Search for single leptoquark and squark production in electron-photon scattering at $\sqrt{s_{\rm ee}}=189$ GeV at LEP

A search for first generation scalar and vector leptoquarks (LQ) as well as for squarks () in R-parity violating SUSY models with the direct decay of the into Standard Model particles has been performed using ee collisions collected with the OPAL detector at LEP at an ee centre-of-mass energy of 189 GeV. The data correspond to an integrated luminosity of about 160 pb. The dominant process for this search is , where a photon, which has been radiated by one of the beam electrons, serves as a source of quarks. The numbers of selected events found in the two decay channels are in agreement with the expectations from Standard Model processes. This result allows to set lower limits at the 95% confidence level on the mass of first generation scalar and vector leptoquarks, and of squarks in R-parity violating SUSY models. For Yukawa couplings to fermions larger than , the mass limits range from 121 GeV to GeV ( GeV to GeV) depending on the branching ratio of the scalar (vector) leptoquark state. Furthermore, limits are set on the Yukawa couplings for leptoquarks and for squarks, and on as a function of the scalar leptoquark/squark mass. Received: 22 May 2001 / Published online: 25 January 2002     

Proton decay and flavor violating thresholds in SO(10) models

Discovery of neutrino mass has put the spotlight on the supersymmetric (SUSY) SO(10) model as a natural candidate for grand unification of forces and matter. However, the suppression of proton decay is a major problem in such SUSY grand unified models. In this Letter we show how to alleviate this problem by simple threshold effects which raise the colored Higgsino masses and the grand unification scale to greater than or similar to 10(17) GeV. There exist only four types of fields arising from different SO(10) representations which can generate this kind of threshold effect. Some of these fields also generate a sizable flavor violation in the quark sector compared to the lepton sector. The b-tau unification can work in these types of models even for intermediate values of tanbeta.     

Renormalization of seesaw neutrino masses in the standard model with two-Higgs doublets

Using the theoretical ambiguities inherent in the seesaw mechanism, we derive the new analytic expressions for both quadratic and linear seesaw formulae for neutrino masses at low energies, with either up-type quark masses or charged lepton masses. This is possible through full radiative corrections arising out of the renormalizations of the Yukawa couplings, the coefficients of the neutrino-mass-operator in the standard model with two-Higgs doublets, and also the QCD-QED rescaling factors below the top-quark mass scale, at one-loop level. We also investigate numerically the unification of top-b-τ Yukawa couplings at the scale M ₁=0.59×10⁸ GeV for a fixed value of tan β=58.77, and then evaluate the seesaw neutrino masses which are too large in magnitude to be compatible with the presently available solar and atmospheric neutrino oscillation data. However, if we consider a higher but arbitrary value of M ₁=0.59×10¹¹ GeV, the predictions from linear seesaw formulae with charged lepton masses, can accommodate simultaneousely both solar atmospheric neutrino oscillation data.     

The b \to X_s \gamma rate and Higgs boson limits in the constrained minimal supersymmetric model

New NLO calculations have become available using resummed radiative corrections. Using these calculations we perform a global fit of the supergravity inspired constrained minimal supersymmetric model. We find that the resummed calculations show similar constraints as the LO calculations, namely that only with a relatively heavy supersymmetric mass spectrum of (1 TeV) the b– Yukawa unification and the rate can coexist in the large scenario. The resummed calculations are found to reduce the renormalization scale uncertainty considerably. The low scenario is excluded by the present Higgs limits from LEP II. The constraint from the Higgs limit in the plane is severe, if the trilinear coupling at the GUT scale is fixed to zero, but is considerably reduced for . The relatively heavy SUSY spectrum required by corresponds to a Higgs mass of GeV in the CMSSM. Received: 14 February 2001 / Revised version: 22 March 2001 / Published online: 29 June 2001     

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

In the light of the gathering evidence for 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 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 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. Received: 22 June 1999 / Published online: 10 December 1999     

