Quark Triplets Research Articles

Heavy vector-like quarks decaying to exotic scalars: a case study with triplets

We investigate the pair production of a vector-like quark triplet with hypercharge 5/3 decaying into top quark and a complex scalar triplet with hypercharge 1 at the LHC. This novel scenario, featuring particles with exotic charges — two quarks with charge 8/3 and 5/3 and a scalar with charge 2 — serves as a unique window to models based on the framework of partial compositeness, where these particles naturally emerge as bound states around the TeV scale. Leveraging on the LHC data we establish exclusion limits on the masses of the vector-like quark and the scalar triplet. Subsequently, we design an analysis strategy aimed at improving sensitivity in the region which is still allowed. Our analysis focuses on two specific regions in the parameter space: the first entails a large mass gap between the vector-like quarks and the scalars, so that the vector-like quarks can decay into the scalars; the second involves a small mass gap, such that this decay is forbidden. To simplify the parameter space, both vector-like quarks and scalars are assumed to be degenerate or almost degenerate within the triplets, such that chain decays between fermions and scalars are suppressed. As a result, we found that final states characterized by a same-sign lepton pair, multiple jets, and high net transverse momentum (i.e. effective mass) will play a pivotal role to unveil this model and, more in general, models characterised by multiple vector-like quarks around the same mass scale during the high luminosity LHC phase.

Extended Z3-graded Lorentz symmetry and quark chromodynamics

We propose a modification of standard QCD description of the color triplet of quarks by introducing a 12-component color generalization of Dirac spinor, with built-in [Formula: see text] grading playing an important algebraic role in quark confinement. In the “color Dirac equations” the [Formula: see text] color symmetry is entangled with the [Formula: see text]-graded generalization of Lorentz symmetry, containing three 6-parameter sectors related by [Formula: see text]-graded maps. The generalized Lorentz covariance requires simultaneous presence of 12 color Dirac multiplets, which lead to the description of all internal symmetries of quarks: besides [Formula: see text], the flavor symmetries and three quark families. We also discuss the generalized gauge fields and show how the Standard Model content appears naturally due to the overall [Formula: see text] symmetry.

Z3-graded colour Dirac equations for quarks, confinement and generalized Lorentz symmetries

We propose a modification of standard QCD description of the colour triplet of quarks by introducing a 12-component colour generalization of Dirac spinor, with built-in Z3 grading playing an important algebraic role in quark confinement. In “colour Dirac equations” the SU(3) colour symmetry is entangled with the Z3-graded generalization of Lorentz symmetry, containing three 6-parameter sectors related by Z3 maps. The generalized Lorentz covariance requires simultaneous presence of 12 colour Dirac multiplets, which lead to the description of all internal symmetries of quarks: besides SU(3)×SU(2)×U(1), the flavour symmetries and three quark families.

Alternative [SU(3)]4 model of leptonic color and dark matter

The alternative [SU(3)]4 model of leptonic color and dark matter is discussed. It unifies at MU∼1014 GeV and has the low-energy subgroup SU(3)q×SU(2)l×SU(2)L×SU(2)R×U(1)X with (u,h)R instead of (u,d)R as doublets under SU(2)R. It has the built-in global U(1) dark symmetry which is generalized B–L. In analogy to SU(3)q quark triplets, it has SU(2)l hemion doublets which have half-integral charges and are confined by SU(2)l gauge bosons (stickons). In analogy to quarkonia, their vector bound states (hemionia) are uniquely suited for exploration at a future e−e+ collider.

