Present studies in physics assume that elementary particles are the building blocks of all matter, and that they are zero-dimensional objects which do not occupy space. The new I-Theory predicts that elementary partic...Present studies in physics assume that elementary particles are the building blocks of all matter, and that they are zero-dimensional objects which do not occupy space. The new I-Theory predicts that elementary particles do indeed have a substructure, three dimensions, and occupy space, being composed of fundamental particles called I-particles. In this article we identify the substructural pattern of elementary particles and define the quanta of energy that form each elementary particle. We demonstrate that the substructure comprises two classes of quanta which we call “attraction quanta” and “repulsion quanta”. We create a model that defines the rest-mass energy of each elementary particle and can predict new particles. Lastly, in order to incorporate this knowledge into the contemporary models of science, a revised periodic table is proposed.展开更多
Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix...Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected.展开更多
One of the biggest unsolved problems in physics is the particle masses of all elementary particles which cannot be calculated accurately and predicted theoretically. In this paper, the unsolved problem of the particle...One of the biggest unsolved problems in physics is the particle masses of all elementary particles which cannot be calculated accurately and predicted theoretically. In this paper, the unsolved problem of the particle masses is solved by the accurate mass formulas which calculate accurately and predict theoretically the particle masses of all leptons, quarks, gauge bosons, the Higgs boson, and cosmic rays (the knees-ankles-toe) by using only five known constants: the number (seven) of the extra spatial dimensions in the eleven-dimensional membrane, the mass of electron, the masses of Z and W bosons, and the fine structure constant. The calculated masses are in excellent agreements with the observed masses. For examples, the calculated masses of muon, top quark, pion, neutron, and the Higgs boson are 105.55 MeV, 175.4 GeV, 139.54 MeV, 939.43 MeV, and 126 GeV, respectively, in excellent agreements with the observed 105.65 MeV, 173.3 GeV, 139.57 MeV, 939.27 MeV, and 126 GeV, respectively. The mass formulas also calculate accurately the masses of the new particle at 750 GeV from the LHC and the new light boson at 17 MeV. The theoretical base of the accurate mass formulas is the periodic table of elementary particles. As the periodic table of elements is derived from atomic orbitals, the periodic table of elementary particles is derived from the seven principal mass dimensional orbitals and seven auxiliary mass dimensional orbitals. All elementary particles including leptons, quarks, gauge bosons, the Higgs boson, and cosmic rays can be placed in the periodic table of elementary particles. The periodic table of elementary particles is based on the theory of everything as the computer simulation model of physical reality consisting of the mathematical computation, digital representation and selective retention components. The computer simulation model of physical reality provides the seven principal mass dimensional orbitals and seven auxiliary mass dimensional orbitals for the periodic table of elementary particles.展开更多
This paper aims at solving several open questions in current neutrino physics: the neutrino mass hierarchy, the Dirac CP violating phase, the absolute mass of neutrinos, the nature of neutrinos (Dirac or Majorana), th...This paper aims at solving several open questions in current neutrino physics: the neutrino mass hierarchy, the Dirac CP violating phase, the absolute mass of neutrinos, the nature of neutrinos (Dirac or Majorana), the Majorana matrix and the absolute value of the effective Majorana neutrino mass. In the research presented in this paper, we have shown that the precise definition of the mass splittings between neutrino mass eigenstates, done in the latest analysis of experimental data, can be of crucial importance for defining the nature of neutrino mass hierarchy. The Standard Model has three generations of fundamental matter particles. Three generations of the charged lepton mass show a hierarchical structure: m<sub>τ</sub> > m<sub>μ</sub> > m<sub>e</sub>. Owing to that, there is a belief and it is considered that neutrinos may follow such hierarchical structure. In our calculations, we have also included the latest data obtained, based on the processing of measurement results, which showed that even with such data, obtained results favor the normal neutrino mass hierarchy. As for the individual neutrino mass calculated in this paper, in today’s neutrino physics it is only known that neutrino mass scale is bounded only from above, and both the Dirac and the Majorana character of neutrinos are compatible with all observations. Among some of the questions resolved in this paper, which are related to the properties of neutrinos, a positive answer was also given to the question of whether light neutrinos are self-conjugate particles or not.展开更多
