Meson decay constants and bare quark masses from duality for current two-point functions

Duality is applied in a quasi-local form to the SU(4) × SU(4) current two-point functions. Interpolating functions for some of their space-time components are assumed to be given by the free quark model. Mass intervals in the finite energy sum rules are taken to be approximately SU(3) × SU(3) invariant and a linear dependence of the hadronic mass spectrum upon the radial quantum number is assumed. The correct order of magnitude of various meson decay constants is reproduced provided the color gauge group is SU(3). The bare uncharmed quark masses are given by the formulae: $\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ M}{}_{\mathrm{\pi }}\text{F}{}_{\mathrm{\pi }}\text{/F}{}_{\mathrm{\pi }}\text{√6 ≌ 40}\text{MeV}\text{, m}{}_{\mathrm{<mtext>s</mtext>}}\text{/m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ 1 = 6}$. The η-η mixing problem is discussed. Predictions are made for the masses and decay constants of the vector mesons of the first L = 2 level of SU(6) × O(3), as well as for the decay constants of the radially excited pseudoscalar mesons; estimates of corrections to PCAC in Goldberger-Treiman relations are presented. The bare charmed quark mass is found to be of the order of 1.1–1.2 GeV. Some decay constants of charmed mesons are evaluated.     

Charmed meson decays and right-handed currents

In the presence of right-handed currents including $\text{(}\text{c}\text{s}\text{)}{}_{\mathrm{<mtext>R</mtext>}}$, it is emphasized that the dominant parity-violating (-conserving) Hamiltonian for nonleptonic decays of charmed hadrons transforms like $\text{45}\text{+}\text{45}{}^1\text{(}\text{20″ +}\text{84}\text{)}$ of SU(4), and leads to distinctive results especially in D⁺ → K_Sπ⁺, F⁺ → μ⁺ν_μ and D⁰ → K^?e⁺ν_e, etc.     

Charmed baryon pair production in e+e− annihilation

Cross sections for charmed baryon pair production near threshold in e⁺e^? annihilation are calculated using pole-dominated form factors modified to take intoccount continuum effects. When the C₀⁺$\text{C}$₀^? production cross section is normalized with the help of data for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{p}\text{X}$ it is found that the total charmed baryon production cross $\text{(}\text{C}{}_0\text{C}{}_0\text{,}\text{C}{}_1\text{C}{}_1\text{,}\text{C}{}_1\text{C}{}_1{}^1\text{+}\text{C}{}_1{}^1\text{C}{}_1\text{,}\text{C}{}_1{}^1\text{C}{}_1{}^1\text{)}$ reaches a peak value of approximately 2.7 nb at √s = 5 GeV.     

Electromagnetic mass differences of the old and the charmed mesons

We predict for M_?⁺?M_?⁰ the values -3.4 ± 0.8 MeV using the ?-ω mixing and the quark model, respectively. The extracted parameters indicate the necessity of a relativistic treatment of the old mesons. The problem of extrapolating these parameters to the charmed mesons is discussed. Under conservative assumptions, we predict 1.7 ? M_D⁰ ? 2.2 MeV and .     

Predictions of duality for the charmed meson masses

The constraints of duality via FESR's are applied to the processes P+P→P+V, using particles with a new quantum number (charm) as both external and internal (resonance saturation) states. The results are independent of any detailed dynamics or symmetry schemes, as well as independent of coupling strengths. We use the masses of the recently-discovered D and D¹ to set the scale. We predict , m_F = 1938 ± 33 MeV, . Thus slopes of Regge trajectories for charmed mesons are predicted to be substantially smaller than those for ordinary mesons.     

