Pion and kaon form factors and heavy vector mesons

A zero parameter model of analytic pion and kaon form factors with supplementary dynamical constraints is presented. Contrary to the general belief the predicted form factors have a t^?2 behaviour and fit the pion space-like data excellently. Some properties of heavy vector mesons are predicted and discussed.     

Pion form factor and its asymptotic behaviour

A simple phenomenological formula is constructed, consistent with the basic principles, providing a definite freedom in the choice of asymptotic behaviour and reflecting all experimentally known features of the pion form factor. The formula is used to test the asymptotic behaviour of the pion form factor both in spacelike and timelike regions simultaneously. The present experimental data require the fall-off t ^–2, which differs from the quark model prediction.On leave of absence fromInstitute of Physics, Slovak Acad. Sci., 899 30 Bratislava 1, Czechoslovakia.One of the authors (S. D.) would like to thank ProfessorAbdus Salam, the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics, Trieste, where the final part of this work was done.     

New high statistics measurement of Ke4 decay form factors and ππ scattering phase shifts

We report results from a new measurement of the K_e4 decay K^±→π⁺π^-e^±ν by the NA48/2 collaboration at the CERN SPS, based on a partial sample of more than 670 000 K_e4 decays in both charged modes collected in 2003. The form factors of the hadronic current (F,G,H) and ππ phase difference (δ=δ_s-δ_p) have been measured in ten independent bins of the ππ mass spectrum to investigate their variation. A sizeable acceptance at large ππ mass, a low background and a very good resolution contribute to an improved experimental accuracy, a factor two better than in the previous measurement, when extracting the ππ scattering lengths a₀ ⁰ and a₀ ². Under the assumption of isospin symmetry and using numerical solutions of the Roy equations, the following values are obtained in the plane (a₀ ⁰,a₀ ²): a₀ ⁰=0.233±0.016stat±0.007syst,a₀ ²=-0.0471±0.011stat±0.004syst. The presence of potentially large isospin effects is also considered and will allow comparison with precise predictions from Chiral Perturbation Theory. PACS 13.20.Eb; 13.75.Lb     

Pion charge form factor and constraints from space-time translations

The role of Poincaré covariant space-time translations is investigated in the case of a relativistic quantum mechanics approach to the pion charge form factor.It is shown that the related constraints are generally inconsistent with the assumption of a single-particle current,which is most often referred to.The only exception is the front-form approach with q + = 0.How accounting for the related constraints,as well as restoring the equivalence of different RQM approaches in estimating form factors,is discussed.Some extensions of this work and,in particular,the relationship with a dispersion-relation approach,are presented.Conclusions relative to the underlying dynamics are given.     

Pion charge form factor and constraints from space-time translations

The role of Poincaré covariant space-time translations is investigated in the case of a relativistic quantum mechanics approach to the pion charge form factor.It is shown that the related constraints are generally inconsistent with the assumption of a single-particle current,which is most often referred to.The only exception is the front-form approach with q ^＋ = 0.How accounting for the related constraints,as well as restoring the equivalence of different RQM approaches in estimating form factors,is discussed.Some extensions of this work and,in particular,the relationship with a dispersion-relation approach,are presented.Conclusions relative to the underlying dynamics are given.     

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.     

Pion electromagnetic form factor in Coulomb gauge QCD

The electromagnetic pion form factor and radius is calculated in a model which can be derived from Coulomb gauge QCD in an instantaneous approximation discussed recently. The results agree well with experimental data without further adjustment of parameters. They are also compared to results obtained in the Nambu-Jona-Lasinio and in the Vector Meson Dominance model.     

