arXiv subjects
Publications and source records attributed to Zurab Berezhiani.
The comparison of the CKM mixing angles with the leptonic mixings implied by the recent atmospheric and solar neutrino data exhibits an interesting complementarity. This pattern can be understood in the context of the SU(5) grand unification, assuming that the fermion mass matrices have Fritzsch-like structures but are not necessarily symmetric. (The present contribution is based on the paper in ref. \cite{az}.)
The atmospheric neutrino data imply large mixing between the $ν_μ$ and $ν_τ$ states, $θ_{23} = (45\pm 12)^\circ$, while the MSW solution to the solar neutrino problem needs very small mixing angle $θ_{12} = (2\pm 1)^\circ$. In the quark sector the situation is rather opposite -- the 23 mixing is tiny, $θ_{23}\simeq 2^\circ$, versus reasonable 12 mixing, $θ_{12}\simeq 13^\circ$. We show that such complementary patterns of the quark and leptonic mixings could naturally emerge in the context of the SU(5) grand unification, assuming that the fermion mass matrices have the Fritzsch-like structures but their off-diagonal entries are not necessarily symmetric. Such a picture exhibits a `see-saw' like correspondence between the quark and leptonic mixing patterns so that the smaller the quark mixing angle is, the larger the corresponding leptonic mixing angle becomes. This fact simply follows from the fermion multiplet structure in SU(5). We also discuss a model with horizontal symmetry U(2) in which the discussed pattern of the mass matrices can arise rather naturally.
We study the effects of possible flavor-violating operators in theories with the TeV scale quantum gravity, in which the ordinary matter is localized on a 3-brane embedded in the space with $N$ extra dimensions, whereas gravity propagates in the bulk. These operators are scaled by the fundamental Planck mass $M_{Pf}\sim$ TeV and must be suppressed by the gauge family symmetries. We study suppression of the most dangerous and model-independent operators. Several points emerge. First, we show that the Abelian symmetries can not do the job and one has to invoke non-Abelian $U(2)_F$ (or $U(3)_F$) symmetries. However, even in this case there emerge severe restrictions on the fermion mixing pattern and the whole structure of the theory. In order not to be immediately excluded by the well-known bounds, the horizontal gauge fields {\it must} be the bulk modes, like gravitons. For the generic hierarchical breaking pattern the four-fermion operators induced by the tree-level exchange of the bulk gauge fields are unsuppressed for $N = 2$. For $N > 3$ the suppression factor goes as a square of the largest $U(2)_F$-non-invariant Yukawa coupling, which implies the lower bound $M_{Pf} > 10$ TeV or so from the $K^0 - \bar K^0$ system. Situation is different in the scenarios when flavor Higgs fields live on a ($3 + N'$)-brane of lower dimensionality than the gauge fields. The further suppression of gauge-mediated operators can be achieved by an explicit construction: for instance, if $U(2)_F$ is broken by a vacuum expectation value of the doublet, the troublesome operators are suppressed in the leading order, due to custodial SO(4) symmetry of the Higgs-gauge quartic coupling.
We discuss an initial condition on the superpotential couplings of an SU(5) theory which allows the R-violating term L d^c Q but avoids the simultaneous presence of L L e^c + d^c d^c u^c. This same condition keeps under control the products of pairs of different couplings lambda_{ijk} L_i d^c_j Q_k, which are more strongly constrained by flavour-changing-neutral-current limits. In our view, this observation makes relatively more plausible the interpretation of the high-Q^2 Hera anomaly, if real, as caused by squark production.
The anomalous gauge $U(1)_A$ symmetry which could emerge in the context of the string theories can be very useful ingredient towards builting the complete supersymmetric SO(10) model. We present an example of the $SO(10)\times U(1)_A$ model which provides the ``all order'' solution to the doublet-triplet splitting problem via the missing VEV mechanism -- the Planck scale corrections only can induce the mu-term naturally of order 1 TeV. An interesting feature of this model is that all relevant GUT scale VEVs are defined by the single dimensional parameter in the Higgs superpotential, so that the SO(10) symmetry breaks down to the MSSM practically at one step, without intermediate stages. The colour Higgsino mediated d=5 operators can be naturally suppressed. We also extend the model by implementing $U(1)_A$ as a horizontal symmetry for explaining the fermion mass and mixing pattern, and obtain a predictive texture for fermion masses. This model implies a moderate value of $\tanβ$ ($\sim 6-10$) and leads to five predictions for the low energy observables. It also leads to the neutrino masses and mixing pattern that could naturally explain both the atmospheric and solar neutrino problems. In addition, a remarkable interplay of the SO(10) and $U(1)_A$ symmetries guarantees an automatic R parity conservation at any order in $M_P^{-1}$, and also suppresses the Planck scale induced B and L violating d=5 operators to the needed level.
