Meson Pole Research Articles

DOMINANCE OF LONG DISTANCE EFFECTS IN THE KL-KS MASS DIFFERENCE

It is argued that the asymptotic behavior of the matrix elements of Hw involving on-mass-shell ground-state mesons with infinite momenta, which were instrumental in explaining the |ΔI|=1/2 rule in the K→ππ decays, actually implies [Formula: see text]. The long distance effects (contributions of PS and vector meson poles and ππ intermediate states) may reproduce the observed KL−Ks mass difference, consistent with the |ΔI|=1/2 rule. Its estimate is however sensitive to the η-η′-… mixing.

The K ∗ pole model of K → ππ decays and final-state interactions

It is shown that final-state interactions can enhance (suppress) substantially the ΔI = 1 2 (ΔI = 3 2 ) K → ππ parity-violating decay amplitude calculated from the K ∗ vector meson pole model. This enhancement (suppression) combined with short-distance QCD corrections to the effective weak interaction almost brings the K ∗ pole model into agreement with experiment.

A study of the ϱ0 meson polarization in π− p reaction at 5 GeV/c

Experimental data onϱ0 meson polarization inπ−p reaction at 5 GeV/c are presented. Change inϱ0 meson polarization for ϱ mesons produced at smallP ⊥ 2 and atP ⊥ 2 ≧ 0·3 or produced in backward direction in CMS is demonstrated. Natural explanation of these phenomena is one pion exchange mechanism and mechanism of quark-antiquark annihilation as observed forϱ0 meson production in¯pp reactions.

Hadronic poles andΩ−nonleptonic decays

Separable contributions to the ${\ensuremath{\Omega}}^{\ensuremath{-}}$ nonleptonic decays are replaced by $K$-meson poles. This leads to a theoretical description which shows that the experimental results support general theoretical ideas such as the Weinberg-Salam electroweak theory, QCD, and SU(6) quark structure of hadrons.

Schematic model of mesons based on analytic propagators

Formation of mesons is studied in a model where the confinement phenomenon is parametrized through entire-analytic and asymptotically free propagators for "would-be interpolating" fields with quark and gluon quantum numbers. It is pointed out that with such propagators the corresponding proper vertices necessarily have principal-value infrared singularities in external ${(\mathrm{mass})}^{2}$ variables. With the simplest $\mathrm{qqg}$ vertex model embodying those singularities, the quark-antiquark Bethe-Salpeter equation driven by dressed one-gluon exchange possesses an exact analytic solution. The solution is studied in a simplified scalar model omitting spinor structure. It exhibits a meson pole in the color-singlet channel only and no cuts, the meson mass depending nonanalytically on the coupling constant. The model illustrates, on a phenomenological level, an unconventional binding mechanism: Field configurations having no particle character---while looking like particles at large momentum transfers---can nevertheless interact to form stable hadrons, through a mechanism that invokes neither a confining potential nor the notion of a constituent mass.

Vector-meson contributions to the isovector electric nucleon form factor

The analysis of space-like data on the isovector part of the electric nucleon form factor GEV(t) is carried out by means of a new analytic parametrisation of GEV(t). The analysis confirms the importance of the short logarithmic cut on the second sheet just below the pi pi threshold coming from nucleon exchange in the pi N scattering amplitude. It also favours the existence of a rho pole on the second Riemann sheet and of rho '- and rho -meson poles on the third Riemann sheet in the variable t. The analysis gives REV=0.87 fm for the isovector electric nucleon radius and estimates the corresponding coupling constants.

The compton effect on a vector meson with consideration of polarization

Using the covariant method of matrix element calculation, an explicit expression is obtained for the differential sections of the Compton effect on a vector meson with consideration of meson (photon) polarization in summing over polarized photons (mesons). The behavior of the sections is analyzed for several special cases.

Possible tests for the ρ meson as a gauge particle

Investigates the existence of a self-coupling, non-Abelian isospin gauge field. The authors assume that the rho meson is the gauge field for the isospin group, and it couples to pions and itself via the prescription of Yang-Mills theory. The decay rho to pi pi gamma would show an effect of a few per cent up to 32% due to this non-linear coupling, as opposed to the normal coupling. The production of a rho -meson pair in e+e- to rho + rho - can also show up such an effect in the rho -meson pole energy region.

