The top quark mass and flavour mixing in a seesaw model of quark masses

The top quark mass and the flavour mixing are studied in the context of a seesaw model of quark masses based on the gauge group SU(2)_L × SU(2)_R × U(1). Six isosinglet quarks are introduced to give rise to the mass hierarchy of ordinary quarks. In this scheme, we reexamine a mechanism for the generation of the top quark mass. It is shown that, in order to prevent the seesaw mechanism to act for the top quark, the mass parameter of its isosinglet partner must be much smaller than the breaking scale of SU(2)_R. As a result the fourth lightest up quark must have a mass of the order of the breaking scale of SU(2)_R, and a large mixing between the right-handed top quark and its singlet partner occurs. We also show that this mechanism is compatible with the mass spectrum of light quarks and their flavour mixing.     

Dynamical quark effects on light quark masses

Light quark masses are calculated in lattice QCD with two degenerate flavors of dynamical quarks. The calculations are made with improved actions with lattice spacing a = 0.22-0.11 fm. In the continuum limit we find m(M&Smacr;)(ud)(2 GeV) = 3.44(+0.14)(-0.22) MeV using the pi and rho meson masses as physical input, and m(M&Smacr;)(s)(2 GeV) = 88(+4)(-6) MeV or 90(+5)(-11) MeV with the K or straight phi meson mass as additional input. The quoted errors represent statistical and systematic combined, the latter including those from continuum and chiral extrapolations, and from renormalization factors. Compared to quenched results, two flavors of dynamical quarks reduce quark masses by about 25%.     

Light quark masses from scalar sum rules

In this work, the mass of the strange quark is calculated from QCD sum rules for the divergence of the strangeness-changing vector current. The phenomenological scalar spectral function which enters the sum rule is determined from our previous work on strangeness-changing scalar form factors [1]. For the running strange mass in the scheme, we find . Making use of this result and the light quark mass ratios obtained from chiral perturbation theory, we are also able to extract the masses of the lighter quarks and . We then obtain and . In addition, we present an updated value for the light quark condensate. Received: 18 October 2001 / Revised version: 22 January 2002 / Published online: 12 April 2002     

Constituent quark masses from modified perturbative QCD

A recently proposed modified perturbative expansion for QCD incorporating gluon condensation is employed to evaluate the quark and gluon self-energy corrections in first approximation. The results predict mass values of 1/3 of the nucleon mass for the light quarks u, d, and s and a monotonously growing variation with the current mass. The only phenomenological input is that is evaluated up to order as a function of the unique parameter C defining the modified propagator, and then C is fixed to give a current estimate of . The light quarks u and d as a result are found to be confined and the s, c, b and t ones show damped propagation modes, suggesting a model for the large differences in stability between the nucleons and the higher resonances. The above properties of quark modes diverge from the fully confinement result following from the similar gluon propagator previously considered by Munczek and Nemirovski. On the other hand, the condensate effects on the gluon self-energy furnish a tachyonic mass shell as predicted by the Fukuda analysis of gluon condensation in QCD. Received: 28 September 2001 / Revised version: 15 November 2001 / Published online: 8 February 2002     

Baryon masses in the broken chiral quark bag

We consider corrections to the baryon mass spectrum when the u and the d quarks are massive, i.e. the pion acquires its physical mass. This breaks explicitely the SU(2) chiral symmetry of the chiral quark model. We also include the massive K- and η-mesons to examine the broken SU(3) and SU(3) × SU(3) symmetries. These small corrections do improve the mass spectrum.     

Isospin violation, light quark masses, and all that

Isospin violation is driven through the light quark mass difference and electromagnetic effects. I review recent progress in extracting the light quark mass difference and tests of the chiral dynamics of Quantum Chromodynamics in various reactions involving light as well as heavy quarks.     

Flavor changing Z0 decay and the top quark

The flavor changing neutral current decay of the Z⁰ boson into charge $\text{2}\text{3}$ quarks in the standard three generation SU(2)_L × U(1) theory of electroweak interactions has been studied. This process occurs first at one-loop order, where it has been calculated without approximation. The possibility of producing the as yet undiscovered top quark by this decay has been considered. The branching ratios are extremely small, independent of the top quark mass and plausible quark mixing matrices if there are three generations, making it unlikely that the top quark will be produced by this mechanism. However, a massive fourth bottom quark could increase the rates.     

