Virtual Pion Research Articles

Pion-nuclear interactions at the SC and beyond

The SC at CERN pioneered most of the lines in nuclear pion physics that were later explored in depth at the meson factories at LAMPF, at SIN or PSI and at TRIUMF. The golden age for these investigations was the period 1965—75, while the later programme with a few exceptions was overwhelmed by the superior intensities and beams at the meson factories. This programme at CERN established most of the general ideas which now are routinely exploited although with a far higher degree of sophistication. The impact has been far-reaching well outside of nuclear physics. The reason for this is that pions are the major nuclear constituent in addition to the neutron and the proton. In the early 1960s very little was known about the quantitative and even qualitative consequences of the pion for nuclear structure, except of course the one-pion-exchange nucleon—nucleon potential as a major explanation for the nuclear force. At the time, nuclear physics was mainly dominated by the recent breakthroughs in the understanding of nuclear shell structure and collective motion as well as by the intricate interplay of the two. There was no particular need for exploring those aspects using pions. At present the situation is very different. The pion degree of freedom is integrated in the mainstream of nuclear physics, solidly established as a principal nuclear feature, while nuclear quark physics now is the frontier that then was occupied by pion physics. Indeed, we have now reached a point at which a large part of modern nuclear pion physics is not even carried out by physical pion beams, but by virtual pions in many forms. All of this change is largely due to the pion programme at the SC. The origin of the programme, like the rest of the nuclear physics programme at the SC, was the crucial decision by Yiki Weisskopf in 1963 to broaden the CERN programme by exploiting this machine for another field instead of shutting it down. His far-sighted idea was that of a symbiosis between particle and nuclear physics with each fertilizing the other one. On the one hand one would exploit the properties of nuclei to learn more about elementary particles and their interactions, and on the other one would probe properties of nuclear structure using the high energy nucleons and mesons as probes. It is very interesting to examine the priorities and the perspectives at the time. In order to stimulate this idea Amos de Shalit and Viki Weisskopf made it known in the middle of 1962 that there would be a small conference at CERN in order to discuss these issues. This was enthusiastically received and, in fact, this meeting was the first in what has now become the PANIC conferences on High Energy Physics and Nuclear Structure, of which the 12th was recently held in Cambridge, MA, with over 700 participants. I had the luck as a rather fresh postdoc to be given the task of organizing this meeting at short notice, both scientifically and materially. Interestingly, it was easy to find logical main speakers on muonic atoms (Hans Sens), strange particle interactions

Recent Developments in Nuclear Physics

Nuclei exhibit features that are described in superficially contradictory terms according to the different degrees of freedom that are excited by probes of different scale in space and in time. After giving some examples I concentrate on the hadron degrees of freedom such as the nucleon, the pion and the .6. isobar. These are the effective degrees of freedom on the level of intermediate resolution: about 0�5-1 fm in distance and correspondingly in time. A prime example is the deuteron :which has a nearly model-independent description in terms of pion physics to very high precision. In nuclear matter the pion propagates in close analogy to the propagation of light in a dielectric. This permits the explanation of a number of features in nuclei related to the chiral symmetry limit in which the pion mass vanishes. A consequence of this description is the analogy of the equations for the pion and its effective field with the Maxwell equations for a dielectric. A pionic collective mode should appear strongly and with characteristic properties for a well chosen probe. It is difficult to explore its properties directly and in particular physical pions are not useful for this purpose. I will discuss different alternatives involving 'virtual pion beams'. There is recent evidence for such a collective state in forward charge exchange reactions throughout the periodic system.

Photon production through A1 resonance in high-energy heavy-ion collisions.

Electromagnetic radiation from excited hadronic matter is one of the best ways to study the properties of the matter. Considering various processes in the hadronic gas, Kapusta et al \cite{Kapusta_photons} have found a $\pi\rho \rightarrow \pi\gamma$ reaction with intermediate virtual pion or rho to be the main source of photons with energy greater than 0.7 GeV. However, at temperatures considered T=100-200 MeV, a $\pi\rho$ pair can easily form an $A_1$(1260) resonance, and we show that this mechanism leads to the photon production rates exceeding those suggested previously. The paper is in LATEX, figures available from authors.

