Narrow Results

The additive quark model is one of the simplest and oldest models for the description of soft processes at high energies, and it still works. We present here a review of this model and verify the rules of quark combinatorics following from it in hadronic Z⁰ decays.

Hadronic spectroscopy can be introduced to students and developed rather far without requiring SU(N) flavor symmetry. In such a "minimalist" presentation, we are naturally led to comment and clarify the concept of the "generalized" Pauli principle.

The use of the binary tetrahedral group (T′) as flavor symmetry is discussed. I emphasize the CKM quark and PMNS neutrino mixings. I present a novel formula for the Cabibbo angle.

Life at Caltech with Murray Gell-Mann in the early 1960's is remembered. Our different paths to quarks, leading to different views of their reality, are described.

Early work on the compositeness of hadrons is reviewed, with emphasis on Quarks and Confinement.

The exciting findings and activities in particle physics in the 50's and 60's will be discussed from an experimentalist's viewpoint. Particular emphasis will be placed on the description of several crucial discoveries (including the omega minus) and on the remarkable insight, guidance, and major contributions of Murray Gell-Mann to the understanding of the symmetry of hadrons which led to the development of the standard model of the strong interactions.

I give a brief review of advances in the strong interaction theory. This talk was delivered at the Conference in honor of Murray Gell-Mann's 80th birthday, 24–26 February 2010, Singapore.

This public lecture was presented at the National University of Singapore on the 5th of March, 2013. It was organized by the Institute of Advanced Studies as part of the Distinguished Public Lecture series.

Soon after the postulation of quarks, it was suggested that they interact via gluons, but direct experimental evidence was lacking for over a decade. In 1976, Mary Gaillard, Graham Ross and the author suggested searching for the gluon via 3-jet events due to gluon bremsstrahlung in e⁺ e^- collisions. Following our suggestion, the gluon was discovered at DESY in 1979 by TASSO and the other experiments at the PETRA collider.

The experimental discovery of the first Yang–Mills non-Abelian gauge particle — the gluon — in the spring of 1979 is summarized, together with some of the subsequent developments, including the role of the gluon in the recent discovery of the Higgs particle.

The quark model emerged from the Gell-Mann–Ne'eman flavor SU(3) symmetry. Its development, in the context of strong interactions, took place in a heuristic theoretical framework, referred to as the Bootstrap Era. Setting the background for the dominant ideas in strong interaction of the early 1960s, we outline some aspects of the constituent quark model. An independent theoretical development was the emergence of hadron duality in 1967, leading to a realization of the Bootstrap idea by relating hadron resonances (in the s-channel) with Regge pole trajectories (in t- and u-channels). The synthesis of duality with the quark-model has been achieved by duality diagrams, serving as a conceptual framework for discussing many aspects of hadron dynamics toward the end of the 1960s.

A composite model of quarks and bosons is proposed in which a spin 1/2 isospin doublet ψ is the basic building block of quarks and bosons in the standard model. The ψ has two components v and w with charges and Q = 0, respectively, that combine to form the three generations of colored quark flavors. A strong force described by a triplet of massless gluons binds the constituents called geminis. The confining constituent non-Abelian SU(2)_C field theory is called constituent dynamics with a confining energy scale Λ_CD. The constituent dynamics condensate spontaneously breaks the electroweak symmetry SU(2)_L×U(1)_Y→U(1)_EM and a triplet of Nambu–Goldstone bosons make the gauge bosons W^± and Z⁰ massive, while retaining a massless photon. A global custodial SU(2)_L×SU(2)_R symmetry guarantees that the symmetry breaking in the weak interaction sector agrees with electroweak data. The non-Abelian SU(2)_C color dynamics satisfies asymptotic freedom, which resolves the gauge and Higgs mass hierarchy problems and makes the model ultraviolet complete. The composite constituent dynamics model can realize a SU(3)_C×SU(2)_L×U(1)_Y electroweak and strong interaction model that satisfies the naturalness principle. The three generations of colorless quarks α and β with charges Q = +1e and Q = 0, respectively, which are predicted to exist in the composite model can form bound states which can be identified with the spectrum of exotic mesons.

