arXiv subjects

Tai Tsun Wu

Publications and source records attributed to Tai Tsun Wu.

26 records · Page 2Linked to original sources

arXiv2002

Theory and application of Fermi pseudo-potential in one dimension

The theory of interaction at one point is developed for the one-dimensional Schrodinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of this one-dimensional problem comes from the fact that the real line becomes disconnected when one point is removed. The general interaction at one point is found to be the sum of three terms, the well-known delta-function potential and two Fermi pseudo-potentials, one odd under space reflection and the other even. The odd one gives the proper interpretation for the delta'(x) potential, while the even one is unexpected and more interesting. Among the many applications of these Fermi pseudo-potentials, the simplest one is described. It consists of a superposition of the delta-function potential and the even pseudo-potential applied to two-channel scattering. This simplest application leads to a model of the quantum memory, an essential component of any quantum computer.

math-ph↗

arXiv2001

Three-Neutrino MSW Effect and the LNW Mass Matrix

We review recent work on analytical solutions to the MSW equations for three neutrino flavours, for exponential and linear potentials. An application to a particular mass matrix is also discussed. The three neutrino masses are determined, respectively, to be 0.001--0.004, and roughly 0.01 and 0.05 eV.

hep-ph↗

arXiv2000

Mikheyev-Smirnov-Wolfenstein Effect for Linear Electron Density

When the electron density is a linear function of distance, it is known that the MSW equations for two neutrino species can be solved in terms of known functions. It is shown here that more generally, for any number of neutrino species, these MSW equations can be solved exactly in terms of single integrals. While these integrals cannot be expressed in terms of known functions, some of their simple properties are obtained. Application to the solar neutrino problem is briefly discussed.

hep-ph↗

arXiv2000

Universal quark-lepton mixing and determination of neutrino masses

If three right-handed neutrinos are added to the Standard Model, then, for the three known generations, there are six quarks and six leptons. It is then natural to assume that the symmetry considerations that have been applied to the quark matrices are also valid for the lepton mass matrices. Under this assumption, the solar and atmospheric neutrino data can be used to determine the individual neutrino masses. Three minima have been found, using the chi^2 fit, and, from these minima, it is determined that the mass of the lightest neutrino is 1.3\times10^-3 eV, that of the next heavier neutrino is 1.3\times10^-2 eV, while the mass of the heaviest neutrino is 3.4\times10^-2, 5.8\times10^-2 or 9.4\times10^-2 eV.

hep-ph↗

arXiv1999

Solar Mikheyev-Smirnov-Wolfenstein Effect with Three Generations of Neutrinos

Under the assumption that the density variation of the electrons can be approximated by an exponential function, the solar Mikheyev-Smirnov-Wolfenstein effect is treated for three generations of neutrinos. The generalized hypergeometric functions that result from the exact solution of this problem are studied in detail, and a method for their numerical evaluation is presented. This analysis plays a central role in the determination of neutrino masses, not only the differences of their squares, under the assumption of universal quark-lepton mixing.

hep-ph↗

arXiv1999

Impact-picture predictions for the $γγ$ total cross section at LEP

We show that the rising total cross section $σ(γγ\to hadrons)$ recently observed by the L3 and OPAL Collaborations at LEP are fully consistent with the impact-picture for high-energy scattering. The impact picture is then used to predict this total cross section at higher energies. These experimental results confirm once more the success of the theoretical approach, which predicted for the first time, nearly thirty years ago, the universal increase of total cross sections at high energies.

hep-ph↗

arXiv1998

Universality of low-energy scattering in (2+1) dimensions

We prove that, in (2+1) dimensions, the S-wave phase shift, $ δ_0(k)$, k being the c.m. momentum, vanishes as either $δ_0 \to {c\over \ln (k/m)} or δ_0 \to O(k^2)$ as $k\to 0$. The constant $c$ is universal and $c=π/2$. This result is established first in the framework of the Schrödinger equation for a large class of potentials, second for a massive field theory from proved analyticity and unitarity, and, finally, we look at perturbation theory in $ϕ_3^4$ and study its relation to our non-perturbative result. The remarkable fact here is that in n-th order the perturbative amplitude diverges like $(\ln k)^n$ as $k\to 0$, while the full amplitude vanishes as $(\ln k)^{-1}$. We show how these two facts can be reconciled.

hep-th↗

arXiv1994

Expanding Protons seen by HERA

We show that the rising total photoproduction cross section recently observed at HERA is entirely consistant with the impact-picture in the theory of expanding protons which was proposed more than twenty years ago. More accurate data, which is expected to be forthcoming soon, will give this prediction a stringent test.

hep-ph↗