Dispersion theory of parity non-conservation in pion-nucleon scattering at low energies

We examine the possibility for testing the weak parity non-conserving (pnc) interaction in pion-nucleon scattering at low energies. We start out analysis by assuming the existence of a pnc πNN coupling which conserves time reversal invariance and has the isospin selection rule ΔI = 1, and the existence of fixed-t dispersion relations obeyed by the pnc invariant amplitudes. By using the nonrelativistic expansion, we then derive dispersion relations for the partial-wave amplitudes.We calculate parity-odd observables in π^?p → π^?p and in π^?p → π⁰n, e.g., the up-down asymmetry α in the total cross section for a polarized target and the longitudinal polarization P of the recoil nucleon. In the conventional Cabibbo model for the weak interaction P and α are found to be of order 10^?7 to 10^?8.We have also examined the t-channel pnc ?-exchange process which has the isospin selection rule ΔI = 0, 2 and found it to contribute dominantly to P in the charge-exchange channel π^?p → π⁰n.     

Effects of final-state interactions in pure annihilation decay of B s 0 → π+π −

The hadronic decay of B _s ⁰ → π ⁺ π ^? is analyzed by using “QCD factorization” (QCDF) method and final-state interaction (FSI). First, the B _s ⁰ → π ⁺ π ^? decay is calculated via QCDF method and the annihilation graphs only exist in this method. Hence, the FSI must be seriously considered to solve the B _s ⁰ → π ⁺ π ^? decay and the K ^+(*) K ^?(*) and \(K^{0(*)} K^{\bar 0(*)}\) via the exchange of K ^0(*) and K ^?(*) mesons are chosen for the intermediate states. To estimate the intermediate state amplitudes, the QCDF method is again used. These amplitudes are used in the absorptive part of the diagrams. The experimental branching ratio of B _s ⁰ → π ⁺ π ^? decay is less than 1.2 × 10^?6 and our results according to the QCDF method and FSI are 0.68 × 10^?8 and 1.18 × 10^?6, respectively.     

ψψ → π0π0 and η → π0ψψ at low energy within the extended Nambu Jona-Lasinio model

Within the Extended Nambu Jona-Lasinio model, we calculate the O(π⁶) counterterms entering the low-energy expansion of the ψψ → π⁰π⁰ and the η → π⁰ψψ amplitudes in Chiral Perturbation Theory. For ψψ → π⁰π⁰ our results are compatible with both the experimental data and the two-loop calculation using meson resonance saturation. For the η decay we find Φ(η → π⁰ψψ) = 0.58 ± 0.3 eV which is in agreement with experiment within one standard deviation. We also give predictions for the neutral pion polarizabilities and compare them with the results obtained from resonance saturation.     

Bound states and scattering from bound states in the light-front field theory dynamics

Starting from the Weinberg rules we derive a covariant form of the relativistic Schrödinger equation and formulate the bound state problem in the light-front field theory dynamics. We present an explicit rule for embodying the two-body subsystem in the three-body space and demonstrate that the cluster decomposition property is explicitly preserved in the light front field theory dynamics. As an application of these results we write amplitudes forπd→nN ^*, πd→πpn, andπd→πd, in the impulse approximation, in terms of the internal bound state wave functions and two-body reducedt-matrix elements.     

The Skyrme model with a U*(1) gauged Wess‐Zumino term in a noncommutative spacetime

The Skyrme model is generalized for a noncommutative spacetime with the Weyl‐operators of SU(2) matrices and the corresponding star‐product. The unitary condition and the topological current can be extended to star‐exponential matrices. The Wess‐Zumino term which breaks unphysical symmetries of the Skyrme action is gauged with the U_*(1) group to allow for electromagnetic processes in a noncommutative spacetime. Apart from corrections to the anomalous decay γ→π⁰π⁺π^– in commuting spacetime, the additional anomalous process γ→π⁰π⁰π⁰ is found in the U_*(1) gauged Wess‐Zumino action for a noncommutative spacetime.     

Theoretical study of deuteron polarization in γ+d → π0+d

The state of polarization of the recoil deuteron in γ+d → π⁰+d on unpolarized and target polarized deuterons is analyzed in detail. A new set of statistical tensors is introduced to describe non-oriented systems, such as the recoil deuteron in γ+d → π⁰+d, and their relationships to the vector and tensor polarization parameters are established. The new statistical tensors reduce, in the case of oriented systems, to Fano's statistical tensors. Numerical results are computed using two different deuteron models for polarized photon asymmetry, polarized target asymmetry and the vector and tensor polarizations of the recoil deuteron, and these are presented at various c.m. pion production angles at different energies in the region of the first π-N resonance. The study of these parameters is suggested as a promising source of information on isoscalar pion photoproduction amplitudes.     

