Effective potential methods and the Higgs mass spectrum in the MSSM

We generalize the analytical expressions for the two-loop leading-log neutral Higgs boson masses and mixing angles to the case of general left- and right-handed soft supersymmetry breaking stop and sbottom masses and left-right mixing mass parameters (m_Q, m_U, m_D, A_t, A_b). This generalization is essential for the computation of Higgs masses and couplings in the presence of light stops. At high scales we use the minimal supersymmetric standard model effective potential, while at low scales we consider the two-Higgs doublet model (renormalization group improved) effective potential, with general matching conditions at the thresholds where the squarks decouple. We define physical (pole) masses for the top quark, by including QCD self-energies, and for the neutral Higgs bosons, by including the leading one-loop electroweak self-energies where the top/stop and bottom/sbottom sectors propagate. For m_Q = m_U = m_D and moderate left-right mixing mass parameters, for which the mass expansion in terms of renormalizable Higgs quartic couplings is reliable, we find excellent agreement with previously obtained results.     

Top-quark-mass enhancement in a seesaw-type quark mass matrix

We investigate the implications of a seesawtype mass matrix, i.e.,M _f?m _LM _F ^?1 m _R, for quarks and leptonsf under the assumption that the matricesm _L andm _R are common to all flavors (up-/down- and quark-/lepton-sectors) and the matricesM _F characterizing the heavy fermion sectors have the form [(unit matrix)+b _f (a democratic matrix)] whereb _f is a flavor parameter. We find that by adjusting the complex parameterb _f, the model can provide thatm _t?m _b while at the same time keepingm _u～m _d without assuming any parameter with hierarchically different values betweenM _U andM _D. The model with three adjustable parameters under the “maximal” top-quark-mass enhancement can give reasonable values of five quark-mass ratios and four KM matrix parameters.     

Top-quark-mass enhancement in a seesaw-type quark mass matrix

We investigate the implications of a seesawtype mass matrix, i.e.,M _f?m _LM _F ^?1 m _R, for quarks and leptonsf under the assumption that the matricesm _L andm _R are common to all flavors (up-/down- and quark-/lepton-sectors) and the matricesM _F characterizing the heavy fermion sectors have the form [(unit matrix)+b _f (a democratic matrix)] whereb _f is a flavor parameter. We find that by adjusting the complex parameterb _f, the model can provide thatm _t?m _b while at the same time keepingm _u??m _d without assuming any parameter with hierarchically different values betweenM _U andM _D. The model with three adjustable parameters under the ??maximal?? top-quark-mass enhancement can give reasonable values of five quark-mass ratios and four KM matrix parameters.     

Stability,elastic properties and electronic structures of L12-ZrAl3 and D022-ZrAl3 up to 40 GPa

The effects of high pressures on structure stability, elastic properties and electronic structures of zirconium trialuminide L1₂- and D0₂₂-ZrAl₃ compounds have been investigated by first-principles calculations within the local density approximation. The equilibrium structure and formation energy show that L1₂-ZrAl₃ is more stable than D0₂₂-ZrAl₃ at the applied pressure. The elastic properties and Debye temperatures of (L1₂, D0₂₂)-ZrAl₃ increase with the increasing pressure and the calculated values in the ground state are in good agreement with the available experiment data. The mechanical anisotropic properties were discussed using the universal anisotropic index A^U. The sound velocities along the [100], [110] and [111] directions were also calculated for both phases. The calculated electronic properties under high pressures suggest that the decreased electronic density of states (DOS) at the Fermi level and the changed charges distribution lead to the observed decrease of the structural stability for (L1₂, D0₂₂)-ZrAl₃ under high pressures.     

D0—⦶D0 mixing: Standard versus non-standard scenarios

D⁰—?D⁰ mixing is estimated in several extensions of the minimal SU(2)_LxU(1) model. In some of these models the theoretical upper bound on this mixing (which is known to be strongly suppressed in the standard model) turns out to be rather large - sometimes even close to the present experimental upper bound.     

