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We try to define "our world" by stating that "we live in the quantum 4-dimensional Minkowski space-time with the force-fields gauge group $SU_c(3) \times SU_L(2) \times U(1) \times SU_f(3)$ built-in from the outset". We begin by explaining what "space" and "time" are meaning for us - the 4-dimensional Minkowski space-time, then proceeding to the quantum 4-dimensional Minkowski space-time. In our world, there are fields, or, point-like particles. Particle physics is described by the so-called Standard Model. Maybe I should explain why, how, and what my Standard Model would be everybody's "Standard Model" some day. Following the thinking underlying the minimal Standard Model and based on the gauge group $SU_c(3) \times SU_L(2) \times U(1) \times SU_f(3)$, the extension, which is rather unique, derives from the family concept that there are three generations of quarks, on (123), and of leptons, on another (123). It yields neutrino oscillations in a natural manner. It also predicts a variety of lepton-flavor-violating rare decays. At the end of the Standard Model, we will provide some clear answers toward two "origin" questions: What is the origin of mass? Another one: what is the origin of fields (point-like particles)?, 13 pages

Granting that the $SU_c(3) \times SU_L(2) \times U(1) \times SU_f(3)$ Standard Model is valid (or, partially valid), for the real world, we propose the $\mu^+ e^-$ collider in the $10^2\, GeV$ range as the family collider. This family collider may work efficiently in producing the family Higgs particles and detecting the effects of family gauge bosons, with the range of sub-sub-fermi's (a few $10^{-2} \, fermi$'s)., Comment: arXiv admin note: substantial text overlap with arXiv:1409.6077, arXiv:1301.6464

We declare that we are living in the quantum 4-dimensional Minkowski space-time with the force-fields gauge-group structure $SU_c(3) \times SU_L(2) \times U(1) \times SU_f(3)$ built-in from the very beginning. From this overall background, we see the lepton world, which has the symmetry characterized by $SU_L(2) \times U(1) \times SU_f(3)$ - the lepton world is also called "the atomic world". From the overall background, we also see the quark world, which experiences the well-known $(123)$ symmetry, i.e., $SU_c(3) \times SU_L((2) \times U(1)$. The quark world is also called "the nuclear world". The $3^\circ\,K$ cosmic microwave background (CMB) in our Universe provides the evidence of that "the force-fields gauge-group structure was built-in from the very beginning". The CMB is almost uniform, to the level of one part in $10^5$, reflecting the massless of the photons. The lepton world is dimensionless in the 4-dimensional Minkowski space-time. That is, all couplings are dimensionless. The quark world is also dimensionless in the 4-dimensional Minkowski space-time. Apart from the "ignition" term, the gauge and Higgs sector, i.e., the overall background, is also dimensionless. Thus, apart the "ignition" term, our world as a whole is dimensionless in the 4-dimensional Minkowski space-time - that is, it is the characteristic of the quantum 4-dimensional Minkowski space-time., Comment: 1 figure. arXiv admin note: substantial text overlap with arXiv:1301.6464

We declare that we live in the quantum 4-dimensional Minkowski space-time with, via the gauge principle, the force-fields gauge-group structure, $SU_c(3) \times SU_L(2) \times U(1)$ applied to the quark world or $SU_L(2) \times U(1) \times SU_f(3)$ applied to the lepton world, built-in from the very beginning. The quark world with the triplets from the "quark" group $SU_Q(3)$ (used to be called "flavor $SU(3)$ symmetry"), which is of nuclear sizes and is protected by $SU_c(3) \times SU_L(2) \times U(1)$ (i.e. the (123) symmetry), can be seen by our world, while the lepton world, as of atomic sizes and protected by $SU_L(2) \times U(1) \times SU_f(3)$ or another (123) symmetry, can also be seen, as singlets of the quark group $SU_Q(3)$, by our world. Apart from the "ignition" term, the entire Standard Model is dimensionless and massless in the quantum 4-dimensional Minkowski space-time; that is, all couplings are dimensionless and there are no mass terms in the quantum 4-dimensional Minkowski space-time. Therefore, there exist the well-studied $3^\circ \,K$ cosmic microwave background (CMB) and the now clustered neutrino halos formed from cosmic background (CB) neutrinos (of three flavors, and antineutrinos), both present in the overall background of our Universe. In theory, it yields neutrino oscillations, as some lepton-flavor-violating processes, in a natural manner., Comment: 24 pages

