Quark Quantum Numbers Research Articles

Definition of fragmentation functions and the violation of sum rules

We point out a problem with the formulation and derivations of sum rules for quark fragmentation functions that impacts their validity in QCD, but which potentially points toward an improved understanding of final states in inclusive hard processes. Fragmentation functions give the distribution of final-state hadrons arising from a parton exiting a hard scattering, and the sum rules for momentum, electric charge, etc. express conservation of these quantities. The problem arises from a mismatch between the quark quantum numbers of the initial quark and the fact that all observed final-state hadrons are confined bound states with color zero. We point that, in a confining theory like QCD, the Wilson line in the operator definition of a fragmentation function entails that the final state in a fragmentation function includes a bound state in the external field generated by the Wilson line. We justify this with the aid of general features of string hadronization. The anomalous bound states are restricted to fractional momentum z=0. They tend to invalidate sum rules like the one for charge conservation when applied to the fragmentation functions inferred from experimental data but not the momentum sum rule. We propose to exploit our ideas in future studies as a way to relate the fragmentation functions extracted from inclusive cross sections to more detailed nonperturbative descriptions of final state hadronization. We also describe scenarios wherein the traditional sum rules might remain approximately valid with a reasonably high degree of accuracy. Published by the American Physical Society 2024

Consideration of Additive Quantum Numbers of Fermions and Their Conservations

Two new flavor quantum numbers D and U for down and up quarks, respectively, are introduced, and then quark quantum number H is proposed as the sum of the flavor quantum numbers of quarks. Moreover, lepton quark-like quantum number HL and finally fermion quantum number F are brought forward. Old and new additive quantum numbers are conserved at three different levels in weak interaction, and F builds up a clear relationship to the electric charge of fermions.

Mass spectrum of the hidden-charm pentaquarks in the compact diquark model

The LHCb collaboration have recently updated their analysis of the resonant J/ \U0001d713 p mass spectrum in the decay {varLambda}_b^0 → J/\U0001d713 p K−, making use of their combined Run 1 and Run 2 data. In the updated analysis, three narrow states, Pc (4312)+, Pc (4440)+, and Pc (4457)+, are observed. The spin-parity assignments of these states are not yet known. We interpret these narrow resonances as compact hidden-charm diquark-diquark- antiquark pentaquarks. Using an effective Hamiltonian, based on constituent quarks and diquarks, we calculate the pentaquark mass spectrum for the complete SU (3) F lowest S- and P -wave multiplets, taking into account dominant spin-spin, spin-orbit, orbital and tensor interactions. The resulting spectrum is very rich and we work out the quark flavor compositions, masses, and JP quantum numbers of the pentaquarks. However, heavy quark symmetry restricts the observable states in Λb-baryon, as well as in the decays of the other weakly-decaying b-baryons, Ξb and Ωb. In addition, some of the pentaquark states are estimated to lie below the J/ \U0001d713 p threshold in Λb-decays (and corresponding thresholds in Ξb- and Ωb-decays). They decay via c overline{c} annihilation into light hadrons or a dilepton pair, and are expected to be narrower than the Pc-states observed. We anticipate their discovery, as well as of the other pentaquark states present in the spectrum at the LHC, and in the long-term future at a Tera-Z factory.

A New Quantum Number Triangular Array That Defines the Internal Organization of Valence Quarks, the Hadron Quark Model, and the CKM Matrix

