Number Of Mesons Research Articles

A Nuclear Model with Explicit Mesons

A nuclear model is proposed where the nucleons interact by emitting and absorbing mesons, and where the mesons are treated explicitly. A nucleus in this model finds itself in a quantum superposition of states with different number of mesons. Transitions between these states hold the nucleus together. The model---in its simplest incarnation---is applied to the deuteron, where the latter becomes a superposition of a neutron-proton state and a neutron-proton-meson state. Coupling between these states leads to an effective attraction between the nucleons and results in a bound state with negative energy, the deuteron. The model is able to reproduce the accepted values for the binding energy and the charge radius of the deuteron. The model, should it work in practice, has several potential advantages over the existing non-relativistic few-body nuclear models: the reduced number of model parameters, natural inclusion of few-body forces, and natural inclusion of mesonic physics.

Meson-baryon effective chiral Lagrangians at orderp4

We construct the three-flavor Lorentz-invariant meson-baryon chiral Lagrangians at the order $p^4$, with which a full one-loop investigation may be performed. One obtains 540 independent terms. The processes with the minimal number of mesons and photons that this order Lagrangians may contribute to are also presented.

Does the empirical meson spectrum support the Hagedorn conjecture?

It has long been conjectured that strong interactions give rise to a Hagedorn spectrum and theoretical arguments have been presented in support of Hagedorn spectrum in large Nc QCD. This paper discusses the extent to which the meson spectrum should be viewed as evidence for a Hagedorn spectrum and argues that data do not provide a strong evidence for the Hagedorn conjecture. The conclusion is based on three reasons. It is shown that ‘realistic’ quark models have a spectrum in which the number of mesons up to 2.3 GeV grows with mass in a very similar way to the spectrum of physical mesons up to 2.3 GeV. However, these models can be shown to not have Hagedorn spectra. It is also shown that the available data are insufficient to determine the Hagedorn temperature. The data can be described with comparable accuracy by various functional forms of the prefactor that yield radically different Hagedorn temperatures. An analysis of the behavior of the spectrum for the various parity–spin–charge conjugation–isospin channels also appears to be inconsistent with what one expects if the data were in the regime dominated by exponential behavior.

New near-threshold mesons

We show that under a number of rather plausible assumptions QCD spectrum may contain a number of mesons which have not been predicted or observed. Such states will have the quantum numbers of two existing mesons and masses very close to the dissociation threshold into the two mesons. Moreover, at least one of the two mesonic constituents itself must be very close to its dissociation threshold. In particular, one might expect the existence of loosely bound systems of D and D∗sJ(2317); similarly, K and f0(980), K̄ and f0(980), K and a0(980) and K̄ and a0(980) can be bound. The mechanism for binding in these cases is the S-wave kaon exchange. The nearness of one of the constituents to its decay threshold into a kaon plus a remainder, implies that the range of the kaon exchange force becomes abnormally long—significantly longer than 1/mK which greatly aids the binding.

Density of pseudoscalar states: Evidence for valence glue.

We claim that experimental meson spectroscopy now requires the existence of constituent gluons. Drawing from several models, we study the number of mesons with given quantum numbers that can be expected in a given mass range, concentrating on pseudoscalars below 2 GeV. Counting only quark-antiquark states gives fewer mesons than are now seen, but including gluon degrees of freedom so that glueballs and hybrid states are allowed remedies this situation.

Surface description of QCD with fermionic quark boundaries

The flux sheet description of pure gauge theories proposed by Bardakei and Greensite is extended to include fermionic quark fields defined on the sheet boundaries. The quark fields are sources and sinks of colour flux and the action remains gauge in variant. It is shown that the partition function contains colour singlet contributions with the quantum numbers of mesons, baryons and exotics.

Three-nucleon potential

The interaction between three nucleons is studied on the basis of the covariant Green's function. A three-nucleon potential is derived from the scattering matrix and is characterized by an expansion in number of mesons exchanged. The complete definition of the potential now depends on the knowledge of the basic meson-nucleon interaction amplitudes to which each term of the expansion is connected. With the neglect of pion-pion interactions, the lowest-order potential, which involves the exchange of two quanta, is given in terms of the renormalized coupling constant and the total cross-section for meson-nucleon scattering. It is argued that in low energies and at large distances, the higher terms in the expansion give no appreciable contribution and so the lowest order suffices for most purposes.

