Supersymmetric U（1） Gange Field Theory with Massive Gauge Field

A new mechanism to introduce the mass of U(1) gauge field in supersymmetric U(1) gauge theory is discussed.The model has the strict local U(1) gauge symmetry and supersymmetry.Because we introduce two vector superfields simultaneously,the model contains a massive U(1) gauge field as well as a massless U(1) gauge field.     

A U（4） QCD Model Using Generalized Yang-Mills Theory

Generalized Yang-Mills theory has a covariant derivative which contains both vector and pseudoscalar gauge bosons. Based on this theory, we construct a U（4） strong interaction model. By using this U（4） generalized Yang-Mills model, we obtain that mesons can be realized as the colorless pseudoscalar gauge bosons. We also obtain a gauge potential solution which can be used to explain the asymptotic behavior and color confinement.     

What can a heavy U(1)_(B-L) Z' boson do to the muon(g-2)_μ anomaly and to a new Higgs boson mass?

The minimal U(1)_(B-L) extension of the Standard Model(B-L-SM) offers an explanation for neutrino mass generation via a seesaw mechanism;it also offers two new physics states,namely an extra Higgs boson and a new Z' gauge boson.The emergence of a second Higgs particle as well as a new Z' gauge boson,both linked to the breaking of a local U(1)_(B-L) symmetry,makes the B-L-SM rather constrained by direct searches in Large Hadron Collider(LHC) experiments.We investigate the phenomenological status of the B-L-SM by confronting the new physics predictions with the LHC and electroweak precision data.Taking into account the current bounds from direct LHC searches,we demonstrate that the prediction for the muon(g-2)_μ anomaly in the B-L-SM yields at most a contribution of approximately 8.9 × 10~(-12),which represents a tension of 3.28 standard deviations,with the current1σ uncertainty,by means of a Z' boson if its mass is in the range of 6.3 to 6.5 TeV,within the reach of future LHC runs.This means that the B-L-SM,with heavy yet allowed Z' boson mass range,in practice,does not resolve the tension between the observed anomaly in the muon(g-2)_μ and the theoretical prediction in the Standard Model.Such a heavy Z' boson also implies that the minimal value for the new Higgs mass is of the order of 400 GeV.     

ELECTROWEAK MODEL AND CONSTRAINTS ON NEW PHYSICS

<正>10.1.Introduction The standard model of the electroweak interactions(SM)[1]is based on the gauge group SU(2)×U(l),with gauge bosons W(μ~i),i=1,2,3,and B_μfor the SU(2)and U(l)factors,respectively,and the corresponding gauge coupling constants g and g'.The left-handed fermion fields of the i~(th)fermion family transform as doubletsΨ_i=(v_i/e_i)and(u_i/d'i)under SU(2),where d'_i=∑_jV_(ij)d_j,and V is the Cabibbo-Kobayashi-Maskawa mixing matrix.[Constraints on V and tests of universality are discussed in Ref.2 and in the Section on"The CKM Quark-Mixing Matrix".The extension of the formalism to allow an analogous leptonic mixing matrix is discussed in the Section     

The B-L+xY Model and the Higgs-strahlung Processes at a Collider

The gauge extension of the standard model with the U(1)_(B-L+xY) symmetry predicts the existence of a light gauge boson Z' with small couplings to ordinary fermions. We discuss its contributions to the muon anomalous magnetic moment a_μ. Taking account of the constraints on the relevant free parameters, we further calculate the contributions of the light gauge boson Z' to the Higgs-strahlung processes e~+e~-→ ZH and e~+e~-→ Z'H.     

