New evaluation of muon (g − 2) hadronic anomaly

The hadronic part a_H of the muon g-factor anomaly $\text{a ≡}\text{(g ? 2)}\text{2}$ is evaluated from latest data on σ(e⁺e^? → hadrons). For a p-wave ππ scattering length of a₁ = 0.04±0.005 we calculate a_H = (66±10) × 10^?9, compared to a(experiment) ? a(QED) = (60±29) × 10^?9. Half of the uncertainty on a_H is associated with the energy interval $\text{0.92 <}\text{s}\text{< 2}\text{GeV}$.     

Asymptotic restrictions and ππ scattering lengths in non-linear chiral SU(2) × SU(2) dynamics

The most general effective lagrangian for ππ scattering, that takes into account the exchange of scalar (0⁺), tensor (2⁺) and ? mesons, is constructed within the framework of non-linear chiral SU(2) × SU(2) dynamics. Asymptotic restrictions proposed by Weinberg are imposed on the amplitude of ππ scattering. These restrictions allow one to obtain four independent sum rules containing particle masses, coupling constants and the coefficient A₂ in an expansion of the symmetry-breaking term in a power series of π². The use of only the f⁰ meson in the obtained sum rules leads to the following values of the ππ scattering lengths, the width of ?(700) → 2π decay, and the parameter A₂: α₀⁰ = 0.92m_π^?1, α₀² = 0.27 m_π^?1, α₁¹ = 0.033 m_π^?3, Γ[ε(700) → 2π] = 390 MeV, A₂ = + 1.6. It is shown that the inclusion of heavier mesons results in some increase of the ππ scattering lengths and the parameter A₂, but a decrease of the value of Γ(? → 2π). The field-algebra requirements lead to negligible changes in the results. Analysis of the sum rules shows the incompatability of the asymptotic restrictions with a symmetry breaking which has the transformation properties of the fourth component of a chiral vector.     

The isosinglet and isovector ππ scattering lengths

The ππ scattering lengthsa ₀ ⁰ ,a ₂ ⁰ anda ₁ ¹ are determined from πN elastic scattering data using interior dispersion relations. The importance of the Born-Term contribution, via unitarity, to the imaginary part of all amplitudes is discussed. Proper consideration of these contributions and the analytic properties of the amplitudes near threshold allows us to obtain from the recent πN partial wave analysis of Pietarinen the following scattering lengths $$\begin{gathered} \mu a_0^0 = 0.27 \pm 0.03,\mu ^3 a_1^1 = 0.032 \pm 0.005, \hfill \\ \mu ^5 a_2^0 = 0.002 \pm 0.001. \hfill \\ \end{gathered} $$      

A study of s - wave π π scattering in the reaction πn → ππp at 2.15 GeV/c

We have studied the 2_π⁰ final states in the reaction π⁺d → π⁰π⁰p(p) at 2.15 GeV/c in a 2 million picture exposure of the PPA rapid cycling deuterium bubble chamber. Two tantalum plates were added to the bubble chamber to convert γ rays which were kinematically constrained to a 2π⁰ hypothesis. The 2π⁰ mass spectrum is observed to saturate s-wave unitarity in the ππ mass region between 0.6 and 0.9 GeV/c², clearly favoring the ‘up-down’ or broad resonance solution for s-wave, I = 0, ππ scattering.     

Lower bounds to the I = 0, I = 2 ππ s-wave scattering lenghts

Roy's exact partial wave equations allow us to find bounds for any linear combination of the isospin I = 0 and s-wave scattering lengths, with positive coefficients. The bound is a function of the quantity a_D = a₂⁽⁰⁾ + a₂⁽²⁾, where a₂^(I) are the D-wave sacttering lengths. Thus, we can draw on the (a₀⁽⁰⁾, a₀⁽²⁾) plane an allowed domain whose boundary is fairly close to the phenomenological region. For a value of a_D = 1.7×10^?3, we find the following particular bounds: a₀⁽⁰⁾??0.49, a₀⁽²⁾??0.29.     