As part of a recent analysis of exclusive two-photon production of W＋W- pairs at the LHC, the CMS experiment used di-lepton data to obtain an ＂effective＂ photon-photon luminosity. We show how the CMS analysis on th...As part of a recent analysis of exclusive two-photon production of W＋W- pairs at the LHC, the CMS experiment used di-lepton data to obtain an ＂effective＂ photon-photon luminosity. We show how the CMS analysis on their 8 TeV data, along with some assumptions about the likelihood for events in which the proton breaks up to pass the selection criteria, can be used to significantly constrain the photon parton distribution functions, such as those from the CTEQ, MRST, and NNPDF collaborations. We compare the data with predictions using these photon distributions, as well as the new LUXqed photon distribution. We study the impact of including these data on the NNPDF2.3QED, NNPDF3.0QED and CT14QEDinc fits. We find that these data place a useful and complementary cross-check on the photon distribution, which is consistent with the LUXqed prediction while suggesting that the NNPDF photon error band should be significantly reduced. Additionally, we propose a simple model for describing the two-photon production of W^＋W^- at the LHC. Using this model, we constrain the number of inelastic photons that remain after the experimental cuts are applied.展开更多
The empirical rule for calculation of electric charges of the elementary particles is offered. The given rule contains two parameters: full number of colors Nc of which color of the given particle is formed and a colo...The empirical rule for calculation of electric charges of the elementary particles is offered. The given rule contains two parameters: full number of colors Nc of which color of the given particle is formed and a color index L - number of colors which the given particle possesses. The offered rule allows calculating electric charges of all elementary particles - leptons, quarks and intermediate vector bosons.展开更多
Based on the thesis that baryons including protons and neutrons are Yang-Mills magnetic monopoles which the author has previously developed and which has been confirmed by over half a dozen empirically-accurate predic...Based on the thesis that baryons including protons and neutrons are Yang-Mills magnetic monopoles which the author has previously developed and which has been confirmed by over half a dozen empirically-accurate predictions, we develop a GUT that is rooted in the SU(4) subgroups for the proton/electron and neutron/neutrino which were used as the basis for these predictions. The SU(8) GUT group so-developed leads following three stages of symmetry breaking to all known phenomenology including a neutrino that behaves differently from other fermions, lepto-quark separation, replication of fermions into exactly three generations, the Cabibbo mixing of those generations, weak interactions which are left-chiral, and all four of the gravitational, strong, weak, and electromagnetic interactions. The next steps based on this development will be to calculate the masses and energies associated with the vacuum terms of the Lagrangian, to see if additional empirical confirmations can be achieved, especially for the proton and neutron and the fermion masses.展开更多
A novel model of charged leptons is presented, which contains two basics hypotheses. The first hypothesis is that the Yukawa coupling between Higgs field and charged leptons is the weak interaction, the Higgs field is...A novel model of charged leptons is presented, which contains two basics hypotheses. The first hypothesis is that the Yukawa coupling between Higgs field and charged leptons is the weak interaction, the Higgs field is a scalar intermediate boson which changes the chirality of charged leptons in the weak interaction. The other hypothesis is that the flavor eigenstates of charged leptons are the superposition states of left-handed and right-handed elementary Weyl spinors before the electroweak symmetry breaking. According to this model, the Yukawa coupling constants between Higgs field and three generations of charged leptons are considered to be a universal constant, and the difference of the masses of different charged leptons is due to the different left-right mixing angles of their flavor eigenstates.展开更多
The BABAR experiment has now completed data taking and with an integrated luminosity of 531 fb^-1 of e^＋e^- collision data has recorded some 480 million tau-pair events. Various studies of suppressed, rare and forbid...The BABAR experiment has now completed data taking and with an integrated luminosity of 531 fb^-1 of e^＋e^- collision data has recorded some 480 million tau-pair events. Various studies of suppressed, rare and forbidden decays of the tau have been conducted, including searches for high-multiplicity decays, for second-class hadronic weak currents, and for lepton-flavour violation.展开更多
In this paper,we investigate the production of a pair of doubly charged leptons associated with a gauge boson V(γ or Z) at future linear colliders via e^+e^-and γγ collisions.The numerical results show that the pos...In this paper,we investigate the production of a pair of doubly charged leptons associated with a gauge boson V(γ or Z) at future linear colliders via e^+e^-and γγ collisions.The numerical results show that the possible signals of the doubly charged leptons may be detected via the processes e^+e~→VX^(++)X^(--)and γγ→VX^(++)X^(--)at future ILC or CLIC experiments.展开更多
