F . It is shown that a single Abelian group suffices as G F . Moreover, the gauge charges are optimized to result in relatively smaller flavour violations in processes involving the first and second generation fermions. The scheme is explicitly implemented on the Standard Model fermions in an anomaly-free manner and is shown to be viable with observed charged fermion masses and quark mixings. Constraints from flavour violations dictate the lower limit on the new physics scale in these types of frameworks. Through optimal flavour violation, it is shown that nearly two orders of magnitude improvement can be achieved on the lower limit, leading to the new physics scale ≥ 10 ³ TeV in this case. Further improvements are possible at the cost of the down quark mass deviating more than 3 σ from its value extracted from lattice calculations. Options for inducing tiny masses for light neutrinos are also discussed.
A mechanism for the masses of third, second, and first generation charged fermions at the tree, 1-loop, and 2-loop levels, respectively, is proposed. The fermionic self-energy corrections that lead to this arrangement are induced through heavy vector bosons of a new gauged flavour symmetry group . It is shown that a single Abelian group suffices as . Moreover, the gauge charges are optimized to result in relatively smaller flavour violations in processes involving the first and second generation fermions. The scheme is explicitly implemented on the Standard Model fermions in an anomaly-free manner and is shown to be viable with observed charged fermion masses and quark mixings. Constraints from flavour violations dictate the lower limit on the new physics scale in these types of frameworks. Through optimal flavour violation, it is shown that nearly two orders of magnitude improvement can be achieved on the lower limit, leading to the new physics scale TeV in this case. Further improvements are possible at the cost of the down quark mass deviating more than from its value extracted from lattice calculations. Options for inducing tiny masses for light neutrinos are also discussed.
We explore the low-scale implications of the Pati-Salam Model including the TeV scale right-handed neutrinos interacting and mixing with the MSSM fields through the inverse seesaw (IS) mechanism in light of the muon anomalous magnetic moment (muon g−2) resolution and highlight the solutions which are compatible with the quasi-Yukawa unification condition (QYU). We find that the presence of the right-handed neutrinos causes heavy smuons as mμ˜≳800 GeV in order to avoid tachyonic staus at the low scale. On the other hand, the sneutrinos can be as light as about 100 GeV, and along with the light charginos of mass ≲400 GeV, they can yield such large contributions to muon g−2 that the discrepancy between the experiment and the theory can be resolved. These solutions also require mχ˜1±≲400 GeV and mχ˜10≲200. We also discuss such light chargino and neutralino along with the light stau (mτ˜≳200 GeV) in the light of current LHC results. Besides, the gluino mass lies in a range ∼[2.5–3.5] TeV, which is tested in near future experiments. In addition, the model predicts relatively light Higgsinos (μ≲700 GeV); hence, the second chargino mass is also light enough (≲700 GeV) to contribute to muon g−2. Light Higgsinos also yield less fine-tuning at the electroweak scale, and the regions compatible with muon g−2 restrict ΔEW≲100 strictly, and this region also satisfies the QYU condition. In addition, the ratios among the Yukawa couplings should be 1.8≲yt/yb≲2.6, yτ/yb∼1.3 to yield correct fermion masses. Even though the right-handed neutrino Yukawa coupling can be varied freely, the solutions bound its range to 0.8≲yν/yb≲1.7.
We consider the low scale implications in the U(1)' extended MSSM (UMSSM). We restrict the parameter space such that the lightest supersymmetric particle (LSP) is always the lightest neutralino. In addition, we impose quasi Yukawa unification (QYU) at the grand unification scale (M_GUT). QYU strictly requires the ratios among the yukawa couplings as y_t/y_b ~ 1.2, y_tau/y_b ~ 1.4, and y_t/y_tau ~ 0.8. We find that the need of fine-tuning over the fundamental parameter space of QYU is in the acceptable range (Delta_EW <= 10^3), even if the universal boundary conditions are imposed at M_ GUT, in contrast to CMSSM and NUHM. UMSSM with the universal boundary conditions yields heavy stops (m_{stop} >~ 2.5 TeV), gluinos (m_gluino >~ 2 TeV), and squarks from the first two families (m_squarks >~ 4 TeV). Similarly the stau mass is bounded from below at about 1.5 TeV. Despite this heavy spectrum, we find Delta_EW >~ 300, which is much lower than that needed for the minimal supersymmetric models. In addition, UMSSM yield relatively small mu-term, and the LSP neutralio is mostly form by the Higgsinos of mass >~ 700 GeV. We obtain also bino-like dark matter (DM) of mass about 400 GeV. Wino is usually found to be heavier than Higgsinos and binos, but there is a small region where mu ~ M_1 ~ M_2 ~ 1 TeV. We also identify chargino-neutralino coannihilation channel and A-resonance solutions which reduce the relic abundance of LSP neutralino down to the ranges compatible with the current WMAP measurements.