A Combined Study of the Pion’s Static Properties and form Factors

We study consistently the pion’s static observables and the elastic and γ* γ → π ⁰ transition form factors within a light-front model. Consistency requires that all calculations are performed within a given model with the same and single adjusted length or mass-scale parameter of the associated pion bound-state wave function. Our results agree well with all extent data including recent Belle data on the γ* γ → π ⁰ form factor at large q ², yet the BaBar data on this transition form factor resists a sensible comparison. We relax the initial constraint on the bound-state wave function and show the BaBar data can partially be accommodated. This, however, comes at the cost of a hard elastic form factor not in agreement with experiment. Moreover, the pion charge radius is about 40 % smaller than its experimentally determined value. It is argued that a decreasing charge radius produces an ever harder form factor with a bound-state amplitude difficultly reconcilable with soft QCD. We also discuss why vector dominance type models for the photon-quark vertex, based on analyticity and crossing symmetry, are unlikely to reproduce the litigious transition form factor data.     

Multipion production in photon-photon collisions

The magnitudes of the matrix elements for γγ→2π⁺2π^?, γγ→π⁺π^?2π⁰, γγ→2π⁺2π^?π⁰, γγ→2π⁺2π^?2π⁰, γγ→3π⁺3π^?3π⁺ and γγ→3π⁺3π^?π⁰are deduced from experimental data as a function of the invariant massW of the system (from 1.0 to 3.0 GeV). It is shown that the data are consistent with a universal energy dependence of the reduced channel amplitudes. A statistical model is shown to describe the peaks in the energy dependence of multipion production in γγ collisions quite well without introducing explicit intermediate resonances.     

Double Regge exchange phenomenology

We construct a double Regge exchange amplitude which has the proper analytic structure and which is phenomenologically viable. The various couplings involved can be estimated using pole extrapolation techniques which are successful in two-body scattering. We explicitly calculate the double Regge exchange contributions to the well-measured, and related, processes K^±p → K⁰π^±p and π^?p → K^?K⁰p. In this way the observed features of the dimeson partial-wave production amplitudes are used to text the double-exchange approach.     

A microscopic model for the pd → tπ+ reaction

A microscopic model for the pd → tπ⁺ reaction is constructed using two-body isobar wave functions containing the Δ(1236). This model results in an analytical form for the reaction cross section and so it is possible to check the validity of those more approximate models that relate the pd → tπ⁺ cross section to the pp → dπ⁺ cross section. The calculations are performed at the three proton lab energies of 400, 470 and 600 MeV.     

The evaluation of the branching ratios of the decays φ(1020)→2π<Superscript>+</Superscript>2π<Superscript>−</Superscript>π<Superscript>0</Superscript>, π<Superscript>+</Superscript>π<Superscript>−</Superscript>3π<Superscript>0</Superscript>

Combining the Okubo-Zweig-Iizuka rule in the decay φ→ρπ→π⁺π^?π⁰ with the ρ→4π decay amplitudes, we calculate the φ→2π⁺2π^?π⁰ and φ→π⁺π^?3π⁰ ones. The partial widths of the above φ decays are evaluated, and the excitation curves in e⁺e^? annihilation are obtained, assuming reasonable particular relations among the parameters characterizing the anomalous terms of the HLS Lagrangian. The evaluated branching ratios B_φ→π⁺_π^?_3π⁰ ≈ 2 × 10^?7 and B_φ→2π⁺_2π^?_π⁰ ≈ 7 × 10^?7 are such that, with the luminosity L=500 pb^?1 attained at DAΦNE φ factory, one may already possess about 1685 events of the decays φ→5π.     

Comparison between γN→π and πN→ϱN in the resonance region up to s=1.75 GeV via the vector-dominance-model

We display the helicity amplitudes for the N_? system for each J^P state of the N_π system in the reaction Nπ→N?. These amplitudes are obtained from a K-matrix fit to amplitudes of the reaction Nπ→Nπ and Nπ→Nππ (via the isobar model). We then take either these amplitudes or the resonance couplings estimated from these amplitudes and compare them to the photoproduction amplitudes via the V.D.M. Two possible kinematics are considered for the N_? system below its threshold. These four methods give a range in which the V.D.M. can be accomodated even at this low energy.     

Transition form factors and light-cone distribution amplitudes of pseudoscalar mesons in the chiral quark model

It is shown that a chiral quark model of the Nambu-Jona-Lasinio type can be used to describe “soft”-momentum parts of the amplitudes with large momentum transfer. As a sample, the processes γ* → γ(π, η, η′), where one of the photons, γ*, has large spacelike virtuality, are investigated. The γ* → γ(π, η, η′) transition form factors are calculated for a wide region of the momentum transfer. The results are consistent with the calculations performed in the instanton-induced chiral quark model and agree with experimental data. The distribution amplitudes of pseudoscalar mesons are derived.     

The vector and tensor exchange contributions to πN → πN

Using fixed-t dispersion relations together with experimental data on π^?p → π⁰n we determine the real and imaginary parts of the s-channel helicity amplitudes (SHA) of the vector (?) exchange contribution to πN → πN. The results are in good agreement with amplitude analyses. We also make comparison with finite-energy sum-rules (FESR) and discuss certain implications. Furthermore, on the basis of two-component duality and FESR we calculate the tensor (f) contribution. The t-structure of the resulting SHA is compared with independent information on hadronic tensor exchanges.     