Simple Model for Strong Interactions

A simple model is proposed which relates elastic and inelastic processes in strong interactions. It is assumed that the basic process in strong interactions is meson production. The meson fields are calculated from a Klein-Gordon equation using a Gaussian source function. It is assumed that there are three types of strong interactions, whose quanta are, respectively, the $\ensuremath{\pi}$ meson, the $K$ meson, and the antibaryon. The sizes of the three corresponding source functions are inversely proportional to the square roots of the masses of the quanta. The three coupling constants are taken to be equal. Elastic scattering is assumed to be the diffraction scattering associated with the inelastic meson-producing processes. We thus obtain predictions for three phenomena in nucleon-nucleon collisions: the differential elastic-scattering cross section; the differential cross section for production of particles; the average number of mesons produced as a function of incident energy. The predictions are in good agreement with all experimental data in the multi-GeV region.

Recent experiments with the C. E. R. N. synchro-cyclotron

The C.E.R.N. synchro-cyclotron is capable of accelerating protons up to an energy of 600 MeV, and when they strike a solid target they produce intense beams of π ± -mesons. The particles produced are relatively slow, and an absorber a few centimetres thick is sufficient to bring them to rest. A large number of mesons can therefore be confined to a small volume for a relatively long time, until they decay or interact with the surrounding matter. μ ± -mesons may also be produced by allowing the π ± -mesons to decay in flight. A very important feature of the μ -meson beams so produced is that they are almost 100% longitudinally polarized; i. e. their spins are alined about the direction of motion and in a given sense. Accurate determinations can thus be made of the way features of the decay process, and of interactions with matter, depend on the spin direction. Further, by making the μ -mesons precess in a strong magnetic field, one can determine quantities like their magnetic and electric dipole moments with high precision. I shall describe experiments recently performed with the C. E. R. N. synchro-cyclotron which give new information about the weak and electromagnetic properties of the π - and μ - mesons.

Search for the decay μ+→e++e−+e+

A search for μ+→e++e−+e+ was conducted using counter techniques. The number of mesons stopped was 109; when multiplied by the efficiency for detecting a three-electron decay, the number became 1.7·107. Five events were seen and are probably due to the decay mode μ+→e++e−+e++ν+\(\bar \nu \). Even assuming them to be due to μ+→e++e−+e+, a new upper limit of 5·10−7 is set for the branching ratio of this mode.

The structure of the nucleon core by the Hartree approximation

A method is proposed to investigate the structure of the nucleon core. A set of equations is derived to define the nucleon core and the meson cloud simultaneously. The equations are formulated by a variational method which enables us to find an approximate solution. The size of the nucleon core is estimated for a non-relativistic nucleon interacting with a neutral scalar.meson. The coupling constant between nucleon and meson is given by the ratio of the sizes of the core and the cloud. It is shown that for ƒ 2/4π ≈1 , the core size may be about half that of the meson cloud, where the number of mesons around the nucleon is about one. The generalization to a more realistic case is also suggested. The renormalization is not considered in this paper.

Theory of the Photodisintegration of the Deuteron

By means of a covariant field-theoretic technique, a formally exact expression is derived for the amplitude for photodisintegration of the deuteron. By expanding the result only in the number of mesons exchanged and by making a series of nonrelativistic approximations, the expression is reduced to one in which the corrections to the conventional dipole matrix element depend only on the amplitude for photomeson production, the renormalized meson-nucleon coupling constant, and the appropriate two nucleon wave functions. One finds that virtual meson effects play little role at energies below 100 Mev, in justification of recent calculations based on the conventional nonrelativistic theory. At higher energies good agreement with the total cross section was obtained by the inclusion of both hard core and tensor force effects in the wave functions. In addition the folded angular distribution could be fitted by using a reasonable extrapolation of the phase shifts in the /sup 1/S/sub 0/ and /sup 1/D/sub 2/ states. (auth)

Magnetic Moment of the Deuteron

A contribution to the deuteron magnetic moment which results from the altered expectation values of nucleon core spins in the bound state is calculated. The adiabatic approximation, in which the $\ensuremath{\pi}$-meson clouds of a static-nucleon model are assumed to follow the orbital motion of the sources, is used. The two-nucleon states are expanded in Heitler-London states; the expectation value of the deuteron magnetic moment operator is related to single-nucleon matrix elements by means of an expansion corresponding to exchange of various numbers of mesons between the nucleons. The single-nucleon matrix elements are evaluated using the Chew-Low-Wick fixed-source theory. If an orbital wave function with a relatively large $D$-state probability is used, the one-meson exchange terms give an increase in the deuteron magnetic moment of about one percent. The two-meson exchange terms are considerably smaller than the one-meson exchange terms.

Interaction of Static Nucleons

The Heitler-London method has been applied to the calculation of the energy of interaction of two nucleons, as given by the fixed-source model. Numerical results are also given for the normalization of the state vector and the number of mesons in the cloud, for the states which comprise the deuteron. Particular attention is given to the rate of convergence of the expansions and the influence of the excited states of the nucleons. The relation to the Tamm-Dancoff method is also discussed in detail. It is shown that in $T=0$ states, the interaction does not appear to differ in any significant way from the one-meson exchange term. In $T=1$ states, on the other hand very large contributions are obtained from the higher order terms. These contributions have such a nature as to suggest that even at low energies it is improper to apply the fixed-source model, with the assumption that the meson cloud follows adiabatically the motion of the nucleons, to $T=1$ states.

