Pion-nucleon vertex function and the one-pion exchange potential

We calculate the πNN vertex function from field theory and dispersion relations. It contains no adjustable parameters, the only input being S- and P- waves for $\text{ππ →}\text{N}\text{N}$. Our vertex function, having an effective cut-off mass of 5μ and an rms radius of 0.52 fm, compares well with previous experimental determinations. We find negligible effects from the 3π dressing of the π propagator. The corrected OPEP is significantly different from the uncorrected OPEP for r < 1.5 fm. The inclusion of the corrected OPEP in meson exchange potentials will improve agreement with phenomenology.     

Determination of the one-pion exchange potential from pn and pp charge exchange scattering

The πNN vertex function is determined from $\text{d}\text{σ}\text{d}\text{t}$ for pn → np and $\text{p}\text{p →}\text{n}\text{n}$ at 8 GeV/c in the interval 0 < ? t < 0.1 GeV². A “regularor mass” of 3.5m_π=488 MeV is found, corresponding to an “extension” of 0.40 fm of the πNN vertex. The resulting OPE potential is discussed.     

Dual parton model and the photoproduction of pseudoscalar and vector mesons in the high energy region

On the basis of the dynamical dual model of strong interactions followed from the parton model of hadrons as discussed in an earlier paper, we study here the photo-production of pseudoscalar and vector mesons in the high energy region. To incorporate the concept of duality, it is taken that any two spin $\text{1}\text{2}$ pointlike constituents (partons) can form a π-meson cluster in the structure of a nucleon and the basic interaction involved in MB scattering is the interaction of the incident meson with the π meson in the structure of the nucleon. In this scheme, the amplitudes for the photoproduction of mesons such as γN → Nπ, γN → N?, and γN → Nω in the high energy region can be related with the amplitudes for the process γπ → ππ, γπ → π?, and γπ → πω, respectively. To calculate the amplitudes for the relevant process we also consider a factor corresponding to the structural rearrangement of partons involved in duality diagrams. To obtain the cross sections, we take into account the photon-vector meson analogy, though the naive form of the vector dominance model (VDM) has not been considered here. From a knowledge of the coupling constants $\text{γ?}{}^2\text{4π}$, $\text{γω}{}^2\text{?π}$, , and we obtain the differential cross sections which are in excellent agreement with experimental results. Also we obtain a good fit for the scattering process γN → Nπ at backward angles. For the vector meson production processes, we have contributions from the diffraction mechanism also apart from the amplitudes considered here. In the region where the contribution from the diffraction part is negligible, we obtain the relation

which is in nice agreement with experiments. Finally, it is shown that, though the vector meson dominance is not considered here, the universality of the vector meson coupling with hadrons follows directly from the present model.     

The pion propagator in relativistic quantum field theories of the nuclear many-body problem

Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models: the scalar-vector theory of Walecka, extended to include π and ρ mesons in a non-chiral fashion, and the linear σ-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pion propagator is evaluated in the onenucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual $\text{N}\text{N}$ loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently. Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored. The techniques developed here allow for a consistent treatment of these models using renormalizable relativistic quantum field theores.     

The magnitude of annihilation and penguin contributions to charm-meson decays

A consistent treatment of color singlet and octet contributions in the spectator constituent gluon model for pseudoscalar meson decays is attempted. The result comes out one order of magnitude too small to explain the observed life-time difference of D⁰ and D⁺. Furthermore, it is found that ‘penguin’ interactions in the annihilation channel may give contributions to the asymmetry of the (D⁰ → K⁺K^?)/(D⁰ → π⁺π^?) ratio of the order of the phase-space difference or larger. Finally, it is argued that annihilation cannot explain the $\text{ΔI =}\text{1}\text{2}$ rule for kaon decays; dynamical effects including the penguin interactions seem still to be needed.     

