Evaluation ofS,T, U parameters, triple gauge boson vertices and some oblique corrections in extraU(1) superstring inspired model

Explicit evaluation of the following parameters has been carried out in the extraU (1) superstring inspired model: (i) As Mz₂ varies from 555 GeV to 620 GeV and (m _t) CDF = 175.6 ± 5.7 GeV (Table 1): (a) S^New varies from -0.100 ± 0.089 to -0.130 ± 0.090, (b) T^New varies from -0.098 ± 0.097 to -0.129 ± 0.098, (c) U^New varies from -0.229 ± 0.177 to -0.253 ± 0.206, (d) Τ_z varies from 2.487 ± 0.027 to 2.486 ± 0.027, (e) A_LR varies from 0.0125 ± 0.0003 to 0.0126 ± 0.0003, (f) A _FB ^b remains constant at 0.0080 ± 0.0007. Almost identical values are obtained for (m _t)D0 = 169 GeV (see table 2). (ii) Triple gauge boson vertices (TGV) contributions: AsMz ₂ varies from 555 GeV to 620 GeV and (m _t) CDF = 175.6 ±5.7 GeV. (a)√s = 500 GeV, asymptotic case: varies from -0.301 to -0.179; varies from -0.622 to -0.379; varies from +0.0061 to 0.0056; varies from -3.691 to -2.186. varies from +0.270 to +0.118; varies from +0.552 to 0.238; varies from +0.0004 to +0.0002; remains constant at -0.110. (b)√s = 700 GeV, asymptotic case: varies from -0.297 to -0.176; varies from -0.609 to -0.370; varies from -0.0082 to -0.0078; varies from -3.680 to -2.171.√s = 700 GeV, nonasymptotic case: varies from -0.173 to -0.299; varies from-0.343 to -0.591; varies from -0.005 to -0.011; remains constant at -0.110. The pattern of form factors values for√s = 1000, 1200 GeV is almost identical to that of√s= 700 GeV. Further the values of the form factors for (m _t)D0 (=169 GeV) follow identical pattern as that of (m _t) CDF form factors values (see tables 5, 6, 9, 10). We conclude that the values of all the form factors with the exception of these of , are comparable or larger than theS, T values and therefore the TGV contributions are important while deciding the use of extraU (1) model for doing physics beyond standard model.     

General theory of renormalization of gauge theories in nonlinear gauges

We discuss the general theory of renormalization of unbroken gauge theories in the nonlinear gauges in which the gauge-fixing term is of the form We show that higher loop renormalization modifiesfα [A] to contain ghost terms of the form and show how the corresponding ghost terms are deduced fromfα [A, c, c] uniquely. We show that the theory can be renormalized while preserving a modified form of BRS invariance by multiplicative and independent renormalizations onA, c, g, η, ζ, τ. We briefly discuss the independence of the renormalized S-matrix from η,ζ, τ.     

Photoelasticity in quasicrystals

The maximum number of non-vanishing and independent second order photoelastic coefficients required by the seven pentagonal and the two icosahedral point groups 5(C₅), (S₁₀), (C_5h ), m2(D_5h ), 52(D₅), 5m(C_5v ), 2m(D_5d ); 235(I), 2/m (I _h )—that describe the quasicrystals symmetry groups in two and three dimensions—is obtained. The schemes of non-vanishing and independent coefficients have been calculated and listed. Finally the results of this group-theoretical study are briefly discussed.     

Effect of heavy quark symmetry on the mass difference ofB-system in minimal left right symmetric model

An estimation of the mass difference of system with heavy quark symmetry formalism is presented. The effective Hamiltonian describing the transition (whereh=b forB _d ⁰ -system) is considered in a manifest left right symmetric (MLRS) model along with contribution from neutral Higgs boson. We use the spin and flavor symmetry for heavy quarks to obtain the transition matrix element 〈B _d ⁰ |ℋ_eff(x)| _d ⁰ 〉 in terms of Isgur-Wise function. Assuming thatB _d ⁰ and states are at rest, we find that Isgur-Wise function turns out to be unity. However using the experimental values of ΔM _K and as input, we find thatM _R=835 GeV andM _H⩾2·9 TeV.     

Event-by-event fluctuations of mean transverse momentum in AuAu collisions in STAR experiment at relativistic heavy-ion collider

We report results on event-by-event fluctuations in mean transverse momentum in AuAu collisions at GeV measured by the STAR experiment at RHIC. The dynamical fluctuations, is found to be about 1.2 ±02% of the mean transverse momentum for particles in pseudo-rapidity range of −0.5 < η < 0.5 and for the top 6% central collisions.     

Contribution of Sea Quarks and Gluons to the Proton Spin

Contributions of sea quark and gluon spins to the proton spin in Drell-Jahn processes and direct production of photons in proton-proton and proton-antiproton collisions are studied in the present work. Analytical expressions for two-spin asymmetries and are derived. In both processes, these asymmetries are studied and analyzed as functions of the kinematic variables , x _T, and x _F. Measurements of two-spin asymmetries and make it possible to determine the individual contributions of sea quark and gluon spins to the proton spin.     

