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We make a numerical study of gauge and Yukawa unification in supersymmetric grand unified models and examine the quantitative implications of fermion mass Ansatze at the grand unified scale. Integrating the renormalization group equations with al(Mz) and az(Mz) as inputs, we find as(Mz) --O.lll(0.122) for Msusu = rnt and a3(Mz) N 0.106(0.116) for Msusv = 1 TeV at oneloop (two-loop) order. Including b and T Yukawa couplings in the evolution, we find an upper limit of mt 5 200 GeV from Yukawa unification. For given mt 5 175 GeV, there are two solutions for P: one with tan p > mtlrnb, and one with sin 0 -. 0.78(mt/150 GeV). Taking a popular Ansatz for the mass matrices at the unified scale, we obtain a lower limit on the topquark mass of mt 2 150(115) GeV for a 3 ( M~) = O.ll(0.12) and an upper limit on the supersymmetry parameter tanp 5 50 if a~( M z ) = 0.11. The evolution of the quark mixing matrix elements is also evaluated. PACS number(s): 12.10.Dm, 12.15.Ff I. I N T R O D U C T I O NThere is renewed interest in supersymmetric grand unified theories (GUT's) [I] t o explain gauge couplings, fermion masses, and quark mixings [2-91. Recent measurements of the gauge couplings at the CERN e+e-collider LEP and in other low-energy experiments [lo, 111 are in reasonably good accord with expectations from minimal supersymmetric GUT's with the scale of supersymmetry (SUSY) of order 1 TeV or below [2]. Supersymmetric GUT's are also consistent with the nonobservation to date of proton decay [12]. In addition to the unification of gauge couplings [13], the unification of Yukawa couplings has been considered to predict relations among quark masses [14-161. With equal b-quark and T-lepton Yukawa couplings at the GUT scale, the mb/m, mass ratio is explained by SUSY GUT's [4,15]. With specific Ansatze for the GUT-scale mass matrices (e.g., zero elements, mass hierarchy, relations of quark and lepton elements), other predictions have been obtained from quark masses and mixings that are consistent with measurements [4,6, 7, 17, 181. The consideration of fermion mass relationships has a long history [19-211 and includes single relations and mass matrices ("textures") without evolution [22-241, and single relations and mass matrices with evolution [25].Our approach is to explore supersymmetric GUT's first with the most general assumptions, and then proceed to add additional GUT unification constraints to obtain more predictions at the electroweak scale. The renormalization-group equations (RGE's) used here are for the supersymmetric GUT's [26, 271 with the minimal particle content above the supersymmetry scale and the standard model RGE's [28] below the supersymmetry scale. In Sec. I1 we explore the running of the gauge couplings in the supersymmetric model at the two-loop level and compare the results to those obtained at the one-loop level. Rather than try to predict the scale of supersymmetry (Msusu) which may be sensitive to unknown and model-dependent effects such as particle thresholds at the GUT scale, we choose two value...

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Supersymmetric field theories can be constructed that violate Lorentz and CPT symmetry. We illustrate this with some simple examples related to the original Wess-Zumino model. DOI: 10.1103/PhysRevD.65.091701 PACS number͑s͒: 11.30.Pb, 11.30.Cp, 11.30.Er A major development in fundamental theoretical physics during the past century has been the understanding of the central role played by spacetime symmetries in nature. Conventional spacetime symmetries, including Lorentz and CPT invariance, are now deeply ingrained in modern theories such as the standard model of particle physics and general relativity. Recent research includes investigations of larger spacetime symmetries, notably supersymmetry ͓1͔, and of the possibility that small violations of conventional spacetime symmetry could arise in an underlying theory at the Planck scale ͓2͔.The essence of spacetime supersymmetry is the existence of transformations between bosons and fermions that yield a translation operator upon anticommutation:where the energy-momentum 4-vector P generates spacetime translations, the spinor Q generates supersymmetry transformations, and ␥ are the Dirac matrices. Many supersymmetric Lorentz-invariant models exist. However, if supersymmetry is relevant to nature, experiment suggests it must be broken. Much of the phenomenology of supersymmetry conducted today is therefore within the context of the ͑minimal͒ supersymmetric standard model ͓3͔ in which soft supersymmetry-breaking but Lorentz-preserving interactions are added by hand. Soft interactions are superrenormalizable, while nonrenormalizable terms are taken to be suppressed by powers of the Planck scale or some other large scale associated with new physics. Soft terms can be motivated by studies of more fundamental theories and could arise from spontaneous breaking of supersymmetry ͓4͔. Their physical implications at low energies can be analyzed in the framework of supersymmetric standard-model extensions including supersymmetry-breaking terms.In a related vein, the physical implications of the breaking of conventional spacetime symmetries can be investigated using a general standard-model extension ͓5͔. Its Lagrangian contains terms violating Lorentz and CPT symmetry. Like the supersymmetry-breaking effects described above, these terms could arise from spontaneous symmetry violation. The nonlocal character of string theories offers a potential source for these terms with a natural origin in spontaneous Lorentz breaking ͓6͔ and provides strong motivation for investigating their physical implications at low energy. The renormalizable sector of the standard-model extension is a local field theory that would dominate Lorentz-and CPT-violating effects in low-energy physics. The requisite causality or positivity issues that result from treating the nonlocal underlying theory as a local field theory emerge at a high-energy scale determined by the Planck mass ͓7͔.In this work, we consider an issue unaddressed in the literature: the existence of fully supersymmetric theories incorpo...

High luminosity muon-muon colliders would provide a powerful new probe of Higgs boson physics through s-channel resonance production. We discuss the prospects for detection of Higgs bosons and precision measurements of their masses and widths at such a machine.