Jet Hadronization via Recombination of Parton Showers in Vacuum and in Medium

We introduce a hadronization algorithm for jet parton showers based on a hybrid approach involving recombination of quarks and fragmentation of strings. The algorithm can be applied to parton showers from a shower Monte Carlo generator at the end of their perturbative evolution. The algorithm forces gluon decays and then evaluates the recombination probabilities for quark-antiquark pairs into mesons and (anti)quark triplets into (anti)baryons. We employ a Wigner phase space formulation based on the assumption of harmonic oscillator wave functions for stable hadrons and resonances. Partons too isolated in phase space to find recombination partners are connected by QCD strings to other quarks. Fragmentation of those remnant strings and the decay of all hadron resonances complete the hadronization process. We find that our model applied to parton showers from the PYTHIA Monte Carlo event generator leads to results very similar to pure Lund string fragmentation. We suggest that our algorithm can be readily generalized to jets embedded in quark-gluon plasma by adding sampled thermal partons from the phase transition hypersurface. The recombination of thermal partons and shower partons leads to an enhancement of pions and protons at intermediate momentum at both RHIC and LHC.

On the Color-Singlet States in Many-Quark Model with the su(4)-Algebraic Structure. I

In the modified Bonn quark model in which quark-pairing and particle-hole interactions are included, color-singlet states are examined in addition to the color-neutral quark-triplet state by a method of boson realization. The region which consists of single-quarks, quark pairs and quark triplets is analyzed.

Annihilation, Strangeness, and QGP

At the nuclear and subnuclear level, the matter is made of nucleons bound in nuclei and each nucleon is formed by a stable triplet of non-strange quarks. In ordinary phenomena quarks cannot be extracted singularly from nucleons; to indicate this fact, they are called confined in nucleons. Unstable non-strange or strange quark triplets and quark-antiquark doublets are produced in hadronic collisions and in antinucleon–nucleon annihilations and also in these cases quarks appear to be confined in systems of two or three quarks. However, it was predicted that ordinary nuclear matter could undergo transitions to excited phases and, in extreme cases, could be transformed into blobs of individual quarks deconfined into plasma, the quark-gluon plasma (QGP). The excited hadron phases are supposed to be generalized systems of mesons and baryons of increasing mass and volume, where, anyway, quarks are confined. These new states of the matter should occur when the attained baryon density is so high that nucleons become very close and fuse into each other; or when the baryon density is low but a hot and high enough meson density is attained [1]. Usually, the phase transitions are studied assuming that the excited blobs behave like thermodynamic systems. This means that they should consist of a large number of particles (thousands or more), which for some time are in equilibrium, that is with definite temperature, pressure, energy, and entropy density [2]; but also non-equilibrium conditions are considered [3]. In this contest, the transition from a hadronic gas to QGP is characterized by a critical temperature Tc which, according to various authors, is expected to be in the interval 150–200 MeV. For instance, a lattice QCD calculation [4] predicts for Tc a value of ∼173 MeV corresponding to an energy density Ed ∼ 700 MeV/fm3, about five times the energy density of the ordinary nuclei (0.14 nucleons/fm3 = 130 MeV/fm3).

Note on Many-Quark Model with su(4) Algebraic Structure

In a many-quark model developed in our previous paper where two-body color pairing and particle-hole type interactions are active, the exact energy eigenstates are re-formed with physically clearer expressions than those derived in our previous paper. By using the re-formed energy eigenstates, two types of the eigenstates in which the pairing correlation and the quark triplet formation separately appear definitely, are unified and this model can be treated for both the strong color correlations and the quark triplet formations.

Errata

In a many-quark model developed in our previous paper where two-body color pairing and particle-hole type interactions are active, the exact energy eigenstates are re-formed with physically clearer expressions than those derived in our previous paper. By using the re-formed energy eigenstates, two types of the eigenstates in which the pairing correlation and the quark triplet formation separately appear definitely, are unified and this model can be treated for both the strong color correlations and the quark triplet formations.

Decay widths of lowest massive Regge excitations of open strings

With the advent of the LHC there is widespread interest in the discovery potential for physics beyond the standard model. In TeV-scale open string theory, the new physics can be manifest in the excitation and decay of new resonant structures, corresponding to Regge recurrences of standard model particles. An essential input for the prediction of invariant mass spectra of the decay products (which could serve to identify the resonance as a string excitation) are the partial and total widths of the decay products. We present a parameter-free calculation of these widths for the first Regge recurrence of the SU ( 3 ) gluon octet, of the U ( 1 ) gauge boson which accompanies gluons in D-brane constructions, and of the quark triplet.

