Narrow Results

We show that we are able to extract the pion electromagnetic form factor by using the recent charged pion electroproduction data from JLab and a simple t-channel diagram. For this purpose we have performed the Q²-independent and dependent analyses. The result of the first analysis is in good agreement with those of previous works and fit the Maris and Tandy model as well as the monopole parametrization which describes a pion radius of 0.672 fm. The result of the second analysis corroborates the findings in the first analysis. Our findings therefore provide a direct proof that at the given kinematics the t-channel diagram really dominates the process. This could also set a new constraint to the phenomenological models that try to describe the process.

The total cross sections for the π⁺π⁻ photoproduction on the deuteron were measured in an energy range of 0.8 to 1.1 GeV. The obtained total cross section for the quasi-free π⁺π⁻ photoproduction on the deuteron was about 60 % of those on the free proton. The cross section for Δ⁺⁺Δ⁻ photoproduction was derived from the non-quasi-free π⁺π⁻ photoproduction events. It was smaller than the previous data.

The pion was introduced by Yukawa as the mediator of nucleon-nucleon interaction to bind nucleons in nucleus. Due to its characteristic properties, however, the pion had not be used until recent years for description of nuclei. We present here a newly developed method to treat the pion exchange interaction in nuclei. We study nuclear structure by using the chiral sigma model lagrangian in the relativistic chiral mean field model with projection. The pion develops mean field and provides a magic number effect. We demonstrate also the ability of treating tensor interaction due to pion exchange in terms of tensor optimized shell model.

Measurements of differential cross sections for pion-nucleon charge exchange, π^-p→π⁰n, in the region of the P₁₁(1440), or Roper, resonance are presented. These data were obtained as part of the baryon spectroscopy program using the Crystal Ball detector at the Alternating Gradient Synchrocyclotron (AGS) at Brookhaven National Laboratory (BNL). Data were taken in 1998 with a liquid hydrogen target and in 2002 with CH₂ and C targets.

The Dubna-Mainz-Taipei (DMT) dynamical model for pion electromagnetic production, which describe well the existing data from threshold up to 1 GeV photon lab energy is presented and used to analyze recent data in the Δ region. We find that within DMT model, the bare Δ is almost spherical while the physical Δ is oblate. The deformation is almost saturated by the pion cloud effects.

Selected results from the study of Double Pomeron Exchange with the Split Field Magnet detector at the CERN Intersecting Storage Rings are presented. This concerns various general features of central pionic systems as well as the spectroscopy in the π⁺π^- channel, emphasizing the production properties of the f₂(1270) meson. This summary refers to a series of publications over a time span of 17 years based on the work of the CCHK^1,2 and ABCDHW^3–7 collaborations at the CERN ISR.

There is experimental evidence of an increase in the temporal component of the weak axial vector current in nuclei. Most of this increase is accounted for by meson exchange currents. We consider further corrections from pions and the sigma mean-field. These corrections, however, are found to reduce the coupling, which is already insufficiently large.

The pion plays an important role for the structure of nucleus and nuclear matter. We propose a new theoretical framework, named the tensor optimized shell model (TOSM) to calculate the tensor interaction together with the unitary correlation operator method (UCOM) for the short range repulsion. We are able to handle the pion exchange interaction directly in the proposed framework. We compare the calculated results for ⁴He with the rigorous calculation to show the power of TOSM to treat the tensor interaction.

The pion plays an important role for the structure of nucleus and nuclear matter. We propose a new theoretical framework, named the tensor optimized shell model (TOSM) to calculate the tensor interaction together with the unitary correlation operator method (UCOM) for the short range repulsion. We are able to handle the pion exchange interaction directly in the proposed framework. We compare the calculated results for ⁴He with the rigorous calculation to show the power of TOSM to treat the tensor interaction. We then discuss the important role of pion in hypernuclei due to excitation of Σ baryon from Λ state.

The Drell–Yan process is an invaluable tool for probing the structure of hadrons, and the pion-induced Drell–Yan process is unique in its sensitivity to several subtleties of the partonic structure. This is a brief review of the pionic Drell–Yan process with particular emphasis on the dilepton angular distributions and nuclear modification of the parton distributions (the EMC effect).

The phase diagram of quantum chromodynamics is conjectured to have a rich structure containing at least three forms of matter: hadronic nuclear matter, quarkyonic matter and quark–gluon plasma. We justify the origin of the quarkyonic phase transition in a chiral-quark model and describe its formulation in terms of Skyrme crystals.