Purpose: The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants, including the quarks, are associated with partial harmonic fractional exponents, , of a fundamental frequency, vF. The model has shown that the properties of the quarks are based on a progression of prime number composites. They also fall on three separate power law lines related to integer factors of the Y-intercept, , of a fundamental electromagnetic line which is scaled by the Rydberg constant, R and Planck’s constant. The quark lines are scaled by the quantum number factors {1, 2, 3}, and their Y-intercepts are referred to as nbem. The goal is to present a new proto-quark model in a six-quark inverted triangular array that defines the global organization of the valence quarks, which determines the hadronic quantum numbers, the standard hadron quark model, and the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Methods: The charm, bottom, top quarks are associated with power law line Y-intercept, nbem equal to 1; the strange and down quarks with nbem equal to 2; and the up quark with nbem equal to 3. An inverted equilateral triangular array with three rows arranged from upper row (triangle base) to bottom row (triangle vertex), is associated respectively with nbem numbers 1, 2, and 3. The novelty of our perspective thus defines a new global valence quark organization which supersedes the Standard hadron composite quark model. The quarks are ordered via relative mass, partial fractions, and nbem quantum number. The top row of our inverted triangle includes the c, b, and t quarks from left to right; the middle row depicts the d and s quarks; and the bottom row, the up quark. Results: Our array depicts a quantum generator of the global organization of the valence quarks defining the composite quark model. The vertices of the triangular array are the up quarks, the midpoints are the down quarks. All weak transitions are from a corner to a midpoint or vice versa. The standard 3 by 3 CKM matrix is generated from the new quark triangle with each up type quark (u, c, and t) transforming to each down type (d, s, and b), with their experimental flavor transition magnitudes given. Conclusion: A new quark quantum number, nbem, is an important discovery that generates a new proto-valence quark triangle that secondarily generates the composite quark model and the CKM matrix.

Chiral symmetry breaking and quark confinement in the nilpotency expansion of QCD

We apply to lattice QCD a bosonization method previously developed in which dynamical bosons are generated by time-dependent Bogoliubov transformations. The transformed action can be studied by an expansion in the inverse of the nilpotency index, which is the number of fermionic states in the structure function of composite bosons. When this number diverges the model is solved by the saddle-point method which has a variational interpretation. We give a stationary covariant solution for a background matter field whose fluctuations describe mesons. In the saddle-point approximation fermionic quasiparticles exist which have quark quantum numbers. They are confined in the sense that they propagate only in pointlike color singlets. Conditions for chiral symmetry breaking are determined, to be studied numerically, and a derivation of a mesons-nucleons action is outlined.

Hadronic fluctuations in the QGP

We analyze fluctuations of quark number and electric charge, in 2-flavour QCD at finite temperature and vanishing net baryon number density. In the hadronic phase we find that an enhancement of charge fluctuations arises from contributions of doubly charged hadrons to the thermodynamics. The rapid suppression of fluctuations seen in the high temperature phase suggests that in the QGP quark number and electric charge are predominantly carried by quasi-particles with the quantum numbers of quarks.

Hadronic fluctuations at the QCD phase transition

We discuss the properties of hadronic fluctuations, i.e., fluctuations of net quark and isospin numbers as well as electric charge, in the vicinity of the QCD transition in isospin-symmetric matter at vanishing quark chemical potential. We analyse second- and fourth-order cumulants of these fluctuations and argue that the ratio of quartic and quadratic cumulants reflects the relevant degrees of freedom that carry the quark number, isospin or charge, respectively. In the hadronic phase we find that an enhancement of charge fluctuations arises from contributions of doubly charged hadrons to the thermodynamics. The rapid suppression of fluctuations seen in the high-temperature phase suggests that in the QGP, net quark number and electric charge are predominantly carried by quasi-particles, with the quantum numbers of quarks.

Standard-model particles and interactions from field equations on spin (9+1)-dimensional space

We consider field equations set on an extended spin space that contain fermion and boson solutions. At given dimension, they determine the scalar symmetries. The standard field equations can be equivalently written in terms of such degrees of freedom, and are similarly constrained. At 9+1 dimensions, the SU(3)×SU(2)L×U(1) gauge groups emerge, as well as solution representations with quantum numbers of related gauge bosons, leptons, quarks, Higgs-like particles and others as leptoquarks. Information on coupling constants is also provided.

