Top Quark

The Standard Model Architecture and Interactions

©  2011 Claude Michael Cassano

    Based on my 1984 linearization of the Klein-Gordon equations, potential functions generalizations of the electric and magnetic field strengths form a basis from which a compound model simply constructs the leptons; the simple differences between the quarks and leptons; how the quarks arose from the leptons; why there are these two types of fermions; and why there are precisely three generations for each of these types. The most elementary particle interactions classify the interactions between strong and weak, and further still between the W and Z type of weak interactions. Two simple conservation requirements give rise to all the fundamental particle interactions, and describe the structure of the weak intermediate envelopes. Further, a simple charge function determines the charge of every object. Further still, the only free assignable parameters for the entire model are four mass constants for each fermion generation.
        This presentation is essentially a summary of my book: "a Mathematical Preon Foundation for the Standard Model"; but starting from the different standpoint of my Helmholtzian operator matrix product, rather than my constructive algebras (developed primarily in "Reality is a Mathematical Model" and "The Weighted Matrix Product").
    Through some ingenious mathematical manipulations, it can be shown that in free space, the thus defined  E  and  B  (generalizations of the electric and magnetic field strengths) also satisfy the Klein-Gordon equations, so have a particle-nature.
    Identifying a particle-nature member R  as either an  E  or a  B  ; each of these members satisfies the Klein-Gordon equation, but only really do so as three-vectors with three components or triplets. And, each bag of triplets must be triplets or triplets of triplets or triplets of triplets of triplets, and so on (i.e.: 3 to the n of triplets).
    The simplest , and thus, most fundamental members are triplets. The next most fundamental is triplets of triplets.
    These will be considered, here.
    Denoting a triplet of triplets by:  S sub R ≡ (R sub1,R sub2,R sub3)
  is a 3 matrix.

    Then we can write: 
                  S sub E ≡ (E sub1,E sub2,E sub3)  , and  S sub B ≡ (B sub1,B sub2,B sub3).
    The leptons and all the colors and flavors of quarks correspond to these
        L's  ,  Λ's  , and  Q's  ; by the associations given, here. 

    The table shown,  may be considered a replica of the one found everywhere, including Wikipedia (except that the quark colors  are explicitly delineated).

    Shown, are examples of hadrons (second order compositions): mesons: and baryons.

    The charge function acts as a linear function on any linear combination of  S sub R  matrix objects, independant of column/generation,.
    The function for mass is a little more complicated, but for the first and second order objects is shown, here.
        As mentioned earlier, this has been a summary of my book, "a Mathematical Preon Foundation for the Standard Model", available on Kindle through amazon.com. Find links to all my books at:

https://sites.google.com/site/themathematicalnatureofreality/config/pagetemplates/books .

We present a search for electroweak production of single top quarks in the electron+jets and muon+jets decay channels. The measurements use ~90 pb^-1 of data from Run 1 of the Fermilab Tevatron collider, collected at 1.8 TeV with the DZero detector between 1992 and 1995. We use events that include a tagging muon, implying the presence of a b jet, to set an upper limit at the 95% confidence level on the cross section for the s-channel process ppbar->tb+X of 39 pb. The upper limit for the t-channel process ppbar->tqb+X is 58 pb.

ABSTRACT We report measurements of the polarization of W bosons from top-quark decays using 2.7 fb^-1 of ppbar collisions collected by the CDF II detector. Assuming a top-quark mass of 175 GeV/c^2, three measurements are performed. A simultaneous measurement of the fraction of longitudinal (f_0) and right-handed (f_+) W bosons yields the model-independent results f_0 = 0.88 \pm 0.11 (stat) \pm 0.06 (syst) and f_+ = -0.15 \pm 0.07 (stat) \pm 0.06 (syst) with a correlation coefficient of -0.59. A measurement of f_0 (f_+) constraining f_+ (f_0) to its standard model value of 0.0 (0.7) yields f_0 = 0.70 \pm 0.07 (stat) \pm 0.04 (syst) (f_+ = -0.01 \pm 0.02 (stat) \pm 0.05 (syst)). All these results are consistent with standard model expectations.

