Mass Formula For Mesons Research Articles

Expanding the concept of in-hadron condensates

The in-pseudoscalar-meson condensate can be represented through the pseudoscalar-meson's scalar form factor at zero momentum transfer. With the aid of a mass formula for scalar mesons, revealed herein, the analogue is shown to be true for in-scalar-meson condensates. The concept is readily extended to all hadrons so that, via the zero momentum transfer value of any hadron's scalar form factor, one can readily extract the value for a quark condensate in that hadron which is a measure of dynamical chiral symmetry breaking.

Flavor symmetry breaking and meson masses

The axial-vector Ward-Takahashi identity is used to derive mass formulas for neutral pseudoscalar mesons. Flavor symmetry breaking entails nonideal flavor content for these states. Adding that the ${\ensuremath{\eta}}^{'}$ is not a Goldstone mode, exact chiral-limit relations are developed from the identity. They connect the dressed-quark propagator to the topological susceptibility. It is confirmed that in the chiral limit the ${\ensuremath{\eta}}^{'}$ mass is proportional to the matrix element which connects this state to the vacuum via the topological susceptibility. The implications of the mass formulas are illustrated using an elementary dynamical model, which includes an Ansatz for that part of the Bethe-Salpeter kernel related to the non-Abelian anomaly. In addition to the current-quark masses, the model involves two parameters, one of which is a mass-scale. It is employed in an analysis of pseudoscalar- and vector-meson bound-states. While the effects of $\mathit{SU}({N}_{f}=2)$ and $\mathit{SU}({N}_{f}=3)$ flavor symmetry breaking are emphasized, the five-flavor spectra are described. Despite its simplicity, the model is elucidative and phenomenologically efficacious; e.g., it predicts $\ensuremath{\eta}\text{\ensuremath{-}}{\ensuremath{\eta}}^{'}$ mixing angles of $~\ensuremath{-}{15}^{\ifmmode^\circ\else\textdegree\fi{}}$ and ${\ensuremath{\pi}}^{0}\text{\ensuremath{-}}\ensuremath{\eta}$ angles of $~{1}^{\ifmmode^\circ\else\textdegree\fi{}}.$

Spectroscopy of tetraquark states

A complete classification of $\mathit{qq}\overline{q}\overline{q}$ tetraquark states in terms of the spin-flavor, color, and spatial degrees of freedom was constructed. The permutation symmetry properties of both the spin-flavor and orbital parts of the $\mathit{qq}$ and $\overline{q}\overline{q}$ subsystems are discussed. This complete classification is general and model independent and it is useful both for model builders and experimentalists. The total wave functions are also explicitly constructed in the hypothesis of ideal mixing; this basis for tetraquark states will enable the eigenvalue problem to be solved for a definite dynamical model. An evaluation of the tetraquark spectrum was obtained from the Iachello mass formula for normal mesons, here generalized to tetraquark systems. This mass formula is a generalization of the Gell-Mann Okubo mass formula, whose coefficients have been upgraded by a study of the latest PDG data. The ground-state tetraquark nonet was identified with ${f}_{0}(600),\ensuremath{\kappa}(800),{f}_{0}(980),{a}_{0}(980)$. The diquark-antidiquark limit was also studied.

SU(3)F Meson Mass Formula from Random PhaseApproximation

We present an SU(3)F meson mass formula from random phaseapproximation. Both the mesons of ground-state pseudoscalaroctet and ground-state vector octet are described quite well bythis mass formula. We also estimate the current and constituent quarkmasses from the naive quark model and the PCAC relation.

Light quark masses, chiral condensate and quark–gluon condensate in quenched lattice QCD with exact chiral symmetry

We determine several quantities in quenched lattice QCD with exact chiral symmetry. For 100 gauge configurations generated with Wilson gauge action at β=6.0 on the 16 3×32 lattice, we compute quenched quark propagators for 13 bare quark masses. The pion decay constant is extracted from the pion propagator, and from which the inverse lattice spacing is determined to be a −1=1.979(6) GeV. The parameters ( δ, A, B) in the pseudoscalar meson mass formula in quenched chiral perturbation theory (q χPT) to one-loop order are determined. Further, we measure the index (topological) susceptibility of these 100 gauge configurations, χ t =(175±6 MeV) 4, from which we obtain an estimate of the mass of η′ in q χPT, and the coefficient of quenched chiral logarithm, both in good agreement with the values determined from the pion masses, as well as with the theoretical estimates. With our values of δ, A, B, the experimental inputs of pion and kaon masses, and the pion decay constant, we determine the light quark masses: m u, d =4.1±0.3 MeV, and m s =92±9 MeV, in the MS scheme at scale μ=2 GeV. Also, we determine the quark condensate 〈 q ̄ q〉=−(250±3 MeV) 3 , and the quark–gluon condensate g〈 q ̄ σ μνF μνq〉=−(434±4 MeV) 5 , in the MS scheme at scale 2 GeV.