Supersymmetry for Fermion Masses

It is proposed that supersymmetry （SUSY） may be used to understand fermion mass hierarchies. A family symmetry ZSL is introduced, which is the cyclic symmetry among the three generation SU（2） doublets. SUSY breaks at a high energy scale - 10^11 GeV. The electroweak energy scale- 100 GeV is unnaturally small No additional global symmetry, like the R-parlty, is imposed. The Yukawa couplings and R-parity violating couplings all take their natural values, which are О（10^0 -10^-2）. Under the family symmetry, only the third generation charged ferrnions get their masses. This family symmetry is broken in the soft SUSY breaking terms, which result in a hierarchical pattern of the fermion masses. It turns out that for the charged leptons, the r mass is from the Higgs vacuum expectation value （VEV） and the sneutrino VEVs, the muon mass is due to the sneutrino VEVs, and the electron gains its mass due to both ZZL and SUSY hreaking. The large neutrino mixing are produced with neutralinos playing the partial role of right-handed neutrinos. │Ve3│, which is for Ve-Vr mixing, is expected to be about 0.1. For the quarks, the third generation masses are from the Higgs VEVs, the second generation masses are from quantum corrections, and the down quark mass due to the sneutrino VEVs. It explains me/ms, ms/me, md 〉 mu and so on. Other aspects of the model are discussed.     

Renormalization group analysis and the top quark mass in the SU(4) × O(4) string model

We perform a two-loop renormalization group analysis for the gauge couplings in the SU(4) × O(4) model. We use the string theory prediction for the unification scale and the experimentally acceptable low energy values for ₃ and sin² θ_w, to determine the magnitudes of the various symmetry breaking scales as well as the value of the common gauge coupling at the unification scale. We solve the coupled differential system for the gauge and top and bottom Yukawa couplings, and determine the top mass as a function of two parameters which could be chosen to be the ratio of the Higgs VEV's that give masses to the up and down quarks and the value of the top coupling at the unification scale. We find a relatively heavy top quark mass which lies in the range 130m_t180 GeV.     

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 × SU(2) _R × 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.     

New formulas and predictions for running fermion masses at higher scales in SM, 2HDM, and MSSM

Including contributions of scale-dependent vacuum expectation values, we derive new analytic formulas and obtain substantially different numerical predictions for the running masses of quarks and charged leptons at higher scales in the SM, 2HDM and MSSM. These formulas exhibit significantly different behaviours with respect to their dependence on gauge and Yukawa couplings from those derived earlier. At one-loop level, the masses of the first two generations are found to be independent of the Yukawa couplings of the third generation in all three effective theories in the small mixing limit. Analytic formulas are also obtained for the running of in 2HDM and MSSM. Other numerical analyses include a study of the third generation masses at high scales as functions of the low-energy values of and the SUSY scale GeV. Received: 1 October 2000 / Revised version: 11 January 2001 / Published online: 12 April 2001     

Neutrino masses, muon g−2, and lepton-flavour violation in the supersymmetric see-saw model

In the light of the recent muon (g_μ−2) result by the E821 experiment at the Brookhaven National Laboratory, we study the event rates of the charged lepton-flavour-violating (LFV) processes in the supersymmetric standard model (SUSY SM) with the heavy right-handed neutrinos (SUSY see-saw model). Since the left-handed sleptons get the LFV masses via the neutrino Yukawa interaction in this model, the event rate of μ→eγ and the SUSY-SM correction to (g_μ−2)/2 (δa_μ^SUSY) are strongly correlated. When the left-handed sleptons have a LFV mass between the first and second generations ( ) in the mass matrix, it should be suppressed by 10⁻³ (10⁻⁹/δa_μ^SUSY) compared with the diagonal components (m_SUSY²), from the current experimental bound on μ→eγ. The recent (g_μ−2) result indicates δa_μ^SUSY10⁻⁹. The future charged LFV experiments could cover . These experiments will give a significant impact on the flavour models and the SUSY-breaking models. In the SUSY see-saw model is proportional to square of the tau-neutrino Yukawa-coupling constant. In the typical models where the neutrino-oscillation results are explained and the top-quark and tau-neutrino Yukawa couplings are unified at the GUT scale, a large LFV mass of is generated, and the large LFV event rates are predicted. We impose a so-called no-scale condition for the SUSY-breaking parameters at the GUT scale, which suppresses the FCNC processes, and derive the conservative lower bound on μ→eγ. The predicted Br(μ→eγ) could be covered at the future LFV experiments.     