Two energies, which are measured in opposite directions, and we consider them as quarks are actually two different kinetic energy of a single proton, the first in the direction of its movement, and the second in the opposite direction.
Quarks are actually locked (confinement) in proton, as is clear from the individual tables.

u and d quarks in the QCD theory really  mass much smaller than 1/3 the mass of a proton.
mass of a proton
1.672621777(74)×10−27  kg[1]
938.272046(21) MeV/c2 [1]
Up quark:  2.3 MeV/c2
Down quark:  4.8 MeV/c2
c quark:  1275 MeV/c2
s quark: 95 MeV/c2
b quark: 4180 MeV/c2
t  quark: 173070 MeV/c2
Why are discovered by quarks in pairs?
u,d   
c,s 
t,b
We show that each particle is accompanied by his twin.
A pair of quarks of one  generation = one speed of proton

We calculate the present expansion of our Universe endowed with relict colored objects - quarks and gluons - that survived hadronization either as isolated islands of quark-gluon "nuggets", or spread uniformly in the Universe. In the first scenario, the QNs can play the role of dark matter. In the second scenario, we demonstrate that uniform colored objects can play the role of dark energy providing the late-time accelerating expansion of the Universe.

CMS is a general purpose experiment, designed to study the physics of pp collisions at 14 TeV at the Large Hadron Collider (LHC). It currently involves more than 2000 physicists from more than 150 institutes and 37 countries. The LHC will provide extraordinary opportunities for particle physics based on its unprecedented collision energy and luminosity when it begins operation in 2007. The principal aim of this report is to present the strategy of CMS to explore the rich physics programme offered by the LHC. This ...

We review the present status of QCD corrections to weak decays beyond the leading logarithmic approximation including particle-antiparticle mixing and rare and CP violating decays. After presenting the basic formalism for these calculations we discuss in detail the effective hamiltonians for all decays for which the next-to-leading corrections are known. Subsequently, we present the phenomenological implications of these calculations. In particular we update the values of various parameters and we incorporate new information on mt in view of the recent top quark discovery. One of the central issues in our review are the theoretical uncertainties related to renormalization scale ambiguities which are substantially reduced by including next-to-leading order corrections. The impact of this theoretical improvement on the determination of the Cabibbo-Kobayashi-Maskawa matrix is then illustrated in

We investigate grand unified theories (GUTs) in scenarios where electroweak (EW) symmetry breaking is triggered by a light composite Higgs, arising as a Nambu-Goldstone boson from a strongly interacting sector. The evolution of the standard model (SM) gauge couplings can be predicted at leading order, if the global symmetry of the composite sector is a simple group $ \mathcal{G} $ that contains the SM gauge group. It was noticed that, if the right-handed top quark is also composite, precision gauge unification can be achieved. We build minimal consistent models for a composite sector with these properties, thus demonstrating how composite GUTs may represent an alternative to supersymmetric GUTs. Taking into account the new contributions to the EW precision parameters, we compute the Higgs effective potential and prove that it realizes consistently EW symmetry breaking with little fine-tuning. The $ \mathcal{G} $ group structure and the requirement of proton stability determine the nature of the light composite states accompanying the Higgs and the top quark: a coloured triplet scalar and several vector-like fermions with exotic quantum numbers. We analyse the signatures of these composite partners at hadron colliders: distinctive final states contain multiple top and bottom quarks, either alone or accompanied by a heavy stable charged particle, or by missing transverse energy.

This report describes a measurement of the top quark mass in $\ppbar$ collisions at a center of mass energy of 1.8 TeV. The data sample was collected with the CDF detector during the 1992--95 collider run at the Fermilab Tevatron, and corresponds to an integrated luminosity of 106 \pb. Candidate $t\bar{t}$ events in the ``lepton+jets'' decay channel provide our most precise measurement of the top quark mass. For each event a top mass is determined by using energy and momentum constraints on the production of the $\ttbar$ pair and its subsequent decay. A likelihood fit to the distribution of reconstructed masses in the data sample gives a top mass in the lepton+jets channel of $176.1\pm 5.1 (stat.)\pm 5.3 (syst.) \gevcc$. Combining this result with measurements from the ``all-hadronic'' and ``dilepton'' decay topologies yields a top mass of $176.1\pm 6.6 \gevcc$.

We present a measurement of the inclusive top quark pair production cross section in pp¯ collisions at s=1.96TeV utilizing data corresponding to an integrated luminosity of 5.3fb-1 collected with the D0 detector at the Fermilab Tevatron Collider. We consider final states containing one high-pT isolated electron or muon and at least two jets, and we perform three analyses: one exploiting

We introduce a toy model implementing the proposal of using a custodial symmetry to protect the Z b_L bbar_L coupling from large corrections. This "doublet-extended standard model" adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an O(4) x U(1)_X = SU(2)_L x SU(2)_R x P_LR x U(1)_X symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged SU(2)_L x U(1)_Y electroweak symmetry by a Dirac mass M for the new doublet; adjusting the value of M allows us to explore the range of possibilities between the O(4)-symmetric (M to 0) and standard-model-like (M to infinity) limits.