Mass Formula For Mesons Research Articles

Two mass relations for mesons from string-quark duality

We generalize a self-consistency equation derived previously by us for the Nambu string to strings carrying SU(6) quantum numbers. The self-consistency equations are derived by considering the propagation of a string with the quantum numbers of the physical vacuum. Since we can map the world sheet that the string sweeps out onto rectangles, and the wave function of the physical vacuum is a constant, the boundary conditions are the same on all four sides of the rectangles. We can then calculate the propagator in two ways and this leads to the self-consistency equations. For the strings carrying SU(6) quantum numbers we consider the propagator o strings with the quantum numbers of the physical vacuum all along the string except for having quark quantum numbers either attached or removed from the ends. We can solve these self-consistency equations in a certain approximation and for this case they lead to mass formulae for mesons that are well satisfied in nature.

An Empirical Mass Formula for Mesons. I

An Empirical Mass Formula for Mesons. I

Meson Mass Formula in Nonet Scheme

Meson Mass Formula in Nonet Scheme

Universality sum rules and SU(3) symmetry breaking

Universality relations which are known to hold experimentally at high energies are used as input to obtain new finite energy sum rules, which provide constraints on amplitudes in the resonance region. An ω-universality sum rule explains the surprising experimental validity of ω-universality at low energies. A ϱ-universality sum rule provides conditions on SU(3) symmetry breaking in the resonance region, which follow from the peculiar character of SU(3) symmetry breaking observed at high energies; namely that trajectories have different intercepts but their couplings satisfy SU(3). “Local ϱ-universality” applied to meson-meson scattering gives the SU(6) mass formulas for vector and pseudoscalar mesons and the universal U(3) relations between couplings obtained from the quark model or duality diagrams.

Diophantine Quantization: Application of the Methods of Algebraic Number Theory to the Theory of Elementary Particles

The Gell-Mann---Okubo broken-$\mathrm{SU}(3)$ meson mass formula is treated as a quadratic Diophantine equation and solved in integers. The relative masses of $\ensuremath{\pi}$, $\ensuremath{\eta}$, $K$, many known ${K}^{*}$, and the probable lowest $L$ may be predicted unambiguously. The requirement of least-integer solutions mandates a unit mass of 70 MeV ($137{m}_{e}{c}^{2}$). Connections between rest masses and angular momenta can be made, and there is evidence of a general linear group.

Generalized Algebraic Mass Formulas. I

It is shown that the SL(2, C)-Poincaré associative algebraic model of Böhm can be extended without essential difficulty to an SL(2, C)-de Sitter model which gives rise to a meson mass formula with both spin and isospin dependence.

A relativistic formulation of the quark model for mesons

Mesons are treated as bound states in quark-antiquark scattering using the Bethe-Salpeter equation (this does not necessarily imply that the properties of mesons are dominated by the Q- Q state). It is shown that the existence of very tightly bound states with a nonrelativistic spinor structure (such as are considered in the usual norelativistic quark model) requires a Dirac scalar potential (or sum of irreducible graphs) as well as small internal three momentum (q 2 ⪡ M Q 2). The assumption that the pseudoscalar mesons have a particular simple relativistic spinor structure leads naturally to the correct value of Γ(π→μν) Γ(K→μν) (in contrast to the usual model) and gives the prediction γ ρ 2:γ φ 2:γ ω 2=M ρ 2: 3M φ 2 cos 2θ : 3M ω 2 sin 2θ (where γ V are the usual V − γ coupling constants and θ is the ω − φ mixing angle) which is compatible with the data. The assumption that the internal momentum is small and the potential is spin-independent can lead to approximate SU(6) symmetry, as in the usual model, although the spinor structure is relativistic. Using the value of the weak axial vector coupling constant for quarks given by the nonrelativistic quark model for baryons, these assumptions lead to the Kawarabayashi-Suzuki relation 2 γ ϱ f π = M ϱ which agrees with experiment. The states which have L = 1 in the usual model are discussed. The model leads naturally to quadratic mass formulae for mesons. The processes π 0→ γγ and η 0→ γγ are discussed using the relativistic formalism.

Mass Formula and "BrokenSU(3)" in an Associative Algebra

An associative algebra, which contains the enveloping algebra of the Poincar\'e group and the enveloping algebra of $\mathrm{SL}(3,c)$, is considered. Its reduction with respect to irreducible representations of $\mathrm{SU}(3)$ is studied and a mass formula is derived, which contains the mass formula for mesons of "broken" $\mathrm{SU}(3)$ as a special case. The results are compared with experimental data.

