Pion Coupling Research Articles

Quantum mass shift of the soliton in the Skyrme model.

The quantum mass shift of the soliton in the Skyrme model has been calculated from all nonzero modes. The calculations were carried out using a method applied earlier to the sine-Gordon model. The mass shifts do not depend on the baryonic spin, therefore they are the same for the nucleon and the $\ensuremath{\Delta}$. Our model parameters are the pion decay constant ${F}_{\ensuremath{\pi}}$, with its experimental value, and the pionic mass ${m}_{\ensuremath{\pi}}$, once in the chiral limit ${m}_{\ensuremath{\pi}}=0$ and also with the experimental value. We justify taking for the Skyrme parameter $e$ the experimental value of ${g}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}$, the mesonic $\ensuremath{\rho}$-pion coupling constant. The results depend on the vibrational energy. In this case an energy cutoff must be introduced. Using renormalization considerations as in the nonlinear $\ensuremath{\sigma}$ model, we have chosen this cutoff to be $e{F}_{\ensuremath{\pi}}=1136$ MeV. Our results (for $e={g}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}=6.11$ and ${F}_{\ensuremath{\pi}}=186$ MeV) are ${M}_{N}=996$ MeV, ${M}_{\ensuremath{\Delta}}=1593$ MeV for ${m}_{\ensuremath{\pi}}=0$; ${M}_{N}=857$ MeV, ${M}_{\ensuremath{\Delta}}=1641$ MeV for ${m}_{\ensuremath{\pi}}=138$ MeV. The spin dependence and the energy contribution of the coupling term between vibrations and rotations are being considered here only in a qualitative way.

Baryon-Meson Couplings in the $q\bar{q}$ Pair-Creation Quark Model. I

Characteristic features of the baryon-meson coupling vertices are studied in terms of a quark model in which quark-antiquark pair-creation processes inherent in the quark-gluon interaction Lagrangian are explicitly incorporated. It is shown that the standard non-relativistic baryon-meson vertex functions are naturally derived from quark exchange diagrams in a way that approximate SU6 relations are apparently satisfied for the coupling constants. Under the assumption of the flavor SU3 symmetry, this formalism yields a simple analytic expression for the coupling constants of S-wave baryons, which contains only one parameter related to the overall strength. The model predictions are examined in conjunction with the available empirical information. The effect of flavor symmetry breaking is also discussed with respect to the pion decay widths of decuplet baryons. Due to the improper treatment of the chiral symmetry in constituent quark models, all the pion coupling constants are universally too small by factor 3 ∼6 in strength.

Relativistic one-boson-exchange model for the nucleon-nucleon interaction.

Nucleon-nucleon data below 300-MeV laboratory energy are described by a manifestly covariant wave equation in which one of the intermediate nucleons is restricted to its mass shell. Antisymmetrization of the kernel yields an equation in which the two nucleons are treated in an {ital exactly} symmetric manner, and in which all amplitudes satisfy the Pauli principle {ital exactly}. The kernel is modeled by the sum of one boson exchanges, and four models, all of which fit the data very well ({chi}{sup 2}{congruent}3 per data point) are discussed. Two models require the exchange of {ital only} the {pi}, {sigma}, {rho}, and {omega}, but also require an admixture of {gamma}{sup 5} coupling for the pion, while two other models restrict the pion coupling to pure {gamma}{sup 5}{gamma}{sup {mu}}, but require the exchange of {ital six} mesons, including the {eta}, and a light scalar-isovector meson referred to as {sigma}{sub 1}. Deuteron wave functions resulting from these models are obtained. Th

Union of chiral and heavy quark symmetries

We describe the chiral symmetric couplings of pions to heavy mesons ( B or D), valid in the portion of phase space where the pions have low momentum. In order to include consistently all low energy excitations, the vector mesons (B ∗ or D ∗) must appear explicitly in the effective lagrangian. The result is then invariant under both the chiral and heavy quark symmetries. We include matrix elements relevant for various weak decays.

The ( π,2 π) reaction on few body systems

A review of the ( π,2 π) reaction studies is presented in this paper, together with some very recent results from experiments performed at TRIUMF and at PSI. The comparison of the experimental results with the available models for the πN → ππN indicates that the ( π,2 π) reaction provides informations on the chiral symmetry breaking parameter, as well as on the pionic couplings g ΔΔπ and g NN ∗ππ .

Recent applications of relativistic equations to the few body problem

Recent numerical results for a relativistic OBE model of the NN interaction, obtained by solving a relativistic equation with one-particle on mass-shell, will be presented and discussed. Two meson exchange models, one with only four mesons (π, σ, ϱ, ω) but with a 25% admixture ofγ5 coupling for the pion, and a second with six mesons (π, σ, ϱ, δ, η) but pureγ5γμ pion coupling, are shown to give very good quantitative fits to the NN scattering phase shifts below 400 MeV, and also a good description of the p40Ca elastic scattering observables. Applications of this model to electromagnetic interactions of the two body system, with emphasis on the determination of relativistic current operators consistent with the dynamics and the exact treatment of current conservation in the presence of phenomenological form factors, will be described.