Asymptotic freedom,light quarks and the origin of the ΔT = 12 rule in the non-leptonic decays of strange particles

A dynamical mechanism for the $\text{ΔT =}\text{1}\text{2}$ rule in the non-leptonic decays of strange particles is considered. The weak interactions are described within the Weinberg-Salam model while the strong interactions are assumed to be mediated by the exchange of an octet of colour vector gluons. It is shown that the effect of the strong interactions gives rise to new operators in the effective Hamiltonian of weak interactions which contain both left- and right-handed fermions. These operators satisfy the $\text{ΔT =}\text{1}\text{2}$ rule, and estimates within the relativistic quark model indicate that their contribution dominates the physical amplitudes of the K → 2π, 3π decays.     

A t-channel isospin analysis of the chew-low plot for NN → N(Nπ) interactions at 5.7 GeV/c

A new approach to the t-channel isospin analysis of ZN → Z′(Nπ) reactions is presented. This approach, useful for $\text{Z = N,}\text{N}\text{, K}{}^{\mathrm{?}}$ when only five independent sets of data are availables, is used to analyse data of $\text{N}\text{N →}\text{N}\text{(Nπ)}$ reactions obtained in a $\text{p}\text{p →}\text{N}\text{N}\text{π}$ experiment at $\text{5.7}\text{GeV}\text{/c}\text{and a}\text{p}\text{d →}\text{N}\text{Nπp}{}_{\mathrm{s}}$ experiment at 5.5 GeV/c. the t behaviour of the different isospin exchange amplitudes, suggests their exchange mechanism production. The mass spectrum, M_πN, of the contributions produced by exchanged isospin I_ex = 1, shows enhancements corresponding to N(1490) N(1670) and Δ(1230) isobars, while the mass spectrum for I_ex = 0 presents only a large bump at ～1350 MeV commonly identified as N¹(1400).     

Polarization observables in π-d scattering

Exact calculations of vector and tensor polarizations are presented for the reaction $\text{π +}\text{d}\text{→ π +}\text{d}$ at T_π = 142 MeV. They are aimed at meeting the apparent demand raised by upcoming pertinent experiments. The effects of (i) deuteron D state, (ii) participating π-N partial waves and (iii) coupling of different π-d orbital angular momenta are found to be very important.     

The πNN vertex function and off-mass-shell πN scattering

We have extended the dispersion relation calculation of the πNN vertex function to include off-shell terms in the πN scattering matrix. These off-shell terms are constrained by the current algebra and PCAC results, and contribute to the $\text{N}\text{N}\text{→ ππ}$ s-wave. As such, they add to the kinematic off-shell effects which Durso, Jackson and VerWest found in the p-terms. The off-shell terms increase the calculated Goldberger-Treiman discrepancy from 0.02 to 0.03, bringing it into agreement with the field theory value of Jones and Scadron (0.035). The calculated discrepancy remains smaller than the experimental value of 0.06±0.01.     

Quantization of linear maps on a torus-fresnel diffraction by a periodic grating

Quantization on a phase space q, p in the form of a torus (or periodized plane) with dimensions Δq, Δp requires the Planck's constant take one of the values h = ΔqΔp/N, where N is an integer. Corresponding to a linear classical map T of points q, p is a unitary operator U mapping quantum states that are periodic in q and p; the construction of U involves techniques from number theory. U has eigenvalues exp(iα). The ‘eigenangles’ α must be multiples of $\text{2π}\text{n(N)}$, where n(N) is the lowest common multiple of the lengths of the classical ‘cycles’ mapped under T by those rational points in q, p which are multiples of $\text{Δq}\text{N}$ and $\text{Δp}\text{N}$ (i.e. n(N) is the ‘period of T mod N′), at least for odd N. If T is hyperbolic, n is a very erratic function of N, and the classical limit N → ∞ is very different from the ‘Bohr-Sommerfeld’ behaviour for parabolic maps. The degeneracy structure of the eigenangle spectrum is related to the distribution of cycle lengths. Computation of the quantal Wigner function shows that eigenstates of U do not correspond to individual cycles.     

