Quark Doublet Research Articles

Z0POLE — A program to calculate the electroweak and QCD radiative corrections to e +e - → f [formula omitted] near the Z 0 resonance

We describe the program Z0POLE that evaluates the one-loop electroweak radiative corrections to the process e +e - → f f (f ≠ e -) near the Z 0 resonance. QCD corrections are included up to O (α 3 s) for light-quark doublets and up to O ( m 2 tα s) for the t-b quark doublet. The program uses a calculational strategy that is based firmly on analytic S-matrix theory. It produces results that are demonstrably exactly gauge-invariant and that can be extended to include still higher-order corrections as they become necessary and available. Calculations are performed in either the popular “on-shell” or MS renormalization schemes. The results produced are accurate to 0.5% in the on-shell scheme and somewhat better for the MS scheme. A highly modular and transparent program structure has been employed. All formulas used in the code are given in this paper or appropriate references supplied.

Phenomenology of the aspon model of CP violation.

The aspon model of spontaneous {ital CP} violation solves the strong {ital CP} problem and gives a new mechanism for weak {ital CP} violation. It predicts a vector quark doublet {ital Q} and a gauge boson {ital A}. The {ital Q{bar Q}} production at Fermilab and the Superconductive Super Collider (SSC) is calculated, production of a {ital Q{bar Q}A} final state at the SSC is computed, and signatures of {ital Q} and {ital A} are discussed.

H±→W±γandH±→W±Zin two-Higgs-doublet models: Large-fermion-mass limit

In two-Higgs-doublet models, the ${H}^{\ifmmode\pm\else\textpm\fi{}}{W}^{\ensuremath{\mp}}V$ vertex ($V=Z or \ensuremath{\gamma}$) does not occur at the tree level, but is generated at one-loop order. We derive explicit formulas for the contribution of a weak doublet of fermions ($t, b$) to the ${H}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{W}^{\ifmmode\pm\else\textpm\fi{}}Z$ amplitude in the limit of large fermion masses that appear in the internal loop. In this limit, the amplitude grows as the square of the fermion masses for ${m}_{t}\ensuremath{\ne}{m}_{b}$, and is constant if ${m}_{t}={m}_{b}$. In contrast, the ${H}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{W}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\gamma}$ amplitude approaches a constant (which depends on $\frac{{m}_{t}}{{m}_{b}}$) in the large-fermion-mass limit. Asymptotic results for the contribution of a heavy supersymmetric family are also given. The observability of ${H}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{W}^{\ifmmode\pm\else\textpm\fi{}}Z$ at a future supercollider requires either ${m}_{{H}^{\ifmmode\pm\else\textpm\fi{}}}<{m}_{t}$ and a large $t$-quark mass, or the existence of a fourth-generation nondegenerate quark doublet.

Multiple weak-boson production via gluon fusion.

We present an effective action for multiple production of longitudinally polarized $W'\mathrm{s}$ and $Z'\mathrm{s}$ via gluon fusion through a loop of a superheavy degenerate doublet of quarks. We utilize the "equivalence" of $\frac{{W}_{L}}{{Z}_{L}}$ with Goldstone bosons. Total cross sections are estimated for up to ten weak bosons at Superconducting Super Collider energies, and their validity is discussed. Our result reproduces the exact calculation of the process $\mathrm{gg}\ensuremath{\rightarrow}\mathrm{ZZ}$ in the relevant limit.

Flavor-changing decays of fourth-generation quarkonium.

We evaluate the flavor-changing neutral-current decays {ital S}({ital v{bar v}}){r arrow}{ital c{bar t}},{ital t{bar c}},{ital a{bar t}},{ital t{bar a}} of the {ital S}-wave quarkonium states formed from the {ital Q}={minus}1/3 charge {ital v} quark of a fourth-generation quark doublet ({ital a},{ital v}). Under favorable mass and mixing conditions these decay modes could occur with branching fractions of order 1%.

Production of heavy quarks from W-gluon fusion.

We show that heavy-quark production via W-italic-gluon fusion in high-energy p-italicp-italic and p-barp-italic collisions is an important source of the heavier member of an SU(2)/sub L-italic/ doublet of quarks if the mass splitting within the doublet is large. W-italic-gluon fusion exceeds the strong production of heavy quarks for mass splittings greater than 300--350 GeV at ..sqrt..s-italic = 10 TeV and 400--450 GeV at ..sqrt..s-italic = 40 TeV. An alternative way to regard W-italic-gluon fusion is as the production of the heavier quark by fusing its light partner with a W-italic boson. We use a distribution function for the light partner to show that this process gives results which agree qualitatively with W-italic-gluon fusion. We also discuss the Drell-Yan production of an SU(2)/sub L-italic/ doublet of heavy quarks via a virtual W-italic boson and corrections to this process from initial gluons. We find that at the Fermilab Tevatron energy ..sqrt..s-italic = 2 TeV, W-italic-gluon fusion exceeds the Drell-Yan production of top quarks for masses above 100 GeV.