The standard model is a successful theory but is lacking a mechanism for neutrino mass generation as well as a solution to the naturalness problem.In the models that are proposed to simultaneously solve the two proble...The standard model is a successful theory but is lacking a mechanism for neutrino mass generation as well as a solution to the naturalness problem.In the models that are proposed to simultaneously solve the two problems,heavy Majorana neutrinos and top partners are usually predicted to lead to a new decay mode of the top partner mediated by the heavy Majorana neutrinos:T→b W^+→b l^+l^+qq^1.In this paper,we will study the observability of such a new signature via the pair production process of a top partner pp→TT→2 b+l^±l^±+4 j in a model independent way.By performing Monte Carlo simulations,we present the 2σexclusion limits of the top partner mass and mixing parameters at the HL-LHC.展开更多
The spin-charge-family theory is a kind of the Kaluza-Klein theories, but with two kinds of the spin connection fields, which are the gauge fields of the two kinds of spins. The SO(13,1) representation of one kind of ...The spin-charge-family theory is a kind of the Kaluza-Klein theories, but with two kinds of the spin connection fields, which are the gauge fields of the two kinds of spins. The SO(13,1) representation of one kind of spins manifests in d = (3 + 1) all the properties of family members as assumed by the standard model;the second kind of spins explains the appearance of families. The gauge fields of the first kind, carrying the space index m = (0,...,3), manifest in d = (3 + 1) all the vector gauge fields assumed by the standard model. The gauge fields of both kinds of spins, which carry the space index (7, 8) gaining at the electroweak break nonzero vacuum expectation values, manifest in d = (3 + 1) as scalar fields with the properties of the Higgs scalar of the standard model with respect to the weak and the hyper charge ( and , respectively), while they carry additional quantum numbers in adjoint representations, offering correspondingly the explanation for the scalar Higgs and the Yukawa couplings, predicting the fourth family and the existence of several scalar fields. The paper 1) explains why in this theory the gauge fields are with the scalar index s = (5,6,7,8) doublets with respect to the weak and the hyper charge, while they are with respect to all the other charges in the adjoint representations;2) demonstrates that the spin connection fields manifest as the Kaluza-Klein vector gauge fields, which arise from the vielbeins;and 3) explains the role of the vielbeins and of both kinds of the spin connection fields.展开更多
The (extremely efficient) standard model of the elementary particles and fields makes several assumptions, which call for explanations. Any theory offering next step beyond the standard model must explain at least the...The (extremely efficient) standard model of the elementary particles and fields makes several assumptions, which call for explanations. Any theory offering next step beyond the standard model must explain at least the existence and properties of families and their members and correspondingly the existence of the scalar Higgs and the Yukawa couplings, which in this model take care of masses of fermions and weak bosons and influence the decaying properties of families. The spin-charge-family theory [1-11] is offering a possible explanation for the assumptions of the standard model—for the appearance of families and their members (for the charges of a family members), for the gauge fields, for the scalar fields—interpreting the standard model as its low energy effective manifestation. The spin-charge-family theory predicts at the low energy regime two decoupled groups of four families of quarks and leptons. The predicted fourth family waits to be observed, while the stable fifth family is the candidate to form the dark matter. In this paper properties of families are analysed. The appearance of several scalar fields, all in the bosonic (adjoint) representations with respect to the family groups, while they are doublets with respect to the weak charge, is presented, their properties discussed, it is explained how these scalar fields can effectively be interpreted as the standard model Higgs and the Yukawa couplings. The spin-charge-family theory predicts that there are no supersymmetric partners of the observed fermions and bosons.展开更多
