Yukawa Coupling Unification Research Articles

Can supersymmetric loops correct the fermion mass relations in SU(5)?

We investigate possibilities for improving the fermion mass relations that arise in grand unified theories (GUTs). Each scenario relies on supersymmetric loop effects alone, without modifying the naive Yukawa unification. We briefly review the case where A terms follow the usual proportionality condition. In this case SUSY effects cannot completely improve the mass relations. Secondly, we employ a new ansatz for the trilinear A terms that satisfies all experimental and vacuum stability bounds, and can successfully modify the mass relations. Finally, we investigate the use of general (nonproportional) A terms, which can contain large off-diagonal entries. In this case, flavor changing neutral current (FCNC) data present an important constraint, but remedying the mass relations appears possible. We do not pretend to present a complete, motivated theory of fermion masses. Rather this paper can be viewed as an existence proof, serving to show that Yukawa coupling unification can occur even within the framework of minimal GUTs.

B−τunification,gμ−2,theb→s+γconstraint, and nonuniversalities

An analysis is given of the $b-\tau$ Yukawa coupling unification in view of the recent result from Brookhaven on $g_{\mu}-2$ and under the constraint of $b\to s+\gamma$. We explore $b-\tau$ unification under the above constraints for nonuniversal boundary conditions for the soft SUSY breaking parameters. We find new regions of the parameter space where significant negative supersymmetric contribution to the b quark mass can arise and $b-\tau$ unification within SU(5) framework can occur with nonuniversal gaugino masses. Specifically we find that for the case where the gaugino mass matrix transforms like a 24 plet one finds a negative contribution to the b quark mass irrespective of the sign of the Higgs mixing parameter $\mu$ when the supersymmetric contribution to $g_{\mu}-2$ is positive. We exhibit regions of the parameter space where $b-\tau$ unification occurs for $\mu>0$ satisfying the constraints of $b\to s+\gamma$ and $g_\mu-2$. The $\mu<0$ case is also explored. The dependence of the accuracy of $b-\tau$ unification defined by $|\lambda_b-\lambda_{\tau}|/\lambda_{\tau}$ on the parameter space is also investigated and it is shown that unification with an accuracy of a few percent can be achieved in significant regions of the parameter space. The allowed parameter space is consistent with the naturalness constraints and the corresponding sparticle spectrum is accessible at the Large Hadron Collider.

Quasifixed-point scenario in a modified nonminimal supersymmetric standard model

The simplest extension of the MSSM that does not contradict LEP II experimental bound on the lightest Higgs boson mass at $\tan\beta\sim 1$ is the modified Next-to-Minimal Supersymmetric Standard Model (MNSSM). We investigate the renormalization of Yukawa couplings and soft SUSY breaking terms in this model. The possibility of $b$-quark and $\tau$-lepton Yukawa coupling unification at the Grand Unification scale $M_X$ is studied. The particle spectrum is analysed in the vicinity of the quasi-fixed point where the solutions of renormalization group equations are concentrated at the electroweak scale.

Supersymmetric SO(10) grand unified models with Yukawa unification and a positive mu term.

Supersymmetric grand unified models based on SO(10) gauge symmetry have many desirable features, including the unification of Yukawa couplings. Including D-term contributions to scalar masses arising from the breakdown of SO(10), Yukawa coupling unification only to 30% can be achieved in models with a positive superpotential Higgs mass. The superparticle mass spectrum is highly constrained and yields relatively light top squarks and charginos. Surprisingly, the pattern of grand unified theory scale soft supersymmetry breaking masses are close to those found in the context of inverted hierarchy models.

Infrared quasifixed solutions in a nonminimal supersymmetric standard model

The considerable part of the parameter space in the MSSM corresponding to the infrared quasi fixed point scenario is almost excluded by LEP II bounds on the lightest Higgs boson mass. In the NMSSM the mass of the lightest Higgs boson reaches its maximum value in the strong Yukawa coupling limit when Yukawa couplings are essentially larger than gauge ones at the Grand Unification scale. In this limit the solutions of the renormalisation group equations are attracted to the infrared and Hill type effective fixed lines or surfaces in the Yukawa coupling parameter space. They are concentrated in the vicinity of quasi fixed points for $Y_i(0)\to\infty$. However the solutions are attracted to such points rather weakly. For this reason when all $Y_i(0)\sim 1$ the solutions of the renormalisation group equations are gathered near a line in the Hill type effective surface. In the paper the approximate solutions for the NMSSM Yukawa couplings are given. The possibility of $b$--quark and $\tau$--lepton Yukawa coupling unification at the scale $M_{X}$ is also discussed.