Nonleptonic Decays of Charmed Mesons under the W-Exchange Dominance Hypothesis

Two- and three-body decays of charmed mesons are studied under the “W-exchange” dominance hypothesis. As for the two-body decays, the branching ratios for them are calculated in the scalar meson pole approximation. It is seen through a phenomenological analysis that the contribution of the annihilation diagram is much smaller than that of the W-exchange. This predicts that the F+→π+η decay is considerably suppressed although it is a Cabibbo favored decay. It is also seen that the new Cabibbo angle θc′ which is defined in the charm changing currents is nearly equal to the old one θc. The soft meson technique combined with a linear approximation is applied to the three-body decays. The calculated value of B(D+→π+π+K-) reproduces considerably well the experimental value, but this method is not successful in the other three-body decays of D mesons. The branching ratios for these decays calculated by assuming that quasi tow-body decays contribute dominantly to these decays are almost consistent with the known data.

Deviation from the exactSU 3 symmetry in hadronic decays of ψ and contributions of electromagnetic interactions

It is assumed that hadronic two-body decays of ψ proceed via the ψ-V (V=ρ, ω, ϕ) mixing and that the strong interactions which induce the ψ→V transition are mediated by gluons. The deviations from the exactSU 3 symmetry in the decays of ψ and the contributions of the amplitudes via the ψ→V transition mediated by a photon are examined semi-phenomenologically by fitting the calculated branching ratios for these decays to the corresponding experimental data. Our results are the following. i) There are sizable deviations (0.3≲β≲0.5) from the exactSU 3 symmetry in the decays of ψ into two-boson final states. They can be understood in terms of the symmetry-breaking effects in the residues of the vector meson poles. ii) The contributions of the amplitudes via the one-photon intermediate state are neither negligibly small nor dominant (|G(u)/E(u)|≈2.8). iii) The relative phase between the amplitudes via the gluon and the one-photon intermediate states is approximately equal to π/2. By using the values of the parameters estimated in this way, the branching ratios for the decays in which the amplitudes via the one-photon intermediate state dominate (in theSU 3 symmetry limit) can be predicted. Γ(f→2γ) is also discussed by using the vector meson dominance hypothesis.

The role of instantons in generation of mesonic mass spectrum

It is suggested that instantons play the leading role in the mixing of s s and u u+ d d quark states in mesonic nonets and in the explanation of the Okubo-Zweig-Iizuka (OZI) rule. The non-diagonal polarization operator Π su = 〈0| T{ j s( x) j u( y)}0〉 is considered where j s = s O s and j u = u O u are the currents of the s and u quarks. It is proved that in the dilute instanton gas approximation for quarks in the external instanton field Π su = 0 for the vector and tensor currents and Π su≠0 for the axial current. Hence, after saturating Π su by the low-lying mesonic states, we obtain the qualitative explanation of the OZI rule. The Q 2 dependence of the non-diagonal polarization operator of the axial currents, Π su( Q 2), is calculated and compared with the η′ meson pole term. Taking account of terms ∼ m q 2 allows one, using the experimentally known ηη′ mixing angle, to find the η′ meson coupling constant with the axial current F η′ ≈ 150 MeV and to estimate the η′ π mixing angle.

High-energy hadron dynamics based on a stochastic-field multieikonal theory

Multieikonal theory, using a stochastic-field representation for collective long-range rapidity correlations, is developed and applied to the calculation of Regge-pole parameters, high-transverse-momentum enhancements, and fluctuation patterns in rapidity densities. If a short-range-order model, such as the one-dimensional planar bootstrap, with only leading $t$-channel meson poles, is utilized as input to the multieikonal method, the pole spectrum is modified in three ways: promotion and renormalization of leading trajectories (suggesting an effective Pomeron above unity at intermediate energies), and a proliferation of dynamical secondary trajectories, reminiscent of dual models. When transverse dimensions are included, the collective effects produce a growth with energy of large-${P}_{T}$ inclusive cross sections. Typical-event rapidity distributions, at energies of a few TeV, can be estimated by suitable approximations; the fluctuations give rise to "domain" patterns, which have the appearance of clusters separated by rapidity gaps. The relations between this approach to strong-interaction dynamics and a possible unification of weak, electromagnetic, and strong interactions are outlined.