Lower and upper variational bounds in calculations of Coulomb and nuclear systems

All formulas that are necessary for deriving not only upper (E _U) but also lower (E _L) variational bounds on the energy of systems featuring a few nonrelativistic particles are obtained with trial functions in the form of expansions in multidimensional Gaussian functions or exponentials. For potentials that are used most widely, all matrix elements are expressed in terms of known functions, a circumstance that simplifies considerably relevant numerical calculations. This is so for systems featuring an arbitrary number of particles in the case of a Gaussian basis and for three-particle systems in the case of an exponential basis. Numerical results for E _U and E _L, which are characterized by record accuracies, are presented for some Coulomb and nuclear systems such as the He atom; the e ⁺ e ^? e ^?, ppμ^?, 3α, and 4α systems; and hypertritium (pnΛ). Lower bounds with exponential trial functions are obtained for the first time (the corresponding formulas are presented for the first time as well); for a Gaussian basis, lower bounds for Coulomb systems have not been known either. Given E _L and E _U, limits within which the exact value of energy, E ₀, lies can be indicated with confidence. Moreover, an analysis of the correlation between E _L and E _U with increasing number of terms in the expansion of the trial function makes it possible to improve the accuracy (at least by one order of magnitude) of the value E _∞ extrapolated to infinity. By considering specific examples, it is shown that the exponential basis is advantageous in relation to the Gaussian one.     

Search for light technimesons

The light neutral colour-singlet spin-zero bosons P⁰ and P³ expected in contemporary extended technicolour theories have some small induced flavour-changing couplings, even in monophagic theories where their couplings are mainly flavour-diagonal. Their non-observation in K⁺ decay means that $\text{m}{}_{\mathrm{<mtext>P</mtext>}}\text{0,3 ? 350}\text{MeV}$, leading one to expect direct quark-lepton transitions mediating K_L0 → μe decay close to the present experimental upper limit. In the absence of some as yet unknown suppression mechanisms, eitherP⁰ and P³ should be observed in bottom decays with a branching ratio approaching 100% (which may already be experimentally excluded) and/or they should be observed in charm decays with branching ratios ? 1% and/or the decay K⁰_L → μe should be detected within an order of magnitude of the present upper limit.     

Singlet-Higgs-Boson signals at hadron colliders

Many extensions of the Standard Model includeSU(2) _L ×U(1) _Y singlet higgs bosons,h ⁰, and also vector-like fermions which couple to it. The production and detection possibilities of such singlet neutral scalars at hadron colliders are considered for different scenarios of vectorlike fermions. We find that for some values of masses and couplings, detection at the CERN large hadron collider (LHC) appears to be a distinct possibility, while at the Fermilab Tevatron upgrade theh ⁰ might be observed only in very favourable circumstances.     

A CP violating mixing matrix compatible with neutral flavour conservation and spontaneous CP violation

A specific ansatz for the Yukawa couplings of a four-generation SU(2)_L×U(1) model with two Higgs doublets is discussed which leads to neutral flavour conservation, spontaneous CP violation and to a genuinely complex mixing matrix. W exchange conserves CP in the limit m_t′ = m_t only. The decay rate for t→b is reduced by factor two compared to the standard model wit three generations. The phenomenological implications for K⁰−K̄⁰ and B⁰−B̄⁰ are investigated.     

Majorana masses,photon gas heating and cosmological constraints on neutrinos

Non-vanishing Majorana masses generally lead to flavor-changing neutral currents in the neutrino sector. It is shown that when both right- and left-handed neutrinos have non-vanishing Majorana masses (M_R≠0 and M_L≠0), flavor-changing neutral currents could be as large as flavor-diagonal ones. However, when only right-handed neutrinos have non-vanishing Majorana masses (M_R≠0 but M_L=0), flavor-changing neutral currents are small. If M_R?D (Dirac masses), they are of $\text{O}\text{((}\text{D}\text{M}{}_{\mathrm{<mtext>R</mtext>}}\text{)}{}^2\text{)}$. If M_R?D, they are $\text{?(}\text{m}{}_{\mathrm{<mtext>L</mtext>}}\text{m}{}_{\mathrm{<mtext>H</mtext>}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where m_L and m_H are masses of light and heavy neutrinos appearing in a flavor-changing process.By using these results we examine cosmological implications of non-vanishing flavor-changing neutral currents. Heavy neutrinos can decay into three light neutrinos at an appreciable rate by exchanging a Z-boson. It is demonstrated that owing to this decay mode, heavy neutrinos of mass larger than 70 keV but less than 2m_e give rise to no contradiction with the standard big bang cosmology in the most general case.We also show that if there exist heavy neutrinos of mass m_H2m_e, their decay at an early era of the universe induces photon gas heating, which alters Cowsik and McClelland's constraint on light neutrino masses to Σm_L < k · 100 eV with the sum running over all Majorana eigenstates. Here the constant k, representing the heating effect of the photon gas, is restricted by the deuterium abundance of the present universe. For instance, Σm_L < 240 eV for m_H ～ 25 MeV and the present baryon density = 3.4 × 10^?31 g · cm^?3.     

