Are there anomalous Z fermion couplings?

The couplings of the fermions to the Z boson are of great importance in establishing the validity of the Standard Model and in looking for physics beyond it. The couplings of the b-quark to the Z boson have been the subject of much experimental study and theoretical interpretation. The apparent excess in the value of , the ratio of the partial width of the Z boson to to its total hadronic width, above the Standard Model expectation reported a few years ago has now become much less significant. However, the measurements of the pole forward-backward asymmetry for b-quarks at the Z pole and of the polarisation parameter , obtained using a polarised electron beam, have improved considerably in accuracy. The latest data are examined and values of the vector and axial-vector b-quark and c-quark couplings to the Z are extracted. The left and right handed couplings are also extracted. It is found that whereas the c-quark couplings are compatible with the Standard Model, those of the b-quark data are only compatible with the Standard Model at about the 1% level. In addition, the individual lepton couplings are extracted and the degree to which the data support the hypothesis of lepton universality is discussed. The sensitivity of the limits from electroweak fits to the Higgs boson mass to these data is examined. Received: 21 December 1998 / Revised version: 12 February 1999 / Published online: 15 April 1999     

Are neutron stars with crystalline color-superconducting cores relevant for the LIGO experiment?

We estimate the maximal deformation that can be sustained by a rotating neutron star with a crystalline color-superconducting quark core. Our results suggest that current gravitational-wave data from the Laser Interferometer Gravitational-Wave Observatory have already reached the level where a detection would have been possible over a wide range of the poorly constrained QCD parameters. This leads to the nontrivial conclusion that compact objects do not contain maximally strained color crystalline cores drawn from this range of parameter space. We discuss the uncertainties associated with our simple model and how it can be improved in the future.     

Empirical lepton-quark mass formula: Four dimensional state space for fermion structure?

It is observed that a simple mass formula of the formm =¯mQ ²(exp) is wholly consistent with experimental measurements and quark model estimates for all 12 fundamental fermions. Here¯m = 433.3 MeV is an input (mean fermion mass) constant,Q is the charge number of the lepton or quark, and is a real root of a quartic equation that brings in a principal quantum numbern (= 0, 1, 2, 3). The charged lepton masses are given accurately to within 0.3 of 1%, all neutrino masses are zero, and the top mass is predicted by the formula to be close tom _t = 163.6 GeV.     

Inverse spectral problem for the 2-sphere Schrödinger operators with zonal potentials

Two basic problems of spectral theory of Schrödinger operators H=–+V(x) on the 2-sphere S ₂ are studied: (Direct problem) calculate large-k asymptotics of eigenvalue clusters {_kj}_j in terms of the potential function V; (Inverse problem) recover V from asymptotics of eigenvalue clusters. We get an explicit solution of the inverse problem and establish local spectral rigidity for zonal potentials V.The research was partly supported by the US NSF Grant DMS-8620231 and the Case Research Initiation Grant.     

Are operators describing b →sγ?

The operators of b→sγ,b→sl+l-are usually regarded as being sufficient to describe b→sγγ,b→sl+l-γwith the statement that contributions from diagrams without an effective vertex b→sγ to processes b→sγγand b→sl+l-γ are negligible.In this work we present a comprehensive analysis of the transition b→sγγand find that 1)Effects due to off-shell quarks in vertex b→sγ on b→sγγ are large; 2)Contributions from diagrams without an effective vertex b→sγ to b→sγγare not negligible compared with others; 3)These effects cancel each other out exactly,so the operators of b→sγ can safely be used to describe b→sγγ.     

What is the problem in the locality problem?

In connection with my previous paper Locality, Reflection, and Wave-Particle Duality [Found. Phys. 17, 813 (1987)], in this paper I distinguish explicitly, in the locality problem, between assertions, deductively established results, interpretations, intuitions, and facts. This clarifies the structure of the problem.     

Where to look for solving the gauge hierarchy problem?

A mass of the Higgs boson close to 126 GeV may give a hint that the standard model of particle physics is valid up to the Planck scale. We discuss perspectives for the solution of the gauge hierarchy problem at high scales. Scenarios with an ultraviolet fixed point have predicted a Higgs boson mass very close to 126 GeV if the fixed point value of the quartic scalar coupling is small. In this case the top quark pole mass should be close to 172 GeV.     

What Are the Conditions for Exponential Time-Cubed Echo Decays?