Impact of the muon anomalous magnetic moment on supersymmetric models

The recent measurement of a_\mu =\frac{g_\mu -2}{2} by the E821 Collaboration at Brookhaven deviates from the quoted Standard Model (SM) central value prediction by 2.6\sigma. The difference between SM theory and experiment may be easily accounted for in a variety of particle physics models employing weak scale supersymmetry (SUSY). Other supersymmetric models are distinctly disfavored. We evaluate a_\mu for various supersymmetric models, including minimal supergravity (mSUGRA), Yukawa unified SO(10) SUSY GUTs, models with inverted mass hierarchies (IMH), models with non-universal gaugino masses, gauge mediated SUSY breaking models (GMSB), anomaly-mediated SUSY breaking models (AMSB) and models with gaugino mediated SUSY breaking (inoMSB). Models with Yukawa coupling unification or multi-TeV first and second generation scalars are disfavored by the a_\mu measurement.

A constraint on Yukawa-coupling unification from lepton-flavor violating processes

We present a new constraint on a lepton mixing matrix V from lepton-flavor violating (LFV) processes in supersymmetric standard models with massive neutrinos. Here we assume Yukawa-coupling unification f ν3 ≃ f top, in which τ-neutrino Yukawa coupling f ν3 is unified into top-quark Yukawa coupling f top at the unification scale M ∗≃3×10 16 GeV. We show that the present experimental bound on μ→ eγ decay already gives a stringent limit on the lepton mixing (typically V 13<0.02 for V 23=1/ 2 ). Therefore, many existing neutrino-mass models are strongly constrained. Future improvement of bounds on LFV processes will provide a more significant impact on the models with the Yukawa-coupling unification. We also stress that a precise measurement of a neutrino mixing ( V MNS) e3 in future neutrino experiments would be very important, since the observation of non-zero ( V MNS) e3 , together with negative experimental results for the LFV processes, have a robust potential to exclude a large class of SUSY standard models with the Yukawa-coupling unification.

Supersymmetric unification at the millennium

We argue that the discovery of neutrino mass effects at Super-Kamiokande implies a clear logical chain leading from the Standard Model, through the MSSM and the recently developed Minimal Left Right Supersymmetric models with a renormalizable see-saw mechanism for neutrino mass, to Left Right symmetric SUSY GUTS : in particular, SO(10) and $SU(2)_L \times SU(2)_R\times SU(4)_c$. The progress in constructing such GUTS explicitly is reviewed and their testability/falsifiability by lepton flavour violation and proton decay measurements emphasized. Susy violations of the survival principle and the interplay between third generation Yukawa coupling unification and the structurally stable IR attractive features of the RG flow in SUSY GUTS are also discussed .

Nonanomalous horizontalU(1)Hgauge model of flavor

A nonanomalous horizontal $\mathrm{U}{(1)}_{H}$ gauge symmetry can be responsible for the fermion mass hierarchies of the minimal supersymmetric standard model. Imposing the consistency conditions for the absence of gauge anomalies yields the following results: (i) unification of leptons and down-type quark Yukawa couplings is allowed at most for two generations; (ii) the $\ensuremath{\mu}$ term is necessarily somewhat below the supersymmetry breaking scale; (iii) the determinant of the quark mass matrix vanishes, and there is no strong $\mathrm{CP}$ problem; (iv) the superpotential has accidental B and L symmetries. The prediction ${m}_{\mathrm{up}}=0$ allows for an unambiguous test of the model at low energy.

Supersymmetric cold dark matter with Yukawa unification

The cosmological relic density of the lightest supersymmetric particle of the minimal supersymmetric standard model is calculated under the assumption of gauge and Yukawa coupling unification. We employ radiative electroweak breaking with universal boundary conditions from gravity-mediated supersymmetry breaking. Coannihilation of the lightest supersymmetric particle, which turns out to be an almost pure B-ino, with the next-to-lightest supersymmetric particle (the lightest stau) is crucial for reducing its relic density to an acceptable level. Agreement with the mixed or the pure cold (in the presence of a nonzero cosmological constant) dark matter scenarios for large scale structure formation in the universe requires that the lightest stau mass is about $2\ensuremath{-}8%$ larger than the B-ino mass, which can be as low as 222 GeV. The smallest allowed value of the lightest stau mass turns out to be about 232 GeV.