Anisotropy Effects in Nucleation for Conservative Dynamics

We analyze metastability and nucleation in the context of a local version of the Kawasaki dynamics for the twodimensional it anisotropic Ising lattice gas at very low temperature. Let LsubsetZ² be a sufficiently large finite box. Particles perform simple exclusion on L, but when they occupy neighboring sites they feel a binding energy U₁<0 in the horizontal direction and U₂<0 in the vertical direction; we assume U₁ges U₂. Along each bond touching the boundary of L from the outside, particles are created with rate rho=e^Db and are annihilated with rate 1, where b is the inverse temperature and D>0 is an activity parameter. Thus, the boundary of L plays the role of an infinite gas reservoir with density rho. We take Din (U₁,U₁+U₂) where the totally empty (full) configuration can be naturally associated to metastability (stability). We investigate how the transition from empty to full takes place under the dynamics. In particular, we identify the size and some characteristics of the shape of the it critical droplet/ and the time of its creation in the limit as btoinfty. We observe very different behavior in the weakly or strongly anisotropic case. In both case we find that Wulff shape is not relevant for the nucleation pattern.     

On the ground state energy of free excitons in group IV and III–V semiconductors

An approximate calculation of the ground state energy of direct and indirect free excitons for group IV and group III–V semiconductors is presented. The basic assumption in this treatment is that the anisotropy of the effective masses can be neglected, however, the degeneracy of the valence band cannot. The resulting exciton ground state energy has the usual form but with a reduced mass \(\overline \mu \) given by ( \(\overline \mu \) )^?1=(m _e)^?1+(m _lh)^?1+(m _hh)^?1. The agreement with experiments is considerably improved as compared to the conventional ground state energy comprising the reduced mass defined as (μ)^?1=(m _e)^?1+(m _hh)^?1. Anisotropy corrections are shown to be of minor importance in many cases. However, for the heavier III–V-compounds the neglect of linear terms inE(k) for the valence band results in more serious errors, which invalidate the present theoretical approach.     

On the mass and mixings of the ZE

The experimental data on the neutral current couplings are used to derive lower bounds on the mass of Z_E, the extra neutral gauge boson appearing in the minimal ‘beyond the standard model’ scenario favoured in superstring compactifications. This is based on the gauge group SU(3)_c×SU(2)_L×U(1)_Y×U(1)_E. Taking sin²θ_w=0.229, m_W=80.76 GeV and m_Z=91.59 GeV it is found that the mixing angle θ between Z and Z_E must satisfy −0.136<sin θ<−0.007 corresponding to m_ZE>152 GeV or, assuming E₆ unification m_ZE>155 GeV.     

Kinetic and mass mixing with three abelian groups

We present the possible mixing effects associated with the low-energy limit of a Standard-Model extension by two abelian gauge groups U₁(1)×U₂(1). We derive general formulae and approximate expressions that connect the gauge eigenstates to the mass eigenstates. Applications using the well-studied groups UB(1), U(1)_B−L, U(1)_Lα−Lβ (Lα being lepton flavor numbers), and UDM(1) (a symmetry acting only on the dark matter sector) are discussed briefly.     

Compound windows of the Hénon-map

For the two-parameter second-order Hénon map, the shapes and locations of the periodic windows-continua of parameter values for which solutions x₀,x₁,… can be stably periodic, embedded in larger regions where chaotic solutions or solutions of other periods prevail-are found by a random searching procedure and displayed graphically. Many windows have a typical shape, consisting of a central “body” from which four narrow “antennae” extend. Such windows, to be called compound windows, are often arranged in bands, to be called window streets, that are made up largely of small detected but poorly resolved compound windows.For each fundamental subwindow-the portion of a window where a fundamental period prevails-a stability measure U is introduced; where the solution is stable, |U|<1. Curves of constant U are found by numerical integration. Along one line in parameter space the Hénon-map reduces to the one-parameter first-order logistic map, and two antennae from each compound window intersect this line. The curves where U=1 and U=−1 that bound either antenna are close together within these intersections, but, as either curve with U=−1 leaves the line, it diverges from the curve where U=1, crosses the other curve where U=−1, and nears the other curve where U=1, forming another antenna. The region bounded by the numerically determined curves coincides with the subwindow as found by random searching. A fourth-degree equation for an idealized curve of constant U is established.Points in parameter space producing periodic solutions where x₀=x_m=0, for given values of m, are found to lie on Cantor sets of curves that closely fit the window streets. Points producing solutions where x₀=x_m=0 and satisfying a third condition, approximating the condition that x_n be bounded as n→−∞, lie on curves, to be called street curves of order m, that approximate individual members of the Cantor set and individual window streets. Compound windows of period m+m^′ tend to occur near the intersections of street curves of orders m and m^′.Some exceptions to what appear to be fairly general results are noted. The exceptions render it difficult to establish general theorems.     