From Sakata Model to Goldberg-Ne'eman Quarks and Nambu QCD Phenomenology and “Right" and “Wrong" Experiments

The basic theoretical milestones were the Sakata SU(3) symmetry, the Goldberg-Ne'eman composite model with SU(3) triplets having baryon number (1/3) and the Nambu color gauge Lagrangian. The transition was led in right and wrong directions by interpreted by phenomenology. A experiment on $\bar p p$ annihilation at rest showed that the Sakata model predictions disagreed with experiment. A bad experiment prevented the use of the Goldberg-Ne'eman triplet model to predict the existence and masses of the of the $\Xi^*$ and $\Omega^-$. More revealed the existence and mass of the $\Xi^*$ and the $\Omega^-$ and the absence of positive strangeness baryon resonances, thus confirming the tenfold way. Further good experiments revealed the existence of the vector meson nonet, SU(3) breaking with singlet-octet mixing and the suppression of the $\phi \to \rho \pi$ decay. These led to the quark triplet model. The paradox of peculiar statistics then arose as the $\Delta^{++}$ and $\Omega^-$ contained three identical spin-1/2 fermions coupled symmetrically to spin (3/2). This led to color and the Nambu QCD. The book Lie Groups for Pedestrians used the Sakata model with the name sakaton for the $pn\Lambda$ triplet to teach the algebra of SU(3) to particle physicists in the U.S. and Europe who knew no group theory. The Sakata model had a renaissance in hypernuclear physics in the 1970's.

Boson–fermion and baryon mapping: Construction of collective subspaces. III. Application of the baryon mapping to many-baryon states

The theory developed in Paper I of this series is applied to the general case of a system consisting of colorfree quark triplets, whose quantum numbers are chosen as collective trifermion indices. The appropriate mapping technique to be used here is the baryon mapping. It is demonstrated that the original multiquark states can be exactly represented by states of colorfree ideal baryons. Besides, collective extended images are derived for a class of fermionic operators leaving the collective fermion space invariant.

Hadronic numerics with quarks of f flavors

According to the ‘‘standard model’’ of particles and fields, hadrons can be formed from a triplet of quarks (baryons), each of which may have any one of f flavors (d, u, s, c, b, etc.), or from a quark–antiquark pair (mesons) each one of which may have any flavor. Some numerics of flavor and electric charge content of baryons and mesons are presented. Multiplicity of symmetry types of baryons based on these simple numerical results is calculated without direct appeal to group theory in the hope that the dimensionality of hadron multiplets that contain the building blocks of normal matter will become more widely understood.

The nucleus as a condensate of collective quark triplets

Starting from an effective hamiltonian for multi-quark systems, we propose a mapping of the quark degrees of freedom onto collective colorless triplets of constituent quarks. We end up with an effective hamiltonian for nucleons, which can be treated by traditional nuclear many-body approximations. In this way, we can describe subnucleonic degrees of freedom in the quantum liquid of nucleons.

Confinement of quarks and gluons in gauge quantum field theory

A SU(3)-gauge quantum field theory with a quark triplet, an antiquark triplet, and a self-conjugate gluon octet as basic fields is investigated. In virtue of a nontrivial coupling between the representation of the translation group and the SU(3)-color charge of the basic fields it is proved: (i) The basic quark, antiquark, and gluon fields are confined. (ii) Every state vector of the physical Hilbert space is a SU(3)-color singlet state. (iii) Poincaré invariance holds in the physical Hilbert space. These results rest on a nonstandard transformation law of the basic fields with respect to translations. Its meaning within the frame of classical Lagrangian field theory for chromodynamics is investigated.

