Bottom-tau Unification Research Articles

Generalized bottom-tau unification, neutrino oscillations and dark matter: Predictions from a lepton quarticity flavor approach

We propose an $A_4$ extension of the Standard Model with a Lepton Quarticity symmetry correlating dark matter stability with the Dirac nature of neutrinos. The flavor symmetry predicts (i) a generalized bottom-tau mass relation involving all families, (ii) small neutrino masses are induced a la seesaw, (iii) CP must be significantly violated in neutrino oscillations, (iv) the atmospheric angle $\theta_{23}$ lies in the second octant, and (v) only the normal neutrino mass ordering is realized.

Bottom-tau unification in supersymmetric SU(5) models with extra matters

We consider $b$-$\tau$ unification in supersymmetric $SU(5)$ grand unified theories (GUTs) with extra matters. The renormalization group runnings of $b$ and $\tau$ Yukawa coupling constants may be significantly affected by the existence of extra matters. If the extra matters interact with the standard model particles (and their superpartners) only through gauge interaction, the ratio of the $b$ to $\tau$ Yukawa coupling constants at the GUT scale becomes suppressed compared to the case without extra matters. This is mainly due to the change of the renormalization group running of the $SU(3)_C$ gauge coupling constant. If the extra matters have Yukawa couplings, on the contrary, the (effective) $b$ Yukawa coupling at the GUT scale can be enhanced due to the new Yukawa interaction. Such an effect may improve the $b$-$\tau$ unification in supersymmetric GUTs.

Bottom-tau unification in a supersymmetric model with anomaly-mediation

We study the Yukawa unification, in particular, the unification of the Yukawa coupling constants of $b$ and $\tau$, in the framework of supersymmetric (SUSY) model. We concentrate on the model in which the SUSY breaking scalar masses are of the order of the gravitino mass while the gaugino masses originate from the effect of anomaly mediation and hence are one-loop suppressed relative to the gravitino mass. We perform an accurate calculation of the Yukawa coupling constants of $b$ and $\tau$ at the grand unified theory (GUT) scale, including relevant renormalization group effects and threshold corrections. In particular, we study the renormalization group effects, taking into account the mass splittings among sfermions, gauginos, and the standard model particles. We found that the Yukawa coupling constant of $b$ at the GUT scale is about $70\ \%$ of that of $\tau$ if there is no hierarchy between the sfermion masses and the gravitino mass. Our results suggest sizable threshold corrections to the Yukawa coupling constants at the GUT scale or significant suppressions of the sfermion masses relative to the gravitino mass.

SUSY SU(5)×S 4 GUT flavor model for fermion masses and mixings with adjoint, large θ 13 PMNS

We propose an $S_{4}$ flavor model based on supersymmetric (SUSY) SU(5) GUT. The first and third generations of \textbf{10} dimensional representations in SU(5) are all assigned to be $1_{1}$ of $S_{4}$. The second generation of \textbf{10} is to be $1_{2}$ of $S_{4}$. Right-handed neutrinos of singlet \textbf{1} and three generations of $\bar{\textbf{5}}$ are all assigned to be $3_{1}$ of $S_{4}$. The VEVs of two sets of flavon fields are allowed a moderate hierarchy, that is $\langle\Phi^{\nu}\rangle \sim \lambda_{c}\langle\Phi^{e}\rangle$. Tri-Bimaximal (TBM) mixing can be produced at both leading order (LO) and next to next to leading order (NNLO) in neutrino sector. All the masses of up-type quarks are obtained at LO. We also get the bottom-tau unification $m_{\tau}=m_{b}$ and the popular Georgi-Jarlskog relation $m_{\mu}=3m_{s}$ as well as a new mass relation $m_{e}=\frac{8}{27}m_{d}$ in which the novel Clebsch-Gordan (CG) factor arises from the adjoint field $H_{24}$. The GUT relation leads to a sizable mixing angle $\theta^{e}_{12} \sim \theta_{c}$ and the correct quark mixing matrix $V_{CKM}$ can also be realised in the model. The resulting CKM-like mixing matrix of charged leptons modifies the vanishing $\theta^{\nu}_{13}$ in TBM mixing to a large $\theta^{PMNS}_{13}\simeq\theta_{c}/\sqrt{2}$, in excellent agreement with experimental results. A Dirac CP violation phase $\phi_{12}\simeq\pm\pi/2$ is required to make the deviation from $\theta^{\nu}_{12}$ small. We also present some phenomenological numerical results predicted by the model.