Flavor diagonal neutral currents from extended hypercolor

We show that there are gauge fields in the extended hypercolor scenario which mix with the neutral Z field of the standard electroweak group and that their masses may be much smaller than the masses of the extended hypercolor field, which transform quarks into hyperquarks, in which case their effects may become visible in low energy experiments. We show how the low energy neutral current parameters are modified in an extended hypercolor model with one quark doublet in 3 colors and one hyperquark doublet in N′ hypercolors.

CP Violation in a Left-Right Symmetric Theory

Recently Sanda and DeshpandeJ) have shown that the Weinberg model 2 ) for two quark doublets of CP nonconservation through charged Higgs boson exchange and based on natural flavor conservation gives an unacceptably large value for the CP violation parameter E' / E, so that the model can probably be ruled out. Therefore it seems to' compel one to accept the KobayashiMaskawa mixing matrix for three quark doublets ) as a powerful candidate responsible for CP nonconservation. This mixing matrix is complex and contains a CP violation phase in itself, and hence the source of CP violation is hidden behind this assumed phase. On the other hand, the Weinberg model reduces the CP violation exclusively to the Higgs sector, allowing for the possibility that CP is a spontaneously broken symmetry. We keep this property, but we analyze, in this paper, the CP violation by the quark-Higgs-boson-interaction') of a left-right symmetric theory of the gauge group, G = SU(2hx SU(2)RX SU(3)color. We use a left-right symmetric interaction Lagrangian between Higgs bosons and quarks')

Supersymmetric SU(7) and normal b quark decay

It is pointed out that a supersymmetric version of SU(7) can accomodate normal b quark decay. The superpartners of a split Higgs multiplet (21 = H αβ ) contains the left-handed b quark doublet.

Composite Model of Quarks and Leptons with Elementary Scalars

The model in Ref.[5] is modified to include three doublets of quarks and leptons so as to recover quark-lepton symmetry. The second model is constructed from two elementary scalars and a fermion and is therefore more economical.

Do spinless constituent quarks exist?

Recent studies indicate a surprising nonrelativistic nature for the u, d, s, c, b quarks, which is suggestive of the constituent-quark viewpoint. Accordingly, we investigate the observed spectrum of elementary particles in the constituent-quark limit of small binding energies. The u, d, s, c, b quarks by themselves do not admit a rigorous constituent-quark representation, but the expanded constituent-quark basis set that we obtain from this investigation includes the u, d, s, c, b quarks as a subset. It also includes a spinless 70 MeV quark isospin doublet which echoes the conventional spin-1/2 u- and d-quark isospin doublet. Although spinless, these 70 MeV constituent quarks do not exhibit the properties of true boson states. A mathematical link between spinless and spinning quarks is provided by the relativistically spinning sphere, which serves empirically as a mechanism for the conversion of 70 MeV quantized and 140 MeV quantized spinless quark masses into similarly quantized spin-1/2 excited-state quark masses. Evidence for these characteristic quark excitations is clearly apparent in the experimental data. The constituent-quark superset that we deduce here accurately reproduces particle mass values, and it accounts for quantities such as magnetic moments and some aspects of particle lifetimes. However, in its present state of development it lacks the predictive power of the conventional set of quarks with respect to quantities such as isotopic spins and strangeness quantum numbers.

Bounds on Particle Masses in Grand Unified Theories with Four Fermion Generations

A requirement, in which coupling constants of all interactions cannot be large and the vacuum should be stable up to the unification mass scale in the grand unified theories, leads to bounds on masses of fermions and a Higgs scalar. We calculate these bounds for a model with a heavy lepton and a heavy quark doublet in the framework of the effective 5U(3)c x 5U( 2) x UO) gauge theory with a single Higgs doublet and four fermion generations. These are applied to grand unified models with 5U(5) or 50(0) in the minimal scheme.

Leptonic and hadronic corrections to mass and propagator ofW andZ bosons

Using the propagator formalism we establish more precisely the effects of fermion loops on the boson mass ratioMW2/MZ2 cos2 θ and on the energy dependence of the form factors associated to time-like or space-likeW, Z and γ exchanges. We calculate the corrections due to higher doublets of quarks including vector meson formation and to higher doublets of leptons for example a large number of neutrino types.

Quark masses and cabibbo angles in an SU(2) L×SU(2) R×U(1) gauge model with permutations symmetry

A gauge model with permutation summetry is generalized to a larger number of quark doublets ( N). The N dependence of the results is discussed.