Mass formula for two-dimensional flavor non-singlet mesons

We analytically and numerically investigate the 't Hooft equations, the lowest order mesonic Light-Front Tamm-Dancoff equations for $\rm SU(N_C)$ and $\rm U(N_C)$ gauge theories, generalized to flavor non singlet mesons. We find the wave function can be well approximated by new basis functions and obtain an analytic and an empirical formulae for the mass of the lightest bound state. Its value is consistent with the precedent results.

A mass formula for light mesons from a potential model

The quark dynamics inside light mesons, except pseudoscalar ones, can be quite well described by a spinless Salpeter equation supplemented by a Cornell interaction (possibly partly vector, partly scalar). A mass formula for these mesons can then be obtained by computing analytical approximations of the eigenvalues of the equation. We show that such a formula can be derived by combining the results of two methods: the dominantly orbital state description and the Bohr–Sommerfeld quantization approach. The predictions of the mass formula are compared with accurate solutions of the spinless Salpeter equation computed with a Lagrange-mesh calculation method.

Light quark masses in quenched QCD with exact chiral symmetry

The parameters in the pseudoscalar meson mass formula in quenched chiral perturbation theory to one-loop order are determined by quenched lattice QCD with overlap Dirac operator, and from which the light quark masses are determined with the experimental inputs of pion and kaon masses, and the pion decay constant. Our results are m u, d =5.3±0.3 MeV, and m s =115±8 MeV, in the MS scheme at scale μ=2 GeV.

S- and P-wave meson spectroscopy in the nonrelativistic quark model

The mass spectrum of the ground state 1S 0 , 3S 1 and orbitally excited 3P 0 , 1P 1 , 3P 1 , 3P 2 mesons is considered in a nonrelativistic constituent quark model. A good description of the mass spectrum of these mesons is obtained with the same constituent quark masses m u = m d =305±2 and m s =483±3 MeV/ c 2. It is suggested that the nonrelativistic quark model describes better the masses of “bare” q q ̄ states, such as found in the K-matrix analysis, than the measured ones, at least for such broad states as the K ∗ 0(1430) . The a 0(980) is a quarkonium in this scheme and belongs to the lightest scalar nonet together with the K ∗ 0(1430) , with the “bare” q q ̄ mass 1191±8 MeV/ c 2, f 0(980) and f 0(1370). The extracted value of the K 1( 3P 1)−K 1( 1P 1) mixing angle ( θ K ) is (31±4)°. A constant in the mass formulae for P-wave mesons might be interpreted as the effective gluon “mass”.

Order of the QCD transition and QCD sum rules.

We propose using the finite-temperature {rho}-meson mass as an order parameter to monitor the QCD transition. This is suggested by the {rho}-meson mass formula that emerges from finite-temperature QCD sum rules in the vector channel, and which encompasses the effects of both quark and gluon condensates. We find that a second-order chiral-restoring transition implies a second-order behavior for the {rho} mass even if the value of the gluon condensate is unaffected by the transition.

Spectrum generating algebra for string-like hadrons. Mass formula for mesons

We explore implications on meson properties of the spectrum generating algebra U(4)⊗SU s(2)⊗SU f( n)⊗SU c(3) with U(4) ⊃ SO(4) dynamic symmetry. We suggest a semi-empirical mass formula consistent with this algebra. We find that this mass formula describes the mass squared of 65 relatively well-established meson states with an average deviation of 5.2%, to be compared with the semi-relativistic quark model approach (QM) which has an average deviation of 6.6%.

Meson Mass Formulae in SU(5)

We present first-order mass formulae for mesons in broken SU(5) and, using the upsilon mass as input, we estimate the masses of the new JP = 0-, 1- and 2+ mesons. We find that the masses of the 0- states exceed those of the corresponding 1- states for single b quark mesons, and that a rather large IS0 - 3S1 splitting occurs for the upsilon family.

X0(958)→ηππdecay andηX0mixing

Within the framework of a broken-SU(6)\ifmmode\times\else\texttimes\fi{}O(3) quark model of Lorentz-invariant hadron-coupling structures, the three-body decay process ${X}^{0}(958)\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\pi}\ensuremath{\pi}$ is investigated with a view to assessing the value of the $\ensuremath{\eta}{X}^{0}$ mixing angle. The model assumes that the amplitude for this process is dominated by a $\ensuremath{\delta}(970)\ensuremath{\pi}$ intermediate state so that ${X}^{0}\ensuremath{\rightarrow}\ensuremath{\delta}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\pi}\ensuremath{\pi}$. The results obtained seem to favor a quadratic mass formula for pseudoscalar mesons with an $\ensuremath{\eta}{X}^{0}$ mixing angle of ---10\ifmmode^\circ\else\textdegree\fi{}, in agreement with recent analyses.