Pion form factor from 480 MeV to 1100 MeV

The pion form factor is measured in the reaction e⁺e^? → π⁺π^? for center of mass energies in the range 480–1100 MeV. Our results are first analysed in terms of the conventional Vector Meson Dominance formalism, and then taking into account the ωπ inelastic channel. The result of this later formalism is a pion form factor (F_π) which fits quite well all the existing data on F_π both in the timelike and spacelike regions, and pion mean square radius of 〈r_π²〉 = 0.460 ± 0.011 fm² or $\text{〈r}{}_{\mathrm{\pi }}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 0.678 ± 0.008}\text{fm}$.     

Pion form factor in the NLC QCD SR approach

We present results of a calculation of the electromagnetic pion form factor within the framework of QCD sum rules with nonlocal condensates and using a perturbative spectral density which includes O(α _s ) contributions.     

Pion Softening and Pion Condensation

Physics of Atomic Nuclei - In this paper after a historical introduction I discuss ideas of a pion softening and pion condensation in a dense nuclear matter, in particular in neutron stars, and a...     

Pion propagation near the QCD chiral phase transition

We point out that, in analogy with spin waves in antiferromagnets, all parameters describing the real-time propagation of soft pions at temperatures below the QCD chiral phase transition can be expressed in terms of static correlators. This allows, in principle, the determination of the soft pion dispersion relation on the lattice. Using scaling and universality arguments, we determine the critical behavior of the parameters of pion propagation. We predict that, when the critical temperature is approached from below, the pole mass of the pion drops despite the growth of the pion screening mass. This fact is attributed to the decrease of the pion velocity near the phase transition.     

Pion phase transition in chiral symmetry breaking model

We show that in the non-linear σ-model, we have a phase transition when the isospin chemical potential is equal to the meson mass. This result is shown to be generally true in the SU(2)×SU(2) symmetry breaking model.     

Pion mass splitting and phase structure in twisted mass QCD

In the framework of Wilson chiral perturbation theory [1], we study the effect induced by a twisted Wilson term, as it appears in twisted mass QCD [2] (with two degenerate quarks). In particular we consider the vacuum orientation and the pion masses. The computations are done to NLO both in the mass and in the lattice spacing (i.e. to O(a ²)). There are no restrictions on the relative size of lattice artifacts with respect to the physical mass, thus allowing, in principle, to bridge between the physical regime and the unphysical one, where lattice artifacts tend to dominate. The inclusion of O(a ²) lattice artifacts can account for the splitting of degeneracy of the three pion masses. Moreover O(a ²) terms are necessary to model non-trivial behaviors of the vacuum orientation such as possible Aoki phases. It turns out that these last two phenomena are determined by the same constant.Received: 21 July 2004, Published online: 1 October 2004     

Pion decays and the pion electromagnetic form factor in a σ-model with quarks

We study in the one-loop approximation the decays of the pion and the pion electromagnetic form factor at low q² in the framework of a σ-model with quarks. The theory has a free parameters the quark and σ masses and the results are very insensitive to their values. We get good approximation for all processes considered except for the ratio of the axial to the vector form factor that appear in the electronic radiative decay of the charged pion. The reason is probably that our model includes the pion-pion interaction only in the isoscalar s-wave at the one-loop level.     

Pion-nucleon phase shifts and Padé approximants

Pion-nucleon phase shifts at low energy are computed in the non-linear σ model and compared with Yukawa and linear σ model results. Unitarization of a germ and dispersion-relation methods are also discussed. We have reproduced exactly the calculation of Filkov and Palyushev but our numerical results disagree with theirs.     

Low energy scattering data and phase shifts

We point out that at any given low energyσ _tot and a ratio of integrated scattering data likeF/B can, in principle, be used unambiguously to finds-andp-wave phase shifts. Thus efforts to obtain other low energy data like elastic dσ/dΩ andP/E are unnecessary. It is also indicated that the mere knowledge whetherF/B is greater than or less than unity enables us to draw important conclusions about the nature of the interaction in thep-state without performing detailed calculations. Thus a strong case is made out for obtaining much more preciseF/B data than are presently available. The discussion refers mainly to low energy ∧p scattering data.