Contributions to the Short Range Nuclear Force from the Quark-Pion Interaction in the Chiral Bag Model

The contributions to the short range nuclear force from the quark-pion interaction in the Chiral Bag Model have been investigated. The antisymmetric wave functions for the physical channels of and are obtained in terms of the group classification and fractional parentage reduction. Assuming six quarks in a spherical bag, the separation of the quark triplets is described in terms of two orbitals—left and right which are composed of the quark S and P states. The results show that the contribution to the short range nuclear force from one pion exchange of the quarks is repulsive about 150 MeV.

Interaction-line descriptions of fields

The property producing a field has a qualitative and a quantitative aspect. The former may appear as1, 2, 3,..., n possibilities in the source particles. Interaction lines representing the field must reflect these possibilities. Thus, one expects there to be1, 2, 3,..., n respective kinds of lines joining particles. The different lines interact with each other as well as with the particles at their ends. For gravitational fields,n is1; for electromagnetic fields,n is2; for chromodynamic fieldsn is3. Rest mass can be created by itself out of energy. But a positive-negative pair is the minimum possibility with electric charges, and a color-anticolor pair with quarks. A triplet of quarks or antiquarks, together with the appropriate neutrino, could also arise out of energy.

Gauge field propagator and the number of fermion fields

The structure of the transverse gluon propagator $D$ of massless quantum chromodynamics is considered in the Landau gauge. The essential differences in the weak-coupling limit $g\ensuremath{\rightarrow}0$ for $\frac{{\ensuremath{\gamma}}_{0}}{{\ensuremath{\beta}}_{0}}>0$ and $\frac{{\ensuremath{\gamma}}_{0}}{{\ensuremath{\beta}}_{0}}<0$ are exhibited. Here ${\ensuremath{\gamma}}_{0}$ and ${\ensuremath{\beta}}_{0}$ are coefficients of lowest-order terms of the anomalous dimension and of the $\ensuremath{\beta}$ function. For SU(3) as the color group and quark triplets, the corresponding flavor conditions are ${N}_{F}\ensuremath{\le}9$ and $10\ensuremath{\le}{N}_{F}\ensuremath{\le}16$, respectively. It was shown previously that for $\frac{{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}_{0}}{{\ensuremath{\beta}}_{0}}>0$ there are inconsistencies with the postulates of local quantum field theory and the requirement that the positive-norm contribution ${D}_{+}$ to $D$ should approach its free-field value for $g\ensuremath{\rightarrow}0$. In the present paper, it is investigated in detail how this requirement is violated assuming that the other postulates hold, including invariance under the renormalization group. Using a specific, simple projection into a subspace of positive norm, it is shown that ${D}_{+}$ diverges like ${({g}^{2})}^{\ensuremath{-}\frac{{\ensuremath{\gamma}}_{0}}{{\ensuremath{\beta}}_{0}}}$, while the free-field value and higher-order terms of $D$ are entirely due to contributions from negative-norm states. In contradistinction, the required dominance of positive-norm states in the weak-coupling limit prevails for $\frac{{\ensuremath{\gamma}}_{0}}{{\ensuremath{\beta}}_{0}}<0$. In particular, the condition is fulfilled that ${D}_{+}$ approaches its free-field value for ${g}^{2}\ensuremath{\rightarrow}0$.

Electromagnetic mass shifts of pseudoscalar mesons in a quark-parton model

Mass differences of pseudoscalar mesons are studied in a model with aSU3 quark triplet. It is shown that the elastic term dominates the pion mass shift.

Charm and the ψ-meson family

The quantum number ‘charm’ was first introduced by Bjorken & Glashow (1964) in their early discussion of the merits of a possible extension of the newly established SU(3) symmetry to an SU(4) symmetry. Some years later, this discussion was taken a step further by Glashow, Iliopoulos & Maiani (1970) in their proposal of a weak interaction model based on currents constructed out of four quark fields, which has turned out to have many virtues, both theoretical and in relation to the experimental data. The fourth quark c, additional to the SU(3) quark triplet (u, d, s), carries charm C = + 1, just as the third quark s carries strangeness s = -1.