Study of process e + e − → π+π−π0π0 at energies √s < 1 GeV with the spherical neutral detector

The cross section for the process e ⁺ e ^? → π⁺π^?π⁰π⁰ has been measured in an experiment with a spherical neutral detector, with the cross section at energies √s < 920 MeV having been measured for the first time. The model of vector dominance describes well the data obtained if the ρ, ρ′, and ρ″ resonances are taken into account. The probability of the decay ρ → π⁺π^?π⁰π⁰ is B(ρ → π⁺π^?π⁰π⁰) = (1.60 ± 0.74 ± 0.18) × 10^?5. The upper limit for the decay ω → π⁺π^?π⁰π⁰ has been improved by two orders of magnitude compared to previous measurements and is B(ω → π⁺π^?π⁰π⁰) < 2 × 10^?4 at a 90% confidence level.     

Investigation of nucleon electromagnetic form factors in the unphysical region by means of the ̄NN → πl + l − reactions

A theoretical investigation of ?NN → πl + l ? processes is carried out. First, the general structure of the differential annihilation rate of very slow antinucleons on nucleons at rest into pion and lepton pairs is derived, then the structure of the electromagnetic current of the ?NN → πγ* transition in the case of S-state annihilation is restored and the general properties of the corresponding form factors are demonstrated. Next, by using the treediagram approximation of the amplitude, those form factors are calculated explicitly and for the special process (?pp) → π⁰γ* → π⁰ l ⁺ l ^? they are shown to be completely described by the magnetic form factor of the proton in the unphysical region. Finally, the effective mass spectra of lepton pairs and the integral coefficients of internal conversion for the ?pp → π⁰ l + l ^? and ?pn → π^? l ⁺ l ^? processes are predicted.     

K*0Σ+ Photoproduction from Threshold to 3.0 GeV

The CLAS collaboration and the CBELSA/TAPS collaboration reported the differential cross section data for K*⁰ photoproduction, and found that the t-channel K exchange dominates the production amplitudes at small scattering angles. The measurement of forward-angle parity spin asymmetry for the γ p → K*⁰Σ⁺ reaction, where the theoretical calculations show an unambiguous signal, would establish the role of the κ(800). The γ p → K*⁰Σ⁺ reaction, where the Σ⁺ was identified through missing mass, on a liquid hydrogen target was measured at the LEPS detector in the energy from threshold to 3.0 GeV by using a linearly polarized photon beam at SPring-8. Decay angular distributions in the rest frame of the K ⁺ π ^? system were fit to extract spin-density matrix elements of the K*⁰ decay.     

ππ partial waves from 0.6 to 1.8 GeV

We use high statistics π^?p → π^?π⁺n data at 17.2 GeV/c to calculate the ππ partial-wave amplitudes in the energy range 0.6<M_ππ< 1.8 GeV. We perform both energy-independent and energy-dependent analyses using Barrelet zero techniques. We find four possible solutions for the partial waves, each containing the leading ?, f, g resonances but with very different lower partial waves. Two solutions contain a ?' resonance in the g region, but it is not possible to establish the existence of other possible broad daughter resonances. We show that accurate measurements of π^?p → π⁰π⁰n should select the physical solution.     

Isospin symmetry violating effects and scattering length extraction from kaon decays

The isospin symmetry breaking effects in the charged kaons decays to two or three pions are considered. In semileptonic decay K ^± → π ⁺ π ^?e^± ν (called K _e4) these effects turn out to be crucial for correct extraction of ππ scattering lengths. Taking in account electromagnetic interaction between the pions in the final state and isospin symmetry breaking due to different masses of charged and neutral pions allows to adjust the values of scattering lengths obtained from experimental data on K _e4 decay and predictions of Chiral Perturbation Theory (ChPT). Final state interactions of pions in the decay K ^± → π ^± π ⁰ π ⁰ leading to the anomaly (cusp) in the π ⁰ π ⁰ invariant mass distribution in the vicinity of charged pions’ threshold are discussed and recent results of accounting of the electromagnetic interaction among charged pions leading to π ⁺ π ^? bound states (pioniumatom) just under the charged pions’ threshold are presented.     

Excited strange mesons and their decays in a chiral U(3)×U(3) Lagrangian

We bosonize the Nambu-Jona-Lasinio quark model with separable nonlocal interactions in order to derive a chiral U(3)×U(3) Lagrangian, containing, besides the usual meson fields, their first radial excitations. The spontaneous breaking of chiral symmetry is governed by the Nambu-Jona-Lasinio gap equation. The first radial excitations of the kaon, K*, and ? are described with the help of two form factors. The decays K*′ → ρK, K*′ → K*π, K*′ → Kπ, ?′ → K*K, ?′ → $\bar KK$ K, K′ → Kρ, K′ → K*π, and K′ → K2π are considered, and a qualitative agreement of our results with the experimental data is found.