Comments on charmed baryon pair production in e+e−-annihilation

We show that the symmetric quark model calculation of charmed baryon pair creation in e⁺e^?-annihilation has an incorrect threshold structure. The cc?-pair creation model possesses the correct s-wave threshold behaviour, if the cc?-pair and diquark pair are created in orbital s-waves. We show that the two models become identical for a specific orbital configuration and discuss implications for the relative production rates of $\text{Λ}{}_{\mathrm{<mtext>c</mtext>}}\text{Λ}{}_{\mathrm{<mtext>c</mtext>}}\text{:Σ}{}_{\mathrm{<mtext>c</mtext>}}\text{Σ}{}_{\mathrm{<mtext>c</mtext>}}\text{:Σ}{}_{\mathrm{<mtext>c</mtext>}}\text{Σ}{}_{\mathrm{<mtext>c</mtext>}}{}^1\text{+Σ}{}_{\mathrm{<mtext>c</mtext>}}{}^1\text{Σ}{}_{\mathrm{<mtext>c</mtext>}}\text{:Σ}{}_{\mathrm{<mtext>c</mtext>}}{}^1{}_{\mathrm{<mtext>c</mtext>}}{}^1$.     

Electromagnetic annihilation of e+e− into quarkonium states with even charge conjugation

We calculate the production of narrow resonances with even charge conjugation ${}^3\text{P}{}_{\mathrm{J}}\text{=1,2}$ in e⁺e^? annihilation in the quarkonium and vectordominance models. We give unitarity bounds for $\text{Γ(}{}^3\text{P}{}_{\mathrm{J}}\text{→ e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{)}$ in terms of $\text{Γ(}{}^3\text{P}{}_{\mathrm{J}}\text{→ γγ)}$ and $\text{Γ(}{}^3\text{P}{}_{\mathrm{J}}\text{→ e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{)}$. The electromagnetic production dominates through the neutral current at low energies independent of details of the model. For masses above 10 GeV the situation is reversed.     

On the semileptonic decay of charmed hadrons

The semileptonic and leptonic decay modes of charmed hadrons produced in e⁺e^? collisions above 4 GeV in the cm have been investigated by selecting events with a single electron plus at least two charged tracks. The electron momentum spectrum peaks near 0.5 GeV/c with few events above 0.7 GeV/c. The spectrum excludes large rates for the decays $\text{D}\text{→}\text{e}\text{v}{}_{\mathrm{<mtext>e</mtext>}}$ and $\text{D}\text{→}\text{e}\text{v}{}_{\mathrm{<mtext>e</mtext>}}\text{π}$, but is compatible with $\text{D}\text{→}\text{e}\text{v}{}_{\mathrm{<mtext>e</mtext>}}\text{K}{}^1\text{(892)}$, $\text{D}\text{→}\text{e}\text{v}{}_{\mathrm{<mtext>e</mtext>}}\text{K}$ or a mixture of both. The semileptonic branching ratio is obtained both by comparing the inclusive electron cross section with the total cross section attributable to charm, and by studying the fraction of events containing a second electron. The semileptonic charm branching ratios obtained are 0.11 ± 0.03 and 0.16 ± 0.06 respectively. A single event with three electrons and hadrons is found, consistent with the estimated background. The 90% confidence upper limit for σ(e⁺e^? → 3e + hadrons) is 0.1 nb.     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

Baryon mass splitting by the strong hyperfine interaction and SU(3) breaking

We calculate mass splittings of strange and non-strange baryons in the [56, 0⁺] and the [70, 1^?]. As the most important spin-dependent force we only analyse the hyperfine interaction. The exact treatment of the quark mass breaking shows contributions which have not been considered in similar investigations up to now. Taking $\text{mλ}\text{m}{}_{\mathrm{<mtext>p</mtext>}}\text{? 2}$ and popular values for the slope of the linear potential a, the strong coupling constant α_s and the p-quark mass, we get excellent results for the four mass splittings 〈Σ-Λ〉, $\text{〈Σ}{}^1\text{? Σ〉}$, 〈Δ-N〉 and $\text{〈Ξ}{}^1\text{? Ξ〉}$ in the [56, 0⁺]. The structure of mass spectrum in the [70, 1^?] is well described, too; the strong SU(3) mixing of Σ and Λ states is seen to be due to the quark mass breaking. Predictions for missing Σ states in the [70, 1^?] as as for splittings between charmed baryons can be made.     