A study of ππ → NN partial-wave amplitudes using hyperbolic dispersion relations

We investigate $\text{ππ →}\text{N}\text{N}$ partial-wave amplitudes, using a spin separation method based on hyperbolic dispersion relations. Partial-wave amplitudes with J ? 3 are dominant in the pseudophysical region between the ππ and $\text{N}\text{N}$ thresholds, but we find clear evidence for J = 4 and J = 5 contributions from regions near and above the $\text{N}\text{N}$ threshold. We isolate J = 2 and J = 3 partial waves and determine the couplings of f₀(1270) and g (1680). Knowing the high-spin contributions, we are able to eliminate thse and to study s- and p-waves. We find evidence for small p-wave contributions above the ?, having the same sign as the ? contributions. We develop methods for determining the I = J = 0 ππ scattering length a₀⁰ and find a₀⁰ = 0.30 ± 0.15.     

Searching for effects of neutrino magnetic moments at reactors and accelerators

The sensitivity of the νe elastic scattering experiments to possible effects of nonzero neutrino magnetic moment (μ) is analyzed and the optimal experimental condition under which such effects are relatively enhanced are found. New, somewhat more restrictive than the previously derived bounds on μ, are obtained on the basis of existing data by the use of selfconsistent statistical analyses: μ_νe < 1.52 × 10^?10e/2m_e and μ_νμ < 1.19 × 10^?9e/2m_e. These bounds are expected to be improved approximately by an order of magnitude in experiments planned to be performed in the near future.     

A new absolute bound on the πoπo s-wave scattering length

We improve substantially the precedent absolute lower bounds on the π^oπ^o S-wave scattering length. The main new feature in our derivation is the exploitation of the known structure of the partial wave left hand cut discontinuity, explicitely exhibited by the Roy equations. The final result is a⁰⁰₀ > ?1.75.     

Upper bounds on Higgs-Boson masses in the Weinberg-Salam model with three Higgs doublets

In the Weinberg-Salam model with three Higgs doublets, the positivity of masses and tree graph unitarity applied on Higgs scattering lead to the following upper bounds on Higgs masses: m_H1^±, m_H2^± < 883 GeV, m_H1⁰ < 500 GeV, m_H2⁰, m_H3⁰ < (958–1633) GeV, m_H4⁰, m_H5⁰ < (360–883) GeV.     

The influence of inelastic πω channel on pion form factor at s<(mω + mπ)2

It is shown that F_π(s) can be calculated in a model independent way if one knows the phase δ₁ and the inelasticity η of the p-wave ππ scattering and also F_π and the form factor of the γ¹ → π°ω transition for s> (m_ω + m_π)². The correction on F_π(s) for s< (m_ω + m_π)² due to the πω state with a strong ?′(1250) allows to explain the discrepancy between ?-dominance predictions and the experimental data.     

Temperature dependence of the rho-meson mass and width

It is shown, to leading order in the virial expansion, that unitarity of the ππ scattering amplitude implies that if the ρ-meson widthΓ _ρ(T) increases with temperature, then the ρ-meson massM _ρ(T) must also increase. The temperature dependence ofM _ρ(T) is explicitly obtained from a simple, but physically motivated, parametrization of theI=J=1 ππ scattering amplitude.     

Macroscopic behaviour of ferromagnets with random and statistically vanishing anisotropy

A model is defined in which the anisotropy tensor is a random function of space point characterised by its mean square value σ and a correlation lenght a_c, and the exchange density A is uniform. If the magnetic moment density is M, it is shown that two dimensionless numbers can be defined a_c/a_p, where a_p is a typical Bloch wall width$\text{(}\text{A}\text{δ}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, and 4πM²/σ they define four types of macroscopic behaviour. For 4πM²/σ<1, the pole fields are a perturbation; if a_c<a_p, as in rare earth amorphous alloys, there is some frustration in the ground state and if a_p <a_c, as in inhomogeneous weak ferromagnets the magnetization direction is mainly fixed by the local anisotropy. For 4πM²/σ#62; 1, as in iron alloys, if a_p#62;a_c one has the case of soft alloys, the shape anisotropy is the dominant effect and if a_p<a_c the usual domain theory applies.     