We believe that the quantum 4-dimensional Minkowski space-time with the force-fields gauge-group structure $SU_c(3) \times SU_L(2) \times U(1) \times SU_f(3)$ built-in from the very beginning is the background for everything. Thus, the self-repulsive, but ``related'', complex scalar fields $\Phi(1,2)$ (the Standard-Model Higgs), $\Phi(3,1)$ (the purely family Higgs), and $\Phi(3,2)$ (the mixed family Higgs), with the first family label and the second $SU_L(2)$ label, co-exist such that they generate all the masses if, and only if, necessary. Note that the ``ignition'' channel is on the elusive $\Phi(3,1)$ channel, yielding the prediction that the Standard-Model (SM) Higgs mass $m_{SM}$ is half of the SM vacuum expectation value $v$. Before the ``ignition'', there is no mass terms, including the Higgs, the quarks, and the leptons. Apart from the ``ignition'' term, all the couplings are dimensionless and thus the theory is determined by the quantum 4-dimensional Minkowski space-time. The multi-GeV or sub-sub-fermi $SU_f(3)$ family gauge fields protect the lepton world from the QED Landau ghost and make them asymptotically free. We try to discuss different ways to deal with infinities (ultraviolet divergences) for the resultant Standard Model (as the consistent and complete theory)., Comment: 4 figures

We ponder about neutrino oscillations; a particle without a clear identity, a neutrino of a given flavor in fact does not satisfy the Dirac equation (which is used to define the mass eigen-states and mass eigen-values). This alters the basic treatment of neutrino oscillations, in that the Dirac spinors are defined as the mass eigen-states while the flavor states can only be given as linear combinations of the mass eigen-states (of Dirac equations). Even though neutrino masses are tiny, the impacts of several neutrino masses in a single reaction or a single decay, such as possible violation of the energy-momentum conservation, should not be overlooked. Among those sources of oscillating neutrinos, we point out that the ultra high energy cosmic rays (UHECR's) such as the proton of energy $10^{18}\, eV$ or higher, used to think of being rather stable, can capture, in the matter media, an electron to convert into an electron-like neutrino and a spectator neutron. This would be the most important neutrino source of the UHECR origin., 4 figures

To describe neutrino oscillations in the sense of quantum mechanics and quantum field theory, we propose to use an off-diagonal neutrino-Higgs (mass) interaction, as discussed originally in a family gauge theory and in the extended Standard Model. For neutrino oscillations which take place presumably between point-like Dirac particles, the proposed description would be unique in the quantum mechanics sense. This may help us to resolve a few outstanding puzzles - the question of why there are only three generations, the question of why the masses of neutrinos are so tiny, the question of why neutrinos oscillate, and the question of why the dark-matter world is so huge (25%) as compared to the visible ordinary-matter world (5%)., 1 figure. arXiv admin note: substantial text overlap with arXiv:1209.5488, arXiv:1212.4944, arXiv:1207.6837, arXiv:1304.4705

The problem of galactic formation and evolution should be solved on the basis of the Standard Model of particle physics. We believe that we live in the quantum 4-dimensional Minkowski space-time with the force-fields gauge-group structure SU_c(3) \times SU_L(2) \times U(1) \times SU_f(3) built-in from the very beginning, i.e., the "background" of our world. From this "background", we can see the lepton world, of atomic sizes, and also the quark world, of (fermi)^3 sizes. Basing on this belief, we study galactic formation and evolution, concluding that our Cosmos should end up with "model" galaxies. A model galaxy is the one in which a spiral visible ordinary-matter galaxy, such as our Milky Way and satellites, is surrounded by a huge dark-matter neutrino halo. As a byproduct (of studying the Standard Model), we find that neutrinos will be the {\it only long-lived} dark-matter particles., 18 pages

We would like to discuss the language to write an extended Standard Model - using renormalizable quantum field theory as the framework; to start with certain basic units together with a certain gauge group. Specifically we use the left-handed and right-handed spinors to form the basic units together with SUc(3) x SUL(2) x U(1) x SUf(3) as the gauge group. We could write down the extended Standard Model, though the details of the Higgs mechanism remains to be worked out. The same general quest appeared about forty years ago - the so-called "How to build up a model". It is timely to address the same question again especially since we could now put together "Dirac similarity principle" and "Higgs minimum hypothesis" as two additional working rules., Comment: arXiv admin note: substantial text overlap with arXiv:1207.6443, arXiv:1209.5488