Threshold pion photoproduction in chiral perturbation theory

We analyze threshold pion photoproduction in the framework of baryon chiral perturbation theory. In case of neutral pion photoproduction, virtual pions generate infrared singularities which modify the familiar form of the low-energy theorem for the electric dipole amplitude E 0+. In particular, we predict E 0+ π 0 p ( s th )=−(1.33±0.09)× −3/ M π+ . We also find a satisfactory description of the recently measured total cross section for γp→ π 0p in the threshold region. The process γn→ π 0n is entirely given by the loop and counterterm contributions. It would be interesting to have an experimental determination of the corresponding cross section in the threshold region. In case of the charged channels, the loop corrections are much more tame.

On the low-energy theorems for threshold pion electroproduction

We consider pion electroproduction at threshold to one loop order in chiral perturbation theory. We derive novel contributions to the low-energy theorems for the S-wave multipoles E 0+ and L 0+ at threshold to order O( μ 2, v) with μ= M π / m the ratio of the pion and nucleon mass and v= k 2/ m 2 related to the four-momentum of the virtual photon. At next-to-leading order, the effect of infrared singularities generated by virtual pions becomes visible. We also discuss the inclusion of photon-nucleon vertex form factors.

The new muon (g−2) experiment at Brookhaven

A new measurement of the muon anomalous magnetic moment (BNL E821) aims to obtain a factor of 20 in precision over the previous CERN measurement which had an accuracy of 7.3ppm. This increase in precision will provide a sensitivity to virtual particles into the TeV mass range and opens a substantial window for the discovery of new physics beyond the standard model. The CERN measurements established the muon as a point-like lepton obeying QED with additional corrections from virtual pions. It also provided constraints on the virtual production of new particles with masses on the order of tens of GeV. By increasing the precision of this measurement by a factor of 20, the experiment will be sensitive to the single-loop radiative contribution from the W and Z bosons with an experimental error ∼ 20% of the magnitude of the effect predicted by the standard model. In addition to experimentally testing electroweak renormalization, this measurement will be sensitive to the presence of “new physics” such as muon substructure to several TeV, supersymmetric particles, an anomalous W-boson magnetic moment, aCP violating muon electric dipole moment, and other physics beyond the standard model. In several cases, the sensitivity of E821 goes well beyond that which will be available at Fermilab, LEPII or the SSC. The construction and preparation of the precision storage ring has begun at Brookhaven. Storage ring completion is anticipated in 1993 and data collection will commence in late 1994.

Pion contribution toK+-nucleus scattering

The contribution of virtual pions to the total ${\mathit{K}}^{+}$-nucleus cross section in the ${\mathit{p}}_{\mathit{L}}$=450--1000 MeV/c region is found to be about 10%. With this contribution, the data can be explained without the assumption of nucleons ``swelling'' in the nucleus.

Neutral pion photoproduction at threshold

We evaluate the neutral pion photoproduction amplitude at threshold to one loop in chiral perturbation theory. Virtual pions generated infrared singularities in the scattering amplitude and modify the familiar low-energy expansion of the electric dipole amplitude E o+ at next-to-leading order.

Currents and Ward-Takahashi identities for nonlocal quantum field theories

We consider a nonlocal quantum field theory, which can be used for the description of a composite particle, such as the nucleon interacting with its virtual pion field. Assuming a global symmetry of the theory, we discuss how to find the corresponding conserved currents. For the case of a U(1) symmetry, we then examine the conditions for second quantization and derive a general Ward-Takahashi identity. The formalism is then applied to the electromagnetic interaction.

Real-pion states formed by a virtual-pion beam:: New family of nuclear excited states

Deeply bound pionic states are discussed from various points of view; highly excited nuclear states as a cluster family of pionic bound states, Σ atom/Σ hypernuclei, halo-like density distributions, virtual pion beam to produce pionic states, etc.

The Nonlinear Effects of Pion-Quark Coupling in the Cloudy Bag Model

The nonlinear pion-quark interaction in the Cloudy Bag Model is investigated. The Hamiltoni­ an is normal-ordered. The vacuum expectation value of pion field squared is evaluated by introduc­ ing some cutoff momentum for the virtual pions. We then calculate gA, including other corrections. The Cloudy Bag ModeF) in which the pion is permitted to penetrate into the bag interior, has achieved reasonable success in explaining some properties of hadrons and the pion-nucleon scattering. This model is given by the following Lagrangian:

The Nonlinear Effects of Pion-Quark Coupling in the Cloudy Bag Model

The nonlinear pion-quark interaction in the Cloudy Bag Model is investigated. The Hamiltonian is normal-ordered. The vacuum expectation value of pion field squared is evaluated by introducing some cutoff momentum for the virtual pions. We then calculate gA, including other corrections.

