Calculation of the pseudoscalar masses from a QCD effective potential

We calculate the effective two-loop potential of QCD with massive quarks in the CJT composite operator formalism. To perform the wave-function renormalization of composite operators we are lead to a condition which corresponds to the Adler-Dashen requirement in the limit of vanishing quark masses. The condition also assures absence of spontaneous breaking of parity. Pseudoscalar masses are calculated from the second derivatives of the effective potential, and a fit is obtained for quark masses m_u = 3.6 MeV, m_d = 7 MeV, m_s = 152 MeV. We also comment on consistuent quark masses and on the effect of heavy quarks.     

Fermion masses in SU(11)

Introducing several different sets of Higgs fields, possible mass spectra for the three light generations of particles in the SU(11) model of Georgi are discussed. For the u, c, t quarks there are only two possibilities: either all have masses of the same order of magnitude, or two masses are of the same order and the third is about $\text{α}{}^2\text{? 10}{}^{\mathrm{?4}}$ smaller. The corresponding masses for d,s, b quarks (and e, μ, τ leptons) are: in the first case, the masses are all same order, but a factor α or α² smaller than u, c, t. In the second case, two masses are all of the same order as the heavier top quarks, the third is smaller by a factor α. Neutrinos get small Majorana masses.     

Mass breaking in a relativistic quark model for mesons

We study symmetry breaking via quark mass differences in a relativistic quark model where mesons are built from heavy (m > 3 GeV) spin $\text{1}\text{2}$) quarks and antiquarks. The meson (squared-)mass differences are linearly related to the number of strange, charmed, etc. quarks in the mesons. We show that the previously assumed SU_n symmetry of the mesonic couplings holds, i.e., quark mass differences only show up in the masses of the external particles, not in the three meson vertex itself.     

The ferromagnetic phase of quark matter in the framework of one gluon exchange and thermodynamics with the density-temperature-dependent particle mass model

In the current work we examine the possibility of ferromagnetism phase of quark matter by using the one gluon exchange interaction and the thermodynamics with the density-temperature-dependent particle masses as well as the normal thermodynamics (with constant masses). We calculate the free energy per particle of the polarized and unpolarized states to discuss the difference between these two phases at various densities and temperatures. In our calculations we assume that the QCD coupling, α_c, is constant (the simple model) or varies with the temperature and the density (the asymptotic freedom); but we keep α_c less than one, because we intend to use the perturbation method to calculate the exchange energy. We also assume that the up and down quarks are massless and do not interact. Only the strange quarks interact with each other via the one gluon exchange interaction. The free and internal energies as well as the effective masses and the pressure are calculated at different densities and temperatures. The results are discussed and a comparison is made with those of Tatsumi. Finally it is shown that the present models do not predict any transition for the strange quark matter to its ferromagnetic phase.     

Generations of massless composite quarks and leptons

We present a QCD-like composite model in which quarks, leptons and technifermions are three-body systems made out of three kinds of massless elementary fermions t, c and w, each carrying technicolor, color and weak gauge interactions, respectively. Discrete symmetries, remnants of the U(1)_A of the original lagrangian, are responsible for the masslessness of all the quarks and leptons and give the precise meaning of the generations. The model exhibits three generations for both quarks and leptons. Small but non-zero masses of the quarks and leptons are produced by the technicolor condensate of the composite technifermions, which thereby leads to the non-trivial Cabibbo mixing. Proton decays are all forbidden at the mass scale of the QCD-like theory.     

Gluon exchange in meson spectroscopy

We discuss the spin structure ofN=L=0 andN=L=1 mesons in terms of the one-gluon exchange model with scalar confinement of quarks. SU(3)_flavour is broken by taking different masses for the quarks and the SU (3) breaking of the nonperturbed hamiltonian is shown to be very important in understanding the hyperfine splittings in the ground state mesons, including the charmed states. A fit to the experimental mass spectrum is performed for theN=L=0 andN=L=1 levels simultaneously. The spin-orbit splittings of the spectrum cannot be explained by the convential terms from gluon exchange and scalar confinement. We argue that additional terms, which break the ideal mixing pattern, have to be present. The inclusion of such a term gives a dramatic improvement in χ² and leads to an almost perfect fit to the data for masses and mixing angles.     