We present the supersymmetric $SU(5)$ models which provide a simple ``all order'' solution to the doublet-triplet splitting problem through the missing doublet mechanism. The crucial role is played by the anomalous $U(1)_A$ gauge symmetry and no additional discrete or global symmetries are needed. Remarkably, such models can be realized even if the 75-plet Higgs is replaced by the standard 24-plet. The same $U(1)_A$ symmetry can also guarantee an exact or approximate conservation of R parity, by suppressing the B and L violating operators to the needed level. The neutrino masses and the proton decay via $d=5$ operators are also examined. We also extend the model by incorporating $U(1)_A$ as a horizontal symmetry for explaining the fermion mass and mixing hierarchy. Interestingly, in this scheme the necessary mild violation of the troublesome $SU(5)$ degeneracy between the down quark and the charged lepton masses can be induced by certain R-parity violating operators.
In an analogy to the case of axion, which converts the $Θ$-angle into a dynamical degree of freedom, we are trying to imagine a situation where the quark mixing angles turn out to be dynamical degrees of freedom (pseudo-Goldstone bosons), and their vacuum expectation values are obtained from the minimization of the vacuum energy. We present an explicit supersymmetric model with horizontal symmetry, where such a mechanism can be realized. It implies one relation between the quark masses and the CKM mixing angles: $s_{13}s_{23}/s_{12}=(m_s/m_b)^2$, which is fulfilled within present experimental accuracy. We believe, however, that the idea might be more general than this concrete model, and it can be implemented in more profound frameworks.
The horizontal symmetry $U(3)_H$ can greatly help in solving the flavor problems in the supersymmetric grand unification. We consider the $SU(5)\times U(3)_H$ model and show that it leads to the remarkable relations between the fermion mass matrices and the soft SUSY breaking terms. Dangerous supersymmetric contributions to the flavor-changing phenomena are naturally suppressed. The possible extensions to the $SO(10)\times U(3)_H$ model are also outlined.
The concept of non-abelian horizontal symmetry $SU(3)_H$ can greatly help in understanding the fermion and sfermion flavour structures in supersymmetric grand unification. For the sake of demonstration the $SU(5)\times SU(3)_H$ model, suggested earlier in ref. \cite{PLB85}, is revisited. We show that under very simple and natural assumption it links the sfermion mass pattern to those of fermions in a remarkable way. All dangerous supersymmetric flavour-changing contributions are naturally suppressed in a general case, independently of the concrete texture for fermion mass matrices. Nevertheless, within this framework we present an example of predictive model for fermion masses and mixing, which leads to 7 consistent predictions for the low energy observables. [Based on talks given at Int. Workshop {\em `SUSY 96'}, Univ. of Maryland, 29 May - 1 June 1996 (to appear on Proceedings), and II US-Polish Workshop {\em `Physics from Planck Scale to Electroweak Scale'}, Warsaw, 28-30 March 1996.]