Shell model of the nucleon

A shell model of the nucleon is described in which the quark-gluon core of the nucleon and the virtual pions around the core separately occupy single-particle states.

Pseudoscalar-pseudovector equivalence in relativistic mean-field theory of nuclear structure

In the Dirac-Hartree-Fock treatment of pion-exchange in symmetric nuclear matter, it has long been known that the pseudoscalar πNN coupling leads to crystallization at an unphysically low value of the nuclear density. For this reason, it has been generally accepted that the pseudovector πNN coupling is the correct prescription. In a chirally-symmetric theory like the linear σ-model the two should be equivalent. Earlier work showed this is the case for pion emission or absorption, to O( g 3); in the present paper it is shown that the pion mean field (virtual pions) can be taken as pseudovector-coupled, to all orders in g.

Goldstone bosons generate peculiar conformal anomalies

We reexamine the low energy theorem for the matrix element 〈0| θ μ μ | γγ〉, where θ μν is the energy-momentum tensor. Virtual pions are shown to generate anomalous contributions. The consequences for the decay of a light Higgs particle into two photons are discussed.

Dispersive effects for the nuclear paramagnetic susceptibility

Dispersive effects coming from pionic degrees of freedom (virtual magnetic pion photoproduction) are shown to reproduce the nucleonic magnetic susceptibility and to yield a parallel quenching in nuclei. The relative importance of low lying nuclear vs.Δ-excitations is discussed and the difference of their role for the magnetic and electric polarizability is pointed out.

Enhancements observed in the two-proton invariant mass distribution in the pionless deuteron breakup at 3.3 GeV/c

A sample of “non-spectator” events in the pionless deuteron breakup at a 3.3 GeV/c momentum has been investigated by means of a 1 m HBC at the JINR, Dubna. The two-proton invariant mass spectrum in the charge exchange channel exhibits two enhancements for masses of 2,010 MeV/c2 and 2,160 MeV/c2.Theoretical calculations taking into account one-pion exchange diagrams and virtual pion absorption by the deuteron have been carried out. It has been shown that the enhancement atM pp=2,010 MeV/c2 can be explained if some kind of singularity near theN-N threshold is required. The observed maximum atM pp=2,160 MeV/c2 is caused mainly by intermediate Δ production and pion absorption on the deuteron.

Reply to "Comment on 'Comparison of approximate chiral-dynamical pi N--> pi pi

It is shown that in forward-angle pion-nucleus double charge exchange reactions leading to double analog states the contribution from the contact diagram of the virtual pion production does not vanish identically. Numerical effects of this diagram in various other double charge exchange reactions should, therefore, be examined case by case.

Effect ofππinteractions inπN scattering

The standard cloudy bag model description of ..pi..N scattering is extended to include contributions at the two-pion level. The ..pi pi.. scattering amplitudes are parametrized in phenomenological, separable forms consistent with the known ..pi pi.. S-italic- and P-italic-wave phase shifts. These amplitudes are embedded in the ..pi..N description to account for scattering of the incident pion from the nucleon's virtual pion cloud. A self-consistent analysis of the coupled ..pi..N, ..pi delta.., and ..pi..N/sup */ (1470) systems results in excellent reproduction of the phase shifts in the ..pi..N P-italic/sub 33/ channel to energies above the pion production threshold. In the P-italic/sub 11/ channel, without two-pion intermediate states, no acceptable fit to the data is possible for any values of the bag parameters. It is shown that the additional attraction provided by ..pi pi.. scattering is essential to reproduce the low-energy phase shifts and fix the sign change at the correct energy.

The effect of conventional nuclear binding on nuclear structure functions

We show that Fermi motion (including the effect of nucleon binding energy), together with a simple ansatz for the dependence of the nucleon structure function on its invariant mass, can explain the major features of recent nuclear structure function data. The close relationship of this work to the earlier explanations of the EMC effect based on an enhancement of the virtual pion field of the nucleus is discussed.