Fixed point and anomaly mediation in partial N=2 supersymmetric standard models

Motivated by the simple toroidal compactification of extra-dimensional SUSY theories, we investigate a partial N =2 supersymmetric(SUSY) extension of the standard model which has an N =2 SUSY sector and an N =1 SUSY sector. We point out that below the scale of the partial breaking of N = 2 to N = 1, the ratio of Yukawa to gauge couplings embedded in the original N =2 gauge interaction in the N =2 sector becomes greater due to a fixed point. Since at the partial breaking scale the sfermion masses in the N = 2 sector are suppressed due to the N = 2 non-renormalization theorem, the anomaly mediation effect becomes important. If dominant, the anomaly-induced masses for the sfermions in the N = 2 sector are almost UV-insensitive due to the fixed point. Interestingly, these masses are always positive, i.e. there is no tachyonic slepton problem. From an example model, we show interesting phenomena differing from ordinary MSSM. In particular, the dark matter particle can be a sbino, i.e. the scalar component of the N = 2 vector multiplet of U(1)_Y. To obtain the correct dark matter abundance, the mass of the sbino, as well as the MSSM sparticles in the N =2 sector which have a typical mass pattern of anomaly mediation, is required to be small. Therefore, this scenario can be tested and confirmed in the LHC and may be further confirmed by the measurement of the N = 2 Yukawa couplings in future colliders. This model can explain dark matter, the muon g-2 anomaly, and gauge coupling unification, and relaxes some ordinary problems within the MSSM. It is also compatible with thermal leptogenesis.     

Supersymmetric standard model from the heterotic string

We present a [FORMULA: SEE TEXT] orbifold compactification of the E8xE8 heterotic string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three 16-plets of SO(10), whereas the Higgs fields do not form complete SO(10) multiplets. The model has large vacuum degeneracy. For generic vacua, no exotic states appear at low energies and the model is consistent with gauge coupling unification. The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings, whereas the other Yukawa couplings are suppressed.     

Comparison of grand unified theories with electroweak and strong coupling constants measured at LEP

Using the renormalization group equations one can evolve the electroweak and strong coupling constants, as measured at LEP, to higher energies in order to test the ideas of grand unified theories, which predict that the three coupling constants become equal at a single unification point. With data from the DELPHI Collaboration we find that in the minimal non-supersymmetric standard model with one Higgs doublet a single unification point is excluded by more than 7 standard deviations. In contrast, the minimal supersymmetric standard model leads to good agreement with a single unification scale of 10^16.0±0.3 GeV. Such a large scale is compatible with the present lower limits on the proton lifetime. The best fit is obtained for a SUSY scale around 1000 GeV and limits are derived as function of the strong coupling constant. The unification point is sensitive to the number of Higgs doublets and only the minimal SUSY model with two Higgs doublets is compatible with GUT unification, if one takes the present limits on the proton lifetime into account.     

A renormalizable SO(10) GUT scenario with spontaneous CP violation

We consider fermion masses and mixings in a renormalizable SUSY SO(10) GUT with Yukawa couplings of scalar fields in the representation . We investigate a scenario defined by the following assumptions. (i) We have a single large scale in the theory, the GUT scale. (ii) The small neutrino masses are generated by the type I seesaw mechanism with negligible type II contributions. (iii) We assume a suitable form of spontaneous CP breaking that induces hermitian mass matrices for all fermion mass terms of the Dirac type. Our assumptions define an 18-parameter scenario for the fermion mass matrices for 18 experimentally known observables. Performing a numerical analysis, we find excellent fits to all observables in the case of both the normal and inverted neutrino mass spectrum.     

Threshold and compactification effects in GUTS

We review general results on threshold effects and their implications on GUTs in the context of LEP data. Among the blooming grand-desert models, threshold effects are computed in the presence of a single real scalar ζ (3, 0, 8) with M_ζ?10¹⁰ GeV leading to experimentally testable predictions on the proton lifetimeτ _p in SU (5) and, in addition, small neutrino masses in SO (10) needed for the solar neutrino flux and the dark matter of the universe. The fine structure constant matching at M_Z is ensured by including threshold effects on the unification coupling. In the minimal SUSY SU (5) such effects at the GUT scale modify the prediction of the supersymmetric mass threshold near the TeV scale and the precision measurments of the Standard Model couplings at M_Z probe into the superheavy mass spectrum. Consequences of theorems proved very useful for threshold, compactification and multiloop effects are discussed. It is noted that in a class of GUTs the highest intermediate scale M_I above which G_224P becomes a good symmetry is not affected by the GUT threshold or compactification effects or multiloop contributions in the range M_I-M_U. But spontaneous compatification effects can decrease the intermediate scale drastically in models where parity and SU(2)_R breakings are decoupled. Low mass W_R-bsosns are permitted in models with decoupled parity and SU (2)_R breakings.     