Comment on “Evaluation of concentration-depth profiles by sputtering in SIMS and AES” by S. Hofmann

The statistics of the sputtering process, which has been used to explain sputterbroadening effect due to surface roughness, has been treated with conditional probabilities. This results in the relationship, , instead of derived by S. Hofmann [Appl. Phys.9, 59 (1976)], where δz,z, and are the depth resolution, sputtered depth and sputtering yield, respectively.     

Chiral symmetry breaking andKN sigma commutator

KN sigma commutator has been calculated in the framework of the (6, )+( , 6) model. It is found that though this model could not be discarded in favour of the (3, )+( , 3) or (8, 8) model, a very large value forKN sigma term is required to get a positive value ofπN sigma term.     

Links between neutrino oscillations,leptogenesis, and proton decay within supersymmetric grand unification

Evidence in favor of supersymmetric grand unification including that based on the observed family multiplet-structure, gauge coupling unification, neutrino oscillations, baryogenesis, and certain intriguing features of quark-lepton masses and mixings is noted. It is argued that attempts to understand (a) the tiny neutrino masses (especially Δm ²(v ₂ – v₃)), (b) the baryon asymmetry of the Universe (which seems to need leptogenesis), and (c) the observed features of fermion masses such as the ratiom _b/m_τ, the smallness ofV _cb and the maximality of seem to select out the route to higher unification based on an effective string-unifiedG(224) =SU(2)_L ×SU(2)_R ×SU(2)^c orSO(10)-symmetry that should be operative in 4D, as opposed to other alternatives. A predictiveSO(10)/G(224)-framework possessing supersymmetry is presented that successfully describes the masses and mixings of all fermions including neutrinos. It also accounts for the observed baryon asymmetry of the Universe by utilizing the process of leptogenesis, which is natural to this framework. It is argued that a conservative upper limit on the proton lifetime within thisSO(10)/G(224)-framework, which is so far most successful, is given by x 10³⁴ years. This in turn strongly suggests that an improvement in the current sensitivity by a factor of five to ten (compared to SuperK) ought to reveal proton decay. Implications of this prediction for the next-generation nucleon decay and neutrino-detector are noted.     

Bounds on neutrino mixing with exotic singlet neutrinos

We examine the effects of mixing induced non-diagonal light-heavy neutrino weak neutral currents on the amplitude for the process (with a=e, μ or τ). By imposing constraint that the amplitude should not exceed the perturbative unitarity limit at high energy , we obtain bounds on light-heavy neutrino mixing parameter sin² where is the mixing angle. In the case of one heavy neutrino (mass mξ) or mass degenerate heavy neutrinos, for Λ=1 TeV, no bound is obtained for mξ<0.50 TeV. However, sin² ≤3.8 × 10⁻⁶ for mξ=5 TeV and sin ≤6.0 × 10⁻⁸ for mξ=10 TeV. For Λ=∞, no constraint is obtained for mξ<0.99 TeV and sin² ≤3.8 × 10⁻² (for mξ=5 TeV) and sin² ≤9.6 × 10⁻³ (for mξ=10 TeV).     

Bivariate averaging functions,translation and scale autocorrelations,Fourier and Mellin transforms,the Wiener-Khinchine theorem and their inter-relationships

We first draw attention to the fact that the position operator, , its translation generator, , and its scale generator, , form an important group of triplet of operators that appear in the Heisenberg uncertainty relation stated in its most general form. The pair forms the phase-space and they have led to Fourier transform pair, the autocorrelation function, the Wiener-Khinchine theorem, and the Wigner function with many different applications to wave phenomena. The importance of the pairs and has been pointed out by Moses and Quesada (1972, 1973, 1974) who showed that we must then consider a Mellin transform pair, a scale autocorrelation function, and a corresponding Wiener-Khinchine theorem. In the present paper, we define and explore properties of a bivariate averaging function defined in a new “phase-space” involving the Mellin transform variable and its partner which can either be the position or momentum, analogous to the Wigner function. The not-necessarily positive feature of the bivariate averaging functions is traced to the general Heisenberg uncertainty mentioned above. The properties and their inter-relationships among the averaging functions are given. We hope this will be of use in discussing physical phenomena involving fractals, turbulence, and near phase transitions where the scaling properties are of importance.     

Positron decay in polymers: Molecular weight dependence in polystyrene

The decay time τ_l ofo-Ps by the electron pickoff process has been measured in polystyrene as a function of molecular weight. For samples below their glass transition temperature τ_l is essentially independent of . In the low molecular weight region, , τ_l increased with decreasing in line with earlier theoretical predictions. The overall behaviour reflects closely the dependence of free volume on . The effects of molecular motion on τ_l are examined and it is concluded that the decay time is insensitive to such motions in polystyrene below the melting point, in contrast to what is observed in polytetrafluoroethylene.     