Vector meson couplings and the obsevability of the K → Kππ decays

The K ∗ → Kππ rate is calculated using vector meson pole dominance in several recent coupling-constant models. Including the effects of the contact interaction, the various models give results ranging from 8 to 86 keV for the decay rate. Taking the ω → 3π and ø → 3π decays into accont, we believe the result of 50 keV to be more reliable upper bound. This is significantly higher than older estimates and within the realm of experimental measurement.

SU(3) symmetry for the vector meson-nucleon interaction

When comparing data on VBB coupling constants with SU(3) one usually assumes Sakurai's idea that the ϱ-meson couples universally to the isovector current. In order to use this assumption one has to continue the coupling from the vector meson pole to t=0. The implications for the coupling constants depend upon how this continuation is carried out. In this paper we present arguments to expect simple continuation properties for VNN form factors defined in analogy with the Sachs electromagnetic form factors, rather than for the vector and tensor form factors. We show that in this case experimental data are consistent with SU(3), Sakurai's universality idea and with Zweig's rule. Furthermore we find F D ratios close to the SU(6) prediction.

Quarks as consequence of duality and factorization

Duality combined with factorization imposes very stringent conditions on theN-meson amplitude. An attempt to make both duality and factorization manifest in the Baker-Coon dual-resonance model results naturally in an operator representation of theN-meson amplitude which is remarkably quarklike. The representation is described in terms ofN sets of operators which are topologically similar to theN quark lines in a Harari-Rosner diagram. These operators may be «pinched» to generate meson poles, and the resulting mesons can be consistently identified as «quark-antiquark pairs». It is suggested that the quark diagram structure is a natural consequence of duality and factorization.

High-energy πN backward-scattering models and continuous-moment sum rules

High-energy models for πN backward scattering are investigated with respect to consistency with low-energy data using CMSR. As low-energyt-channel input, ππ phase shifts are used below the KK threshold and narrow-width approximations for higher meson poles. Real parts are restricted to appear in thes-channel physical region. A pole model with a double zero in Nα and a « geometrical delta » model reproduce the data on πN → πN and NN → ππ when the parameters are determined by CMSR.

Finite - width effects and subtraction corrections for theA2→3πdecay

Effects of interference between $\ensuremath{\rho}$-meson poles in the different channels and of subtraction terms for the ${A}_{2}\ensuremath{\rightarrow}3\ensuremath{\pi}$ decay are estimated. Goldberg's formula for the interference correction is discussed and tested by numerical calculations. The FDR-FESR (finite dispersion relation-finite-energy sum rules) technique is used to estimate the correction due to the subtraction. It is found that the effect of a finite $\ensuremath{\rho}$ width and also the subtraction effect lead to small corrections to the decay width.

Comment on theη→3πpuzzle in the (3,3¯) model

By including a ${u}_{3}$ term in ${H}_{\mathrm{em}}$ and taking into account rapidly varying meson poles, we show that the nonvanishing $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ amplitude is consistent with pion PCAC and current algebra. In this case, the $\ensuremath{\sigma}$ term ${\ensuremath{\sigma}}_{\ensuremath{\eta}\ensuremath{\eta}}^{\ensuremath{\pi}\ensuremath{\pi}}$ must be substantially larger than that obtained in the Gell-Mann-Oakes-Renner (3, $\overline{3}$) scheme.

Observation of vector meson production in inclusive pp reactions

We have measured cross sections, rapidity and transverse momentum distributions, and vector meson polarization for the reactions pp→ ϱ o +anything, pp→ ω+charged particles, and pp→ K ∗±+ anything at incident laboratory momenta of 12 and 24 GeV/ c. We discuss various consequences of our results as well as possible connections with lepton pair production.

Properties of Polarization Density Matrix in Regge-Pole Models

We study two-body (or quasi-two-body) parity-conserving reactions with unpolarized beam and target. From the general considerations of angular momentum and parity conservation we derive the structure of the density matrices of the final particles. This structure becomes conspicuous when one uses transversity quantization with a special reordering for the lines and columns. We study the predictions of a single Regge trajectory exchange model. We derive the consequences of reality and factorization of residue functions, and of parity conservation at each vertex. The results are summarized in two tables. For the cases of low-spin particles we give these results in a geometrical form. As an example we plot some experimental data on $Q$-meson polarization.