Tau Yukawa Coupling Research Articles

Yukawa unification in SO(10)

In simple SO(10) SUSY GUTs the top, bottom and tau Yukawa couplings unify at the GUT scale. A naive renormalization group analysis, neglecting weak scale threshold corrections, leads to moderate agreement with the low energy data. However, it is known that intrinsically large threshold corrections proportional to $\mathrm{tan}\ensuremath{\beta}\ensuremath{\sim}{m}_{t}{(M}_{Z}{)/m}_{b}{(M}_{Z})\ensuremath{\sim}50$ can nullify these t, b, \ensuremath{\tau} mass predictions. In this paper we turn the argument around. Instead of predicting fermion masses, we use the constraint of Yukawa unification and the observed values ${M}_{t},$ ${m}_{b}{(m}_{b}),$ ${M}_{\ensuremath{\tau}}$ to constrain SUSY parameter space. We find a narrow region survives for $\ensuremath{\mu}>0$ with $\ensuremath{\mu},$ ${M}_{1/2}\ensuremath{\ll}{m}_{16},$ ${A}_{0}\ensuremath{\approx}\ensuremath{-}1.9{m}_{16}$ and ${m}_{16}>1200 \mathrm{GeV}.$ Demanding Yukawa unification thus makes definite predictions for Higgs boson and sparticle masses. In particular, we find a light Higgs boson with a mass ${m}_{h}^{0}=114\ifmmode\pm\else\textpm\fi{}5\ifmmode\pm\else\textpm\fi{}3 \mathrm{GeV}$ and a light top squark with ${(m}_{{t}_{1}}{)}_{\mathrm{MIN}}\ensuremath{\sim}450 \mathrm{GeV}$ and ${m}_{{t}_{1}}\ensuremath{\ll}{m}_{{b}_{1}}.$ In addition, we find a light chargino and a neutralino LSP. It is also significant that in this region of parameter space the SUSY contribution to the muon anomalous magnetic moment ${a}_{\ensuremath{\mu}}^{\mathrm{SUSY}}<16\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}.$

Can precision measurements of slepton masses probe right handed neutrinos?

In a supersymmetric model, the presence of a right handed neutrino with a large Yukawa coupling $f_{\nu}$ would affect slepton masses via its contribution to the renormalization group evolution between the grand unification and weak scales. Assuming a hierarchichal pattern of neutrino masses, these effects are large for only the third generation of sleptons. We construct mass combinations to isolate the effect of $f_{\nu}$ from mass corrections already expected from tau Yukawa couplings. We then analyze the size of these effects, assuming that the Super-Kamiokande data constrain 0.033 eV $\alt m_{\nu_{\tau}} \alt 0.1$ eV and that neutrino masses arise via a see-saw mechanism. We also explore whether these effects might be detectable in experiments at future $e^+e^-$ linear colliders. We find that $m_{\tnu_{\tau}}$ needs to be measured with a precision of about 2-3% to measure the effect of $f_{\nu}$ if the neutrino and top Yukawa couplings unify at the grand unification scale. In a simple case study, we find a precision of only 6-10% might be attainable after several years of operation. If the neutrino Yukawa coupling is larger, or in more complicated models of neutrino masses, a determination of $\ttau_1$ and $\tnu_{\tau}$ masses might provide a signal of a Yukawa interaction of neutrinos.

Slepton flavor mixing and neutrino masses

It is pointed out that important contribution to neutrino masses and mixing can come from flavour violating slepton exchange. For low and intermediate $\tan\beta$ such effects can dominate over the usual tau Yukawa coupling effects included in the renormalization group evolution. The mixing angles satisfy then the relation different from the fixed point solution of the renormalization group equation, and the desired neutrino mass splitting can be generated.

