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Our Universe is described jointly by Einstein's relativity principle and the quantum principle; there the existence of the smallest units of matter, such as electrons, neutrinos, quarks, and photons, is well established and the smallest units of matter are described by the Standard Model. Based on these, we have a clear picture for the propagation of ultra high energy cosmic rays (UHECR's), for energies greater than $E > 10^{13}\, eV$ but less than $E < 10^{26}\, eV$, in the cosmic medium of the Cosmic Microwave Background (CMB) and of the cosmic background neutrinos (CB$\nu$'s). We find that the CMB plays a pivot role in this energy range, so that the observed "knee(s)" and the "ankle" could be understood in reasonable terms. What we might observe at the energy near $10^{25}\,eV$', the so-called "$W^\pm$ bursts" or "$Z^0$ bursts", is briefly discussed. Meanwhile, in the early Universe, the CB$\nu$'s, in view of the tiny neutrino mass, gave rise to the clustering phenomenon, resulting in a neutrino halo attached to each visual ordinary-matter object, such as the Earth, the Sun, and stars - with the $PeV$ neutrinos near the surface of the Fermi-Dirac sphere of the neutrino halo of the Earth playing the most fundamental role., Comment: 16 pages

We present an extension of the QCD sum rule method in the external fields so as to determine the induced pseudoscalar coupling constant g_P, which tests the validity of the partially conserved axial current (PCAC) hypothesis. This is essentially that we pick out the "higher-order" effects of both the hadron and quark (QCD) sides. A specific QCD sum rules for g_P is obtained and its prediction is briefly analyzed. It turns out that the final prediction on g_P is extremely stable. In view of the versatile nature of the present QCD sum rule methods, we appendix some discussions on the possible future of the method.

Within a covariant Bethe-Salpeter approach a rank-six separable neutron-proton interaction kernel for the triplet coupled $^3S_1$-$^3D_1$ partial-wave state is constructed. Two different methods of a relativistic generalization of initially nonrelativistic form factors parametrizing the kernel are considered. The model parameters are determined by fitting the elastic $^3S_1$ and $^3D_1$ phase shifts and the triplet scattering length as well as the asymptotic $D/S$ ratio of the deuteron wave functions and the deuteron binding energy. The $D$-state probability constraints 4-7\% are taken into account. The deuteron magnetic moment is calculated. The half-off-shell properties are further demonstrated by the Noyes-Kowalski functions. The first test of the constructed kernel is performed by calculating the deuteron electrodisintegration at three different kinematic conditions., Comment: 17 pages, 12 figures

The multirank separable kernels of the neutron-proton interaction for uncoupled $S$ and $P$ partial waves (with the total angular momentum $J$=0,1) are proposed. Two different methods of a relativistic generalization of initially nonrelativistic form factors parametrizing the kernel are considered. Using the constructed kernels the experimental data for phase shifts in the elastic neutron-proton scattering for the laboratory energy up to 3 GeV and low-energy parameters are described. The comparison of our results with other model calculations are presented., Comment: 24 pages, 6 figures, 3 tables

A new version of the separable kernel of the nucleon-nucleon interaction in the Bethe-Salpeter approach is presented. The phase shifts are fitted to recent experimental data for singlet and uncoupled triplet partial waves of the neutron-proton scattering with total angular momenta J=0,1. The results are compared with other model calculations., Comment: 10 pages, 5 figures, 3 tables

The neutron fraction in the very high energy cosmic rays near the Greisen-Zatsepin-Kuzmin (GZK) cutoff energy is analyzed by taking into account the time dilation effect of the neutron decays and also the pion photoproduction behaviors above the GZK cutoff. We predict a non-trivial neutron fraction above the GZK cutoff and a negligibly small neutron fraction below. However, there should be a large antiproton fraction in the high energy cosmic rays below the GZK cutoff in several existing models for the observed cosmic-ray events above and near the GZK cutoff. Such a large antiproton fraction can manifest itself by the muon charge ratio $\mu^+/\mu^-$ in the collisions of the primary nucleon cosmic rays with the atmosphere, if there is no neutron contribution. We suggest to use the muon charge ratio as one of the information to detect the composition of the primary cosmic rays near or below the GZK cutoff., Comment: 5 LaTex pages

