Deviation from the standard model in the decay <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript> → <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">νγ</Emphasis>

A precise investigation of radiative pion decay (π⁺ → e⁺νγ) in a pion beam from the meson factory of the Paul Scherrer Institute (Switzerland) was performed by the PIBETA Collaboration with the aid of the PIBETA detector. This resulted in finding 41 601 events of radiative pion decay in three kinematical regions. The absolute values of the branching ratio for radiative pion decay were determined in each of these regions. To a precision approximately four times higher than that known previously, the ratio of the axial-vector to the vector form factor was found to be γ ≡ F _A /F _V = 0.443 (15), the latter being fixed at F _V = 0.0259. The number of events found in the kinematical region specified by photon energies of E_γ > 55.6 MeV, positron energies of E _e > 20.0 MeV, and angles of θ_{γ, e} > 40° between the momenta of the corresponding particles (B region) was 5233. In region B, the measured branching ratio for radiative pion decay, R_π→evγ(expt) = 11.6(3) × 10^?8, proved to be smaller by eight standard deviations than that which follows from the Standard Model, R_π→evγ (theor) = 14.34(1) × 10^?8.     

Study of the charge dependence of the pion–nucleon coupling constant on the basis of data on low-energy nucleon–nucleon interactions

The relation between quantities that characterize the pion–nucleon and nucleon–nucleon interactions is studied with allowance for the fact that, at low energies, nuclear forces in nucleon–nucleon systems are mediated predominantly by one-pion exchange. On the basis of the values currently recommended for the low-energy parameters of the proton–proton interaction, the charged pion–nucleon coupling constant is evaluated at g_π²±/4π = 14.55(13). This value is in perfect agreement with the experimental value of g_π²±/4π = 14.52(26) found by the Uppsala Neutron Research Group. At the same time, the value obtained for the charged pion–nucleon coupling constant differs sizably from the value of the pion–nucleon coupling constant for neutral pions, which is g_π² 0/4π = 13.55(13). This is indicative of a substantial charge dependence of the coupling constant.     

Analysis of the photoproduction of pions by means of fixed t dispersion relations. I

An absolute prediction for the photoproduction of pions on protons is given in the region of the first pion nucleon resonance. The imaginary part of the amplitude was approximated by the resonant magnetic dipole amplitudeM ₁₊ ^3/2 taken from the theory of CGLN. With this approximation the real part of the amplitude was calculated by means of fixedt dispersion relations and discussed in terms of multipoles.π ⁺-andπ ⁰-excitation curves atΘ=90° for unpolarized as well as plane-polarizedγ's are compared with the experiments. In the appendix we give tables of the differential cross sections in the c.m. system.     

Quark microscopic picture for vector and pseudoscalar mesons in the nucleon and their quasielastic knockout by high-energy electrons

A technique for projecting a multiquark wave function in the microscopic model of a ³P⁰ scalar fluctuation onto the virtual-decay channels N → N + ρ and N → N + π is formulated (at a more general level for the latter than previously). The amplitude for the electromagnetic transition ρ + γ _T ^* → π in electron-induced quasielastic rho-meson knockout followed by rho-meson conversion to a pion is considered. Theoretical results obtained in this way are contrasted against available experimental data, and reasonable agreement is found for cross-section values. This confirms a universal character of the ³P₀ model. The precision of relevant experiments is as yet insufficient for comparing the momentum distribution of the rho meson from the channel N → N + ρ with its theoretical counterpart.     

Using a chiral anomaly to determine the number of colors

The N_c dependence of PPPγ vertices, where P is a pseudoscalar meson and N_c is the number of colors, is analyzed with allowance for the N_c dependence of the quark charges. It is shown that the reactions Kγ → Kπ and π^±γ → π^±η and the decay η → π⁺π^?γ are the best processes for determining N_c. The cross section σ(π^?γ → π^?η) as measured by using the VES facility at IHEP agrees with the value of N_c=3.     

Experimental investigation of ρ<Superscript>0</Superscript> photoproduction on the pion in the H1 experiment

Experimental results on quasielastic photoproduction of the ρ⁰ meson in association with a neutron, obtained at the HERA collider, are presented. The total and differential cross sections of the γp → ρ⁰ nπ⁺ reaction at the positron–proton center-of-mass energy of √s =319 GeV are measured. The data collected with the H1 detector in 2006 and 2007 correspond to an integrated luminosity of 1.16 pb^?1. The kinematic region of the photon–proton cms energy of 20 < W _γp <100 GeV, photon virtuality of Q ² < 2 GeV², and the ρ⁰ transverse momentum below 1 GeV/c is analyzed. Secondary neutrons with energies x _L > 0.35 (in proton-energy units) and emission angles below 0.75 mrad are selected. The model of double peripheral exchange, in which the ρ⁰ is elastically produced via the photon interaction with the virtual pion from the proton–neutron vertex, is employed for interpreting the results. The cross section for the ρ⁰ elastic photoproduction on the pion, γπ⁺→ ρ⁰π⁺, is extracted in the one-pion-exchange approximation. The magnitude of the cross section suggests that the γp → ρ⁰ nπ⁺ reaction is significantly affected by absorption.     

Formfaktor des π-Mesons und Struktur der Nukleonen

Recent measurements of electron-proton scattering at Stanford have shown that the electric and magnetic form factors are not equal. Therefore, the isotopic vector parts of the form factorsG _e ^v andG _m ^v are recalculated with unsubtracted dispersion relations in the 2π-approximation. For the isotopic scalar parts we useG _e ^s (s)≈G _e ^v (s) andG _m ^s (s)≈ 0 which is known to be valid for moderate energy-momentum transfers. We obtain a simple closed expression for the electromagnetic form factor of the pionF _π in terms of the scattering lengtha ₁ and the effective ranger ₁ of the π-π-scattering in the stateL=T=1.a ₁ is roughly known from pion production by pions. With this value and a suitabler ₁,F _π has a resonance in the region of time-like energy-momentum transfer; and the pion rms-radius becomes\(\overline {v_\pi ^2 } = (0.82 \times 10^{ - 13} cm)^2 \). The calculated anomalous magnetic moment, the electric and the magnetic rms-radii of the proton are then within 10% of the experimental values, the electric charge within 30%. Moreover, the proton form factors are different from each other and up to an energy-momentum transfer of\(s = \frac{{ - q^2 }}{{m_\pi ^2 }} = 23\) within the experimental error of the new measurements. The deviations for higher values of the energy-momentum transfer may be explained in terms of the isotopic scalar parts of the form factors. In this case the electric form factor of the neutron will be different from zero in that region and the magnetic form factor of proton and neutron will no longer be equal. For comparison with other experiments we also calculate the π⁺?π^? cross section with neglect of other states thanL=T=1. Under this assumption the π?π cross section has a resonance for low energy-momentum transfer.     

Photoproduction ofρ- andω-mesons in the peripheral model

Photoproduction ofρ- andω-mesons on nucleons is considered. The possible matrix elements according to the peripheral model are constructed and the cross section is calculated,π,η,σ (ABC) and vector meson exchange is taken into account. The angular distribution for the decay pions of polarizedρ's is discussed with particular reference to peripheral production     

Pion electromagnetic form factor in QCD sum rules

The electromagnetic form factor of the π meson is calculated in terms of the QCD sum rules for a pion axial-vector current with allowance made for the radiative QCD corrections. The derived dependence of the pion form factor on the square of the transferred momentum Q² is in good agreement with the experimental data. The QCDc orrections are shown to make a large contribution, and they should be taken into account in a rigorous theoretical analysis.     

QCD quark distributions in mesons

The valence-quark distributions in the π meson and in transversely and longitudinally polarized ρ mesons in the region of intermediate x are obtained on the basis of generalized QCD sum rules. Power-law corrections up to d=6 are taken into account. The quark distributions in the pion agree with those found from the data on Drell-Yan processes. A comparison of the results for the π and ρ mesons show that polarization effects are very significant and that the distribution functions do not have SU(6) symmetry.     

Pion-pion interaction andK 2x03C0;x03C0;x03C0;-decay

The enhancement of theK _2π ⁺ -decay compared to theK _2π ⁰ -decay is discussed on the basis of the\(|\mathop {\Delta {\rm I}}\limits^ \to | = \tfrac{1}{2}\)-rule. The enhancement factor is calculated by dispersion methods which yield an expression depending only on the phase shift of the two pion system in theJ=0,I=0,2 state. This expression has been studied in the framework of simple models for the two-pion interaction in order to obtain a survey of the possibilities for the cause of the anomalous large ratioK _2π ⁺ /K _2π ⁰ . Only characteristic cases have been considered and, as far as possible, experimental results of theπ-π-interaction are taken into account.     

Correlations between pions of low relative momenta

Two-particle pion correlations in exclusive πp and pp interactions at \(\sqrt s = 2.9 - 4\) GeV are studied in the region of low relative 4-momenta. Relevant correlation functions are obtained with allowance for the results of calculations based on the model of quark-gluon strings and the FRITIOF model. Positive correlations that make it possible to estimate the spatial size of the pion source are observed for pairs of identical pions. No correlations are observed for pairs featuring one charged and one neutral pion.     

Tests of discrete symmetries with the neutral kaon system at the KLOE and KLOE-2 experiments

The KLOE-2 experiment continues and extends the program of its predecessor KLOE in the field of discrete symmetry tests with the K meson system, among other studies which comprise light meson spectroscopy, dark matter searches and γγ physics. Together, KLOE and KLOE-2 have recorded the largest sample (almost 8 fb^??1) of e⁺e^? collisions at the energy equal to ? meson mass, amounting to 2.4 × 10¹⁰ of produced ? mesons. We report on the latest results and ongoing analyses of KLOE and KLOE-2 concerning discrete symmetry tests and measurements of symmetry-violating observables. A measurement of the CPT violation sensitive asymmetry in semileptonic decays of K˙S with 1.7 fb^??1 of KLOE data will be presented, which improves the sensitivity w.r.t. previous measurements about twice. Moreover, status of direct tests of T and CPT in transitions of neutral kaons performed with the ? →K˙SK˙L → πeν, 3π⁰(2π) processes will be reported, followed by the search of the CP-violating decay K˙S → 3π⁰ using the data recently acquired by KLOE-2.     

Electromagnetic Interactions of Mesons and the π<Emphasis Type="Italic">a</Emphasis><Subscript>1</Subscript> Diagonalization

It has been demonstrated that, contrary to the commonly accepted viewpoint, electromagnetic interactions cannot be consistently included in the Nambu–Jona-Lasinio model within vector meson dominance. This refers to the procedure for removing the πa₁ transition in the effective meson Lagrangian. By the example of the a₁(1260)→γπ⁺π^- radiative decay, it has been demonstrated that the gauge invariance condition for the amplitude gives rise to an electromagnetic vertex describing the direct emission of a photon and a pion by a quark–antiquark pair. Surface terms appearing in the calculation of an anomalous triangular quark diagram, where one of the vertices is the interaction violating the vector-dominance hypothesis, play a key role in satisfying the Ward identities.     

On the dependence of the single-spin asymmetry of charged pions on kinematical variables

The experimental single-spin asymmetry (A _N ) of charged pions produced in proton-proton and proton-nucleus collisions is analyzed phenomenologically as a function of kinematical variables. It is shown that the c.m. pion threshold energy (E ₀ ^c.m. ) above which |A _N | is positive depends on the reaction energy √s and on the particle-production angle θ ^c.m.. The dependence of the single-spin asymmetry on the kinematical variables in the region specified by the inequalities 0.7 < p _T < 2.7 GeV/c and E ^c.m. > E ₀ ^c.m. exhibits a scaling behavior. The dependence of A _N on √s proves to be significant at moderate and low energies. Formulas that make it possible to predict the behavior of A _N for charged pions over a broad region of kinematical variables are derived.     

Inclusive neutral-pion production in <Emphasis Type="Italic">d</Emphasis>C and <Emphasis Type="Italic">d</Emphasis>Cu interactions at a momentum of 4.5 GeV/. per nucleon

The cross sections for inclusive neutral-pion production in the reactions d + C → π⁰ + x and d + Cu → π⁰ + x at a momentum of 4.5 GeV/c per nucleon were measured over the kinematical region specified by the inequalities Θ_π≤16° and E_π≥2 GeV (in the laboratory frame). From the ratio of the cross sections for neutral-pion generation on carbon and copper nuclei, the exponent n in the parametrization Ed³σ/d³p ～ A _T ⁿ is obtained as a function of the cumulative number X in the range 0.6 ≤ X ≤ 1.8 and as a function of the square of the transverse momentum in the range 0.04 ≤ P _t ² ≤ 0.40 (GeV/c)². The probabilities of the formation of six-quark configurations in the D, ⁴He, and ¹²C nuclei are estimated. The double-differential cross section for the reaction d + C → π⁰ + x is determined for the first time by using a data sample containing more than 40 000 neutral pions.     

Production of exotic Λ hypernuclei via mesonic beams

We study the production of neutron-rich hypernuclei _Λ ¹² Be, _Λ ¹⁶ C, and _Λ ¹⁰ Li by the (π^?, K⁺) and (K^?, π⁺) reactions in flight and treat two different mechanisms of production. The first mechanism is a two-step process with meson charge exchange (e.g., π^?p → π⁰n, π⁰p → K⁺Λ). The other mechanism is one-step production (π^?p → K⁺Σ^?) proceeding via a small Σ^? component, arising in Λ hypernuclei due to ΛN–ΣN coupling, as a doorway state. Typically, the two-step mechanism is more productive. The forward differential cross section of the ¹⁰B(π^?,K⁺) reaction is about 70 nb/sr at an incident momentum of 1.05 GeV/c. On the other hand, the one-step process can serve as a direct measurement of the Σ admixture if the two-step contribution is suppressed by a suitable choice of the reaction kinematics.     

Production of Heavy Helium <Superscript>5</Superscript>Hе in the Absorption of Stopped Pions by <Superscript>10,11</Superscript>B Nuclei

Helium ⁵Hе states are sought in missing-mass (MM) spectra from reactions of the absorption of stopped pions: ¹⁰В(π^?, dt)Х and ¹¹В(π^?, tt)Х. The experiment is conducted using the LANL accelerator equipped with a two-arm semiconductor charged-particle spectrometer. The parameters of the ground state agree with the literature data. The best fit for the first excited level is obtained at E_r = 1.8(5) MeV and Γ = 4.7(7) MeV. Neither of the two reactions produce statistically significant evidence for the presence of highly excited (E_x ≥ 20 MeV) states of ⁵Hе.     

Investigation of zero-frequency solutions to the pion dispersion equation

The instability of nuclear matter is considered for the case where it is generated by the vanishing of the frequencies of collective excitations belonging to specific types (specifically, excitations that have the pion quantum numbers J ^π = 0^?). The behavior of zero-frequency solutions to the pion dispersion equation is analyzed versus the strength G′ of spin—isospin particle—hole interaction. It is shown that there exists a strength value G′_tr (|G′_tr| ? 1) such that, for G′ < G′_tr, zero-frequency solutions are excitations of the ω _P type, while, for G′ ≥ G′_tr, such solutions are excitations of the ω _c type. Excitations of the ω _P type for G′ < ?1 describe the instability of nuclear matter against small density fluctuations (Pomeranchuk’s instability), while excitations of the ω _c type are responsible for the instability associated with pion condensation at G′ ≈ 2. For stable nuclear matter, the solutions ω _P(κ) and ω _c (κ) lie on unphysical sheets of the complex plane of frequency.