Can one test technicolour?

We estimate the couplings to ordinary particles of the lightest bound states in technicolour theories and discuss the resulting phenomenology. We compute their couplings to light gauge bosons through axial anomalies and also estimate their non-anomalous couplings at low energies. We estimate their couplings to fermions under the general simplifying assumption that each fermion acquires its mass from a unique technifermion condensate (“monophagy”), in which case they are naturally flavour conserving and relatively well-defined. We find that the classic Higgs search experiments (ttoponium → H⁰ + γ, e⁺e^? → H⁺H^?, e⁺e^? → Z⁰ + H⁰) enable one to make a decisive discrimination between elementary and composite models of spontaneous symmetry breaking. We also emphasize the interest of improving experimental limits on K_L⁰ → μe in the context of dynamical symmetry breaking models.     

Can the superstring inspire the standard model?

We discuss general features of models in which the E₈ × E′₈ heterotic superstring is compactified on a specific Calabi-Yau manifold. The gauge group of rank-6 in four dimensions is supposed to be broken down at an intermediate scale m_I to the standard model group SU(3)_C × SU(2)_L × U(1)_Y, as a result of two neutral scalar fields acquiring large vacuum expectations (vev's) in one of many flat directions of the effective potential. We find that it is difficult to generate such an intermediate scale by radiative symmetry breaking, whilst such models have prima facie problems with baryon decay mediated by massive particles and with non-perturbative behaviour of the gauge couplings, unless m_I ≳ 10¹⁶ GeV. Rapid baryon decay mediated by light particles, large neutrino masses, other Δ L ≠ 0 processes and flavour-changing neutral currents are generic features of these models. We illustrate these observations with explicit calculations in a number of different models given by vev's in different flat directions.     

Gamma-ray-L-x-ray directional correlations in182W

Directional correlations between gamma radiation andL x-rays in¹⁸²W have been measured. The x-rays are emitted following the internal conversion process of the 100.1 keV 2⁺ → 0⁺ transition. The experimental results for anisotropies involving gamma radiation emitted in the 1189.0 keV transition andL x-rays are A(γ?L _l )=?0.073(27),A(γ?L _α)=?0.0102(45),A(γ?L _β)=?0.0031(35), andA(γ?L _γ)=?0.007(13). The value deduced for the coefficientU ₂(e) pertaining to the converted transition isU ₂(e)=0.52(8) in reasonable agreement with the theoretically expected value 0.410. A note is given on the use of internal conversion radial matrix elements.     

Signals of new gauge bosons at futuree + e − colliders

We analyze possible indirect signals of additional neutral gauge bosons at futuree ⁺ e ^? colliders, concentrating onSU(2) _L ×U(1) _y ×U(1) _y , andSU(2) _L ×SU(2) _R ×U(1) effective theories. We develop a simple formalism to describe these effects and make a careful study of radiative corrections, in particular initial state radiation, which will be shown to have important implications. To make realistic estimates of the sensitivity to the new gauge boson effects, we use a model detector fore ⁺ e ^? annihilation at a center of mass energy of 500 GeV. Using a number of selected physical observables we then show that masses considerably higher than the total energy (up to a factor of 6) can be probed and that distinction between various theoretical models is possible.     

Aspects of left-right symmetric models in superstring phenomenology

The general features of low-energy, rank-six left-right symmetric models as inspired by the superstring are examined. Particular attention is paid to the mass-mixing matrix of the exotic and downtype quarks. It is found that the class of models based on the groupSU(3) _C ×SU(2) _L ×SU(2) _N ×U(1) _L ×U(1) _R is plagued with the problem of unnatural fine tuning. Models based on the other left-right group, namelySU(3) _C ×SU(2) _L ×SU(2) _N ×U(1) _L ×U(1) _R , work rather well from the points of view investigated. In this case a parameter fitting is presented which is compatible with the lowering of the group rank by two units via radiative breaking, without conflicting either with weak universality or with lepton conservation. The unification scale comes in the 10¹⁷ GeV mass range, the intermediate (righthanded) scale is quite low, not exceeding the 10⁴ GeV range, and the Weinberg angle is correct. Good prospects are also obtained for proton decay and neutrino masses.