Mass formulas for mesons and baryons in the quark model

A unified mass formula is given, linear both for mesons and baryons. The spin-spin interaction and the annihilation interaction of strange quark pairs is proposed to be much weaker than that of non-strange quark pairs.

Boson mass squared formula and spurions

We have obtained the GMO mass formula for PS mesons directly in terms of the masses squared, to all orders in an S-PS-PS coupling constant, assuming that the principal contributions to δm 2 are due to the single boson intermediate states and to the non-vanishing of the vacuum expectation values of some scalar fields.

Meson Mass Formulas for the 405 Multiplet ofSU(6)

Mass formulas for mesons in a 405-dimensional representation of $\mathrm{SU}(6)$ are derived. A table of the particles and their quantum numbers is given for the $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}{(2)}_{J}$ and the $\mathrm{SU}(4)\ensuremath{\bigotimes}\mathrm{SU}{(2)}_{S}$ chains, along with the recoupling transformations which relate the chains. The results are in a form which may be applied to the newly discovered positive-parity mesons, in particular, the ${2}^{+}$ nonet. Under the assumption that the 27-plet of ${2}^{+}$ mesons is much higher up, a quadratic relation is found for the ${2}^{+}$ nonet which is satisfied within experimental errors.

BrokenU(3)Symmetry and Semileptonic Weak Interactions

A phenomenological field-theoretic model of $U(3)$-symmetry breakdown is proposed. It allows a unified treatment of both mass renormalization and field renormalization of the phenomenological fields associated with particles. Specifically, we have calculated the renormalization effects on the semileptonic weak coupling constants. Based on our model, it is shown that the empirically observed damping factor for $|\ensuremath{\Delta}Y|=1$ transitions cannot be explained by symmetry-breaking effects and therefore the Cabibbo angle is intrinsic to weak-interaction theory. From our calculation, we expect a 20% renormalization effect on all $|\ensuremath{\Delta}Y|=1$ axial-vector coupling constants for baryon leptonic decays. This renormalization effect is supported by the present experimental information about the $\frac{{G}_{A}}{{G}_{V}}$ ratio of lambda beta decay. To make a sharp test of our model, more accurate experimental data concerning the $\frac{{G}_{A}}{{G}_{V}}$ ratios of the baryon leptonic decays are required. Our model also reproduces the Ademollo-Gatto theorem on the nonrenormalization of the $|\ensuremath{\Delta}Y|=1$ vector transitions and Okubo's speculated mass formulas for vector mesons.

A model of strongly interacting particles

An oscillator (or noncompact group) model of strongly interacting particles is given. Mass formulae for baryons, baryon resonances and vector mesons are derived. Possible existence of new pseudoscalar mesons is discussed.

Intermultiplet Mass Formula for Mesons

An $\mathrm{SU}(6)$ intermultiplet mass formula for mesons is presented which relates the average masses of the pseudoscalar and vector octets and the ${X}^{0}$ singlet. The meson mass splittings are also related to the baryon mass splittings on the basis of a bootstrap model of the baryon supermultiplet.

Broken symmetries and mass formulae for vector mesons

The question of which kind of mass formulae [(mass)2vs. (mass)-2] are correct for a multiplet of vector mesons is studied. It is shown that from a field-theoretic point of view, one does not have a clear a priori preference for either kind of formulae.

Propriétés de l'étrangeté et une formule de masse pour les mésons vectoriels

A mass-formula for vector mesons is proposed, and the role of strangeness in mass-formulae discussed.

Large symmetry-breaking meson-baryon interactions

The general structure of the symmetry-breaking meson-baryon interactions within the framework of the three-dimensional unitary-unimodular group is investigated. It is suggested that the symmetry-breaking terms are not necessarily small compared with the symmetry-preserving terms, and that the mass formulae for mesons and baryons follow as a result of certain cancellations in the self-energies of these particles. An estimate based on the second-order self-energy calculations leads to an intrinsic mass of about 870 MeV for mesons as well as baryons, and accounts for all the observed mass splittings between the meson and baryon multiplets in terms of the symmetry-breaking interactions.

ω-ϕ mixing and the mass formula for pseudoscalar mesons in a non-perturbative model

ω-ϕ mixing and the mass formula for pseudoscalar mesons in a non-perturbative model