Elastic backwardpd-scattering in Δ-resonance region

Contribution ofΔ-resonance mechanism to elastic backwardpd-scattering overT ₀ =0.5–0.8 GeV range of incident energy is analyzed. As distinct from [1–3], the parameters ofNN?NΔ amplitudes in the phenomenology of one-mesonπ- andρ-exchange are determined frompp→pnπ ⁺ reaction immediately in the kinematic region where the processpd→dp occurs. It has been found as a result that in the vicinity of the region whereΔ-isobar is present on-mass-shell, the coherent sum of the amplitudes ofΔ-resonance mechanism, relativistic one-nucleon exchange and single scattering predicts thepd→dp cross-section to be twice smaller than the experimental one and does not describe the tensor polarization oft ₂₀ deuteron. Possible causes of this discrepancy as well as the relation between the mechanisms ofpd→dp process and the data on reactions of quasi-elastic knock-out of fast deuterons by protons (p,pd) from light nuclei, are discussed.     

Exact solution of a model for πd induced reactions and its application to pion-nucleus reactions

Reduction techniques are applied to πd elastic scattering and π-absorption in a theory without anti-nucleons. In a one-pion approximation we derive two sets of exact coupled-channel equations for respectively the amplitudes T_πd,NN, T_{Nδ, NN} and T_{πd, πd}, T_{d, NΔ}- Alternatively we express in terms of the absorption amplitude T_{πd, NN} available solutions for a three-body problem restricted to the πd and NΔ channels. We explicitly demonstrate that our model (which comes close to the one of Thomas, Mizutani and Koltun) strictly respects the Pauli principle and avoids double-counting. Using the same technique we determine amplitudes for the (π, 2N) reaction and for π (in)elastic scattering on general nuclei in terms of amplitudes amongst the NN, NNπ channels. Both the elastic amplitude and the πA optical potential are shown to decompose into a multiple scattering part based on an input πN amplitude without the P₁₁ partial wave and calculable absorption corrections.     

Spin-parity analysis of the nπ+ system produced in the reaction π+p → π+π+n at 16GeV/c

A spin-parity analysis of the nπ⁺ system produced in the reaction π⁺p → π⁺π⁺n at 16 MeV/c has shown apart from the mass enhancements associated with the known resonances Δ⁺(1238), N¹(1520) and N¹(1688) there is an enhancement peaked at M(nπ⁺) ? 1.35 GeV, ∑0.2 GeV wide. For masses below M(nπ⁺) ? 1.35 GeV this enhancement is predominantly due to $\text{J}{}^{\mathrm{P}}\text{=}\text{1}\text{2}{}^{\mathrm{?}}$ states, predominate. The presence of $\text{J}{}^{\mathrm{P}}\text{=}\text{1}\text{2}{}^{\mathrm{?}}$ states indicates that the rule ΔP = (?1)^ΔJ is strongly violated in the diffractive process N → Nπ, and hence it cannot be considered a specific characteristic of all diffractive processes.     

Large-pTπ0 production with pion beams and dominance of the subprocess quark + quark → baryon + antiquark

We compare the predictions of the subprocesses M + q → M + q, q + $\text{q}$ → M + M, q + q → B + q?, for large-p_Tπ⁰ inclusive production in π^?p collisions, with the data. Calculations performed with various models show, in a model independent way, that q + q → B + q? is dominant in pp collisions.     

Investigation of rare non-strange decay modes of the f meson in Π+p interactions at 5GeVc

Rare decay modes of the f meson are studied in the final states Δ⁺⁺π⁺π^?π⁺π^?, Δ⁺⁺π⁺π^?MM and Δ⁺⁺π⁺π^?π⁺π^?MM. The ratio $\text{Γ (f → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{π}{}^0\text{)}\text{Γ(f → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$ is 0.23 ± 0.09 and Γ(f → 4 π) saturates the f inelasticity. A 2 s.d. upper limit of 0.09 is found for the branching ratio $\text{(f → ηη)}\text{(f → 2π)}$.     