We identify a class of supersymmetric SO(10) model in which imposing essentially perfect t-b-τ Yukawa coupling unification at the grand unification scale yields lightest CP-even (SM-like) Higgs boson mass around 125 GeV. The squark and gluino masses in these models exceed 3 TeV. The model predicts only neutralino-stau coannihilation scenario in order to obtain the desired relic dark matter density.
Radiative flavor models where the hierarchies of Standard Model (SM) fermion
masses and mixings are explained via loop corrections are elegant ways to solve
the SM flavor puzzle. Here we build such a model in the context of Mini-Split
Supersymmetry (SUSY) where both flavor and SUSY breaking occur at a scale of
1000 TeV. This model is consistent with the observed Higgs mass, unification,
and WIMP dark matter. The high scale allows large flavor mixing among the
sfermions, which provides part of the mechanism for radiative flavor
generation. In the deep UV, all flavors are treated democratically, but at the
SUSY breaking scale, the third, second, and first generation Yukawa couplings
are generated at tree level, one loop, and two loops, respectively. Save for
one, all the dimensionless parameters in the theory are O(1), with the
exception being a modest and technically natural tuning that explains both the
smallness of the bottom Yukawa coupling and the largeness of the Cabibbo angle.
We revisit a class of supersymmetric SO(10) models with t-b-τ Yukawa coupling unification condition, with emphasis on the prediction of the Higgs mass. We discuss qualitative features in this model that lead to a Higgs mass prediction close to 125 GeV. We show this with two distinct computing packages, Isajet and SuSpect, and also show that they yield similar global features in the parameter space of this model. We find that t-b-τ Yukawa coupling unification prefers values of the CP-odd Higgs mass m
A
to be around 600–800 GeV, with all colored sparticle masses above 3 TeV. We also briefly discuss prospects for testing this scenario with the ongoing and planned direct dark matter detection experiments. In this class of models with t-b-τ Yukawa unification, the neutralino dark matter particle is heavy (
≳ 400 GeV), which coannihilates with a stau to yield 1 the correct relic abundance.
It is shown that in SO(10) models where the large solar and atmospheric neutrino angles come from the charged-lepton mass matrix being “lopsided”, there is a characteristic relation between the 13 mixing angle of the neutrinos and the size of the Dirac CP-violating phase in the lepton sector. This is illustrated in a recently proposed realistic and predictive model.
A nonsupersymmetric grand unified theory can exhibit a “radiative fermion mass hierarchy”, in which the heavier quarks and leptons get mass at tree level and the lighter ones get mass from loop diagrams. Recently the first predictive model of this type was proposed. Here it is analyzed numerically and it is shown to give an excellent fit to the quark and lepton masses and mixings, including the CP violating phase δCKM. A relation between the neutrino angle θ13 and the atmospheric neutrino angle is obtained.
We report a recent study on lepton masses within a beyond standard model with
a SU(3) family symmetry model. In this scenario ordinary heavy fermions, top
and bottom quarks and tau lepton become massive at tree level from Dirac
See-saw mechanisms implemented by the introduction of a new set of
weak singlet vector-like fermions U,D,E,N, with N a sterile neutrino. The
sterile neutrinos allow the implementation of a general
tree level See-saw Majorana neutrino mass matrix with four massless
eigenvalues. Hence, light fermions, including light neutrinos, obtain masses
from one loop radiative corrections mediated by the massive SU(3) gauge bosons.
Recent analysis shows the existence of a space parameter region where the vector-like fermion masses are within a scale of a few TeV's. This
BSM model is able to accommodate the known spectrum of quark masses and mixing
in a non-unitary as well as the charged lepton masses. We
report a preliminary solution for ordinary charged lepton masses at the scale, a and SU(3) gauge boson masses of .
A detailed numerical analysis on neutrino masses and mixing is in progress
and hopefully shall be reported soon.