Superparticle mass spectra fromSO(10)grand unified models with Yukawa coupling unification

We examine the spectrum of superparticles obtained from the minimal $\mathrm{SO}(10)$ grand unified model, where it is assumed the gauge symmetry breaking yields the minimal supersymmetric standard model (MSSM) as the effective theory at ${M}_{\mathrm{GUT}}\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{16}$ GeV. In this model, unification of Yukawa couplings implies a value of $\mathrm{tan}\ensuremath{\beta}\ensuremath{\sim}45--55.$ At such high values of $\mathrm{tan}\ensuremath{\beta},$ assuming universality of scalar masses, the usual mechanism of radiative electroweak symmetry breaking breaks down. We show that a set of weak scale sparticle masses consistent with radiative electroweak symmetry breaking can be generated by imposing non-universal GUT scale scalar masses consistent with universality within $\mathrm{SO}(10)$ plus extra D-term contributions associated with the reduction in rank of the gauge symmetry group when $\mathrm{SO}(10)$ spontaneously breaks to $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}U(1).$ We comment upon the consequences of the sparticle mass spectrum for collider searches for supersymmetry. One implication of $\mathrm{SO}(10)$ unification is that the light bottom squark can be by far the lightest of the squarks. This motivates a dedicated search for bottom squark pair production at $p\overline{p}$ and ${e}^{+}{e}^{\ensuremath{-}}$ colliders.

Calculable sparticle masses with radiatively driven inverted mass hierarchy

Supersymmetric models with an inverted mass hierarchy (IMH: multi-TeV first and second generation matter scalars, and sub-TeV third generation scalars) can ameliorate problems arising from flavor changing neutral currents, CP violating phases and electric dipole moments, while at the same time satisfying conditions on naturalness. It has recently been shown that such an IMH can be generated radiatively, making use of infra-red fixed point properties of renormalization group equations given Yukawa coupling unification and suitable GUT scale boundary conditions on soft SUSY breaking masses. In these models, explicit spectra cannot be obtained due to problems implementing radiative electroweak symmetry breaking (REWSB). We show that use of SO(10) D-term contributions to scalar masses can allow REWSB to occur, while maintaining much of the desired IMH. A somewhat improved IMH is obtained if splittings are applied only to Higgs scalar masses.

Gauge and Yukawa unification in SUSY with bilinearly broken R-Parity

In a supersymmetric model where R-Parity and lepton number are violated bilinearly in the superpotential, which can explain the solar and atmospheric neutrino problems, we study the unification of gauge and Yukawa couplings at the GUT scale. We show that bottom-tau Yukawa coupling unification can be achieved at any value of tanβ, and that the strong coupling constant prediction from unification of gauge couplings is closer to the experimental value compared with the MSSM. We also study the predictions for V cb in a Yukawa texture ansätze.

Neutrino mixing and the pattern of supersymmetry breaking

We study the implications of a large νμ–ντ mixing angle on lepton flavour violating radiative transitions in supersymmetric extensions of the standard model. The transition rates are calculated to leading order in ϵ, the parameter which characterizes the flavour mixing. The uncertainty of the predicted rates is discussed in detail. For models with modular invariance the branching ratio BR(μ→eγ) mostly exceeds the experimental upper limit. In models with radiatively induced flavour mixing the predicted range includes the upper limit, if the Yukawa couplings in the lepton sector are large, as favoured by Yukawa coupling unification.

Up–down unification, neutrino masses, and rare lepton decays

In a recent paper, we showed that tree level up–down unification of fermion Yukawa couplings is a natural consequence of a large class of supersymmetric models. They can lead to viable quark masses and mixings for moderately large values of tan β with interesting and testable predictions for CP violation in the hadronic sector. In this letter, we extend our discussion to the leptonic sector focusing on one particular class of these models, the supersymmetric left–right model with the seesaw mechanism for neutrino masses. We show that fitting the solar and the atmospheric neutrino data considerably restricts the Majorana–Yukawa couplings of the leptons in this model and leads to predictions for the decay τ→ μ+ γ, which is found to be accessible to the next generation of rare decay searches. We also show that the resulting parameter space of the model is consistent with the requirements of generating adequate baryon asymmetry through lepton-number violating decays of the right-handed neutrino.