Three-nucleon force in the quark compound bag model

A model of the three-nucleon force is derived from the one-pion-exchange interaction between the nucleon and a six-quark bag excited during the NN collision at short distances. The parameters determining the excitation of the six-quark bag are taken from the quark-compound bag model of NN scattering up to 1 GeV. The pionic couplings with the bag states are deduced from the cloudy bag model. Their effect on the binding energy of the three-nucleon system is calculated and found to be about - 0.05 MeV. Future development of the model is discussed.

A hamiltonian approach to the roper resonance

The breathing modes along with the spin-isospin zero modes of the ω-stabilized skyrmion are quantized using Dirac's method. The result is a hamiltonian for the nucleon, the δ-isobar and the Roper with explicit meson couplings. The linear pion coupling is used to evaluate the decay width of the Roper into πN.

Photoproduction of delta and Roper resonances in the cloudy bag model.

The photoproduction of delta and Roper resonances has been calculated within the framework of the cloudy bag model. Two alternative formulations, the original pseudoscalar surface coupling and the pseudovector volume coupling of pions, have been used, and the results are compared. The helicity amplitudes are in fair agreement with experimental data, the prediction for the small ${E}_{1+}$/${M}_{1+}$ ratio for delta production is -1.8% for a bag radius of 1 fm and pseudovector coupling.

Exchange currents and the internal structure of the nucleon in quark models

The influence of internal nucleon structure on meson exchange currents has been investigated, in the framework of the nonrelativistic constituent quark model and the MIT bag model with massless quarks. In comparison with the conventional theory of exchange currents, one finds different strengths for the model-dependent higher-order terms and no ambiguity between pseudoscalar and pseudovector pion couplings. Furthermore, the retardation and excitation effects in the many-body system have to be treated consistently, in order to preserve gauge invariance. In this way one obtains 'damping' factors, which differ in structure from the phenomenological form factors.

Infrared treatment of higher anomalies and their consequences.

Ward identities leading to higher-order anomalies are discussed from an infrared point of view. As a result a new proof of the relations between various couplings of photons, pions, and axial-vector currents is obtained.

The goldstone pion in SU(2) lattice QCD at low quark mass: Scaling and finite size effects

Results for the pion sector of an extensive numerical simulation of quenched SU(2) QCD with staggered fermions are presented. A wide range of quark masses, gauge couplings and lattice sizes is investigated. The systematic and statistical errors are carefully analyzed. Finite size effects occurring on small lattices and/or at low quark masses are studied in detail. When they are absent or weak, we find that the pion mass and coupling constant verify approximate scaling behaviour at low quark mass for β ≳ 2.4. We determine the K and π coupling constants to be in the ratio 1.25(5). At β = 2.3, we show that the square pion mass contains a substantial contribution which is non-linear in the quark mass and renders chiral limit extrapolations less reliable.

The 2π-exchange potential for pseudovector coupling of pions and nucleons

A 2 pi -exchange (TPE) potential for pseudovector coupling of pions and nucleons is derived by transforming the Dirac equation into a Schrodinger-like form. The resulting TPE potential is spin dependent and attractive in all states of the NN and NN systems and describes part of the intermediate-range interaction. A comparison is made with the Hamada-Johnston potential and with the TPE potential obtained from different approaches.

Bethe-Salpeter dynamics for two-photon processes

Recent experimental data on single hadron production by two-photon beams inpetra andpep have provided a unique opportunity for testing specific models of confinement through a study of one of their cleanest predictionsviz the γγ →H amplitudes. Motivated by this new facility, aqcd-oriented Bethe-Salpeter model of harmonic confinement, which has already been found to describe rather well several classes of hadronic data (from mass spectra to electromagnetic and pionic couplings), is now employed for a detailed comparison of its predictions onP → γγ andT → γγ couplings with the data. The agreement is quite good for all cases except one (η → γγ).

Role of hadronic dynamics in proton decay

Aspects of hadronic dynamics which play a crucial role in proton decay (exclusive and inclusive) are examined in the context of a comprehensive Bethe-Salpeter (BS) formalism forq\(\bar q\) andqqq systems, under harmonic confinement. The BS model which is characterized by two basic parameters—the universal spring constant\(\tilde \omega \) GeV and the quark massm q =0.28 GeV, has already provided an impressive set of agreements in respect of a large number and variety of hadronic observables (mass spectra, and an extensive list of e.m. and pionic couplings of both mesons and baryons). TheSU(5) GUT parameters, on the other hand, are kept fixed at the ‘standard’ values, (see e.g. Langacker's review). The absolute normalization of the baryon, which is rather crucial in this case, is fixed with reference to the (topologically equivalent) process of its ‘dissociation’ into three quarks by a hard photon, which makes use of the structure function sum rule\(\int\limits_0^1 {dxF_2^p (x)/x = \sum {Q_i^2 } } \), instead of the usual BS normalization (which amounts to the conservation of charge). Thee+ inclusive rate, which is about three times that of thee+π0 mode, works out at0.54×10 −33 yr −1 which is smaller than most contemporary calculations by two orders of magnitude. Other exclusive modes are also consistent with the above estimate. The theoretical implications of these results vis a vis contemporary calculations as well as current experimental searches are discussed.