The t-b-tau unification with positive Higgs mass parameter \mu\ in the
minimal supersymmetric standard model prefers "just so" Higgs splitting and a
light gluino < 500 GeV which appears to be ruled out by the recent LHC
searches. We reanalyze constraints on soft supersymmetry breaking parameters in
this scenario allowing independent splittings among squarks and Higgs doublets
at the grand unification scale and show that it is possible to obtain t-b-tau
unification and satisfy experimental constraints on gluino mass without raising
supersymmetry breaking scale to very high value ~ 20 TeV. We discuss the origin
of independent squark and Higgs splittings in realistic SO(10) models. Just so
Higgs splitting can be induced without significantly affecting the t-b-tau
unification in SO(10) models containing Higgs fields transforming as
10+\bar{126}+126+210. This splitting arises in the presence of non-universal
boundary conditions from mixing between 10 and other Higgs fields. Similarly,
if additional matter fields are introduced then their mixing with the matter
multiplet 16 is shown to generate the squark splitting required to raise the
gluino mass within the t-b-tau unified models with positive \mu.
We address two fundamental aspects of flavor physics: the mass hierarchy and the large lepton mixing angles. On one side, left–right flavor symmetry realizes the democratic mass matrix patterns and explains why one family is much heavier than the others. On the other side, discrete flavor symmetry such as A4 leads to the observed tribimaximal mixing for the leptons. We show that, by explicitly breaking the left–right flavor symmetry into the diagonal A4, it is possible to explain both the observed charged fermion mass hierarchies and quark and lepton mixing angles. In particular we predict a heavy 3rd family, the tribimaximal mixing for the leptons, and we suggest a possible origin of the Cabibbo and other mixing angles for the quarks.
In this paper we present the main results of our investigation of the single-charm scalar tetraquarks and their SU(3)
representations: , , and . We use the
Fermi-Breit interaction Hamiltonian with SU(3) flavor symmetry breaking to
determine the masses of the single-charm tetraquarks. We also discuss mass
spectra obtained from meson and baryon mass fits. The mass spectra are very
similar to those obtained with Glozman-Riska hyperfine interaction, and they
indicate that some of the experimentally detected states may have tetraquark
nature.
I report low energy results on the study of fermion masses and mixing for
quarks and leptons, including neutrinos within a SU(3) flavor symmetry model,
where ordinary heavy fermions, top and bottom quarks and tau lepton become
massive at tree level from {\bf Dirac See-saw} mechanisms implemented by the
introduction a new set of weak singlet vector-like fermions
U,D,E,N, with N a sterile neutrino. Light fermions obtain masses from one
loop radiative corrections mediated by the massive SU(3) gauge bosons. Recent
results shows the existence of a low energy space parameter where this model is
able to accommodate the known spectrum of quark masses and mixing in a non-unitary as well as the charged lepton masses. Motivated by the
recent LSND and MiniBooNe short-baseline neutrino oscillation experiments we
fit for the 3+1 scenario the neutrino squared mass differences , and . The model
predicts the D vector like quark mass in the range and
horizontal gauge boson masses of few TeV. These low energy predictions are
within LHC possibilities. Furthermore, the above scenario enable us to suppress
simultaneously the tree level processes for and
meson mixing mediated by these extra horizontal gauge bosons
within current experimental bounds.