Neutrino masses, mixing angles and the unification of couplings in the MSSM

In the light of the gathering evidence for $\nu_{\mu}-\nu_{\tau}$ neutrino oscillations, coming in particular from the Super-Kamiokande data on atmospheric neutrinos, we re-analyze the unification of gauge and Yukawa couplings within the minimal supersymmetric extension of the Standard Model (MSSM). Guided by a range of different grand-unified models, we stress the relevance of large mixing in the lepton sector for the question of bottom-tau Yukawa coupling unification. We also discuss the dependence of the favoured value of $\tan\beta$ on the characteristics of the high-energy quark and lepton mass matrices. In particular, we find that, in the presence of large lepton mixing, Yukawa unification can be achieved for intermediate values of $\tan\beta$ that were previously disfavoured. The renormalization-group sensitivity to the structures of different mass matrices may enable Yukawa unification to serve as a useful probe of GUT models.

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.

Haggling over the fine-tuning price of LEP

We amplify previous discussions of the fine-tuning price to be paid by supersymmetric models in the light of LEP data. The whole range of tan β is discussed, including large values. In the minimal supergravity model with universal gaugino and scalar masses, a small fine-tuning price is possible only for intermediate values of tan β and for a small range of superpartner masses. Moreover, the fine-tuning price in this region is significantly higher if we require β-τ Yukawacoupling unification. We interpret the significant increase after LEP of the fine-tuning price in the minimal supergravity model as a message for theory and not for the experiment. For possible choices of low-energy parameters in the MSSM consistent with present experimental constraints and, optionally, with some other theoretical assumptions such as ifb-τ Yukawa-coupling unification, a measure of the amount of fine tuning becomes an interesting criterion for the naturalness of various theoretical models for mass terms in the MSSM Lagrangian. In particular, we emphasize that the fine-tuning price will depend on the actual solution to the μ problem. We illustrate the relevance of this fact by considering a simple ansatz of linear dependence of μ on M 1 2 or A 0, showing that big price reductions are obtained in such cases. Significant price reductions are also obtained for large tan β if non-universal soft Higgs mass parameters are allowed. We also study input relations between MSSM parameters suggested in some interpretations of string theory: the price may depend significantly on these inputs, potentially providing guidance for building string models. However, in the available models the fine-tuning price may not be reduced significantly.

New limits on the SUSY Higgs boson mass

We present new upper limits on the light Higgs boson mass m h in supersymmetric models. We consider two gravity-mediated models (with and without universal scalar masses) and two gauge-mediated models (with a 5 + 5 or 10 + 10 messenger sector). We impose standard phenomenological constraints, as well as SU(5) Yukawa coupling unification. Requiring that the bottom and tau Yukawa couplings meet at the unification scale to within 15%, we find the upper limit m h <114 GeV in the universal supergravity model. This reverts to the usual upper bound of 130 GeV with a particular nonuniversality in the scalar spectrum. In the 5 + 5 gauge-mediated model we find m h <97 GeV for small tan β and m h ≃116 GeV for large tan β, and in the 10 + 10 model we find m h <94 GeV. We discuss the implications for upcoming searches at LEP-II and the Tevatron.

Higgs limit and b→ sγ constraints in minimal supersymmetry

New limits on the Higgs mass from LEP and new calculations on the radiative (penguin) decay of the b-quark into sγ restrict the parameter space of the Constrained Minimal Supersymmetric Standard Model (CMSSM). We find that for the low tan β scenario only one sign of the Higgs mixing parameter is allowed, while the high tan β scenario is practically excluded, if one requires all sparticles to be below 1 TeV and imposes radiative electroweak symmetry breaking as well as gauge and Yukawa coupling unification. For squarks between 1 and 2 TeV high tan β scenarios are allowed. We consider especially a new high tan β=64 scenario with triple unification of all Yukawa couplings of the third generation, which shows an infrared fixed point behaviour. The upper limit on the mass of the lightest Higgs in the low (high) tan β scenarios is 97±6 (120±2) GeV, where the largest error originates predominantly from the uncertainty in the top mass.