Mass formula for mesons and quark-line rule in u-, d- and c-quark sector

Mass formula for mesons and quark-line rule in u-, d- and c-quark sector

Meson mass formula in broken SUN symmetry and its applications

Group theory of SU 5 and SU 6 symmetry is developed explicitly. Meson mass formula of Borchardt-Mathur-Okubo type is generalized to broken SU N in a form suitable for computer calculation. The result is applied to SU 5 and SU 6 cases, by assuming two possible assignments: (1) 3.95 or upsilon 5.97 GeV is the new lowest state of J PC = 1 −− member of SU 5 symmetry, and (2) 3.95 and 5.97 GeV states are new 1 −− members of SU 5 and SU 6, respectively. The derived wave functions and other consistency checks do not exclude above two possibilities in the sense of currently accepted Okubo-Zweig-Iizuka rule. A further check of the validity of the model in future experiments is suggested from a close examination of the group theoretical structures studied in this paper and available information.

Meson mass formula in broken SU N symmetry and its applications : H. Hayashi, Department of Physics, Faculty of Education, Shizuoka University, Shizuoka, Japan; I. Ishiwata, Shizuoka Public Health Laboratory, Shizuoka, Japan; S. Iwao, Department of Physics, College of Liberal Arts, Kanazawa University, Kanazawa, Japan; M. Shako, Data Processing Center, Kanazawa University, Kanazawa, Japan; and S. Takeshita, Shizuoka Environmental Pollution

Meson mass formula in broken SU N symmetry and its applications : H. Hayashi, Department of Physics, Faculty of Education, Shizuoka University, Shizuoka, Japan; I. Ishiwata, Shizuoka Public Health Laboratory, Shizuoka, Japan; S. Iwao, Department of Physics, College of Liberal Arts, Kanazawa University, Kanazawa, Japan; M. Shako, Data Processing Center, Kanazawa University, Kanazawa, Japan; and S. Takeshita, Shizuoka Environmental Pollution

Relativistic bound states: a mass formula for vector mesons

The problem of interaction in relativistic quantum mechanics remains certainly one of the most attractive in particle physics. Interesting approaches have been proposed by DmAC (~), BAKA~IJIAN and THOMAS (2) and FOLDY (3). More recently some hope was born with the development of theories at infinite momentum (4), using the nonrelativistic structure of the Poincar4 group; but, if the success of such an approach is evident in the current algebra scheme, its use for describing interacting relativistic systems in the general case seems still uncertain. The success of the theory of quarks in hadron physics is one of the motivations for the interest of a relativistic description of bound states. The concept of quarks prisoner of hadrons they build up has led physicists to introduce appealing notions such as colour, gluon theory and more recently bag theories. To these attempts one must add the symmetric harmonic-oscillator quark model (5) for baryons in which quarks constituting baryons are assumed linked by harmonic-oscillator forces (**): first presented in the nonrelativistic scheme (7), its generalization to the relativistic case (s) does not appear so easy. Note at this point a recent paper (9) in which a model for relativistic bound-state perturbation theory is presented. However, it appears very important to have a relativistic t reatment of quarks. Let us recall the transformation from current to constituent quarks obtained by MELOSH (10) in a relativistic free quark model: this transformation can be simply interpreted as a Wigner's rotation (~), and so could not appear in a nonrelativistic t reatment .

SU(3) invariance in radiative decays and the vector meson masses

Assuming SU(3) covariance for a vector field inspired from local duality for the current propagator, we calculate successfully the meson radiative decays. A new vector meson mass formula is also obtained leading to exactly ideal mixing. Possible difficulties from ϱ'(1250) → ωπ are emphasized.

Radiative Decays of the Vector Mesons and the Meson Mixing Angles

A general SU(3) analysis of vector meson and pseudoscalar meson radiative decays is carried out. Two solutions are obtained, corresponding either to an inverse-square mass formula or to a linear mass formula for vector mesons that lead to reasonable agreement with most of the radiative decays. (AIP)

Meson mass formula from duality

A general mass formula for meson levels in the symmetric-group dual resonance model is written in terms of the corresponding quark-model quantum numbers.Received 7 April 1975DOI:https://doi.org/10.1103/PhysRevD.12.2164©1975 American Physical Society