Impact of radiative corrections on sterile neutrino scenarios

In sterile neutrino scenarios, radiative corrections induce mass splittings proportional to the top Yukawa coupling, in contrast to the three active neutrino case where the induced splittings are proportional to the tau Yukawa coupling. In view of this, we have analyzed the stability of the four-neutrino schemes favored by oscillation experiments, consisting in two pairs of nearly degenerate neutrinos separated by the LSND gap. Requiring compatibility with the measurements of the abundances of primordial elements produced in Big Bang Nucleosynthesis, we find that when the heaviest pair corresponds to the solar neutrinos (mainly an admixture of nu_e - nu_s) the natural mass splitting is 3-5 orders of magnitude larger than the observed one, discrediting the scenario from a theoretical point of view. On the contrary, the scheme where the heaviest pair corresponds to the atmospheric neutrinos (mainly an admixture of nu_mu - nu_tau) is safe from radiative corrections due to the small sterile component of these mass eigenstates.

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.

Supersymmetric b- tau unification, gauge unification, and fixed points.

The equality assumption of the b and tau Yukawa couplings at the grand-unification scale can strongly constrain the allowed parameter space of supersymmetric models. We examine the constraints in the case that there is a discrepancy > 10% in the gauge coupling unification assumption (which necessarily implies large perturbations at the grand scale). The constraints are shown to diminish in that case [most significantly so if alpha_{s}(M_{Z}) \approx 0.11]. In particular, the requirement that the t Yukawa coupling, h_{t}, is near its quasi-fixed point may not be necessary. We discuss the colored-triplet threshold as a simple example of a source for the discrepancies, and comment on its possible implications. In addition, we point out that supersymmetric (as well as unification-scale) threshold corrections to h_{t} shift the fixed-point curve in the m_{t} - \tan\beta plane. The implications for the prediction of the Higgs boson mass are briefly discussed.

Extending the Symmetries of the Standard Model

We discuss the possibilities for determining the parameters of the Standard Model by extending its symmetries. Supersymmetry combined with a stage of unification is capable of determining the magnitude of the gauge couplings and explaining the pattern of spontaneous breaking. We consider how further family symmetries may determine the qualitative struc­ ture of the fermion masses and mixing angles. Finally we explore the possibility that the dynamics of the low-energy theory may determine the magnitude of the Yukawa couplings via its fixed point structure and hence give a complete theory of the fermion masses. With the advent of precision measurements of the parameters of the Standard Model we have been able to test quantitatively the possibility of supersymmetric unifi­ cation in several areas. In particular the couplings are found to come together at a scale 0(10 1 6 GeV) the values corresponding to the SU(5) normalisation of the U(l) coupling with sin 2 (0w) = 3/8 (this is not the case in the Standard Model where the couplings are some six standard deviations apart). The idea the soft SUSY breaking terms unify may be tested too because the Higgs mass as well as the squark and slepton mass are unified and deviate at low energy only through calculable radiative corrections. The exciting thing about soft mass unification is that it gives a reason why the pattern of symmetry breaking in the Standard Model is the way it is. Due to the large top mass and associated Yukawa coupling the RG equations drive the Higgs mass squared neg­ ative, triggering electroweak breaking. Due to the QCD radiative corrections the top squark masses which also feel the top Yukawa coupling are not driven negative giving a simple explanation for the observed pattern of symmetry breakdown. Such unification predictions encourage us in the belief there is some extension of the symmetries of the Standard Model. However there still remains much to explain. In particular the pattern of fermion masses and mixing angles suggests the need for further symmetries and indeed simple relationships do appear· at high scales. The measured values of the bottom quark and the T lepton masses are consistent with their equality at the unification scale. l), 2 ) Indeed this simplicity might extend to the top quark sector for it is a viable possibility that the top, bottom and tau Yukawa couplings are all equal and governed by the infra-red structure of the theory. 3 ) However the pattern of light masses and mixing angles appears at first sight to be too complicated to be explained by such simple unification ideas. In this talk I wish to show that this is not the case and that a very simple extension of the Standard Model is capable of generating both the qualitative and quantitative structure of the full set of fermion masses and mixing