Bottom-tau unification by neutrinos in a nonsupersymmetric SU(5) model

We show that Yukawa couplings of bottom quarks and tau leptons can be unified in a non-supersymmetric SU(5) model. We introduce an arbitrary number of right-handed neutrinos. Their masses and Yukawa couplings that satisfy the unification condition by renormalization group evolution are shown. In the case that the grand unification scale is $10^{15.5}$GeV and three right-handed neutrinos have the same mass, the upper bound on their mass is $\sim 10^{14.1}$GeV.

The interplay between GUT and flavour symmetries in a Pati-Salam × S4 model

Both Grand Unified symmetries and discrete flavour symmetries are appealing ways to describe apparent structures in the gauge and flavour sectors of the Standard Model. Both symmetries put constraints on the high energy behaviour of the theory. This can give rise to unexpected interplay when building models that possess both symmetries. We investigate on the possibility to combine a Pati-Salam model with the discrete flavour symmetry $S_4$ that gives rise to quark-lepton complementarity. Under appropriate assumptions at the GUT scale, the model reproduces fermion masses and mixings both in the quark and in the lepton sectors. We show that in particular the Higgs sector and the running Yukawa couplings are strongly affected by the combined constraints of the Grand Unified and family symmetries. This in turn reduces the phenomenologically viable parameter space, with high energy mass scales confined to a small region and some parameters in the neutrino sector slightly unnatural. In the allowed regions, we can reproduce the quark masses and the CKM matrix. In the lepton sector, we reproduce the charged lepton masses, including bottom-tau unification and the Georgi-Jarlskog relation as well as the two known angles of the PMNS matrix. The neutrino mass spectrum can present a normal or an inverse hierarchy, and only allowing the neutrino parameters to spread into a range of values between $\lambda^{-2}$ and $\lambda^2$, with $\lambda\simeq0.2$. Finally, our model suggests that the reactor mixing angle is close to its current experimental bound.

Can Symmetric Texture Reproduce the Unitarity Triangle and mb/m ?

We study the SUSY SO(10) GUT with the symmetric two-zero textures of the quark/lepton mass matrix which realize the Georgi-Jarlskog relations in down-type quark and charged lepton masses. We show that the important constraints on such a framework come from the bottom-tau unification and the observed value of sin 2 beta, one of the angles in the CKM unitarity triangle. We investigate the symmetric two-zero textures assumed at the GUT scale by solving the MSSM renormalization group equations with right-handed neutrino threshold effects. Our results indicate that the value of tan (beta) over tilde is large and the representation of the Higgs field which couples to the third generation of left- and right-handed neutrinos is restricted by the bottom-tau unification condition. The textures with a vanishing 1-2 (and 2-1) element for up-type quarks and a vanishing 1-3 (and 3-1) element for down-type quarks are favored by the observed value of sin 2 beta.