We try to envision that there might be a dark-matter world and neutrinos, especially the right-handed ones, might be coupled directly with dark-matter particles in the dark-matter world. The candidate model would be the extended Standard Model based on SU_c(3)\times SU_L(2)\times U(1)\times SU_f (3)\times SU_R(2), with the search of the detailed version through the aid of the two working rules, "Dirac similarity principle" and "minimum Higgs hypothesis"., Comment: 1 figure. arXiv admin note: substantial text overlap with arXiv:1203.1407, arXiv:1207.6443

The physics of the 20th Century is governed by two pillars, Einstein's relativity principle and the quantum principle. At the beginning of the 21st Century, it becomes clear that there exist the smallest units of matter, such as electrons, neutrinos, and quarks; their behaviors are described by the Standard Model. It was believed that the temperature of the early Universe was once 300 GeV, or higher, at $10^{-11} sec$, and then going through the electroweak phase transition. But the mass phase transition happens in the purely imaginary temperature. Later on, its temperature was 150 MeV at $3.3 \times 10^{-5} sec$, and then going through the "QCD cosmological phase transition". We attempt to use the Standard Model, a completely dimensionless theory apart from the negative "ignition" term, to conclude that the EW or mass phase transition {\it does not exist}. On the front of QCD cosmological phase transition, the intriguing question about the latent heat (energy) is discussed and its role is speculated., 24 pages, 1 figure

We introduce the "Dirac similarity principle" that states that only those point-like Dirac particles which can interact with the Dirac electron can be observed, such as in the Standard Model. We emphasize that the existing world of the Standard Model is a Dirac world satisfying the Dirac similarity principle and believe that the immediate extension of the Standard Model will remain to be so. On the other hand, we are looking for Higgs particles for the last forty years but something is yet to be found. This leads naturally to the "minimum Higgs hypotheses". Now we know firmly that neutrinos have tiny masses, but in the minimal Standard Model there is no natural sources for such tiny masses. If nothing else, this could be taken as the clue as the signature of the existence of the extra heavy $Z^{\prime 0}$ since it requires the extra Higgs field, that would help in generating the neutrino tiny masses. Alternatively, we may have missed the right-hand sector for some reason. A simplified version of the left-right symmetric electroweak model has the simplest Higgs sector (in which there is one standard left-hand Higgs doublet together with the image right-handed Higgs doublet), of which the Higgs sector also satisfies the "minimum Higgs hypothesis". Or, if we question the origin of the family symmetry, we may consider to enlarge it to the family gauge symmetry. It transpires very feeble family interactions. All the above possibilities satisfy both the so-called "Dirac similarity principle", the "minimum Higgs hypothesis", and renormalizability.

We now know firmly that neutrinos have tiny masses, but in the minimal Standard Model there is no natural sources for such tiny masses. On the other hand, the extra heavy Z^{\prime 0} requires the extra Higgs field, the particle generating the mass. Here I propose that the previous 2+2 Higgs scenario could be a natural framework for mass generations for both the neutrinos and the extra Z^{\prime)}. These particles are classified as the "dark matter". Hopefully all the couplings to the "visible" matter are through the neutrinos and the extra Z^{\prime 0}, explaining naturally why the dark matter is so dark to see.

Even though neutrinos and antineutrinos are everywhere in the Universe, their critical importance might be overlooked, especially because that at least one species of neutrinos has the mass 0.058 eV, far larger than the cosmic thermalization temperature 1.9^\circ K. The non-zero mass makes neutrinos participate the galaxy formation from the very beginning, in view of the process of clustering. Unlike the cosmic microwave background (CMB), the cosmic background neutrinos (CB\nu) cannot be uniform. Thus, we wish to examine the questions such as: Is there some new source for neutrinos or antineutrinos, that might be detectible experimentally? Is there some new interaction of neutrinos with the visible world, that may be of numerical importance at, e.g., the ultra high energies (\ge 10^{13} eV)? One major conclusion is that, on the basis of the Standard Model, neutrinos would eventually become the {\it only} dark-matter species left in our Universe. Our Cosmos is limited in energy for various particles, electrons or photons without threshold, while protons or neutrinos having the following hurdles to overcome in reaching extreme energies such as 10^{18} eV. In an electron-rich medium, the threshold is 10^{15} eV for an ultra high energy (UHECR) proton, due to p + e^- \to n + \nu_e. On the other hand, the cosmic background neutrinos would cut off UHECR neutrinos of greater than 10^{13} eV if at least one kind of neutrinos has the mass 0.05 eV (as suggested by the experimental value of 0.058 eV), due to \nu +{\bar \nu}_{CB} \to e^- + e^+; this, plus the clustering due to mass, gives us some hope that this effect might be detectible., Comment: 17 pages