Diffusion of precessing spins through a constant field gradient is well-known to produce two distinctive features: an exp(-bt(3)) decay of the echo amplitude in response to two pulses and a much slower decay of the Carr-Purcell echo train. These features will appear whenever the spin frequency is described by a continuous random-walk. The present work shows that this may also occur in the presence of motions with long correlation times tau(c)-continuous Gaussian frequency noise with an exponential autocorrelation has the correct properties over time durations smaller than tau(c). Thus, time-cubed echo decays will occur in situations other than physical diffusion. The decay rate of the Carr-Purcell echo train is shown to vary with the pulse spacing tau whenever the correlation time tau(c) is long; the slower Carr-Purcell decay compared to the two-pulse echo decay is not unique to diffusion. Simulations are presented that display time-cubed decays. The simulations confirm two important criteria: the echo time must be less than tau(c) and the frequency noise must consist of nearly continuous variations, as opposed to step-like changes. These criteria define the range of physical parameters for which time-cubed decays will be observable.     

On eigenvalue estimates for the Dirac–Witten-type operators

We give optimal lower bounds for the eigenvalues of the Dirac–Witten-type operators associated with the _e0$e_0$-Killing connection and imaginary Killing connection, in terms of the mean curvature and the scalar curvature. The limiting cases are then studied and lead to interesting geometric situations.     

What mass are the smallest protohalos?

We calculate the kinetic-decoupling temperature for weakly interacting massive particles (WIMPs) in supersymmetric (SUSY) and extra dimensional models that can account for the cold-dark-matter abundance determined from cosmic microwave background measurements. Depending on the parameters of the particle-physics model, a wide variety of decoupling temperatures is possible, ranging from several MeV to a few GeV. These decoupling temperatures imply a range of masses for the smallest protohalos much larger than previously thought--ranging from 10(-6)M(+ in a circle) to 10(2)M(+ in a circle). We expect the range of protohalos masses derived here to be characteristic of most particle-physics models that can thermally accommodate the required relic abundance of WIMP dark matter, even beyond SUSY and extra dimensions.     

Can four-fermion contact interactions at one-loop explain the new atomic parity violation results?

We investigate the possibility that four-fermion contact interactions give rise to the observed deviation from the standard model prediction for the weak charge of cesium, through one-loop contributions. We show that the presence of loops involving the third generation quarks can explain such a deviation. Received: 28 March 2000 / Revised version: 12 May 2000 / Published online: 9 August 2000     

On the gap problem for the sequence ∥mβ∥

We discuss the gap problem for the sequence m used in our previous Letter (D. H. Mayer, Lett. Math. Phys. 16, 139–143 (1988)).     

Feynman path integrals and the trace formula for the Schrödinger operators

We study Schrödinger operators of the form on ^d , whereA ² is a strictly positive symmetricd×d matrix andV(x) is a continuous real function which is the Fourier transform of a bounded measure. If _n are the eigenvalues ofH we show that the theta function is explicitly expressible in terms of infinite dimensional oscillatory integrals (Feynman path integrals) over the Hilbert space of closed trajectories. We use these explicit expressions to give the asymptotic behaviour of (t) for smallh in terms of classical periodic orbits, thus obtaining a trace formula for the Schrödinger operators. This then yields an asymptotic expansion of the spectrum ofH in terms of the periodic orbits of the corresponding classical mechanical system. These results extend to the physical case the recent work on Poisson and trace formulae for compact manifolds.Partially supported by the USP-Mathematisierung, University of Bielefeld (Forschungsprojekt Unendlich dimensionale Analysis)     

Does the planck mass run on the cosmological-horizon scale?

Einstein's theory of general relativity contains a universal value of the Planck mass. However, one may envisage that in alternative theories of gravity the effective value of the Planck mass (or Newton's constant), which quantifies the coupling of matter to metric perturbations, can run on the cosmological-horizon scale. In this Letter, we study the consequences of a glitch in the Planck mass from subhorizon to superhorizon scales. We show that current cosmological observations severely constrain this glitch to less than 1.2%.     

Can symmetry non-restoration solve the monopole problem?

We reexamine a recently proposed non-inflationary solution to the monopole problem, based on the possibility that spontaneously broken Grand-Unified symmetries do not get restored at high temperature. We go beyond leading order by studying the self-consistent one-loop equations of the model. We find large next-to-leading corrections that reverse the lowest order results and cause symmetry restoration at high temperature.