QCD sum rules with finite masses

The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections is analyzed in a systematic discussion of the IR- and UV-divergencies, leading in general to a finite number of corrections. The results are demonstrated for a system of two massless quarks and two heavy scalar quarks.We wish to thank Dr. Lech Mankiewicz for very helpful discussions. This work was supported by DFG (G. Hess program).     

Relations between the masses of the superpartners of leptons and quarks,the goldstino coupling and the neutral currents

The mass² splittings between leptons and quarks and their spin-0 partners under supersymmetry are related to the goldstino couplings. The bosonic partner of the goldstino cannot be the photon itself. But it should be, in part, a linear combination of the various neutral gauge bosons. As a result, mass relations constrain the neutral current structure of the theory. They require the existence of at least two neutral gauge bosons in addition to the photon and suggest the possibility of a universal mass² splitting between leptons and quarks and their spin-0 partners.     

Speculations on quark observation

Results of non-perturbative calculations in several models of relativistic quantum field theory lead to the concept of a stable particle whose mass is not well defined. Assuming that quarks are such particles, we propose several possible methods of quark observation.     

Neutrino emissivity from strange matter having density dependent quark masses

We have analyzed the equilibrium composition of quark matter consisting of approximately equal number of up, down and strange quarks, based upon the confinement mechanism of Fowler et al. (1981) and Plümmer et al. (1984) in which the quark masses are considered density dependent. Using this model, we calculate the neutrino emissivity rate and the neutrino mean free path in quark matter and compare the results with Iwamoto (1982). We find that the emissivity rate is a slowly increasing function of the density, while the values of mean free path are slightly on the higher side than those of Iwamoto.     

Flavour mixing and quark masses in sequential flavour dynamics

We discuss the mixing of quark flavours in sequential flavour dynamics in the case of an arbitrary number of quark generations. For n generations the dominant weak interaction mixing is described by n ? 1 mixing angles, which are computed in terms of the quark masses.     

Theories of quark confinement

It is conjectured that a non-Abelian gauge theory based on the color SU(3) group will confine quarks. Various techniques that have been applied to this question are reviewed. These include approximate methods based on strong coupling expansions of Hamiltonian and Euclidian lattice theories, instanton improvements on perturbation theory, and solutions of truncated Dyson-Schwinger equations for the gauge field propagator. Formal results based on electric-magnetic duality arguments and on the study of loop field theories are presented. Deconfinement at high temperatures, the inclusion of light quarks, and a possible reconciliation with a hypothetical discovery of free quarks are discussed.     

Quark masses

Because of the observed similarity between leptons and quarks, any lepton mass formula can be applied with proper modification to estimate the quark masses. In this work such an application of Rosen's (1978) lepton mass formula is attempted.     

On mass spectrum in SQCD. Unequal quark masses

The N = 1 SQCD with N _c colors and two types of light quarks, N _l flavors with the smaller mass m _l and N _h = N _F − N _l flavors with the larger mass m _h , N _c < N _F < 3N _c , 0 < m _l ≤ m _h ≪ Λ _Q , is considered within the dynamical scenario in which quarks can form a coherent colorless diquark condensate 〈$ \bar Q $ \bar Q Q〉. There are several phase states at different values of the parameters r = m _l /m _h . N _l , and N _F . Properties of these phases and their mass spectra are described.     

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.     

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.     

Moments of heavy quark correlators with two masses: Exact mass dependence to three loops

We compute moments of non-diagonal correlators with two massive quarks. Results are obtained where no restriction on the ratio of the masses is assumed. Both analytical and numerical methods are applied in order to evaluate the two-scale master integrals at three loops. We provide explicit results for the latter which are useful for other calculations. As a by-product we obtain results for the electroweak ρ parameter up to three loops which can be applied to a fourth generation of quarks with arbitrary masses.