The QCD axion fails to solve the strong CP problem unless all explicit PQ violating, Planck-suppressed, dimension n<10 operators are forbidden or have exponentially small coefficients. We show that all theories with a QCD axion contain an irreducible source of explicit PQ violation which is proportional to the determinant of the Yukawa interaction matrix of colored fermions. Generically, this contribution is of low operator dimension and will drastically destabilize the axion potential, so its suppression is a necessary condition for solving the strong CP problem. We propose a mechanism whereby the PQ symmetry is kept exact up to n=12 with the help of the very same flavor symmetries which generate the hierarchical quark masses and mixings of the SM. This "axion flavor protection" is straightforwardly realized in theories which employ radiative fermion mass generation and grand unification. A universal feature of this construction is that the heavy quark Yukawa couplings are generated at the PQ breaking scale. Comment: 16 pages, 2 figures
We study flavour violation in a supersymmetric SO(10) implementation of the type II seesaw mechanism, which provides a predictive realization of triplet leptogenesis. The experimental upper bounds on lepton flavour violating processes have a significant impact on the leptogenesis dynamics, in particular they exclude the strong washout regime. Requiring successful leptogenesis then constrains the otherwise largely unknown overall size of flavour-violating observables, thus yielding testable predictions. In particular, the branching ratio for mu -> e gamma lies within the reach of the MEG experiment if the superpartner spectrum is accessible at the LHC, and the supersymmetric contribution to epsilon_K can account for a significant part of the experimental value. We show that this scenario can be realized in a consistent SO(10) model achieving gauge symmetry breaking and doublet-triplet splitting in agreement with the proton decay bounds, improving on the MSSM prediction for alpha_3(m_Z), and reproducing the measured quark and lepton masses. Comment: 40 pages, 10 figures. Accepted for publication in JHEP
Assuming that the leptons and quarks other than top are massless at tree level, we show that their masses may be induced by loops involving the top quark. As a result, the generic features of the fermion mass spectrum arise from combinations of loop factors. Explicitly, we construct a renormalizable model involving a few new particles, which leads to 1-loop bottom and tau masses, a 2-loop charm mass, 3-loop muon and strange masses, and 4-loop masses for first generation fermions. This realistic pattern of masses does not require any symmetry to differentiate the three generations of fermions. The new particles may produce observable effects in future experiments searching for mu to e conversion in nuclei, rare meson decays, and other processes. Comment: 29 pages; Introduction expanded, references added
We point out that, in a class of SO(10) models with matter fields in 16 and 10 representations and type II realization of the seesaw mechanism, the light neutrino masses and the CP asymmetry needed for leptogenesis are controlled by one and the same set of couplings. The generated baryon asymmetry then directly depends on the low-energy neutrino parameters, with no unknown seesaw-scale flavour parameters involved; in particular, the necessary CP violation is provided by the CP-violating phases of the lepton mixing matrix. We compute the CP asymmetry in triplet decays for this scenario and show that it can lead to successful leptogenesis.
We explore in detail the effective matter fermion mass sum-rules in a class of renormalizable SUSY SO(10) grand unified models where the quark and lepton mass and mixing patterns originate from non-decoupling effects of an extra vector matter multiplet living around the unification scale. If the renormalizable type-II contribution governed by the SU(2)_L-triplet in 54_H dominates the seesaw formula, we obtain an interesting correlation between the maximality of the atmospheric neutrino mixing and the proximity of y_s/y_b to V_cb in the quark sector.
In theories in which different regions of the universe can have different values of certain physical parameters, we would naturally find ourselves in a region where they take values favorable for life. We explore the range of such viable values of the mass parameter in the Higgs potential, μ2. For μ2<0, the requirement that complex elements be formed suggests that the Higgs vacuum expectation value v must have a magnitude less than 5 times its observed value. For μ2>0, baryon stability requires that |μ|≪MP, the Planck mass. Smaller values of |μ2| may or may not be allowed depending on issues of element synthesis and stellar evolution. We conclude that the observed value of μ2 appears reasonably typical of the viable range, and a multiple-domain scenario may provide a plausible explanation for the closeness of the QCD scale and the weak scale.
We argue that the observed quark and lepton masses are related at momenta larger than 1015 GeV as follows: mb = mτ, mμ = 3ms and me = md/3. We construct a model in which these factors of three arise naturally — because quarks come in three colors.
We study a coset-space unification model for families based on E-7/SU(5) x U(1)(3). We find that qualitative structure of quark and lepton mass matrices in this model describes very well the observation. We stress, in particular, that the large mixing angle, sin(2)2 theta(v mu v tau) similar or equal to 1, required for the atmospheric neutrino oscillation reported by the SuperKamiokande collaboration, is naturally obtained, which is a consequence of unparallel family structure in the present coset-space unification.
It is shown that, in a model in which up-type and down-type fermions acquire mass from different Higgs doublets, the anthropic tuning of the Higgs mass parameters can explain the fact that the observed masses of the d and u quarks are nearly the same with d slightly heavier. If Yukawa couplings are assumed not to scan (vary among domains), this would also help explain why t is much heavier than b. It is also pointed out that the existence of dark matter invalidates some earlier anthropic arguments against the viability of domains where the standard model Higgs has positive mu2, but makes other even stronger arguments possible.
We show that the existence of a hierarchy of masses among light fermions, with typical mass ratios (..cap alpha../..pi..) (where ..cap alpha.. is the unified gauge coupling at the unification mass scale), is a natural feature of a certain class of grand unification schemes that have recently been discussed.