The properties of charmed baryon (Λc+) and the proton revisited

A statistical model for baryons was suggested leading to an analytical expression for the square modulus ∥ψ(r)∥² of baryon wavefunctions, which is not only free of constituent quark masses but also devoid of the interaction parameters of the effective linear potential in which a quark moves. Using ∥ψ(r)∥² as an input the lifetimes of the newly established charmed baryon ($\text{Λ}{}_{\mathrm{c}}{}^{\mathrm{+}}$) and the proton were studied and compared with other existing theoretical estimates.     

Some properties of heavy lepton families

The simplest four-quark SU(2) ? U(1) models with an anomally-free heavy lepton sector can have two charged heavy leptons and one or two neutral leprons. Such models also explain the rise in R (the ratio of hadronic to muon pair production in e⁺e^? collisions). We study some consequences of different choices of leptonic numbers for L₁ and L₂. In particular, we derive, the leptonic decay width when several final-stae leptons are massive; the cross section for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{L}{}_1\text{L}{}_2$ production; the branching ratio for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{L}{}_2\text{L}{}_2\text{→}\text{e}\text{3μ+}\text{missing energy}$.     

Hyperfine structure of CH3OH

Hyperfine structure of the (0, 0, 1) - (1, 0, 1) transition of methanol has been investigated by beam absorption and of the (J, 1, 3?) → (J, 1, 3+) transitions for J = 2, 3, and 6 by beam-maser spectroscopy. The best-fit results for the spin-rotation and spin-spin coupling constants $\text{C}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$ and $\text{D}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$, respectively, are in kHz¹: $\text{C}{}_{101}{}^{\mathrm{(1)}}\text{= 2.4(10)}$, $\text{C}{}_{101}{}^{\mathrm{(2)}}\text{= ?0.6(10)}$, $\text{D}{}_{101}{}^{\mathrm{(1)}}\text{= ?13.8(9)}$, $\text{D}{}_{101}{}^{\mathrm{(2)}}\text{= 7.0(9)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(1)}}\text{= ?5.0(10)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(2)}}\text{= ?5.5(10)}$ and ($\text{C}{}_{\mathrm{J13?}}{}^{\mathrm{(2)}}\text{- C}{}_{\mathrm{J13+}}{}^{\mathrm{(2)}}\text{) = 0.98(9)}$.     

Asymptotic energy scale factors for pseudoscalar meson scattering and charmed meson couplings

Energy scale factors ν₀ for PP → PP scattering amplitudes are related via the absence of exotic resonances to ratios of tensor to vector coupling strengths. These same ratios are extracted from FESR's for non-exotic reactions. The scale factors obtained are all of the order of 1.0 GeV²or less, independent of quantum numbers. This contradicts the expectations of dual amplitudes in which ν₀ = 1/α′, and trajectory slopes are smaller for charmed mesons. Decay widths for tensor mesons are predicted. An observed SU(3) violation for the ratio $\text{A}{}_2\text{→}\text{K}\text{K}\text{/}\text{K}{}^7\text{→}\text{K}\text{π}$ is shown to be consistent with the FESR results. Charmed meson decays are predicted to be factors of 2–3 larger than those predicted by SU(4).     

l-type doubling transitions in Δ states of OCS

Molecular beam electric resonance spectroscopy has been used to measure the l-type doubling transitions in carbonyl sulfide. Transitions in J = 4 to J = 20 have been observed for the (02²0) vibrational state and for J = 1 and J = 2 for the (03¹0) state. The data has been analyzed to give the v = 2 energy separation $\text{E}{}_{\mathrm{<mtext>\Delta </mtext>}}{}^0\text{- E}{}_{\mathrm{<mtext>\Sigma </mtext>}}{}^0\text{= ?5.7861(2) + 8.36(1) × 10}{}^{\mathrm{?5}}\text{J(J + 1)}\text{cm}{}^{\mathrm{?1}}$, and the vibrational dependence of q to be 86.52(9)(v₂ + 1) KHz. The dipole moment of the (02²0) vibrational state is 0.6936(3) D.     