Matter unification in warped supersymmetric [formula omitted

We construct models of warped unification with a bulk SO(10) gauge symmetry and boundary conditions that preserve the SU(4)_C x SU(2)_L x SU(2)_R Pati-Salam gauge group (422). In the dual 4D description, these models are 422 gauge theories in which the apparent unification of gauge couplings in the minimal supersymmetric standard model is explained as a consequence of strong coupling in the ultraviolet. The weakness of the gauge couplings at low energies is ensured in this 4D picture by asymptotically non-free contributions from the conformal sector, which are universal due to an approximate SO(10) global symmetry. The 422 gauge symmetry is broken to the standard model group by a simple set of Higgs fields. An advantage of this setup relative to SU(5) models of warped unification is that matter is automatically required to fill out representations of 422, providing an elegant understanding of the quantum numbers of the standard-model quarks and leptons. The models also naturally incorporate the see-saw mechanism for neutrino masses and bottom-tau unification. Finally, they predict a rich spectrum of exotic particles near the TeV scale, including states with different quantum numbers than those that appear in SU(5) models.

Bottom-tau unification in a supersymmetric SU(5) grand unified theory and constraints fromb→sγand muong−2

An analysis is made on bottom-tau Yukawa unification in supersymmetric (SUSY) SU(5) grand unified theory (GUT) in the framework of minimal supergravity, in which the parameter space is restricted by some experimental constraints including $\mathrm{Br}(\stackrel{\ensuremath{\rightarrow}}{b}s\ensuremath{\gamma})$ and muon $g\ensuremath{-}2.$ The bottom-tau unification can be accommodated to the measured branching ratio $\mathrm{Br}(\stackrel{\ensuremath{\rightarrow}}{b}s\ensuremath{\gamma})$ if superparticle masses are relatively heavy and the Higgsino mass parameter $\ensuremath{\mu}$ is negative. On the other hand, if we take the latest muon $g\ensuremath{-}2$ data to require positive SUSY contributions, then wrong-sign threshold corrections at the SUSY scale upset the Yukawa unification with more than $20%$ discrepancy. It has to be compensated by superheavy threshold corrections around the GUT scale, which constrains models of flavor in SUSY GUT. A pattern of the superparticle masses preferred by the three requirements is also commented upon.

Supersymmetry unification predictions for mtop, Vcb and tan β

We study the predictions for M_top, tan(beta) and V_cb in a popular texture ansatze for the fermion mass matrices. We do this both for the Minimal Supersymmetric Standard Model (MSSM) and for the simplest model (MSSM-BRpV) where a bilinear R-Parity violating term is added to the superpotential. We find that taking the experimental values for M_top and V_cb at 99 % C.L. and the GUT relations h_b=h_tau and (V_cb)^2=h_c/h_t within 5 %, the large tan(beta) solution, characteristic in the MSSM with bottom--tau unification, becomes disallowed. In contrast the corresponding allowed region for the MSSM-BRpV is slightly larger. We also find that important modifications occur if we relax the texture conditions at the GUT scale. For example, if the GUT relations are imposed at 40 %, the large tan(beta) branch in the MSSM becomes fully allowed. In addition, in MSSM-BRpV the whole tan(beta)-M_top plane become allowed, finding unification at any value of tan(beta).

Nearly degenerate neutrinos, supersymmetry and radiative corrections

If neutrinos are to play a relevant cosmological role, they must be essentially degenerate with a mass matrix of the bimaximal mixing type. We study this scenario in the MSSM framework, finding that if neutrino masses are produced by a see-saw mechanism, the radiative corrections give rise to mass splittings and mixing angles that can accommodate the atmospheric and the (large angle MSW) solar neutrino oscillations. This provides a natural origin for the $\Delta m^2_{sol} << \Delta m^2_{atm}$ hierarchy. On the other hand, the vacuum oscillation solution to the solar neutrino problem is always excluded. We discuss also in the SUSY scenario other possible effects of radiative corrections involving the new neutrino Yukawa couplings, including implications for triviality limits on the Majorana mass, the infrared fixed point value of the top Yukawa coupling, and gauge coupling and bottom-tau unification.