Higgs boson production in pp andp\bar p collisionscollisions

The associated production of Higgs particles andZ (W) bosons inpp and collisions is studied. The total cross-section of the processpp →HXl ⁺ l ⁻ is estimated.     

Inhomogeneous contact processes on trees

We consider an inhomogeneous contact process on a tree of degreek, where the infection rate at any site isλ, the death rate at any site in isδ (with 0 <δ ⩽ 1) and that at any site in is 1. Denote by the critical value for thehomogeneous model (i.e.,δ=1) on and byϑ(δ, λ) the survival probability of the inhomogeneous model on . We prove that whenk > 4, if , a subtree embedded in , with 1 ⩽σ ⩽ √k, then three existsδ _c ^σ strictly between ( ) and 1 such that ( ) whenδ >δ _c ^σ andϑ(δ, λ _c( ) > 0 whenδ <δ _c ^σ ; ifS={o}, the origin of , then for anyδ ε (0, 1).     

NMR dynamics in disordered magnets

The excitation dynamics of site diluted magnets can be described at low energies (long length scales) by magnons, and above a crossover frequency, ω_c, (short length scales) by fractons. The density of fracton states is given by , where is the fracton dimensionality. Dilution gives rise to a characteristic length ξ∝(p−p _c)^ν, wherep _c is the critical concentration for (magnetic) percolation. The crossover frequency ω_c is proportional to ξ^-1[1+(θ/2)], where θ is the rate at which the diffusion constant decays with distance for diffusion on an equivalent network. A fractal dimensionD describes the density of magnetic sites on the infinite network, and . For percolating networks, for all dimensions ≥2. Neutron scattering structure factor measurements by Uemura and Birgeneau compare well with calculations using fracton concepts. Magnons are extended at low energies, while the fracton states are geometrically localized, with a wave function envelope proportional to exp . Here, is the fracton length scale at frequency ω. The exponentd _ϕ lies between 1 andd _min, the chemical length index (of the order of 1.6 in three dimensions). The localization of the magnetic excitations causes a spread in the NMR relaxation rates. A given nuclear moment will experience only a limited set of fracton excitations, resulting in an overall non-exponential decay of the NMR relaxation signal. When strong cross-relaxation is present, the relaxation will be exponential, but the temperature dependence will be strongly altered from the concentrated result.     

Mesonic decays of τ− lepton: Effects of neutrino mass and mass mixing

Experimentally established mesonic decays ofτ ⁻ lepton have been reexamined with the inclusion of the effects of finite neutrino mass and the associated mass mixing in the form of Kobayashi-Maskawa mixing matrix. A comparison with the experimentally predicted decay probabilities provides limits for thev _τ mass which are finite in all decays except for the lower limit in mass mixing case of the decayτ ⁻→K*⁻ (892)+v _τ for which MeV. The large error in this value is because of (i) large errors in the experimental values of life time and branching ratio for this decay and (ii) thekm mixing used in the calculations. The ratio of parity-violating to parity-conserving terms in the differential decay probabilities of various decays differs slightly from their values corresponding to those with varishingv _τ mass.     

Nonabelian orbifolds and the boson-fermion correspondence

For a positive integerl divisible by 8 there is a (bosonic) holomorphic vertex operator algebra (VOA) associated to the spin lattice _l . For a broad class of finite groupsG of automorphisms of we prove the existence and uniqueness of irreducibleg-twisted -modules and establish the modular-invariance of the partition functionsZ(g, h, ) for commuting elements inG. In particular, for any finite group there are infinitely many holomorphic VOAs admittingG for which these properties hold. The proof is facilitated by a boson-fermion correspondence which gives a VOA isomorphism between and a certain fermionic construction, and which extends work of Frenkel and others.Supported by NSA grant MDA904-92-H-3099.Supported by NSF grant DMS-9122030.     

CP invariance: A point of view

That the longlived componentL ofK ₀ has bothcp=+1 andcp=−1 modes of decay is often cited as evidence of violation ofcp invariance. The careful ones find the compelling evidence to be the non-dilution of the regeneration interference pattern when the incidentK ₀ beam is mixed even substantially with . However the two phenomena comprehensively imply thatL has acp=+1 componentL ₊ and acp=−1 componentL ₋ and that the longlived component of bothK ₀ and are one and the sameL. This does not demand abandoningcp invariance. It does imply that is not thecp conjugate ofK ₀.     

High resolution measurement of bragg cut-off in beryllium

Bragg cut-off for plane of polycrystalline beryllium of various lengths of 300 and 116 K has been measured with an energy resolution of 5 μeV. The natural width of the cut-off is 12.5±1.5 μeV, independent of temperature and length of beryllium and also of physical characteristics and certain metallurgical treatments of the powder. Such blocks of beryllium would be suitable for designing a ΔT-window spectrometer with resolution ⩾20 μeV. Bragg cut-offs corresponding to (0002) and planes of beryllium have been separated for the first time. These can also be used for producing additional energy windows in a ΔT-window spectrometer, thus increasing its efficiency. Paper entitled ‘ΔT-window spectrometer’ will appear in the November issue of Pramana.