A unified model with a generalized gauge symmetry and its cosmological implications

A unified model is based on a generalized gauge symmetry with groups [SU3c ]color×(SU2×U1)×[U1b×U1l].It implies that all interactions should preserve conservation laws of baryon number, lepton number, and electric charge, etc. The baryonic U1 b, leptonic U1 l and color SU3 c gauge transformations are generalized to involve nonintegrable phase factors. One has gauge invariant fourth-order equations for massless gauge fields, which leads to linear potentials in the [U1b ×U1l] and color [SU3c ] sectors. We discuss possible cosmological implications of the new baryonic gauge field. It can produce a very small constant repulsive force between two baryon galaxies(or between two anti-baryon galaxies), where the baryon force can overcome the gravitational force at very large distances and leads to an accelerated cosmic expansion. Based on conservation laws in the unified model, we discuss a simple rotating dumbbell universe with equal amounts of matter and anti-matter, which may be pictured as two gigantic rotating clusters of galaxies. Within the gigantic baryonic cluster, a galaxy will have an approximately linearly accelerated expansion due to the effective force of constant density of all baryonic matter. The same expansion happens in the gigantic anti-baryonic cluster. Physical implications of the generalized gauge symmetry on charmonium confining potentials due to new SU3 c field equations, frequency shift of distant supernovae Ia and their experimental tests are discussed.     

Quark confinement,new cosmic expansion and general Yang-Mills symmetry

We discuss a unified model of quark confinement and new cosmic expansion with linear potentials based on a general(SU_3)_(color)×(U_1)baryon symmetry. The phase functions in the usual gauge transformations are generalized to new ‘action integrals'. The general Yang-Mills transformations have group properties and reduce to usual gauge transformations in special cases. Both quarks and ‘gauge bosons' are permanently confined by linear potentials. In this unified model of particle-cosmology, physics in the largest cosmos and that in the smallest quark system appear to both be dictated by the general Yang-Mills symmetry and characterized by a universal length. The basic force between two baryons is independent of distance. However, the cosmic repulsive force exerted on a baryonic supernova by a uniform sphere of galaxies is proportional to the distance from the center of the sphere. The new general YangMills field may give a field-theoretic explanation of the accelerated cosmic expansion. The prediction could be tested experimentally by measuring the frequency shifts of supernovae at different distances.     

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.     

Benchmarking the simplest slave-particle theory with Hubbard dimer

Slave-particle method is a powerful tool to tackle the correlation effect in quantum many-body physics. Although it has been successfully used to comprehend various intriguing problems, such as Mott metal–insulator transition and Kondo effect, there is still no convincing theory so far on the availability and limitation of this method. The abuse of slave-particle method may lead to wrong physics. As the simplest slave-particle method, Z2 slave spin, which is widely applied to many strongly correlated problems, is highly accessible and researchable. In this work, we will uncover the nature of the Z2 slave-spin method by studying a two-site Hubbard model. After exploring aspects of properties of this toy model, we make a comparative analysis of the results obtained by three methods:(i) slave-spin method on mean-field level,(ii) slave-spin method with gauge constraint, and(iii) the exact solution as a benchmark. We find that, protected by the particle–hole symmetry, the slave-spin mean-field method can recover the static properties of ground state exactly at half filling. Furthermore, in the parameter space where both U and T are small enough, the slave-spin mean-field method is also reliable in calculating the dynamic and thermal dynamic properties. However, when U or T is considerably large, the mean-field approximation gives ill-defined behaviors, which result from the unphysical states in the enlarged Hilbert space.These findings lead to our conclusion that the accuracy of slave particle can be guaranteed if we can exclude all unphysical states by enforcing gauge constraints. Our work demonstrates the promising prospect of slave-particle method in studying complex strongly correlated models with specific symmetry or in certain parameter space.     

Ξ_(bb) and Ω_(bbb) molecular states

Using the vector exchange interaction in the local hidden gauge approach,which in the light quark sector generates the chiral Lagrangians and has produced realistic results for ?_c,Ξ_c,Ξ_b and the hidden charm pentaquark states,we study the meson-baryon interactions in the coupled channels that lead to the Ξ_(bb) and ?_(bbb) excited states of the molecular type.We obtain seven states of the Ξ_(bb) type with energies between 10408 and 10869 MeV,and one ?_(bbb) state at 15212 MeV.     