2-loop supersymmetric renormalization group equations includingR-parity violation and aspects of unification

We present the complete 2-loop renormalisation group equations of the superpotential parameters for the supersymmetric standard model including the full set of R-parity violating couplings. We use these equations to do a study of (a) gauge coupling unification, (b) bottom-tau unification, (c) the fixed-point structure of the top quark Yukawa coupling, and (d) two-loop bounds from perturbative unification. For large values of the R-parity violating coupling, the value of \alpha_S(M_Z) predicted from unification can be reduced by 5% with respect to the R-parity conserving case, bringing it to within 2\sigma of the observed value. Bottom-tau Yukawa unification becomes potentially valid for any value of \tan\beta\sim 2-50. The prediction of the top Yukawa coupling from the low \tan\beta, infra-red quasi fixed point can be lowered by up to 10%, raising \tan\beta up to a maximum of 5 and relaxing experimental constraints upon the quasi-fixed point scenario. For heavy scalar fermion masses of order 1 Tev the limits on the higher family \Delta L\not=0 operators from perturbative unification are competitive with the indirect laboratory bounds. We calculate the dependence of these bounds upon \tan \beta.

Gauge and Yukawa unification with broken R-parity

We study Yukawa coupling unification in the simplest extension of the Minimal Supersymmetric Standard Model (MSSM) which incorporates R-parity violation through a bilinear superpotential term. In contrast to what happens in the MSSM, we show that bottom-tau unification at the scale M GUT where the gauge couplings approximately unify can be achieved for any value of tan β by choosing appropriately the sneutrino vacuum expectation value. Moreover, we show that in contrast with the MSSM where large tan β solutions exist, in our case for sufficiently large sneutrino VEV ν 3 , large tan β becomes incompatible with bottom-tau unification .

Effects of a 126-dimensional Higgs scalar on bottom-tau unification and the quasi-infrared fixed point

In the presence of ${\bf 126 + \bar{126}}$ Higgs multiplets in a SO(10) theory, the fermion masses get contributions from an induced vacuum expectation value (VEV) of a $SU(2)_L$ doublet residing in ${\bf 126}$ which differentiates between quarks and leptons by a relative sign leading to a significant correction to the prediction of the mass ratio of the bottom quark and the tau lepton for ranges of the mass of this extra doublet. We perform a two-loop renormalization group analysis of the minimal version of the one-step supersymmetric SO(10) model to display this and re-calculate the corrections to the top quark mass in the presence of such an induced VEV. We show that these effects make the infra-red fixed point scenario consistent with experimental results.

Possible dynamical determination of mt, mb and mτ

Motivated by four-dimensional superstring models, we consider the possibility of treating the Yukawa couplings of the Minimal Supersymmetric Standard Model (MSSM) as dynamical variables of the effective theory at the electroweak scale. Assuming bottom-tau unification, we concentrate on the top and bottom Yukawa couplings, and find that minimizing the effective potential drives them close to an effective infrared fixed line. Requiring an acceptable bottom-top mass ratio leads in principle to an additional constraint on the MSSM parameter space. As a by-product, we give new approximate analytical solutions of the renormalization group equations for the MSSM parameters.

Implications of a heavy top in supersymmetric theories

In the context of the radiative electroweak symmetry breaking scenario, we investigate the implications of a heavy top quark mass, close to its infrared fixed point, on the low energy parameters of the minimal supersymmetric standard model. We use analytic expressions to calculate the Higgs masses as well as the supersymmetric masses of the third generation. We further assume bottom-tau unification at the GUT scale and examine the constraints put by this condition on the parameter space ($\tan\beta$,$\alpha_3$), using the renormalization group procedure at the two-loop level. We find only a small fraction of the parameter space where the above conditions can be satisfied, namely $1\le \tan\beta \le 2$, while $0.111\le\alpha_3(M_Z) \le 0.118$. We further analyse the case where all three Yukawa couplings reach the perturbative limit just after the unification scale. In this latter case, the situation turns out to be very strict demanding $\tan\beta\sim 63$.