Exceptional confinement in G(2) gauge theory

We study theories with the exceptional gauge group G(2). The 14 adjoint “gluons” of a G(2) gauge theory transform as {3}, { 3 ̄ } and {8} under the subgroup SU(3), and hence have the color quantum numbers of ordinary quarks, anti-quarks and gluons in QCD. Since G(2) has a trivial center, a “quark” in the {7} representation of G(2) can be screened by “gluons”. As a result, in G(2) Yang–Mills theory the string between a pair of static “quarks” can break. In G(2) QCD there is a hybrid consisting of one “quark” and three “gluons”. In supersymmetric G(2) Yang–Mills theory with a {14} Majorana “gluino” the chiral symmetry is Z(4) χ . Chiral symmetry breaking gives rise to distinct confined phases separated by confined–confined domain walls. A scalar Higgs field in the {7} representation breaks G(2) to SU(3) and allows us to interpolate between theories with exceptional and ordinary confinement. We also present strong coupling lattice calculations that reveal basic features of G(2) confinement. Just as in QCD, where dynamical quarks break the Z(3) symmetry explicitly, G(2) gauge theories confine even without a center. However, there is not necessarily a deconfinement phase transition at finite temperature.

Grand unification in higher dimensions

We have recently proposed an alternative picture for the physics at the scale of gauge coupling unification, where the unified symmetry is realized in higher dimensions but is broken locally by a symmetry breaking defect. Gauge coupling unification, the quantum numbers of quarks and leptons and the longevity of the proton arise as phenomena of the symmetrical bulk, while the lightness of the Higgs doublets and the masses of the light quarks and leptons probe the symmetry breaking defect. Moreover, the framework is extremely predictive if the effective higher dimensional theory is valid over a large energy interval up to the scale of strong coupling. Precise agreement with experiments is obtained in the simplest theory— SU(5) in five dimensions with two Higgs multiplets propagating in the bulk. The weak mixing angle is predicted to be sin 2 θ w =0.2313±0.0004, which fits the data with extraordinary accuracy. The compactification scale and the strong coupling scale are determined to be M c≃5×10 14 GeV and M s≃1×10 17 GeV , respectively. Proton decay with a lifetime of order 10 34 years is expected with a variety of final states such as e + π 0, and several aspects of flavor, including large neutrino mixing angles, are understood by the geometrical locations of the matter fields. When combined with a particular supersymmetry breaking mechanism, the theory predicts large lepton flavor violating μ→ e and τ→ μ transitions, with all superpartner masses determined by only two free parameters. The predicted value of the bottom quark mass from Yukawa unification agrees well with the data. This paper is mainly a review of the work presented in hep-ph/0103125, hep-ph/0111068, and hep-ph/0205067 [1–3].

Recent results from CLEOII: charm physics

In the last decade the CLEO II collaboration, using the CESR e + e − storage ring, has accumulated nearly 15 fb −1 of luminosity. in the energy region around 10.5 GeV, corresponding to the production of more than 3·10 7 charmed particles (apart from daughters of B meson decay). This has produced new results in the spectroscopy of charmed baryons and mesons and a much improved limit on D 0 - D 0 mixing. We present evidence for an excitation of the Ξ c , seen in both charge states; namely, the Ξ′ c , the J p = 1 2 + c{sq} state, which is symmetric under exchange of light quark quantum numbers. Another state is seen in the decays to Ξ c + π + π − and Ξ c 0 π + π − via an intermediate Ξ c ∗ , and is consistent with the Ξ c1 , the J p = 3 2 − p-wave state analogous to the Λ c1 +(2625). The mass differences relative to the ground state are: M( Ξ c +′) − M( Ξ c ) = (107.8 ± 1.7 ± 2.5) MeV/ c 2, M( Ξ c 0′) − M( Ξ c ) = (107.0 ± 1.5 ± 2.5) MeV/ c 2, M( Ξ c1 +) − M( Ξ c +) = (348.6 ± 0.6 ± 1.0) MeV/ c 2, and M( Ξ c1 0) − M( Ξ c 0) = (347.2 ± 0.7 ± 2.0) MeV/ c 2. We have made the first (preliminary) measurements of the natural widths of the Σ c ++ and Σ c 0 baryons: Γ ++ = (2.98 −.35 +.38 ± 0.5) MeV, and Γ 0 = (2.63 −.33 +.36 ± 0.5) MeV. In the charmed meson sector we find evidence for a wide 1 + state, the D 1 0(2460). Its mass is (2.461 −.034 +.041 ± .010 ± .032) GeV; its width is (290 −74 +101 ± 26 ± 36) MeV. We find no supporting evidence for the D ∗′+ , a purported radial excitation claimed by the Delphi group at a mass of (2637 ± 2 ± 6) MeV. Finally we are able, using “wrong-sign” (DCSD) Kπ decays to make the following measurements: 1) the observed ratio of DCSD decays relative to the Cabibbo-allowed rate is R ws = (0.34 ± 0.7 ± .06)%, 2) the mixing parameters are bounded, at 95% confidence, by x ′2 < .001 and −.059 < y′ < .003. x′ and y′ are, in the absence of final state phase differences, the real and imaginary parts of | frsol| δM/ Γ.