The problem of fermion masses and mixings is discussed in the context of supersymmetric grand unification theories. Some predictive frameworks based on the $SU(5)$, $SO(10)$ and $SU(6)$ models are reviewed. [Based on lectures delivered at the ICTP Summer School on `High Energy Physics and Cosmology', Trieste, Italy, 3-28 July 1995 (to appear on Proceedings), and XIX Int. Conference on {\em Particle Physics and Astrophysics in the Standard Model and Beyond}, Bystra, Poland, 19-26 September 1995]
The first fermion family might play a key role in understanding the structure of flavour: a role of the mass unification point. The GUT scale running masses $\bar{m}_{e,u,d}$ are rather close, which may indicate an approximate symmetry limit. Following this observation, we present a new predictive approach based on the SUSY $SO(10)$ theory with $\tanβ\sim 1$. The inter-family hierarchy is first generated in a sector of hypothetical superheavy fermions and then transfered inversely to ordinary quarks and leptons by means of the universal seesaw mechanism. The Yukawa matrices are simply parametrized by the small complex coefficients $\eps_{u,d,e}$ which are related by the $SO(10)$ symmetry properties. Their values are determined by the ratio of the GUT scale $M_X\simeq 10^{16}$ GeV to a higher (possibly string) scale $M\simeq 10^{17}-10^{18}$ GeV. The suggested ansatz correctly reproduces the fermion mass and mixing pattern. By taking as input the masses of leptons and $c$ and $b$ quarks, the ratio $m_s/m_d$ and the value of the Cabibbo angle, we compute the $u,d,s$ quark masses, top mass and $\tanβ$. The top quark is naturally in the 100 GeV range, but with upper limit $M_t<165$ GeV, while the lower bound $M_t>160$ GeV implies $m_s/m_d>22$. $\tanβ$ can vary from 1.4 to 1.7. The proton decaying $d=5$ operators $qqql$ are naturally suppressed.
In most supersymmetric models the stability of the proton is ensured by invoking R-parity. A necessary ingredient to enforce R-parity is the possibility of distinguishing the lepton superfields from the Higgs ones. This is generally achieved either by assuming different charges under some matter parity, or by assigning the superfields to different representations of a unified gauge group. We want to put forward the idea that the replica of the fermion generations, which constitute an intrinsic difference between the fermions and the Higgs superfields, can give a clue to understand R-parity as an accidental symmetry. More ambitiously, we suggest a possible relation between proton stability and the actual number of fermion generations. We carry out our investigation in the framework of non-Abelian horizontal gauge symmetries. We identify $SU(4)_H$ as the only acceptable horizontal gauge group whichcan naturally ensure the absence of R parity violating operators, without conflicting with other theoretical and phenomenological constraints. We analyze a version of the supersymmetric standard model equipped with a gauged horizontal $SU(4)_H$, in which R-parity is accidental. The model predicts four families of fermions, it allows for the dynamical generation of a realistic hierarchy of fermion masseswithout any ad hoc choice of small Yukawa couplings, it ensures in a natural way the heaviness of all the fourth family fermions (including the neutrino) and it predicts a {\it lower} limit for the $τ$-neutrino mass of a few eV. The scale of the breaking of the horizontal symmetry can be constrained rather precisely in a narrow window around $\sim 10^{11}$ GeV. Some interesting astrophysical and cosmological implications of the model are addressed as well.
The supersymmetric $SU(6)$ model equipped by the flavour-blind discrete gauge symmetry $Z_3$ is considered. It provides simultaneous solution to the doublet-triplet splitting problem, $μ$-problem and leads to natural understanding of fermion flavour. The Higgs doublets arise as Goldstone modes of the spontaneously broken {\em accidental} global symmetry $SU(6)\times U(6)$ of the Higgs superpotential. Their couplings to fermions have peculiarities leading to the consistent picture of the quark and lepton masses and mixing, without invoking the horizontal symmetry or zero texture concepts. In particular, the only particle that has direct $O(1)$ Yukawa coupling with the Higgs doublet is top quark. Other fermion masses arise from the higher order operators, with natural mass hierarchy described in terms of small ratios $\eps_Σ=V_Σ/V_H$ and $\eps_H=V_H/M$, where $V_H$ and $V_Σ$ correspondingly are the $SU(6)$ and $ SU(5)$ symmetry breaking scales, and $M$ is a large (Planck or string) scale. The model automatically implies $b-τ$ Yukawa unification. Specific mass formulas are also obtained, relating the down quark and charged lepton masses. Neutrinos get small ($\sim 10^{-5}\,$eV) masses which can be relevant for solving the solar neutrino problem via long wavelength vacuum oscillation.