We advocate the extraterrestrial solar neutrino physics (etSNP) as a means of investigating solar neutrino physics (SNP). As we already know, the dominant and subdominant (vacuum) oscillation lengths would be approximately one kilometer and one hundred kilometers. On the other hand, we know so far that the matter-enhanced oscillations take place only in the core of the Sun. Thus, the etSNP, i.e. solar neutrino physics that could be extracted outside the Earth, would assume a special unique role. The etSNP experiments include (1) a satellite (detector) around the Earth or around the Jupiter or others (to provide the shadow, for the matter-enhanced neutrino oscillations), (2) during the Sun-Venus-Earth eclipse or similar, and (3) the chemical compositions of the geology type (as in the Jupiter or in the Venus, to study the origins of these planets). To be specific, we note that the reactions induced by the ^8B solar neutrinos, in view of the sole high energy nature (E_\nu^{max}=14.03 MeV), would be most interesting in the solar environment. Moreover, the experiments such as the chemical compositions of the geology type (on the Venus or Jupiter) and the matter-enhanced oscillations when the Sun-Venus-Earth eclipse, or the Sun-Mercury-Earth eclipse, may also be interesting.

We all know that in our family of particle physics we have three generations but still don't know why - the so-called "family problem". On other hand, in view of the masses and oscillations, the neutrinos now present some basic difficulty in the Standard Model. In this note, I propose that on top of the SU_c(3) \times SU(2) \times U(1) standard model there is an SU_f (3) extension - a simple SU_c(3) \times SU(2) \times U(1) \times SU_f (3) extended standard model. The family gauge bosons (familons) are massive through the so-called "colored" Higgs mechanism while the remaining Higgs particles are also massive. The three neutrinos, the electron-like, muon-like, and tao-like neutrinos, form the basic family triplets. Hopefully all the couplings to the "visible" matter are through the neutrinos, explaining why dark matter (25 %) is more than visible matter (5 %) in our Universe., 3 pages

The scenario that some first-order phase transitions may have taken place in the early Universe offers us one of the most intriguing and fascinating questions in cosmology. Indeed, the role played by the latent "heat" or energy released in the phase transition is highly nontrivial and may lead to some surprising, important results. In this paper, we take the wisdom that the cosmological QCD phase transition, which happened at a time between 10^(-5) sec and 10^(-4) sec or at the temperature of about 150 MeV and accounts for confinement of quarks and gluons to within hadrons, would be of first order. To get the essence out of the scenario, it is sufficient to approximate the true QCD vacuum as one of degenerate theta-vacua and when necessary we try to model it effectively via a complex scalar field with spontaneous symmetry breaking. We examine how and when "pasted" or "patched" domain walls are formed, how long such walls evolve in the long run, and we believe that the significant portion of dark matter could be accounted for in terms of such domain-wall structure and its remnants. Of course, the cosmological QCD phase transition happened in the way such that the false vacua associated with baryons and many other color-singlet objects did not disappear (that is, using the bag-model language, there are bags of radius 1.0 fermi for the baryons) - but the amount of the energy remained in the false vacua is negligible. The latent energy released due to the conversion of the false vacua to the true vacua, in the form of "pasted" or "patched" domain walls in the short run and their numerous evolved objects, should make the concept of the "radiation-dominated" epoch, or of the "matter-dominated" epoch to be re-examined., Comment: 16 pages, 1 figure