Fermion masses generated by radiative corrections in aSU(2) L ×SU(2) R ×U(1) B-L model

A new model based on aSU(2) ^R ×SU(2) ^L ×U(1) ^B-L gauge symmetry group is presented. Fermion masses are generated by radiative corrections.     

Global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on bipartite lattices

In this paper the global symmetry of the Hubbard model on a bipartite lattice is found to be larger than SO(4). The model is one of the most studied many-particle quantum problems, yet except in one dimension it has no exact solution, so that there remain many open questions about its properties. Symmetry plays an important role in physics and often can be used to extract useful information on unsolved non-perturbative quantum problems. Specifically, here it is found that for on-site interaction U ≠ 0 the local SU(2) × SU(2) × U(1) gauge symmetry of the Hubbard model on a bipartite lattice with N_a^D sites and vanishing transfer integral t = 0 can be lifted to a global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with t > 0. (Examples of a bipartite lattice are the D-dimensional cubic lattices of lattice constant a and edge length L = N_aa for which D = 1, 2, 3,... in the number N_a^D of sites.) The generator of the new found hidden independent charge global U(1) symmetry, which is not related to the ordinary U(1) gauge subgroup of electromagnetism, is one half the rotated-electron number of singly occupied sites operator. Although addition of chemical-potential and magnetic-field operator terms to the model Hamiltonian lowers its symmetry, such terms commute with it. Therefore, its 4^N_aD energy eigenstates refer to representations of the new found global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry. Consistently, we find that for the Hubbard model on a bipartite lattice the number of independent representations of the group SO(3) × SO(3) × U(1) equals the Hilbert-space dimension 4^N_aD. It is confirmed elsewhere that the new found symmetry has important physical consequences.     

Quark-lepton symmetry and B − L as the U(1) generator of the electroweak symmetry group

We seek an interpretation of the U(1) part of the electroweak symmetry group in terms of the quantum number B ? L. We show that the electroweak symmetry group, for which U(1) can be interpreted as a local B ? L symmetry, is the left-right symmetry group SU(2)_L × SU(2)_R × U(1)_L+R. The equating of U_L+R(1) to U_B?L(1) should lead to physical consequences which are not shared by standard gauge theory. B ? L may also help to explain the inversion of quark and lepton mass spectra.     

Spinor-inverted solution to thirring model and its generalization to U(n) symmetry

Using the properties of massless free Fermi fields in (1-1) dimensions, it is shown that the spinor inverted form of Klaiber's operator solution to Thirring model is also a scale-invariant solution of the model. But unlike the former it admits a nonvanishing SU(n) current coupling in the generalization of the model to include U(n) symmetry. The value of this coupling constant is fixed and equals Dashen-Frishman number $\text{?4π}\text{(n + 1)}$. The general form of the 2m-point function is given and operates product expansions are exhibited in terms of composite local operators. Scale dimensions of all the bilinear and quadrilinear local operators with U(n) symmetry are computed and are found to depend on n. However, different parts of a composite local operator belonging to different irreducible U(n) representations have the same dimension.     

Aspects of UA (1) breaking in the Nambu and Jona-Lasinio model

The six-quark instanton induced ’t Hooft interaction, which breaks the unwanted U_A (1) symmetry of QCD, is a source of perturbative corrections to the leading order result formed by the four-quark forces with the U_L (3) × U_R (3) chiral symmetry. A detailed quantitative calculation is carried out to bosonize the model by the functional integral method. We concentrate our efforts on finding ways to integrate out the auxiliary bosonic variables. The functional integral over these variables cannot be evaluated exactly. We show that the modified stationary phase approach leads to a resummation within the perturbative series and calculate the integral in the “two-loop” approximation. The result is a correction to the effective mesonic Lagrangian which may be important for the low-energy spectrum and dynamics of the scalar and pseudoscalar nonets.     