Hidden quantum numbers of the groupS(3) as a classification scheme of the generations of leptons and quarks in a subfermion model

In preceding papers electroweak gauge bosons, leptons and quarks have been assumed to arise from two-particle and three-particle bound states of subfermions, where the subfermion dynamics is governed by a non-linear spinor-field equation with appropriate regularization and globalSU(2)×U(1) invariance. The bound states were classified according to a shell model scheme and theSU(2)×U(1) quantum numbers. It has been shown that the effective dynamics of three-particle states with symmetric configurations in isospin-superspin degrees of freedom coincides with the phenomenologicalSU(2)×U(1) unbroken gauge theory. In this paper we extend these results to the inclusion of the three generations of leptons and quarks. This is done by considering three-particle bound states with mixed symmetry in isospin-superspin space which had been calculated in a previous paper. Apart from symmetry breaking and left-right asymmetry, the effective dynamics of these three-subfermion bound states and the two-particle bound states yields theSU(2)×U(1) gauge theory with the correct phenomenological quantum numbers of leptons, quarks and gauge bosons including the three generations.

Quark solitons from effective action of QCD

We derive an effective low-energy action for QCD in 4 dimensions. The low energy dynamics is described by chiral fields transforming nontrivially under both color and flavor. We use the method of anomaly integration from the QCD action. The solitons of the theory have the quantum numbers of quarks. They are expected to be the constituent quarks of hadrons. In two dimensions our result is exact, namely the bosonic gauged action of WZW.

Qualitons from QCD

Qualitons, topological excitations with the quantum numbers of quarks, may provide an accurate description of what is meant by constituent quarks in QCD. Their existence hinges crucially on an effective Lagrangian description of QCD in which a pseudoscalar colour-octet of fields enters as a new variable. We show here how such new fields may be extracted from the fundamental QCD Lagrangian using the gauge-symmetric collective field technique.

Constituent quarks as solitons

We exhibit soliton solutions of QCD in two dimensions that have the quantum numbers of quarks. They exist only for quarks heavier than the dimensional gauge coupling, and have infinite energy, corresponding to the presence of a string carrying the non-singlet color flux off to spatial infinity. The quark solitons also disappear at finite temperature, as the temperature, as the temperature-dependent effective quark mass is reduced in the approach to the quark/hadron phase transition.

Standard model gauge group and realistic fermions from the most symmetric cosetM klm