Phenomenology of the minimal supergravitySU(5) model

The minimal grand unified supergravity model is discussed. Requiring radiative breaking of the electroweak gauge symmetry, the unification of b and tau Yukawa couplings, a sufficiently stable nucleon, and not too large a relic density of neutralinos produced in the Big Bang constrains the parameter space significantly. In particular, the soft breaking parameter m_1/2 has to be less than about 130 GeV, and the top quark Yukawa coupling has to be near its (quasi) fixed point. The former condition implies m_gluino < 400 GeV and hence very large production rates for gluino pairs at the LHC, while the latter constraint implies that the lighter stop and sbottom eigenstates are significantly lighter than the other squarks, leading to characteristic signatures for gluino pair events.

Infrared fixed points and fixed lines in the top-bottom-tau sector in supersymmetric grand unification

The two-loop “top-down” renormalization group flow for the top, bottom and tau Yukawa couplings, from μ = M GUT ⋍ O(10 16 GeV) to μ ⋍ m t , is explored in the framework of supersymmetric grand unification; reproduction of the physical bottom and tau masses is required. Instead of following the recent trend of implementing exact Yukawa coupling unification i) a search for infrared (IR) fixed lines and fixed points in the m t pole −tan β plane is performed and ii) the extent to which these imply approximate Yukawa unification is determined. In the m t pole −tan β plane two IR fixed lines, intersecting in an IR fixed point, are located. The more attractive fixed line has a branch of almost constant top mass, m t pole ⋍ 168–180 GeV (close to the experimental value), for the large interval 2.5 ≲ tan β ≲ 55; it realizes tau-bottom Yukawa unification at M GUT approximately. The less attractive fixed line as well as the fixed point at m t pole ⋍ 170 GeV, tan β ⋍ 55 implement approximate top-bottom Yukawa unification at all scales μ. The renormalization group flow is attracted towards the IR fixed point by way of the more attractive IR fixed line. The fixed point and lines are distinct from the much quoted effective IR fixed point m t pole ⋍ O(200 GeV) sin β.

Predictive fermion mass matrix Ansa-umltze in nonsupersymmetric SO(10) grand unification.

We investigate the status of predictive fermion mass ansatzes which make use of the grand unification scale conditions $m_e=m_d/3$, $m_\mu =3m_s$, and $\mid V_{cb}\mid =\sqrt{m_{c}/m_{t}}$ in non-supersymmetric SO(10) grand unification. The gauge symmetry below an intermediate symmetry breaking scale $M_I$ is assumed to be that of the standard model with either one Higgs doublet or two Higgs doublets . We find in both cases that a maximum of 5 standard model parameters may be predicted within $1\sigma$ experimental ranges. We find that the standard model scenario predicts the low energy $\mid V_{cb}\mid$ to be in a range which includes its experimental mid-value 0.044 and which for a large top mass can extend to lower values than the range resulting in the supersymmetric case. In the two Higgs standard model case, we identify the regions of parameter space for which unification of the bottom quark and tau lepton Yukawa couplings is possible at grand unification scale. In fact, we find that unification of the top, bottom and tau Yukawa couplings is possible with the running b-quark mass within the $1\sigma$ preferred range $m_b=4.25\pm 0.1\, GeV$ provided $\alpha_{3c}(M_Z)$ is near the low end of its allowed range. In this case, one may make 6 predictions which include $\mid V_{cb}\mid$ within its $90\%$ confidence limits. However unless the running mass $m_b>4.4\, GeV$, third generation Yukawa coupling unification requires the top mass to be greater than

Implications of Yukawa unification for the Higgs sector in supersymmetric grand-unified models.