Sequential two-photon spectroscopy of some ion-pair states of IBr

Molecular constants of the first E 0⁺ ion-pair state of IBr vapor have been determined using polarization-labeling spectroscopy applied to the sequential transitions E 0⁺ ← B′ 0⁺ ← X 0⁺, while the second f 0⁺ ion-pair state is reported and characterized for the first time. A least-squares, simultaneous analysis of data for the I⁷⁹Br and I⁸¹Br isotopes gives the following constants (in cm^?1) for I⁷⁹Br:

$\text{E}\text{state}\text{: T}{}_{\mathrm{<mtext>e</mtext>}}\text{= 39487.32(12), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{= 119.518(21), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{ξ}{}_{\mathrm{<mtext>e</mtext>}}\text{= 0.2109(12)}$

,

$\text{ω}{}_{\mathrm{<mtext>e</mtext>}}\text{y}{}_{\mathrm{<mtext>e</mtext>}}\text{= ? 2.34(22) × 10}{}^{\mathrm{?4}}\text{, B}{}_{\mathrm{<mtext>e</mtext>}}\text{= 2.9701(14) × 10}{}^{\mathrm{?2}}$

,

$\text{α}{}_{\mathrm{<mtext>e</mtext>}}\text{= 5.43(59) × 10}{}^{\mathrm{?5}}\text{,}\text{and}\text{γ}{}_{\mathrm{<mtext>e</mtext>}}\text{= ? 6.8(16) × 10}{}^{\mathrm{?7}}$

.

$\text{F}\text{state}\text{: T}{}_{\mathrm{<mtext>e</mtext>}}\text{= 45382.58(17), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{= 128.805(66), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{ξ}{}_{\mathrm{<mtext>e</mtext>}}\text{= 0.3630(69)}$

,

$\text{ω}{}_{\mathrm{<mtext>e</mtext>}}\text{y}{}_{\mathrm{<mtext>e</mtext>}}\text{= ? 9.7(22) × 10}{}^{\mathrm{?4}}\text{, B}{}_{\mathrm{<mtext>e</mtext>}}\text{= 3.0073(30) × 10}{}^{\mathrm{?2}}\text{,}\text{and}\text{α}{}_{\mathrm{<mtext>e</mtext>}}\text{= 8.52(48) × 10}{}^{\mathrm{?5}}$

. Preliminary data for the first $\text{Ω}\text{= 1}$ ion-pair state, accessed in the sequence $\text{1(}{}^3\text{P}{}_2\text{) ← A(}\text{Ω}\text{= 1) ← X 0}{}^{\mathrm{+}}$, indicate that T_e is ?30 cm^?1 higher in energy than that of the E state.     

Gravitational collapse in quantum mechanics with relativistic kinetic energy

It is proved that the quantum mechanical Hamiltonian $\text{H = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{N}}\text{(p}{}^2\text{+ m}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? κ Σ}{}_{\mathrm{i>j}}\text{|x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{|}{}^{\mathrm{?1}}$ for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^?1 (resp. $\text{N ≤ c}{}_{\mathrm{f}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). H is unbounded from below if N ≥ c_b^lκ^?1 (resp. $\text{N ≥ c}{}_{\mathrm{f}}{}^{\mathrm{l}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).     

Weak decays of the charmed baryon C0+ and the inclusive yield of Λ and p

We calculate the decay rates of the charmed baryon state C₀⁺(2.26) into 25 two body and quasi two body states involving baryons and mesons with $\text{J}{}^{\mathrm{P}}\text{=}\text{1}\text{2}{}^{\mathrm{+}}\text{,}\text{3}\text{2}{}^{\mathrm{+}}\text{, 0}{}^{\mathrm{?}}\text{and}\text{1}{}^{\mathrm{?}}$. These modes yield a width of Γ = 16.3 × 10¹²s^?1and an inclusive yield of $\text{Λ/}\text{p}\text{? 40\%}$.     

Effects of multiplicity on charm semileptonic decay distributions

We consider the effects of multiplicity in semileptonic decays of charmed D(1.87) mesons, produced near threshold in e⁺e^? collisions. We calculate the decay distributions from uncorrelated D → (nπ)Kev and resonance dominated $\text{D}\text{→}\text{K}{}^1\text{e}\text{v}$ modes. Recent data from DORIS suggest that modes with two or more final hadrons dominate strongly.