Meson Lagrangians in a superconductor quark model

On the basis of a effective “superconductivity”-type four-quark interaction, phenomenological Lagrangians are obtained for interactions of scalar, pseudoscalar, vector, and axial vector meson nonets. The Lagrangians include mass terms breaking chiral and U(3) invariance and corresponding to the quark masses m_u ≠ m_d ≠ m_s. It is shown that upon introducing boson fields the masses of current quarks in the initial Lagrangian are replaced by the masses of constituent quarks in the phenomenological boson Lagrangians. Estimates of these masses are presented. Electromagnetic interactions are considered, and the vector dominance model is derived. The widths of various meson decays are calculated.     

Inverse seesaw in NMSSM and 126 GeV Higgs boson

We consider extensions of the next-to-minimal supersymmetric model (NMSSM) in which the observed neutrino masses are generated through a TeV scale inverse seesaw mechanism. The new particles associated with this mechanism can have sizable couplings to the Higgs field which can yield a large contribution to the mass of the lightest CP-even Higgs boson. With this new contribution, a 126 GeV Higgs is possible along with order of 200 GeV masses for the stop quarks for a broad range of tan β. The Higgs production and decay in the diphoton channel can be enhanced due to this new contribution. It is also possible to solve the little hierarchy problem in this model without invoking a maximal value for the NMSSM trilinear coupling and without severe restrictions on the value of tan β.     

Enhancement of CP-violating phenomena at tree level due to heavy quark propagator singularities

We discuss new interesting CP-violating phenomena in scattering processes resulting from heavy quarks with masses larger than the W-mass (m _q >M _W ). Such a situation is connected with a singularity in the heavy quark propagator which, properly regularized, gives rise to measurable CP-odd effects. The observability of these CP-odd signals in the most representative Kobayashi-Maskawa (KM) models (like fourth generation model, left-right symmetric model and two Higgs doublet model) is investigated. We find that the necessary conditions for measurable CP-asymmetries imply the enlargement of the Standard Model (SM) in the generations of quarks. In addition a significant mixing between the fourth and the other generations is required.     

Triangular and <Emphasis Type="Italic">Y</Emphasis>-shaped hadrons in QCD

Gauge-invariant extended configurations are considered for the three fundamental (quarks) or adjoint (gluons) particles. For quarks, it is shown that the Y-shaped configuration is the only one possible. For adjoint sources, both Y-shaped and triangular configurations may exist. The corresponding static potentials are calculated by the method of field correlators and, in the case of baryons, shown to be consistent with the lattice simulations. For adjoint sources the potentials of Y-shaped and Δ-shaped configurations turn out to be close to each other, which leads to almost degenerate masses of 3^??3g glueballs and odderon trajectories.     

Order αs corrections to intermediate boson masses

We present the order α_s corrections to the masses of the Z and W bosons in the standard model. For the low mass quarks u, d, c and s the corrections are small and positive. Due to the Coulomb singularity which appears in the vector boson self-energy graph with one gluon exchange, we find a negative contribution from the t, b doublets.     

Weak decays of charm and quark masses

We calculate the effects of finite quark masses for the semileptonic and nonleptonic decays of charmed particles. The total lifetimes of charmed particles are not sensitive to the masses of the quarks in the final state. However the semileptonic branching ratios changes considerably. Using conventional constituent quark masses, one expect e.g. B_e(D⁺)≈ 21%. The brancing ratios and lifetimes of the charmed particles are estimated, taking into account the annihilation hypothesis.     