Mass of the t-quark in SU(2) × U(1)

Using permutation symmetry for the Higgs couplings we find the quark and lepton masses to approximately satisfy m μ : m τ : m L…= m s: m b: m′ b…= m c: m t: m′ t… A more accurate calculation leads to m t ≈ 26 GeV. If there is a fourth lepton and a fourth quark doublet, we anticipate their masses to be m L∼30 GeV, m′ t∼450 GeV and m′ b∼ 100 GeV.

Weak interactions of ultra heavy fermions (II)

We discuss the weak interactions of ultra heavy fermions at low and high energy in the SU(2) L × U(1) gauge theory. Using partial-wave unitarity at high energy we establish critical fermion mass values beyond which strong couplings occur in the theory and the perturbation expansion fails. The critical masses are ( 500 √N ) GeV for quarks and ( 1.0 √N ) TeV for leptons, where N is the number of nearly degenerate SU(2) L doublets of quarks and leptons respectively. At low energies, far below their production threshold, we show that ultra heavy fermions would induce large, observable one-loop radiative corrections. One of these corrections (obtained also by Veltman) implies, using present experimental data, an upper limit of ∼700 GeV for a heavy lepton in an SU(2) L doublet with a massless neutrino.

Generalized charge symmetry and charmed particle decays

We introduce the charge symmetry operation within the c, s and p, n quark doublets and study its consequences for weak decays proceeding via the GIM current. Numerous relations between various decays are obtained. Combined with CP we find an interesting pattern of allowed and suppressed amplitudes for charmed meson and baryon processes. The results are compatible with the present meagre experimental information.

Natural suppression of symmetry violation in gauge theories: Muon- and electron-lepton-number nonconservation

We analyze the circumstances under which the violations of an approximate symmetry in a unified gauge theory of weak interactions are naturally suppressed; in particular, we investigate approximate muon- and electron-type lepton-number conservation as an example of such a symmetry. Extending earlier work, we propose a unified treatment of this symmetry together with strangeness conservation by the weak neutral current and $\mathrm{CP}$ invariance. The rate for the decay $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ is calculated for a general SU(2) \ifmmode\times\else\texttimes\fi{} U(1) gauge model. From this and a similar study of the decay $\ensuremath{\mu}\ensuremath{\rightarrow}\mathrm{ee}\overline{e}$ we derive a set of conditions which guarantees that the violation of muon- and electron-type lepton-number conservation is naturally strongly suppressed. As part of this, we compute the nondiagonal electromagnetic vertex to one-loop order for an arbitrary SU(2) \ifmmode\times\else\texttimes\fi{} U(1) gauge theory. We then focus on the phenomenological predictions of a particular gauge model with three left-handed doublets of leptons and quarks. These include the existence of charged and neutral heavy leptons and of small violations of $\ensuremath{\mu}$-$e$ universality and the relation ${G}_{F}^{\ensuremath{\beta}}sec{\ensuremath{\theta}}_{C}={G}_{F}^{\ensuremath{\mu}}$. Other muon- and electron-number-violating effects include nonvanishing rates for the decays ${K}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}e\overline{\ensuremath{\mu}}$ and ${K}_{L}\ensuremath{\rightarrow}e\overline{\ensuremath{\mu}}$ and for the reactions $\ensuremath{\mu}+N\ensuremath{\rightarrow}e+N$ and ${\ensuremath{\nu}}_{\ensuremath{\mu}}+N\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+X$.

Nonleptonic decays of charmed F meson and the existence of (c, λ) R doublet

It is shown that the analysis of decay modes of the charmed pseudoscalar meson F ± into 3π and K ±K S 0 may provide a sensitive test for the existence of a right-handed c and λ quark doublet.

Strong-coupling calculations of the hadron spectrum of quantum chromodynamics

We present calculations of the low-energy mass spectrum and matrix elements of quantum chromodynamics. We employ an isospin doublet of massless quarks and analyze the theory from the strong-coupling limit using a particularly simple lattice Hamiltonian. In the strong-coupling limit the vacuum state has exact local color symmetry, but spontaneously breaks those elements of chiral symmetry which are present in the lattice Hamiltonian. Expansions for masses ($\ensuremath{\pi},\ensuremath{\rho},\ensuremath{\omega},\ensuremath{\sigma},{A}_{1},B,f,$ and nucleon) and matrix elements ${g}_{A}$ in the reciprocal coupling constant are analytically continued to the continuum limit using Pad\'e approximants. The results are in surprisingly good agreement with experiment except for the pion mass. This single failure is traced to the lack of full chiral symmetry in the theory for large lattice spacing and the lack of significant spin-spin forces in low orders of strong-coupling perturbation theory. Higher-order calculations should resolve this problem, but a more realistic Hamiltonian suggested by renormalization-group analyses also looks promising.