The gluon and quark condensates and their temperature dependence are investigated within QCD premises. The input for the former is a gauge invariant $gg$ kernel made up of the direct (D), exchange (X) and contact(C) QCD interactions in the lowest order, but with the perturbative propagator $k^{-2}$ replaced by a `non-perturbative $k^{-4}$ form obtained via two differentiations: $ \mu^2 \partial_m^2 (m^2+k^2)^{-1}$, ($\mu$ a scale parameter), and then setting $m=0$, to simulate linear confinement. Similarly for the input $q{\bar q}$ kernel the gluon propagator is replaced by the above $k^{-4}$ form. With these `linear' simulations, the respective condensates are obtained by `looping' up the gluon and quark lines in the standard manner. Using Dimensional regularization (DR), the necessary integrals yield the condensates plus temperature corrections, with a common scale parameter $\mu$ for both. For gluons the exact result is $$ = {36\mu^4}\pi^{-3}\alpha_s(\mu^2)[2-\gamma - 4\pi^2 T^2/(3\mu^2)]$$. Evaluation of the quark condensate is preceded by an approximate solution of the SDE for the mass function $m(p)$, giving a recursive formula, with convergence achieved at the third iteration. Setting the scale parameter $\mu$ equal to the universal Regge slope $1 GeV^2$, the gluon and quark condensates at T=0 are found to be $0.586 Gev^4$ and $(240-260 MeV)^3$ respectively, in fair accord with QCD sum rule values. Next, the temperature corrections (of order $-T^2$ for both condensates) is determined via finite-temperature field theory a la Matsubara. Keywords: Gluon Condensate, mass tensor, gauge invariance, linear confinement, finite-temperature, contour-closing. PACS: 11.15.Tk ; 12.38.Lg ; 13.20.Cz, Comment: 13 pages (LaTeX) including 2 figures

Isospin symmetry breaking in the quark condensates, $< \bar dd> \not= < \bar uu>$, is a fundamental parameter in both the QCD sum rule studies and the chiral perturbation theory. In this article, we apply the QCD sum rule method to treat the hyperon mass difference ${1\over 2}(m_{��^-}+m_{��^0})-m_{��^+}$ in order to obtain a reasonable estimate on such isospin symmetry breaking parameter $��$ defined as $(< \bar dd>-< \bar uu>)/ < \bar uu>$. Note that the electromagnetic contributions to the particular mass difference are expected to cancel almost completely. Using the light-quark mass difference $m_d-m_u=4\pm 1$ MeV and the experimental data ${1\over 2}(m_{��^-}+m_{��^0})-m_{��^+}$$=5.62\pm 0.13$ MeV, we obtain $��= -0.011\pm 0.001$, a value which is slightly larger than the commonly adopted value and is of smaller uncertainty., 10 pages, 2 figures, Latex

We calculate the on-shell $��^0$-$��$ mixing parameter $��$ with the method of QCD sum rule. Our result is $��(m^2_{��^0}) =(-)(0.5\pm 0.1)$MeV. The electromagnetic interaction is not included.

The method of QCD sum rules in the presence of external elctromagnetic fields is used to calculate the $��$ magnetic moment $��_{��^-}$ and $��^0$-$��$ transition magnetic moment $��_{��^0��}$, with the susceptibilities obtained previously from the study of octet baryon magnetic moments. The results $��_{��^-}=-1.92��_N$ and $��_{��^0��}=1.5��_N$ are in good agreement with the recent experimental data.

We use QCD spectral sum rules to extract the Sigma_c and Lambda_c magnetic moments. The elctromagnetic field is treated as the external field. We adopt the value of the susceptibility chi=-4.5 GeV^{-2}, which is determined from an overall analysis of the octet baryon magnetic moments. Our result for Sigma_c is in agreement with the quark model prediction, while slight deviation exists from the Lambda_c., Comment: Latex file, two postscript figures

In the presence of the nontrivial QCD ground state or vacuum, nonlocal condensates are used to characterize the quark or gluon propagator, or other Green functions of higher order. In this paper, we wish to show that, by taking the large $N_c$ limit (with $N_c$ the number of color) in treating higher-order condensates, a closed set of coupled differential equations may be derived for nonlocal condensates. As a specific example, the leading-order equations for the nonlocal condensates appearing in the quark propagator are derived and explicit solutions are obtained. Some applications of our analytical results are briefly discussed., Comment: 13 pages, plain TeX, MIT-CTP-2606

The method of QCD sum rules in the presence of the external electromagnetic $F_{\mu\nu}$ field is used to analyze radiative decays of charmed or bottomed mesons such as $D^{\ast}\to D\gamma$ and $B^{\ast}\to B\gamma$, with the susceptibilities obtained previously from the study of baryon magnetic moments. Our predictions on $D^{\ast}$ decays agree very well with the experimental data. There are differences among the various theoretical predictions on $B^{\ast}$ decays but the data are not yet available., Comment: 11 pages, LateX