Glueball spectrum from N_f=2 lattice QCD study on anisotropic lattices

The lowest-lying glueballs are investigated in lattice QCD using N_f = 2 clover Wilson fermions on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion masses of mπ～938 MeV and 650 MeV. The quark mass dependence of the glueball masses has not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67)GeV at mπ～938 MeV and 650 MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of ∈_ijkTrB_iD_jB_k, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter(around 1 GeV) and compatible with the expected masses of the flavor singlet qq meson. This indicates that the operator ∈ijk TrBiDjBk and the topological charge density couple rather differently to the glueball states and qq mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.     

Using radiative corrections to bound substructure

Composite models predict the existence of excited quarks and leptons. We find bounds for the masses of possible excited leptons and for the substructure scale by using radiative corrections at theZ scale. A non-decoupling scenario arises naturally which induces upper bounds on these masses as a function of the substructure scale.     

A<Subscript>4</Subscript> model for the quark mass matrices

We propose a model for the quark masses and mixings based on an A₄ family symmetry. Three scalar SU(2) doublets form a triplet of A₄. The three left-handed-quark SU(2) doublets are also united in a triplet of A₄. The right-handed quarks are singlets of A₄. The A₄-symmetric scalar potential leads to a vacuum in which two of the three scalar SU(2) doublets have expectation values with equal moduli. Our model makes an excellent fit of the observed |V_ub/V_cb|. CP symmetry is respected in the charged gauge interactions of the quarks.     

A minimalSU(2)×U(1)×U(1) electroweak model with mirror fermions

We present a minimal extension of the standard electroweak model, which accommodates mirror fermions, based onSU(2)×U(1)×U(1). Mirror mixing happens through sterile neutrino states and induces radiative mixing for charged leptons. Quarks and mirror quarks are not mixed with each other, consistent with the suppression of flavour changing neutral currents. Higgs sector, fermion masses and neutral currents are discussed. In this scheme there can be a secondZ boson as light as 0.2TeV.     

Pion decays and the pion electromagnetic form factor in a σ-model with quarks

We study in the one-loop approximation the decays of the pion and the pion electromagnetic form factor at low q² in the framework of a σ-model with quarks. The theory has a free parameters the quark and σ masses and the results are very insensitive to their values. We get good approximation for all processes considered except for the ratio of the axial to the vector form factor that appear in the electronic radiative decay of the charged pion. The reason is probably that our model includes the pion-pion interaction only in the isoscalar s-wave at the one-loop level.     

Replication of lepton and quark fields and stability of the proton in N = 2 SUSY GUTs

We show that in N = 2 SUSY GUTs, leptons and quarks tend to combine with their mirror partners and to acquire very large masses proportional to the grand-unification mass. We solve this problem by means of a replication of lepton and quark fields. Grand-unification now associates light leptons and quarks with heavy ones of masses ? m_X or 2m_X. The latter carry a non-vanishing value of the central charge 〈Z〉 = ± m_X or ± 2m_X (which may be viewed as the fifth or sixth component of the covariant momentum). The exchanges of the grand-unification gauge bosons do not induce proton decay, and the proton is stable, in minimal N = 2 SUSY GUTs. Moreover the grand-unification mass does not get renormalized.     

A connection between ν-dimensional Yang-Mills theory and (ν−1)-dimensional,non-linear σ-models

We study non-linear σ-models and Yang-Mills theory. Yang-Mills theory on the ν-dimensional lattice ? ^v can be obtained as an integral of a product over all values of one coordinate of non-linear σ-models on ? ^v?1 in random external gauge fields. This exhibits two possible mechanisms for confinement of static quarks one of which is that clustering of certain two-point functions of those σ-models implies confinement of static quarks in the corresponding Yang-Mills theory. Clustering is proven for all one-dimensional σ-models, for theU(n) ×U(n) σ-models,n=1, 2, 3, ..., in two dimensions, and for the SU(2) × SU(2) σ-models for a large range of couplingsg ² ? O(ν). Arguments pertinent to the construction of the continuum limit are discussed. A representation of the expectation of Wilson loops in terms of expectations of random surfaces bounded by the loops is derived when the gauge group is SU(2),U(n) or O(n),n=1, 2, 3, ..., and connections to the theory of dual strings are sketched.