Based on the space spherical symmetry of 3-dimensional and the translational symmetry of time and the uncertainty principle, a 4-dimensional space-time cylinder model of quarks and leptons is established. With this mo...Based on the space spherical symmetry of 3-dimensional and the translational symmetry of time and the uncertainty principle, a 4-dimensional space-time cylinder model of quarks and leptons is established. With this model, equations of the special relativity can be extended more perfectly, thereby achieving a unity of the special relativity and quantum mechanics in deeper level. New equations can not only interpret issues explained by old equations but also solve several important pending problems. For example, a formula to strictly calculate the coefficient ξ of Lorentz invariance violation (LIV) is derived, to above 4 × 1019 eV UHECR protons the calculated |ξ| -30, although there is the LIV effect it is too weak to change the GZK cutoff, which is consistent with observations of HiRes and Auger;Also, a relation formula between the Hubble constant and several basic constants is derived, thus theoretically calculated H0 = 70.937 km·s-1·Mpc-1, which is well consistent with the final observation result of HST Key Project. In addition, an unusual effect predicted by new equations can be experimentally tested in the electron storage ring;a preliminary experiment result has hinted its signs of existence.展开更多
文摘Present studies in physics assume that elementary particles are the building blocks of all matter, and that they are zero-dimensional objects which do not occupy space. The new I-Theory predicts that elementary particles do indeed have a substructure, three dimensions, and occupy space, being composed of fundamental particles called I-particles. In this article we identify the substructural pattern of elementary particles and define the quanta of energy that form each elementary particle. We demonstrate that the substructure comprises two classes of quanta which we call “attraction quanta” and “repulsion quanta”. We create a model that defines the rest-mass energy of each elementary particle and can predict new particles. Lastly, in order to incorporate this knowledge into the contemporary models of science, a revised periodic table is proposed.
文摘Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected.
文摘One of the biggest unsolved problems in physics is the particle masses of all elementary particles which cannot be calculated accurately and predicted theoretically. In this paper, the unsolved problem of the particle masses is solved by the accurate mass formulas which calculate accurately and predict theoretically the particle masses of all leptons, quarks, gauge bosons, the Higgs boson, and cosmic rays (the knees-ankles-toe) by using only five known constants: the number (seven) of the extra spatial dimensions in the eleven-dimensional membrane, the mass of electron, the masses of Z and W bosons, and the fine structure constant. The calculated masses are in excellent agreements with the observed masses. For examples, the calculated masses of muon, top quark, pion, neutron, and the Higgs boson are 105.55 MeV, 175.4 GeV, 139.54 MeV, 939.43 MeV, and 126 GeV, respectively, in excellent agreements with the observed 105.65 MeV, 173.3 GeV, 139.57 MeV, 939.27 MeV, and 126 GeV, respectively. The mass formulas also calculate accurately the masses of the new particle at 750 GeV from the LHC and the new light boson at 17 MeV. The theoretical base of the accurate mass formulas is the periodic table of elementary particles. As the periodic table of elements is derived from atomic orbitals, the periodic table of elementary particles is derived from the seven principal mass dimensional orbitals and seven auxiliary mass dimensional orbitals. All elementary particles including leptons, quarks, gauge bosons, the Higgs boson, and cosmic rays can be placed in the periodic table of elementary particles. The periodic table of elementary particles is based on the theory of everything as the computer simulation model of physical reality consisting of the mathematical computation, digital representation and selective retention components. The computer simulation model of physical reality provides the seven principal mass dimensional orbitals and seven auxiliary mass dimensional orbitals for the periodic table of elementary particles.
文摘This paper aims at solving several open questions in current neutrino physics: the neutrino mass hierarchy, the Dirac CP violating phase, the absolute mass of neutrinos, the nature of neutrinos (Dirac or Majorana), the Majorana matrix and the absolute value of the effective Majorana neutrino mass. In the research presented in this paper, we have shown that the precise definition of the mass splittings between neutrino mass eigenstates, done in the latest analysis of experimental data, can be of crucial importance for defining the nature of neutrino mass hierarchy. The Standard Model has three generations of fundamental matter particles. Three generations of the charged lepton mass show a hierarchical structure: m<sub>τ</sub> > m<sub>μ</sub> > m<sub>e</sub>. Owing to that, there is a belief and it is considered that neutrinos may follow such hierarchical structure. In our calculations, we have also included the latest data obtained, based on the processing of measurement results, which showed that even with such data, obtained results favor the normal neutrino mass hierarchy. As for the individual neutrino mass calculated in this paper, in today’s neutrino physics it is only known that neutrino mass scale is bounded only from above, and both the Dirac and the Majorana character of neutrinos are compatible with all observations. Among some of the questions resolved in this paper, which are related to the properties of neutrinos, a positive answer was also given to the question of whether light neutrinos are self-conjugate particles or not.