We study an extension of the supersymmetric standard model with four families and gauged horizontal symmetry $SU(4)_H$, in which R parity automatically follows as a consequence of gauge invariance and of the field content of the model. Beyond ensuring R parity conservation, the horizontal symmetry allows for the dynamical generation of a hierarchical pattern of fermion masses, without the need of any ad hoc choice of small Yukawa couplings. The structure of the mass matrices implies that the fourth family does not mix with the other three, and that the $b',t',τ',ν'$ masses are all naturally in the 100 GeV range. The model has other interesting phenomenological implications. The scale of the horizontal symmetry breaking is constrained by cosmological and astrophysical arguments to be $\sim 10^{11}$ GeV. Then the late $b'$ decays could explain a magnitude of the isotropic cosmic gamma flux. In addition, a lower bound of a few eV is found for the mass of the $τ$-neutrino, which can thus provide a hot component for the cosmological dark matter. Due to R parity conservation, the lightest supersymmetric particle is stable and can provide the cold component. The $ν_e$ and $ν_μ$ masses can naturally be in the correct ranges for a solution of the solar or atmospheric neutrino problems via neutrino oscillations.
The doublet-triplet splitting problem is perhaps the most problematic aspect of supersymmetric grand unified theories. It can be argued that the most natural reason for the Higgs doublets to be light is that they are pseudo-Goldstone bosons associated with the spontaneous breakdown of an accidental global symmetry. In this paper we discuss the possibility of implementing this idea in the SU(6) model of refs. \cite{Zur,Bar2,Bar3,Bar4}. We show that although it is simple to generate an accidental symmetry of the renormalizable terms of the potential, it is quite difficult to construct a model which allows for the preservation of the accidental symmetry in the nonrenormalizable terms. We summarize the constraints on such models and then give three different ways to construct a superpotential where the dangerous mixing terms are sufficiently suppressed even in the presence of nonrenormalizable operators. With these examples we demonstrate the existence of consistent models implementing the Higgs as pseudo-Goldstone boson scheme. We extend one of the three examples to include fermion masses. We also show that when restricted to regular group embeddings the only possible models without light triplets are trivial generalizations of the SU(6) model we consider.
The supersymmetric $SU(6)$ model accompanied by the flavour-blind discrete symmetry $Z_3$ can succesfully deal with such key problems of SUSY GUTs, as are the gauge hierarchy/doublet-triplet splitting, $μ$-problem and flavour problem. The Higgs doublets arise as Goldstone modes of the spontaneously broken {\em accidental} global $SU(6)\times U(6)$ symmetry of the Higgs superpotential. Their couplings to fermions have peculiarities leading to the consistent picture of the quark and lepton masses and mixing, without invoking any of horizontal symmetry/zero texture concepts. In particular, the only particle that has direct Yukawa coupling with the Higgs doublet is top quark. Other fermion masses appear from the higher order operators, with natural mass hierarchy. Specific mass formulas are also obtained. [On the basis of talks given at the Int. Workshop "Physics from Planck Scale to Electroweak Scale", Warsaw, Poland, 21-24 September 1994, and at the III Trieste Conference "Recent Developments in the Phenomenology of Particle Physics", Trieste, Italy, 3-7 October 1994.]
The up-down splitting within quark families increases with the family number: m_u ~ m_d, m_c > m_s, m_t >> m_b. We show an approach that realizes this feature of the spectrum in a natural way. We suggest that the mass hierarchy is first generated by radiative effects in a sector of heavy isosinglet fermions, and then projected to the ordinary light fermions by means of a seesaw mixing. The hierarchy appears then inverted in the light fermion sector. We present a simple left-right symmetric gauge model in which the P- and CP-parities and an isotopical "up-down" symmetry are softly (or spontaneously) broken in the Higgs potential. Experimentally consistent predictions are obtained. The Cabibbo angle is automatically in the needed range: Theta_C ~ 0.2. The top quark is naturally heavy, but not too heavy: m_t < 150 GeV.
Zee-type models with Majorons naturally incorporate the 17 keV neutrino but in their minimal version fail to simultaneously solve the solar neutrino puzzle. If there is a sterile neutrino state, we find a particularly simple solution to the solar neutrino problem, which besides $ν_{17}$ predicts a light Zeldovich-Konopinski-Mahmoud neutrino $ν_{light}=ν_e+ν_μ^c$ with a magnetic moment being easily as large as $10^{-11}μ_B$ through the Barr-Freire-Zee mechanism.