The SU(5) unification-scale relation h_b=h_tau between the b and tau Yukawa couplings severely constrains tan beta and m_t (even more so if h_t=h_b= h_tau holds) in supersymmetric models. We examine the implications of these constraints for the Higgs sector assuming universal soft breaking terms, and emphasize that both of these relations impose unique characteristics in terms of symmetries and of the spectrum. We further study the tan beta near 1 scenario, which is suggested by h_b=h_tau, and, in particular, the loop- induced mass of the light Higgs boson. We compare the effective potential and renormalization group methods and stress the two-loop ambiguities in the calculation of the mass. These and a large enhancement to the loop correction due to t-scalar left-right mixing considerably weaken the upper bound. Nevertheless, we find that for this scenario the Higgs boson is probably lighter than 110 GeV, and typically lighter than 100 GeV. Thus, it is in the mass range that may be relevant for LEPII. Our numerical results are presented in a self-contained manner in section V. In separate appendices we discuss the global symmetries of the Higgs potential, the issue of false (color-breaking) vacua, two-loop calculations, and the effect of an additional Higgs singlet. We show that the approximate constraints that are often used to eliminate color-breaking vacua are not always relevant.

On the unification of couplings in the minimal supersymmetric standard model

The unification of gauge and Yukawa couplings within the minimal supersymmetric standard model is studied at the two loop level. We derive an expression for the effective scale, T SUSY, which characterizes the supersymmetric particle threshold corrections to the gauge couplings, and demonstrate that T SUSY is only slightly dependent on the squark and slepton masses, and strongly dependent on the higgsino masses as well as on the mass ratio of the gauginos of the strong and weak interactions. Thus, if the gaugino masses proceed from a common soft supersymmetry breaking term at the unification scale, and there is no significant gaugino-higgsino mixing, T SUSY will have a strong dependence on the supersymmetric mass parameter μ. Moreover, the value of the top quark Yukawa coupling necessary to achieve the unification of bottom and tau Yukawa couplings is also governed by T SUSY, and its yield predictions for the top quark mass which are close to the quasi infrared fixed point results associated with the triviality bounds on this quantity. From the requirement of perturbative consistency of the top quark Yukawa sector of the theory, we obtain constraints on the allowed splitting of the supersymmetric spectrum, which, for certain values of the running bottom quark mass, m b, are stronger than those ones coming from the experimental constraints on the strong gauge coupling. For example, for m b( M b) ⩽ 4.1 GeV, which approximately corresponds to a physical mass M b ⩽ 4.7 GeV, we obtain that, for moderate values of tan β, perturbative unification may be achieved only if α 3( M Z) ⩽ 0.124.

A detailed comparison of LEP data with the predictions of the minimal supersymmetric SU(5) GUT

We confront the precise LEP determinations of sin 2 θ w and the strong coupling α 3( m z 0 with the predictions of the minimal supersymmetric SU(5) GUT. We incorporate O( α em α 3) effects in the extraction of sin 2 θ w from LEP data. We incorporate distinct thresholds for the supersymmetric partners of the different species of Standard Model particles, parameterized in terms of a scalar mass m 0 and a gaugino mass m 1 2 that are assumed to be universal at the GUT scale. We also allow for uncertainties in the top, higgs and higgsino masses. We use the full two-loop renormalization group equations including top, bottom and tau Yukawa couplings. We show that GUT threshold effects are small because proton stability prevents triplet Higgs particles from weighing much less than 10 16 GeV. Using 1−σ errors for the experimental inputs and plausible ranges for unknown supersymmetric model parameters, in particular an upper bound of 300 GeV on the higgs mixing parameter μ, we find that either 3.0×10 12 TeV>m 1 2 >21 TeV or m 1 2 <65 GeV , with the intermediate range allowed at the 2 − σ level. An upper bound of μ=500 GeV excludes m 1 2 from 80 GeV to 5 TeV at 1 − σ, and an upper bound of μ=1 TeV excludes m 1 2 from 110 GeV to 620 GeV at 1 − σ. It is not possible at present to fix the supersymmetry breaking scale with any precision.