Separation of S-wave pseudoscalar and pseudovector amplitudes in π−P↑ → π+π−n reaction on polarized target

A new analysis of S-wave production amplitudes for the reaction π^?p↑ → π⁺π^?n on a transversely polarized target is performed. It is based on the results obtained by the CERN-Cracow-Munich collaboration in the ππ energy range from 600 MeV to 1600 MeV at 17.2 GeV/c π^? momentum. Energy-independent separation of the S-wave pseudoscalar amplitude (π exchange) from the pseudovector amplitude (a ₁ exchange) is carried out using assumptions much weaker than those in all previous analyses. We show that, especially around 1000 MeV and around 1500 MeV, the a₁ exchange amplitude cannot be neglected. The scalarisoscalar ππ phase shifts are calculated using fairly weak assumptions. Below the KK? threshold we find two solutions for the π — π phase shifts, for which the phases increase slower with the effective π — π mass than the P-wave phases. Both solutions are consistent with a broad f ₀(500) but only one is similar to the well-known “down” solution. We find also the third solution (with a somewhat puzzling behavior of inelasticity) which exhibits a narrow f ₀(750) claimed by Svec. All the solutions undergo a rapid change at the KK? threshold. Above 1420 MeV the phase shifts increase with energy faster than those obtained without the polarized-target data. This phase behavior as well as an increase of the modulus of the a₁-exchange amplitude can be due to the presence of the f ₀(1500).     

High-pT pion production in ππ interactions

Charged pion production in high energy π^-π^- interactions is studied in the p_T region of 1–2 GeV/c. The characteristics of pion production in π^-π^- interactions are compared with those in π^-p and pp interactions. The p_T dependence of pion production in these reactions follows a systematic trend which indicates that high-p_T pion production for ππ interactions as well as for πp and pp interactions proceeds via quark-quark scattering as predicted by QCD.     

Meson-meson potentials from lattice QCD and inverse scattering

Potentials between light-light and heavy-light mesons are computed from meson-meson Green’s functions in the framework of quenched lattice QCD with Kogut-Susskind fermions. Comparisons with a full QCD simulation and a simulation using an O(a ²) tree-level and tadpole improved gauge action show that dynamic quarks and lattice discretization errors have no drastic influence. Calculations from inverse scattering theory propose a similar shape for $K\bar K$ potentials, whereas a good qualitative agreement with ππ potentials could not be obtained.     

Lower bound to the π0π0 S-wave scattering length

Starting from analyticity, unitarity and crossing symmetry of the π⁰π⁰ elastic scattering amplitude we derive an inequality between the S- and D-wave scattering lengths (a₀ and a₂, respectively) of the form: $\text{a}{}_0\text{>?23.5}\text{a}{}_2\text{+141a}{}_2$. Using the phenomenological value of a₂ we can improve in this way the lower bound to a₀.     

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.     

The ππ total cross section: Its scale and massless pion limit

The question of the scale of the ππ total cross section is considered. We first give a simple intuitive argument for expecting cross sections in the massless chiral world to be finite. Assuming the universality of P-f Regge couplings, we give a simple dispersion theoretic evaluation of the asymptotic ππ total cross section, σ^ππ. We deduce an algebraic expression for σ^ππ and find that its scale is determined by 1/m_?² or, equivalently, 1/f_π² — just as Pagels conjectured. This relation has a smooth, finite limit as m_π tends to zero. Numerically, we obtain σ^ππ = 17 ± 4mb for physical mass pions and 14 ± 3mb for massless pions.