One of the main sources of the information about nuclear resonances are partial wave analyses (PWA) of pion-proton elastic scattering. Nearly all of the data available for PWA were obtained more than 20 years ago with old measurement techniques. The talk presents new high precision data obtained recently by the EPECUR collaboration. The experiment features high statistics and better than 1 MeV resolution in the invariant mass thus allowing searches for narrow resonances with the coupling to the πp channel as low as 5%. The experimental setup consists of a 25 cm long liquid hydrogen target in a non-magnetic spectrometer of wire drift chambers with hexagonal structure. The measurements started in 2009. 3 billions of triggers are already collected with positive and negative pion beams in the beam momentum range 820-1330 MeV/c.

The large transverse single spin asymmetries (SSA) of high $x_F$ inclusive hadrons produced in polarized proton collisions are usually explained by means of collinear twist-3 multi-parton correlations. In this picture these asymmetries can originate from initial-state twist-3 parton distributions in the polarized proton and/or through the coupling between proton transversity and twist-3 fragmentation functions. The measurement of SSA for forward inclusive hadrons produced in $pp$ collisions out to high transverse momentum helps to examine the validity and interplay of these initial- and final-state models. These models can be further explored by investigating the dependence of the SSA on event topologies. We present our latest status on the measurement of SSA for forward inclusive ${\pi }^0$ detected within $2.8<\eta <4.0$ in $\sqrt{s}$ = 500 GeV $pp$ collisions as well as its dependence on event topologies. We will also present our analysis of Sivers and Collins asymmetries for forward jet-like events consisting of multi-photon final states. The measurements are based on the data taken in 2011 with integrated luminosity $\sim$ 22 $p{b}^{-1}$.

We compute the pion Generalized Parton Distribution (GPD) in a valence dressed quarks approach. We model the Mellin moments of the GPD using Ansätze for Green functions inspired by the numerical solutions of the Dyson-Schwinger Equations (DSE) and the Bethe-Salpeter Equation (BSE). Then, the GPD is reconstructed from its Mellin moment using the Double Distribution (DD) formalism. The agreement with available experimental data is very good.

The main experimental works, where dipole polarizabilities of charged pions have been determined, are considered. Possible reasons for the differences between the experimental data are discussed. In particular, it is shown that the account of the $\sigma$-meson gives a significant correction to the value of the polarizability obtained in the latest experiment of the COMPASS collaboration. We present also new fit results for the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ reaction.

During the INT-18-3 workshop, we presented an analysis of unpolarized Drell-Yan pair production in pion-nucleus scattering with a particular focus into the pion Transverse Momentum Distributions in view of the future Electron Ion Collider. The transverse distributions of the pion calculated in a Nambu–Jona-Lasinio framework, with Pauli-Villars regularization, were used. The pion Transverse Momentum Distributions evolved up to next-to-leading logarithmic accuracy is then tested against the transverse momentum spectrum of dilepton pairs up to a transverse momentum of 2 GeV. We found a fair agreement with available pion-nucleus data. This contribution joins common efforts from the TMD and the pion structure communities for the Electron Ion Collider.

In this talk, I will overview recent studies on the evolution of the shell structure in stable and exotic nuclei, and will show results of related shell-model calculations. This shell evolution is primarily due to the tensor force. The robust mechanism and some examples will be presented. Such examples include the disappearance of existing magic numbers and the appearance of new ones. The nuclear magic numbers have been believed, since Mayer and Jensen, to be constants as 2, 8, 20, 28, 50, … This turned out to be changed, once we entered the regime of exotic nuclei. This shell evolution develops at many places on the nuclear chart in various forms. For instance, the Island of Inversion picture has been changed considerably.

The correlations of secondary pions in annihilation and non-annihilation channels are investigated.

Numerous attempts to create a model that would exactly reproduce the N* - and Δ - resonances spectrum (that was presented in the Review of Particle Physics) failed. The existing models usually predicted considerably more resonances (twice or more in number) than were found in elastic πN - scattering. This problem is known as the problem of "missing" resonances. The recent partial wave analysis (PWA) SP06 that was made at George Washington University (2006) and included the modern experimental data revealed considerably fewer (approximately half) the N*- and Δ-resonances than those presented in the Review of Particle Physics (RPP) tables (2006). This disagreement invites further experimental investigation of the pion-nucleon interactions. Recent spin rotation parameter A and R measurements of the PNPI and PNPI-ITEP collaborations resolved a part of the twofold ambiguities of the PWA's. These results were used in the last PWA of the George Washington University (GWU) groups. The proposal for the additional measurements of the differential cross section and spin-rotation parameters R and A in the resonance region of the πN interactions is motivated. Such additional experiments are necessary to resolve the problem of the narrow (Γ < 30 MeV) baryon resonances existing and to complete monosemantic PWA of the πN elastic scattering.

The following sections are included:

• Introduction

• Neutron Star Model

• Relativistic Mean Field Model with Kaons (Pions)

• Conclusions

• Bibliography