The proper field of a physical nucleon

The energy values of Tomonaga's intermediate coupling equation for a physical nucleon are obtained from the asymptotic solutions of the equation when the number of mesons is very large. The energy values can be determined immediately from the requirement that the asymptotic solutions should contain only positive integer powers of meson emission operators. The possibility that the asymptotic solution for the ground state will give a good description of the situation at small distances from the core of nucleons is discussed. The result is consistent with the view that the production of meson showers by high energy nucleon collisions is due to the shaking off of meson clouds during collisions. No inconsistency with the low energy experiments is introduced by this picture of shower production.

Nucleon-antinucleon forces in the intermediate coupling theory

A semi-phenomenological approach to meson theory is used in order to calculate the nucleon-antinucleon complex interaction responsible for the scattering and annihilation of antinucleons in hydrogen. It is assumed that the main part of the imaginary potential is due to processes involving virtual annihilation into an arbitrary number of mesons, all of them but one being emitted or absorbed in a p-state. An effective Hamiltonian is derived for such processes, from which a static interaction can be calculated, the nucleon and antinucleon being treated as fixed sources. The intermediate coupling theory of Tomonaga is extended to the two-body problem and applied first to the calculation of ordinary nuclear forces and of the real part of the nucleon-antinucleon interaction. The annihilation Hamiltonian is then treated approximately by the intermediate coupling method. The imaginary part of the potential is found to have a range of the order of 2 to 3.10-3 cm, beyond which it becomes a weakly oscillating function of the nucleon-antinucleon distance. The physical meaning of this result is discussed, as well as the effects which would tend to sharpen the definition of the emitted pions multiplicity. In particular, a method is proposed to investigate, in the framework of the intermediate coupling theory, the influence of the excited states of the nucleon-antinucleon system.

The structure of the nucleon

We derive from the fixed source meson theory an exact relation connecting the structure of the physical nucleon to the mesonnucleon scattering amplitudes. General formulae are obtained for the charge and current densities of the meson cloud of the nucleon. Using these results it is possible to obtain an upper limit of 5.5 meson masses for the cut-off and of 1.65 for the average number of mesons in the cloud. The nucleon magnetic moments take the correct experimental values ±1.9 in correspondence of a cut-off to 5 meson masses.

Adiabatic nuclear potential for large values of the coupling constant

A method for the calculation of the adiabatic potential between two fixed nucleons is proposed giving a sequence of approximations in which at each stage only a limited number of mesons and pairs is taken into account. By means of a variational principle the adiabatic potential is approximated with a sequence of fractions of polynomials ing2, whose coefficients contain only the potentials calculated by Levy and Klein with perturbation methods. The convergence of the sequence does not depend on the magnitude of the coupling constant and, when the limit exists, it is an analytic continuation of the series in powers ofg2 outside its radius of convergence.

Multiple Meson Production

IT has recently been reported by Daniel et al.1 that in high-energy collisions between nucleons, besides π-mesons, some heavier mesons of about 1,300 me mass are also created. The purpose of the present note is to estimate the theoretical probability of emission of a heavy meson in a collision process, using the statistical theory developed by Fermi2. The collision is studied in the centre-of-mass system of the particles and it is assumed that the total energy W (W is the energy in the centre-of-mass system) is suddenly released in a small volume, surrounding the nucleons (M = mass of the nucleon, μ = mass of π-meson). One then calculates statiscally the probability that a certain number of mesons are created.

The Differential Range Spectrum of Cosmic-Ray Mesons

A counter-controlled cloud chamber has been used to investigate the differential range spectrum of mesons at sea level. The chamber contains eight lead plates each 7\textonehalf{} in. wide and one-half in. thick. A lead absorber of variable thickness, up to 27 in., may be placed above the chamber. The number of mesons observed the stop in the chamber per unit time has been found for various thicknesses of absorber above the chamber. A plot of the counting rate of particles which stop versus the thickness of absorber above the chamber reveals a broad low peak which has its maximum at a 6-in. thickness of absorber. The counting rate at the peak is 2.20\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ count/sec./sterad/g, about 10 percent higher than the counting rate with no absorber. Correction has been made for particles lost through scattering in the absorber. The corrected results show a more marked peak whose maximum occurs with a 9-in. thickness of absorber. The counting rate at the maximum of the corrected curve is 3.73\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ count/sec./sterad/g.