Bethe-Salpeter few-quark dynamics and the pion degree of freedom

The pionic interaction of baryon (qqq) states is formulated in a Bethe-Salpeter (BS) model of harmonic confinement, characterized by a universal spring constant (omega-tilde = 0.15 GeV) and the quark mass (m/sub q/ = 0.28 GeV) concerned, on lines similar to those developed recently for pionic couplings of meson (qq-bar) states, wherein the pionic degree of freedom is governed by the same BS dynamics as for other qq-bar states, and not introduced by hand as an independent entity. The algebraic structures of the matrix elements for NN..pi.. and ..delta..N..pi.. couplings are strongly reminiscent of the quark-pair-creation model, as found recently for meson couplings (rho..pi pi.., ..omega..rho..pi..). A Lorentz-invariant adaptation of the resulting pion-baryon form factors, on lines identical to those employed successfully to the meson couplings, leads to the parameter-free predictions (4..pi..)/sup -1/(G/sub NNpi/)/sup 2/ = 13.02 and GAMMA(..delta -->..N..pi..) = 104.6 MeV, both within 10% of experiment. It is stressed that these pionic results are consistent with the one-pion-exchange-potential structure.

Complete mass spectra of $$q\bar q$$ and $$Q\bar q$$ mesons with improved Bethe-Salpeter dynamics of confinementmesons with improved Bethe-Salpeter dynamics of confinement

The Bethe-Salpeter (bs) dynamics of harmonic confinement developed byanm and collaborators over the last three years and already applied with considerable experimental success to various hadron spectra and coupling structures has been significantly improved through (i) a more exact treatment of a certain momentum-dependent operator\(\hat Q_q \) appearing in thebs equation, using the techniques of SO (2, 1) Lie algebra, and (ii) a sharpened definition of theqcd Coulomb term, so as to yield unambiguous values for different flavour sectors. The resulting mass spectra of light\((q\bar q)\) meson towers and semi-heavy\((Q\bar q)\) quarkonia which are most sensitive to the improved treatment of\(\hat Q_q \), reveal excellent agreement with experiment, one in which only slight changes in the reduced spring constant\((\tilde \omega )\) and quark masses (mq) over the earlier parametrizations are involved. These changes are however found to have a negligible effect on the (already good) numerical values of the other predictions (electroweak and pionic couplings) depending on the\(q\bar q\) andqqq wave functions. A critical assessment of the strong and weak points of this method is madevis-a-vis other related approaches.

Up-down quark mass difference: Couplings of pions to nucleons or isobars and low-energy nucleon-nucleon scattering

We investigate effects of the up-down quark mass difference on the couplings of pions to nucleons or isobars. The calculated $\ensuremath{\pi}\mathrm{NN}$ and $\ensuremath{\pi}\mathrm{N}\ensuremath{\Delta}$ couplings are used to derive the long-range one-pion-exchange potential and the intermediate-range attraction for the three different cases: p-p, n-p, and n-n. The resultant potentials are then used to determine numerically the low-energy scattering parameters, including both the scattering length $a$ and the effective range $r$. Our results indicate that a reasonable up-down quark mass difference such as 10 MeV yields a value for $|{a}_{\mathrm{pp}}|\ensuremath{-}|{a}_{\mathrm{nn}}|$ of about + 0.6 fm, which is sizable from the experimental point of view. Our results also suggest that the large observed value for $|{a}_{\mathrm{np}}|\ensuremath{-}|{a}_{\mathrm{nn}}|$ can be understood primarily as a manifestation of the pion mass difference.[NUCLEAR REACTIONS Application of quark models to nuclear physics; effects of the up-down quark mass difference on couplings of pions to nucleons or isobars; charge dependence and charge symmetry breaking in low energy nucleon-nucleon scattering.]

Divergence of the quark self-energy in the second quantized chiral bag model

When summing over the intermediate quark states of a spherical cavity, the quark self-energy of the chiral bag model, in lowest order of the pion coupling, is shown to generate a series of terms, each one growing linearly with the angular variable κ. However, there is a cancellation between terms for different κ, which finally leads to an overall linearly divergent series.

Chiral invariance in the soliton bag model

The soliton bag model of quark confinement is shown to give the same pionic coupling as the cloudy bag model, explicitly independent of details of the soliton field. The Goldberger-Treiman relation is satisfied in this development.