We present a unified gauge model of weak and electromagnetic interactions, which has the following features: (a) Chiral U(2)L×U(2)R is an exact "natural" symmetry of strong interactions in zeroth order and therefore its violations (which arise in order g4 are computable, and adjusting parameters suitably we can get (√2ε0+ε8)/(√2ε0-2ε8)∼α; (b) violations of isospin symmetry as observed in, for example, ΔI≠0 mass differences are, then, computable and of order α; (c) this model can be extended to include leptons in such a way that me/mμ is computable and is of order g4. We also speculate on the possibility of spontaneous CP violation arising as a higher-order effect.
In conventional quantum electrodynamics both the electron mass and the muon mass are free parameters, so that their ratio is arbitrary. In a unified theory of weak and electromagnetic interactions, this need not be the case. We examine models in which only the muon mass appears as a counterterm. The electron is massless in zeroth order, but develops a finite and calculable mass of order αmμ. Unfortunately, the precise value of the electron mass depends on details of the models, and in particular on masses of unobserved vector bosons.
A model based on the grand unifying group SO(10) is described which
leads to a realistic hierarchy of masses for the quarks and leptons. The
SU(5) prediction me~md is obviated in a simple
way. Some simplification of the Higgs structure is achieved. Only Higgs
representations appearing in the fermion-fermion operator are employed.
Current solar and atmospheric neutrino oscillation data seem to favor a bimaximal pattern for neutrino mixings where the matrix elements Ue2 and Uμ3 are of order one, while Ue3 is much smaller. We show that such a pattern can be obtained quite easily in theories with “lopsided” mass matrices for the charged leptons and the down type quarks. A relation connecting the solar and atmospheric neutrino mixing angles is derived, tan2θatm≃1+tan2θsol, which predicts sin22θatm≃0.97 corresponding to the best fit LMA solution for solar neutrinos. Predictive schemes in SO(10) realizing these ideas are presented. A new class of SO(10) models with lopsided mass matrices is found which makes use of an adjoint VEV along the I3R direction, rather than the traditional B−L direction.
A mechanism is presented for generating fermion masses as a reflection of the superheavy fermions existing in a class of grand unified theories. By means of it we propose a way of understanding how, giving a driving mass term for the top-generation, the charm-generation mass results as a relative first-order perturbation in the unified gauge coupling g2/4π ≈ 10−2, and the up-generation mass as a second-order perturbation. An illustrative calculation of the charm-generation mass is described in a model based on E6.
We present a supersymmetric standard model with three gauged Abelian symmetries, of a type commonly found in superstrings. One is anomalous, the other two are family symmetries. It has a vacuum in which only these symmetries are broken by stringy effects. It reproduces all observed quark and charged lepton Yukawa hierarchies, and the value of the Weinberg angle. It predicts three massive neutrinos, with mixing that can explain both the small angle MSW effect, and the atmospheric neutrino anomaly. The Cabibbo angle is expressed in terms of the gauge couplings at unification. It conserves R-parity, and proton decay is close to experimental bounds. Comment: 26 pages
It has recently been shown how to break SO(10) down to the Standard Model in a realistic way with only one adjoint Higgs. The expectation value of this adjoint must point in the B-L direction. This has consequences for the possible form of the quark and lepton mass matrices. These consequences are explored in this paper, and it is found that one is naturally led to consider a particular form for the masses of the heavier generations. This form implies typically that there should be large (nearly maximal) mixing of the mu- and tau-neutrinos. An explanation that does not involve large tan beta also emerges for the fact that b and tau are light compared to the top quark. Comment: 20 pages, LaTeX, clarification of statements about multiple adjoint Higgs fields in the context of superstring theory
Typically in unified theories the neutrino mixing angles, like the
Cabibbo-Kobayashi-Maskawa (CKM) angles of the quarks, are related to the small
mass ratios between fermions of different generations and are therefore quite
small. A new approach for explaining the intergenerational mass hierarchies is
proposed here which, while giving small CKM angles, naturally leads to neutrino
angles of order unity. Such large mixing angles may be required for a
resolution of the atmospheric neutrino anomaly and may also be relevant for the
solar neutrino puzzle. The mechanism presented here provides a framework in
which novel approaches to the fermion mass question can arise. In particular,
within this framework a variant of the texture idea allows highly predictive
models to be constructed, an illustrative example of which is given. It is
shown how the neutrino mixing angles may be completely determined in such
schemes.
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