Threshold and compactification effects in GUTS

We review general results on threshold effects and their implications on GUTs in the context of LEP data. Among the blooming grand-desert models, threshold effects are computed in the presence of a single real scalar ζ (3, 0, 8) with M_ζ≃10¹⁰ GeV leading to experimentally testable predictions on the proton lifetimeτ _p in SU (5) and, in addition, small neutrino masses in SO (10) needed for the solar neutrino flux and the dark matter of the universe. The fine structure constant matching at M_Z is ensured by including threshold effects on the unification coupling. In the minimal SUSY SU (5) such effects at the GUT scale modify the prediction of the supersymmetric mass threshold near the TeV scale and the precision measurments of the Standard Model couplings at M_Z probe into the superheavy mass spectrum. Consequences of theorems proved very useful for threshold, compactification and multiloop effects are discussed. It is noted that in a class of GUTs the highest intermediate scale M_I above which G_224P becomes a good symmetry is not affected by the GUT threshold or compactification effects or multiloop contributions in the range M_I-M_U. But spontaneous compatification effects can decrease the intermediate scale drastically in models where parity and SU(2)_R breakings are decoupled. Low mass W_R-bsosns are permitted in models with decoupled parity and SU (2)_R breakings.     

Hierarchy of quark masses in the isotopic doublets in N=1 supergravity models

In the framework of some generic softly broken SUSY models we study the SU (2) × U(1) breaking by radiative corrections, starting with the Yukawa couplings which at the Planck scale M_P satisfy h^t = h^b. Physically acceptable solutions exist with the heirarchy of VEVs: ν₂/ν₁ ≈ m_t/m_b provided m_t ⩾ 50 GeV. When the SUSY breaking is driven only by the gaugino mass the solutions uniquely predict ν₂=O(10)ν₁ and the top mass in the range 50–65 GeV. Also, the mass ratio in the second quark generation can be accounted for.     

New formulas and predictions for running masses at higher scales in MSSM

The effects of the scale dependent vacuum expectation values (VEVs) on the running masses of quarks and leptons in non-SUSY gauge theories have been considered by a number of authors. Here we use RGEs of the VEVs, and the gauge and Yukawa couplings in the MSSM to analytically derive new one loop formulas for the running masses above the SUSY breaking scale. Some of the masses exhibit a substantially different behaviour with respect to their dependence on the gauge and Yukawa couplings when compared with earlier formulas in the MSSM derived ignoring RGEs of VEVs. In particular, the masses of the first two generations are found to be independent of the Yukawa couplings of the third generation in the small mixing limit. New numerical estimates at the two loop level are also presented. Received: 30 July 1999 / Published online: 6 April 2000     

Large top-quark mass and nonlinear representation of flavor symmetry

We consider an effective theory (ET) approach to flavor-violating processes beyond the standard model, where the breaking of flavor symmetry is described by spurion fields whose low-energy vacuum expectation values are identified with the standard model Yukawa couplings. Insisting on canonical mass dimensions for the spurion fields, the large top-quark Yukawa coupling also implies a large expectation value for the associated spurion, which breaks part of the flavor symmetry already at the UV scale Lambda of the ET. Below that scale, flavor symmetry in the ET is represented in a nonlinear way by introducing Goldstone modes for the partly broken flavor symmetry and spurion fields transforming under the residual symmetry. As a result, the dominance of certain flavor structures in rare quark decays can be understood in terms of the 1/Lambda expansion in the ET.     

Higgs boson couplings to bottom quarks: two-loop supersymmetry-QCD corrections

We present two-loop supersymmetry (SUSY) QCD corrections to the effective bottom Yukawa couplings within the minimal supersymmetric extension of the standard model (MSSM). The effective Yukawa couplings include the resummation of the nondecoupling corrections Deltam_{b} for large values of tanbeta. We have derived the two-loop SUSY-QCD corrections to the leading SUSY-QCD and top-quark-induced SUSY-electroweak contributions to Deltam_{b}. The scale dependence of the resummed Yukawa couplings is reduced from O(10%) to the percent level. These results reduce the theoretical uncertainties of the MSSM Higgs branching ratios to the accuracy which can be achieved at a future linear e;{+}e;{-} collider.