A brief survey on Kaluza-Klein theories is given. It is emphasized that for a maximally supersymmetric universe, the only way to do Kaluza-Klein theory is through supergravity. Bearing this in mind, a seven-dimensional internal compact manifold,Mklm,is considered. It is described as being the most general type of coset spaces containing the standard model groupsSU(3) ⊗SU(2) ⊗U(1).Mklmis obtained as a compactification ofD=11 supergravity. It is shown that contary to the manifoldsMpqr,the topology of the spacesMklmis not sensitive to the integers,k, l, m but rather to the 6 parameters that parametrize the subalgebraSU(2) ⊗U(1)′ ⊗U(1)″ taken to be the stability group ofMklm.This gives the spacesMklma much richer topology and thus a much wider class of solutions ofD=11 theory. Also, the most general expressions for the “geometrical” coupling constant are obtained. A consistency condition with the low-energy standard model, with and without supersymmetry, is established. A harmonic expansion analysis is made, it is shown thatMklmmanifold possesses a spinor structure for a given class of parameters. It is shown that for two classes of parametersL 0+ klm andL 0− klm the manifoldMklmbecomes the 8-dimensional coset spaceLklmfor which classes it is seen to be consistent with theSU(3) ⊗SU(2) ⊗U(1) quark and lepton quantum numbers. TheSU(3) ⊗SU(2) ⊗U(1) invariant solutions ofD=11 supergravity are studied. It is shown that all solutions break supersymmetry except for two mirror solutions for whichN=2 supersymmetry is preserved. The 8-dimensional coset manifoldLklmis then considered; it is obtained as a minimal increase on the manifoldMklm.

State vectors in higher-dimensional gravity with kinematic quantum numbers of quarks and leptons

We examine the question of whether fundamental fermions can be regarded as topological solitons (geons) of a theory of pure quantum gravity in n + 4 dimensions. In particular, we consider the quantum gravitational field for ( n + 4)-dimensional space-times which have asymptotic Kaluza-Klein behavior: asymptotic topology of the form R 4 × G/H and a metric that is asymptotically the direct sum of the Minkowski metric on R 4 and the natural symmetric metric on G/H. We argue that if there is a nonsingular theory of pure quantum gravity (a theory that, below Planck energy, involves only the space-time metric), then there are stable ground states with the kinematical quantum numbers of fundamental fermions: that is, states which have spin 1 2 and belong to the fundamental representation of G . Multi-valued representations of the asymptotic symmetry group can arise from diffeomorphisms (diffeos) of the ( n + 3)-dimensional space that are not isotopic to the identity. In a path integral approach, the creation of fundamental fermions (topological geons) requires a space-time in which the topology of space-like hypersurfaces changes and in which the relevant diffeos on the final ( n + 3)-space (containing the geons) are not extendible to diffeos of the ( n + 4)-space-time. We prove that such pair-creation geometries occur in a lorentzian as well as euclidean framework and that the diffeos are not extendible. Although zero-mass modes of finite-size fermions need not belong to a real representation of the internal group, it is not difficult to prove that, independent of the fermion size, one cannot avoid mirror fermions. There is, however, an interesting loophole: A nonzero vacuum expectation value of a Higgs-like vector constructed from the metric can break chiral invariance without changing the lowest-order Einstein-Yang-Mills form of the gravitational lagrangian.

New tripreon models with semisimple metacolor groups.

A systematic analysis of the chiral tripreon models with $\mathrm{SU}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(M)$-metacolor symmetry is made. Unique solutions to the 't Hooft anomaly-matching condition with the Bars constraint are obtained for SU(3)\ifmmode\times\else\texttimes\fi{}SO(5) models which also satisfy complementarity. Both the metacolor group and the gauged color-flavor subgroup of the metaflavor group are asymptotically free. A model which has a low-metacolor-energy scale and three generations of composite fermions with the quantum numbers of quarks and leptons of the standard model is obtained.

Relating the fundamental coupling constants via a stability principle

We proposed a dynamical stability principle related to the interplay of electromagnetic and weak interactions and predict sin 2θ w in terms of the lepton and quark quantum numbers in good agreement with its empirical value. The application of our stability principle to the interplay of electromagnetic and strong interactions yields a value for the γϱ 0 transitions strength (and thus implicitly for α α s ) , which is satisfactory, if one takes into account the crudeness of the approximations involved.

Probabilistic derivation of parton splitting functions.

We show that the parton splitting functions defined by Altarelli and Parisi can be derived in a completely probabilistic manner. In this approach, the apparent infrared divergences in the Altarelli-Parisi calculation cancel between gain and loss terms in the splitting functions, and momentum and quark quantum number conservation are satisfied automatically without the imposition of extra constraints. We discuss the relation of the probabilistic approach to the usual leading-logarithm diagrammatic analysis.