基金Supported by the U.S.National Science Foundation(PHY-1417326,PHY-1719914)the National Natural Science Foundation of China(11465018)
文摘As part of a recent analysis of exclusive two-photon production of W＋W- pairs at the LHC, the CMS experiment used di-lepton data to obtain an ＂effective＂ photon-photon luminosity. We show how the CMS analysis on their 8 TeV data, along with some assumptions about the likelihood for events in which the proton breaks up to pass the selection criteria, can be used to significantly constrain the photon parton distribution functions, such as those from the CTEQ, MRST, and NNPDF collaborations. We compare the data with predictions using these photon distributions, as well as the new LUXqed photon distribution. We study the impact of including these data on the NNPDF2.3QED, NNPDF3.0QED and CT14QEDinc fits. We find that these data place a useful and complementary cross-check on the photon distribution, which is consistent with the LUXqed prediction while suggesting that the NNPDF photon error band should be significantly reduced. Additionally, we propose a simple model for describing the two-photon production of W^＋W^- at the LHC. Using this model, we constrain the number of inelastic photons that remain after the experimental cuts are applied.
文摘The empirical rule for calculation of electric charges of the elementary particles is offered. The given rule contains two parameters: full number of colors Nc of which color of the given particle is formed and a color index L - number of colors which the given particle possesses. The offered rule allows calculating electric charges of all elementary particles - leptons, quarks and intermediate vector bosons.
文摘Based on the thesis that baryons including protons and neutrons are Yang-Mills magnetic monopoles which the author has previously developed and which has been confirmed by over half a dozen empirically-accurate predictions, we develop a GUT that is rooted in the SU(4) subgroups for the proton/electron and neutron/neutrino which were used as the basis for these predictions. The SU(8) GUT group so-developed leads following three stages of symmetry breaking to all known phenomenology including a neutrino that behaves differently from other fermions, lepto-quark separation, replication of fermions into exactly three generations, the Cabibbo mixing of those generations, weak interactions which are left-chiral, and all four of the gravitational, strong, weak, and electromagnetic interactions. The next steps based on this development will be to calculate the masses and energies associated with the vacuum terms of the Lagrangian, to see if additional empirical confirmations can be achieved, especially for the proton and neutron and the fermion masses.
文摘A novel model of charged leptons is presented, which contains two basics hypotheses. The first hypothesis is that the Yukawa coupling between Higgs field and charged leptons is the weak interaction, the Higgs field is a scalar intermediate boson which changes the chirality of charged leptons in the weak interaction. The other hypothesis is that the flavor eigenstates of charged leptons are the superposition states of left-handed and right-handed elementary Weyl spinors before the electroweak symmetry breaking. According to this model, the Yukawa coupling constants between Higgs field and three generations of charged leptons are considered to be a universal constant, and the difference of the masses of different charged leptons is due to the different left-right mixing angles of their flavor eigenstates.
文摘The BABAR experiment has now completed data taking and with an integrated luminosity of 531 fb^-1 of e^＋e^- collision data has recorded some 480 million tau-pair events. Various studies of suppressed, rare and forbidden decays of the tau have been conducted, including searches for high-multiplicity decays, for second-class hadronic weak currents, and for lepton-flavour violation.
基金Supported in part by the National Natural Science Foundation of China under Grants Nos.11275088,11205023,11375248the Program for Liaoning Excellent Talents in University under Grant No.LJQ2014135
文摘In this paper,we investigate the production of a pair of doubly charged leptons associated with a gauge boson V(γ or Z) at future linear colliders via e^+e^-and γγ collisions.The numerical results show that the possible signals of the doubly charged leptons may be detected via the processes e^+e~→VX^(++)X^(--)and γγ→VX^(++)X^(--)at future ILC or CLIC experiments.