In this paper, we report an analysis of partial momentum fractions carried by quarks and gluons in six alternative phenomenological models of proton structure function valid in limited small $x$ regions: $x_{a_i}\le x\le x_{b_i}$, $i=1$ to 6; the limits being determined by phenomenological range of validity in each model. Since the physics of small $x$ is not completely understood at this point, we have considered both self-similarity-based as well as QCD-based models. The procedure by which one can determine the applicability ranges in $x$ and $Q^2$ of the models is presented. We find that while the self-similarity-based models with linear rise in $Q^2$ has limited phenomenological ranges of validity, an improved version with linear rise in $log{Q}^2$ has a wider phenomenological range. We then compare the partial momentum fractions in all the small $x$ models. Our analysis implies that the role of small $x$ sea quarks in calculating the second moments of parton distribution is minor one. We have also made a comprehensive comparison of all the phenomenological models considered to the available perturbative QCD, lattice QCD as well as Ads/QCD results.

Transverse momentum dependent (TMD) parton distributions, also referred to as unintegrated parton distribution functions (UPDFs), are produced via the Kimber–Martin–Ryskin (KMR) prescription. The GJR08 set of parton distribution functions (PDFs) which are based on the valence-like distributions is used, at the leading order (LO) and the next-to-leading order (NLO) approximations, as inputs of the KMR formalism. The general and the relative behaviors of the generated TMD PDFs at LO and NLO and their ratios in a wide range of the transverse momentum values, i.e. $k_t^2=10$, $10^2$, $10^4$ and $10^8{\mathrm{\text{GeV}}}^2$ are investigated. It is shown that the properties of the parent valence-like PDFs are imprinted on the daughter TMD PDFs. Imposing the angular ordering constraint (AOC) leads to the dynamical variable limits on the integrals which in turn increase the contributions from the lower scales at lower $k_t^2$. The results are compared with our previous studies based on the MSTW2008 input PDFs and it is shown that the present calculation gives flatter TMD PDFs. Finally, a comparison of longitudinal structure function $(F_L)$ is made by using the produced TMD PDFs and those that were generated through the MSTW2008-LO PDF from our previous work and the corresponding data from H1 and ZEUS collaborations and a reasonable agreement is found.

This study is devoted to investigate the implementation of machine learning methodologies in the prediction of Quark–anti-Quark bound state spectrum. Predictions are produced by using variety of machine learning (ML) approaches, such as ridge regression, random forest regression, linear regression and K-nearest neighbors regression methods. The forecasts are then evaluated and contrasted in order to determine the optimal performance. Furthermore, systematic comparison of the considered ML methods in terms of percentage of performance is done. Each of the four strategies yielded comparable results. With accuracy of 99%, the ridge regression model exhibited the highest level of predictive performance.

The fermionic properties of quarks and leptons are determined by their weak interactions, the ultimate sources of which are their nonzero weak charges, and they are distinguished from each other by the strong interaction, which applies to quarks but not to leptons. There is no obvious reason why electric charge should be relevant to the distinction, but quarks are all required, in the conventional picture, to have electric charges, while leptons are not. It is as though the strong interaction requires electric charge to be present even though it is defined to be electric charge independent. It is proposed that the solution of this mystery lies in subtle aspects of the SU(3) × SU(2) × U(1) symmetry breaking of the three interactions and is a consequence of the way in which this symmetry breaking arises.

Pauli’s principle is generalized for the case of the Z₃ grading replacing the usual Z₂ grading, leading to ternary commutation relations and ternary algebras. Invariant cubic forms on such algebras are introduced, with the SL(2,C) arising naturally as their invariance group in the case of lowest dimension, with two generators only. The wave equation generalizing the Dirac operator for the Z₃-graded case is introduced, whose diagonalization leads to a third-order equation. The solutions of this equation cannot propagate because their exponents contain a non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry.