Measurement of cross sections for processes involving <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilation to hadrons at the VEPP-2M collider

Results obtained by measuring, in experiments at the VEPP-2M e ⁺ e ^? collider with the CMD-2 and SND detectors at the Novosibirsk Institute of Nuclear Physics, cross sections for e ⁺ e ^? → hadrons annihilation processes at energies in the range 360 ≤ √s ≤ 1380 MeV are surveyed. The measured cross sections and the vector-meson parameters deduced from an analysis of these cross sections are presented. The cross section for the process e ⁺ e ^? → π ⁺ π ^? is compared with the spectral function for the decay τ ^? → π ^? π ⁰ ν _τ.     

37 Years with the light scalar mesons. The learned lessons

Attention is paid to the production mechanisms of light scalars that reveal their nature. We reveal the chiral shielding of the σ(600) meson. We show that the kaon loop mechanism of the ? radiative decays, ratified by experiment, is four-quark transition and points to the four-quark nature of light scalars. We show also that the light scalars are produced in the two photon collisions via four-quark transitions in contrast to the classic P wave tensor qq? mesons that are produced via two-quark transitions γγ → qq?. We study the mechanism of production of the light scalar mesons in the D _s ⁺ → π⁺π^? e ⁺ν decays: D _s ⁺ → ss?e ⁺ν → [σ(600) + f ₀(980)]e ⁺ν → π⁺π^? e ⁺ν, and compare it with the mechanism of production of the light pseudoscalar mesons in the D _s ⁺ → (η/η′)e ⁺ν decays: D _s ⁺ → ss?e ⁺ν → (η/η′)e ⁺ν. As a result we find support to four-quark nature of light scalars. In the end, we outline the future research program.     

Energy scan of cross sections for <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>–</Superscript> annihilation into quarkonia and light hadrons in the Belle experiment

The cross sections of the reactions e⁺e^– → ?(nS)π⁺π^? (n = 1, 2,3) and e⁺e^– → h _b (nP)π⁺π^? (n = 1, 2) are measured as a function of the cms collision energy from their thresholds up to 11.02 GeV using the data of the Belle experiment operating at the KEKB e⁺e^– collider. The peaks of the ?(10 860) and ?(11020) resonances are observed in the cross sections with an insignificant contribution of the continuum. The decay ?(11020) → h _b (nP)π⁺π^? is found to fully proceed through intermediate isovector states Z _b (10610) and Z _b (10650).     

Application of the hidden local symmetry effective chiral Lagrangian to evaluation of the <Emphasis Type="Italic">ω</Emphasis>(782), <Emphasis Type="Italic">ϕ</Emphasis>(1020) → 5<Emphasis Type="Italic">π</Emphasis> decay widths

The amplitudes obtained from the effective chiral Lagrangian with anomalous terms based on hidden local symmetry are applied to the evaluation of the partial widths of the decays ω → 2π⁺2π^?π⁰ and ω → π⁺π^?3π⁰. Combining the Okubo-Zweig-Iizuka rule, applied to the five-pion final state, with the Adler condition of vanishing of the amplitude at the vanishing of four-momentum of any final pion in the chiral limit, the ? → 2π⁺2π^?π⁰ and ? → π⁺π^?3π⁰ decay amplitudes are also calculated. The partial widths of the above decays are evaluated, and the resonance excitation curves in e⁺e^? annihilation are obtained, assuming reasonable particular relations among the free parameters characterizing the anomalous terms of the Lagrangian. The evaluated branching ratios \(Br_{\phi \to \pi + \pi - 3\pi ^0 } \approx 2 \times 10^{ - 7} \) and \(Br_{\phi \to 2\pi + 2\pi - \pi ^0 } \approx 5 \times 10^{ - 7} \) are such that with the luminosity L = 500 pb^?1, attained at the DAΦNE ? factory, one may already possess about 1340 events of the decays ? → 5π.     

Analysis of the production of Higgs boson pairs at the one-loop level in the minimal supersymmetric standard model

Within theminimal supersymmetric standardmodel, the amplitudes and total cross sections for the processes e ⁺ e ^? → hh, e ⁺ e ^? → hH, e ⁺ e ^? → HH, and e ⁺ e ^? → AA are calculated in the first order of perturbation theory with allowance for a complete set of one-loop diagrams in the m _e → 0 approximation. Analytic expressions are obtained for the quantities under consideration; numerical results are presented in a graphical form. It is shown that the cross section for the process e ⁺ e ^? → hh is larger than those for the other processes (and is on the same order of magnitude as the cross section for the corresponding processes in the Standard Model). In the case of the collision energy equal to √s = 500 GeV, an integrated luminosity in the region ∫ ? ≥ 500 fb^?1, and a longitudinal polarization of the e ⁺ e ? beams used, 520, 320, and 300 production events are possible in the processes e ⁺ e ^? → hh (at M _h = 115 GeV), e ⁺ e ^? → HH, and e ⁺ e ^? → AA (at M _H,A = 120 GeV), respectively. Even at M _H,A ≈ 500 GeV and √s = 1.5 TeV, not less than 200 events for each of the processes can be accumulated. The cross section for the process e ⁺ e ^? → hH is small (about 10^?2 fb), which complicates the detection of the sought signal significantly.     

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.     

Energy dependence of the cross sections for the e<Superscript>+</Superscript>e<Superscript>–</Superscript> → hadrons process near the production threshold for the <Emphasis Type="Italic">N</Emphasis><Emphasis Type="Italic">N̄</Emphasis> pair

The energy dependence of the cross sections for the processes e⁺e^? → π⁺π^?π⁰, K⁺K^?, ηπ⁺π^?, ωπ₀, and K⁺K^?π⁺π^? is studied near the production threshold for a nucleon–antinucleon pair. It is shown that, within the measurement errors, the cross sections in question behave smoothly in this energy region.     

Contribution of the π<Superscript>0</Superscript>γ and ηγ intermediate states to vacuum polarization and the muon anomalous magnetic moment

Using new experimental data, we calculated, with a high precision, a contribution to the muon anomalous magnetic moment from the vacuum-polarization intermediate states π⁰γ and ηγ taking into account a correction for the trapezoidal rule: aμ(π⁰γ+aμ(ηγ)=(53.1± 1.5)×10^?11. We also determined a small contribution from the e⁺e^?π⁰, e⁺e^?η, and μ⁺μ^?π⁰ intermediate states, which was found to be equal to 0.5×10^?11.     

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.     

Analytic calculation of feynman amplitudes

A new method is proposed for calculating amplitudes of processes involving spin-1/2 fermions. The method is based on the use of the isotropic-vierbein vectors in Minkowski space and the basis spinors associated with them. The amplitudes for the electron-positron interaction processes e^?e⁺ → ff and e^?e⁺ → W^?W⁺ and the amplitude for one of the possible diagrams for the process e⁺e^? → e⁺e^?e⁺e^?e⁺e^? are calculated in order to test and illustrate the potential of the method.     

Determination of quark-antiquark component of the photon wave function for <Emphasis Type="Italic">u,d, s</Emphasis> quarks

Based on the data for the transitions π⁰, η, η′ → γγ*(Q²) and reactions of the e⁺e^? annihilations e⁺e^? → ρ⁰, ω, ? and e⁺e^? → hadrons at 1<E _e+e? <3.7 GeV, we determine the light-quark components of the photon wave function \(\gamma * (Q^2 ) \to q\bar q(q = u,d,s)\) for the region 0 ? Q² ? 1 (GeV/c)².     

Conserved vector current and decays τ<Superscript>−</Superscript> → η(η′)π<Superscript>−</Superscript>π<Superscript>0</Superscript>ν<Subscript>τ</Subscript>

We use experimental data on e ⁺ e ^? → (η′)π⁺π^? and conservation of vector current to estimate the branching fractions of τ^? decay to η(η′)π^?π⁰ν_τ. The obtained values are compared to the experimental results.     

Observation of coherent <Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript> electroproduction on deuterons at large momentum transfer

The first experimental results for the coherent π⁰ electroproduction on a deuteron, e+d → e+d+π⁰, at large momentum transfer, are reported. The experiment was performed at Jefferson Laboratory at an incident electron energy of 4.05 GeV. A large pion production yield has been observed in the kinematical region 1.1<Q²<1.8 GeV², from the threshold to 200-MeV excitation energy in the dπ⁰ system. The Q² dependence is compared with theoretical predictions.     

Isospin violation in mixing and decays of <Emphasis Type="Italic">ρ</Emphasis> and <Emphasis Type="Italic">ω</Emphasis> mesons

The influence of isospin-violating (ρ⁰, ω) mixing is discussed for any pair of decays of ρ⁰, ω into the same final state. It is demonstrated, in analogy to the CP violation in neutral kaon decays, that isospin violation can manifest itself in various forms: direct violation in amplitudes and/or violation due to mixing. In addition to the known decays (ρ⁰, ω) → π⁺π^? and (ρ⁰, ω) → π⁰γ, the pair of decays to e⁺e^? and the whole set of radiative decays with participation of ρ⁰, ω (in initial or final states) are also shown to be useful and promising for studies. Existing data on these decays agree with the universal character of the mixing parameter and indirectly support enhancement of ρ⁰ → π⁰γ in respect to ρ^± → π^±γ. Future precise measurements will allow one to separate different forms of isospin violation and elucidate their mechanisms.     

Pseudoscalar Higgs boson in experiments at <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> colliders

The potential of experiments at e ⁺ e ^? colliders to search for a signal of a new pseudoscalar Higgs boson and to study its CP properties is analyzed. A new Higgs boson coupling to the b quark and τ lepton, which is parameterized in a model-independent way as m _b /v(a + iγ₅ b), is chosen to be an indicator of its CP nature. We study the e ⁺ e ^? → τ⁺τ^?vv, e ⁺ e ^? → b \(\bar b\)vv, and e ⁺ e ^? → e ⁺ e ^? b \(\bar b\) processes highly sensitive to anomalous Higgs boson couplings due to the dominant contributions from the vector boson fusion processes W*W* → H and Z*Z* → H in the central region. It is shown that the study of polarization of particles in the final state could help to separate the contributions from the scalar and pseudoscalar Higgs bosons. For instance, the consideration of the cascade decays of τ leptons in the e ⁺ e ^? → τ⁺τ^?vv process allows one to determine reliably the CP state of the Higgs boson as well as the value and the sign of the b parameter. As a result of our analysis, we develop a search strategy for a signal of a new pseudoscalar Higgs boson in future experiments at linear e ⁺ e ^? colliders, which will allow one to understand the CP nature of the Higgs boson and set the bounds on its couplings to fermions.     

Effects of four-fermion contact interactions in the Bhabha process at linear electron-positron colliders

For the case of longitudinally polarized primary beams, effects are investigated that are induced by four-fermion contact interactions in the process e⁺e^? → e⁺e^? occurring at linear electron-positron colliders of energy in the range \(\sqrt s = 0.5 - 1 TeV\). Model-independent constraints on the parameters of four-fermion contact interactions are obtained. It is shown that the sensitivity of the Bhabha process to the parameter Λ_LR is considerably higher than the sensitivity of the leptonic process e⁺e^? → μ⁺μ^?; at the same time, the sensitivities of these processes to the parameters Λ_RR and Λ_LL are commensurate.     

Rare meson decay in supersymmetric theory with nonconservation of <Emphasis Type="Italic">R</Emphasis>-parity

The decay of mesons K ⁺ → π ^? l ⁺ l′⁺ and D ⁺ → K ^? l ⁺ l′⁺ (l, l′ = e, μ) involving a change of lepton number ΔL = 2 is considered in a supersymmetric extension of the standard model in which R-parity is not conserved due to trilinear Yukawa interactions. The obtained estimates for the probabilities of these decays are significantly lower than the direct experimental upper limits.     

Dielectron Production in Pion-Nucleon Reactions at Intermediate Energies

Dielectron production in the πN interaction at not large energies is studied assuming that the electron- positron pair is produced from splitting of the virtual time-like photon. It allows us to get the interesting information on a nucleon form factor in the time-like region of four momentum transfer squared. The dominant contribution of the Δ-isobar creation in the intermediate state at incident pion momenta of about 0.3–0.4 GeV/c is shown. The experimental distributions over the angle and effective mass \({M_{{e^ + }{e^ - }}}\) of the e⁺e^? pair are described satisfactorily. This stimulated us to present theoretical predictions for the \({M_{{e^ + }{e^ - }}}\) distribution in the process π^?p → ne⁺e^? at different incident momenta, which could be verified, for example, by the HADES experiments.     

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.     

Nonadiabatic theory of diamagnetic susceptibility of molecules

A nonadiabatic theory of diamagnetic susceptibility of molecules is presented in which the electrons and nuclei are considered to be a united system of charged particles whose motion is simultaneously per-turbed by a magnetic field. It is found that on separating out the translational motion of the molecule as a whole, there is certain freedom in choosing the phase of the wave function. Its optimum choice corresponds to the gauge of the vector potential with which two contributions opposite in sign to the magnetic susceptibility—the first order diamagnetism and the second order paramagnetism—have minimum magnitudes. Expressions for non-adiabatic calculations of the diamagnetic susceptibility of atoms and molecules are derived. The diamagnetic contributions to the energy of the hydrogen, helium, and lithium atoms, the hydrogen molecule, the π^?μ^?π⁺μ⁺ and p ^? K ^? p ⁺ K ⁺ mesomolecules, and the positronium molecule e ^? e ^? e ⁺ e ⁺ are calculated. The nonadiabatic contribution of the nuclear motion to the diamagnetic susceptibility amounts to 0.01–0.1% for ordinary atoms and molecules, is increased by several hundred times on passing to mesomolecules, and reaches 50% for the positronium molecule.