基金supported by the National Natural Science Foundation of China(NNSFC)under grant Nos.11847208 and 11705093the Jiangsu Planned Projects for Postdoctoral Research Funds under grant No.2019K197。
文摘The standard model is a successful theory but is lacking a mechanism for neutrino mass generation as well as a solution to the naturalness problem.In the models that are proposed to simultaneously solve the two problems,heavy Majorana neutrinos and top partners are usually predicted to lead to a new decay mode of the top partner mediated by the heavy Majorana neutrinos:T→b W^+→b l^+l^+qq^1.In this paper,we will study the observability of such a new signature via the pair production process of a top partner pp→TT→2 b+l^±l^±+4 j in a model independent way.By performing Monte Carlo simulations,we present the 2σexclusion limits of the top partner mass and mixing parameters at the HL-LHC.
文摘The spin-charge-family theory is a kind of the Kaluza-Klein theories, but with two kinds of the spin connection fields, which are the gauge fields of the two kinds of spins. The SO(13,1) representation of one kind of spins manifests in d = (3 + 1) all the properties of family members as assumed by the standard model;the second kind of spins explains the appearance of families. The gauge fields of the first kind, carrying the space index m = (0,...,3), manifest in d = (3 + 1) all the vector gauge fields assumed by the standard model. The gauge fields of both kinds of spins, which carry the space index (7, 8) gaining at the electroweak break nonzero vacuum expectation values, manifest in d = (3 + 1) as scalar fields with the properties of the Higgs scalar of the standard model with respect to the weak and the hyper charge ( and , respectively), while they carry additional quantum numbers in adjoint representations, offering correspondingly the explanation for the scalar Higgs and the Yukawa couplings, predicting the fourth family and the existence of several scalar fields. The paper 1) explains why in this theory the gauge fields are with the scalar index s = (5,6,7,8) doublets with respect to the weak and the hyper charge, while they are with respect to all the other charges in the adjoint representations;2) demonstrates that the spin connection fields manifest as the Kaluza-Klein vector gauge fields, which arise from the vielbeins;and 3) explains the role of the vielbeins and of both kinds of the spin connection fields.
文摘The (extremely efficient) standard model of the elementary particles and fields makes several assumptions, which call for explanations. Any theory offering next step beyond the standard model must explain at least the existence and properties of families and their members and correspondingly the existence of the scalar Higgs and the Yukawa couplings, which in this model take care of masses of fermions and weak bosons and influence the decaying properties of families. The spin-charge-family theory [1-11] is offering a possible explanation for the assumptions of the standard model—for the appearance of families and their members (for the charges of a family members), for the gauge fields, for the scalar fields—interpreting the standard model as its low energy effective manifestation. The spin-charge-family theory predicts at the low energy regime two decoupled groups of four families of quarks and leptons. The predicted fourth family waits to be observed, while the stable fifth family is the candidate to form the dark matter. In this paper properties of families are analysed. The appearance of several scalar fields, all in the bosonic (adjoint) representations with respect to the family groups, while they are doublets with respect to the weak charge, is presented, their properties discussed, it is explained how these scalar fields can effectively be interpreted as the standard model Higgs and the Yukawa couplings. The spin-charge-family theory predicts that there are no supersymmetric partners of the observed fermions and bosons.
文摘Based on the space spherical symmetry of 3-dimensional and the translational symmetry of time and the uncertainty principle, a 4-dimensional space-time cylinder model of quarks and leptons is established. With this model, equations of the special relativity can be extended more perfectly, thereby achieving a unity of the special relativity and quantum mechanics in deeper level. New equations can not only interpret issues explained by old equations but also solve several important pending problems. For example, a formula to strictly calculate the coefficient ξ of Lorentz invariance violation (LIV) is derived, to above 4 × 1019 eV UHECR protons the calculated |ξ| -30, although there is the LIV effect it is too weak to change the GZK cutoff, which is consistent with observations of HiRes and Auger;Also, a relation formula between the Hubble constant and several basic constants is derived, thus theoretically calculated H0 = 70.937 km·s-1·Mpc-1, which is well consistent with the final observation result of HST Key Project. In addition, an unusual effect predicted by new equations can be experimentally tested in the electron storage ring;a preliminary experiment result has hinted its signs of existence.