The conflict between natural flavor conservation of Higgs couplings and cabibbo mixing in SU(2)L × U(1)

The general problem of conservation of strangeness and other quark flavors by the exchange of several neutral Higgs mesons is investigated in SU(2)_L × U(1). We find that the horizontal symmetries necessary to enforce this conservation conflict with the known Cabibbo mixing. In particular, if the quarks form an irreducible representation of the horizontal symmetry, the mixing angles are all trivial (i.e., 0 or $\text{π}\text{2}$); if they form a reducible representation, it is possible to have some nontrivial mixing angles, but only if there are several unmixed generations of quarks with exactly the same relative pattern of masses and mixings.     

Deformation of nuclei as a function of angular momentum in the U(6) ⊃ SU(3) model

In the framework of a hybrid rotational model, proposed recently by Moshinsky as a consequence of a comparison between the Gneuss and Greiner extension of the Bohr and Mottelson model and the interacting boson model, we study the shape of nuclei by calculating the average of the expectation value of the square of the deformation parameter β with respect to the rotational states with the same angular momentum belonging to a given irreducible representation of SU(3). This work generalises to three dimensions the corresponding analysis carried out in two dimensions by Chacón, Moshinsky, and Vanagas. We use the canonical chain for U(3), i.e., the chain U(6) ? U(3) ? U(2) ? U(1), to obtain an analytical formula for the quantity studied. We bring out the overall stretching effect of the angular momentum on the shape of nuclei. The influence of other parameters, such as the boson number and the irreducible representation of SU(3), is also studied.     

Interacting boson-fermion model of collective states II. Boson-fermion symmetries connected with the U(5) limit

The boson-fermion symmetries, which are connected with the U^(B)(5) limit of the interacting boson model are discussed. These symmetries arise when the bosons have U(5) symmetry and the fermions occupy a single-particle orbit with spin $\text{j =}\text{1}\text{2}$ (Spin(3) limit), $\text{j =}\text{3}\text{2}$ (Spin(5) limit), or $\text{j =}\text{3}\text{2}\text{,}\text{5}\text{2}$ (U^(B+F)(5) ? U^(F)(2) limit). Closed expressions for energy spectra, electromagnetic transition rates, static moments, and (one and two) nucleon transfer reaction intensities are derived.     

A supersymmetricSU(5)×U(1) model with natural gauge hierarchy

We present a supersymmetricSU(5)×U(1) model. This model has the following features. The gauge hierarchy is naturally generated by the quadratically divergent nature of the Fayet-IliopoulosD term. TheSU(5)×U(1) gauge symmetry breaks uniquely intoSU(3) _W ×SU(2) _c ×U(1) _y at an energy scale of 10^17–18GeV. The non-vanishing vacuum expectation value of an auxiliary field component ofU(1) gauge vector multiplet induces the breaking ofSU(2) _W ×U(1) _y . It gives a mass of 10^2–3GeV to scalar quarks and scalar leptons at the tree level. The renormalization group analysis shows that the color fine structure constant α _C (M _W ) becomes somewhat small and the Weinberg angle sin²θ _W (M _W ) somewhat too large in a simple version of the model.     

Thermal expansion and magnetostriction in Pr(n+2)(n+1)Nin(n−1)+2Sin(n+1) compounds

Thermal expansion and magnetostriction of members of a homologous series of compounds based on the alloy series Pr_(n+2)(n+1)Ni_n(n−1)+2Si_n(n+1) have been measured. The crystal structures of these compounds are closely interrelated because they form trigonal prismatic columns in which the number of trigonal prisms that form the base of the trigonal columns is determined by the value of n in the chemical formula. Two compositions were investigated, Pr₅Ni₂Si₃ and Pr₁₅Ni₇Si₁₀, corresponding to n=3$n=3$ and n=4,$n=4,$ respectively. The results were analyzed and used to determine the location of magnetic phase transitions by calculating the magnetic contribution to thermal expansion using the Gruneisen–Debye theory. This allowed more precise determination of the magnetic transition temperatures than could be achieved using the total thermal expansion. The results show two phase transitions in each material, one corresponding to the Curie temperature and the other at a lower temperature exhibiting characteristics of a spin reorientation transition.