We propose a method to investigate the scenario that cosmic relic neutrinos are highly clustered around stars and galaxies, or dark-matter clusters, rather than uniformly distributed in the universe. Such a scenario can be detected or constrained by the interaction of high energy cosmic ray protons and nuclei with the cosmic neutrinos. There should be observable signature in the energy spectra of cosmic ray protons and nuclei for a neutrino clustering factor beyond $10^{13}$. We provide a relation on the signature onset positions between proton and nuclei spectra, and discuss possible support from existing experiments. It is also suggested that the relative abundance of cosmic ray nuclei may detect or constrain the cosmic neutrinos with smaller clustering., Comment: 8 Latex Pages

We have made a needed correction to our earlier paper (nucl-th/9511002), which contains a sign error. With this correction, the weak parity-violating pion-nucleon coupling is about 3 x 10^(-7)., Comment: 4 pages

The light cone QCD sum rules are derived for the $\pi NN$ coupling $g_{\pi NN}$ and $\pi NN(1535)$ coupling $g_{\pi NN^\ast}$. The contribution from the excited states and continuum is subtracted cleanly through double Borel transformation. We first improve the original sum rule for $g_{\pi NN}$ and determine the value of the pion wave function at the middle point $\phi_\pi (u_0 ={1\over 2})=(1.5\pm 0.2)$ at $\mu =1$GeV, which is a fundamental nonperturbative quantity like the quark condensate. Our calculation shows that the $\pi N N(1535)$ coupling is strongly suppressed., Comment: Submitted to Phys. Rev. C

We apply the method of QCD sum rules in the presence of external electromagnetic fields $F_{\mu\nu}$ to the problem of the electromagnetic decays of various vector mesons, such as $\rho\to\pi\gamma$, $K^\ast\to K\gamma$ and $\eta'\to\rho\gamma$. The induced condensates obtained previously from the study of baryon magnetic moments are adopted, thereby ensuring the parameter-free nature of the present calculation. Further consistency is reinforced by invoking various QCD sum rules for the meson masses. The numerical results on the various radiative decays agree very well with the experimental data., Comment: To appear in Phys. Lett. B

We use the method of QCD sum rules in the presence of an external pion field to investigate isospin symmetry breakings in pion-nucleon couplings. Possible manifestations of such isospin symmetry breaking are examined in the context of low-energy nucleon-nucleon ($NN$) scattering. We discuss numerical results in relation to both the existing data and other theoretical predictions., Comment: 14 pages, 4 figures (upon request), LateX

We use QCD sum rules to obtain the weak parity-violating pion-nucleon coupling constant $f_{\pi NN}$. We find that $f_{\pi NN}\approx 2\times 10^{-8}$, about an order of magnitude smaller than the ``best estimates'' based on quark models. This result follows from the cancellation between perturbative and nonperturbative QCD processes not found in quark models, but explicit in the QCD sum rule method. Our result is consistent with the experimental upper limit found from $^{18}$F parity-violating measurements., Comment: 13 pages, uses LaTex; figures can be obtained from any of the authors: Henley@phys.washington.edu, Kisslinger@kelvin. phys.cmu.edu, Hwang@mitlns.mit.edu

We use QCD sum rules to obtain the weak parity-violating pion-nucleon coupling constant $f_{\pi NN}$. We find that $f_{\pi NN}\approx 3\times 10^{-8}$, up to an order of magnitude smaller than the ``best estimates" based on quark models. This result follows from the cancellation between perturbative and nonperturbative QCD processes not found in quark models, but explicit in the QCD sum rule method. Our result is consistent with the experimental upper limit found from $^{18}$F parity-violating measurements., Comment: 13 pages, latex, 5 figures