Evidence for double dissociation in K-p interactions at 14.3 GeV/c

We have studied the reaction K^-p → K^-π⁺π^-π⁺π^-p at 14.3 GeV/c to search for evidence of the double dissociation process $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{QN}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1$. In the channel $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{K}{}^{10}\text{(890)}$π₁^-π₂^-Δ⁺⁺ (1236) there is evidence for simultaneous production of low-mass enhancements in the $\text{K}{}^{10}\text{π}{}_1{}^{\mathrm{-}}$ and Δ⁺⁺(1236)π₂^- subsystems which correspond to the $\text{Q}\text{→}\text{K}{}^1\text{(890)π}$ and $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1\text{→ Δπ}$ decay modes. In this particular final state the double fragmentation system is produced with a cross section of the order of a few microbarns. Our data are consistent with the factorizable pomeron exchange model of double diffractive dissociation.     

Isospin analysis of the reactions pp→N(Nπ) at 12 and 24 GeV/c

The reaction pp → nucleon + nucleon + pion at 12 and 24 GeV/c is analyzed in terms of the isospin amplitudes for the production of the (Nπ) system. The energy dependence of the $\text{I(}\text{N}\text{π) =}\text{1}\text{2}$ amplitude is weak, while the $\text{I(}\text{N}\text{π) =}\text{3}\text{2}$ contribution shows the strong energy dependence known from meson exchange reactions. The slope parameter B of the dσ/dt′ distributions of the $\text{I(}\text{N}\text{π)=}\text{1}\text{2}$ contribution is a strong function of the (Nπ) mass, decreasing sharply from about 12 GeV^?2 at threshold to about 4 GeV^?2 above 1700 MeV. Comparing our results for the $\text{I(}\text{N}\text{π) =}\text{1}\text{2}$ cross section with those of similar investigations in πp and Kp reactions, we find that factorisation is valid within experimental errors. The results support the conclusion that the $\text{I(}\text{N}\text{π) =}\text{1}\text{2}$ contribution is dominated by diffraction dissociation of the proton.     

The mixing and decays of isoscalar mesons

The predictions of a linear mass mixing model for pseudoscalar and vector mesons, which incorporates the effects of radial excitations, are examined. Several analyses are made fitting in each case to a different experimental value of $\text{Γ(ψ →η'γ)}\text{Γ(ψ→ηγ)}$ upon which the η-η′ mixing pattern is very sensitive. Predictions for radiative transitions among the mesons and for the ratio of production amplitudes $\text{σ}\text{(π}{}^{\mathrm{?}}\text{p→η′n)}\text{σ}\text{(π}{}^{\mathrm{?}}\text{p→ηn)}$ are compared with experiments. Results indicate a preferred value of 3.1 for $\text{Γ(ψ→η′γ)}\text{Γ(ψ→ηγ)}$.     

Meson decays in the non-relativistic quark model

Treating light as well as heavy pseudoscalar and vector mesons as non-relativistic quarkonia, we calculate various decay modes, including lowest QCD corrections. All decay modes studied are in good agreement with experiment, indicating that the quarkonium treatment is applicable to light mesons η, η′, π, also. Consistency of the quarkonium and current algebra treatments for the process π⁰ → 2λ leads to $\text{f}{}_{\mathrm{\pi }}\text{= (}\text{3}\text{2π}\text{)m}{}_{\mathrm{<mtext>u</mtext>}}\text{{1 ? (0.62/4π)α}{}_{\mathrm{<mtext>s</mtext>}}\text{(μ)},}\text{where}\text{m}{}_{\mathrm{<mtext>u</mtext>}}$ is the constituent u-quark mass, and $\text{f}{}_{\mathrm{\pi }}\text{? 93}\text{MeV}$.     

Coherent π0 production in neutrino reactions

We have calculated the cross section and angular distribution of the neutral current process $\text{ν +}\text{N}\text{→ ν +}\text{N}\text{+ π}{}^0$ involving the coherent interaction of a neutrino with a complex nucleus. A contrast is made to incoherent production ν + n → ν + n + π⁰ on a single nucleon. The results are compared with observations from some recent experiments.