Pion–nucleon amplitude near threshold: the sigma-term and scattering lengths beyond few loops

The pion–nucleon amplitude is considered in the vicinity of the elastic scattering threshold within a relativistic dynamical model dressing the πNN and πNΔ vertices self-consistently with an infinite number of meson loops. The dressing is formulated as solution of a system of coupled integral equations incorporating unitarity, crossing symmetry and analyticity constraints. The calculated scattering lengths and the sigma-term agree with recent data analyses. The dressing is important in this model both below and at threshold. The contribution of the Δ resonance is discussed, including effects of the consistent dressing of the πNΔ vertex. A comparison with the approaches of chiral perturbation theory and the Bethe–Salpeter equation is outlined.     

Fixed-t partial wave analysis of πN scattering

The last full Karlsruhe PW analysis of πN scattering was finished ca. 20 years ago. After that a huge pile of new accurate πN scattering data has emerged, with which the old analysis is not completely compatible. We are making a highly modernized version of the old analysis to all (recent and old) data, aiming to pay particular attention to the discrepancies between different data sets and to the handling of the experimental errors as well as to the electromagnetic corrections and the effects of isospin breaking.     

The NN → NNη reaction close to threshold

The pp → ppη and np → npη reactions at energies near the η production threshold are studied in a non-relativistic one boson exchange model, where the N^* (1535 MeV) S11 resonance is excited through the exchange of π, η, and ω mesons and subsequently decays into an ηN pair. Energy integrated cross sections and energy spectra of the out going η's are reported. Providing NN and ηN final state interactions are taken into account coherently, the model reproduces both the scale and energy dependence of the cross section for the pp → ppη reactions up to 100 MeV. Final state interaction corrections due to the nucleon-nucleon and meson-nucleon forces influence strongly the scale and shape of the cross sections. The shape of the energy spectra of the outgoing η's provides a clear signature of the ηN force.     

πN scattering and electromagnetic corrections in the perturbative chiral quark model

We apply the perturbative chiral quark model to give predictions for the electromagnetic O(p²) low-energy couplings of the ChPT effective Lagrangian that define the electromagnetic mass shifts of nucleons and first-order (e²) radiative corrections to the πN scattering amplitude. We estimate the leading isospin-breaking correction to the strong energy shift of the π⁻p atom in the 1s state, which is relevant for the experiment “Pionic Hydrogen” at PSI.     

On the pp → ppη(η′) reactions near threshold

The production rate for η′ in pp → ppη′ at rest is calculated in a covariant one boson exchange model, previously applied to study π⁰ and η production in NN collisions. The transition amplitudes for the elementary BN → η′N processes with B being the meson exchanged (B = π, σ, η, , ω and a₀) are taken to be the sum of s- and u-channels with a nucleon in the intermediate states, and an a₀ meson pole in a t-channel. The couplings of the η′ to hadrons are a factor 0.4 weaker than the respective η-hadron couplings, as suggested by a quark model and a singlet-octet mixing angle θ = −23°. The model reproduces near threshold cross sections for the quasielastic processes π⁻p → nη(η′) and pp → ppη(η′) reactions.     

1/N expansion and the correlation energy of nuclear matter in the relativistic σω model

We propose the 1/N expansion method, where N can be identified with 2 due to the isospin SU(2), as a systematic expansion scheme for the relativistic meson-nucleon many-body theory. We derive a general formula for the computation of the effective action in the σω model based on the 1/N expansion, utilizing the functional integral method. In this scheme the leading contribution coincides with the familiar Hartree approximation. The elimination of the Landau ghost from the meson propagators in the subgraphs, which appears to be essential for our formulation, is also established.

As an application we compute the energy density of nuclear matter beyond the Hartree approximation including the next-to-leading order contributions in the 1/N expansion. In this order, one should include the ring energy contribution as a correlation energy addition to the exchange energy contribution. We find that we can describe the nuclear matter saturation properties without drastic changes of the overall physical picture which emerged in the Hartree approximation. The important role of the repulsive contribution due to the vacuum polarization effects in the ring energy is emphasized.     

The relativistic stripping model of (p, π) reactions in the Δ resonance region

The relativistic stripping model is presented for the (p, π⁺) reaction in the Δ-resonance region. The Dirac impulse approximation and a Dirac-Hartree calculation are used for the proton nucleus interaction and neutron bound state wave function respectively. The Δ-hole model is employed for the pion-nucleus interaction. This model is applied to the reaction ¹⁶O(p, π⁺)¹⁷O(g.s.).     

Double pion photoproduction on the nucleon: study of the isospin channels

A model for the γp → π⁺π⁻p reaction developed earlier is extended to account for all isospin channels. The model includes N, Δ(1232), N^*(1440) and N^*(1520) as intermediate baryonic states and the meson as an intermediate 2π resonance. Although many terms contribute to the cross section, some channels exhibit particular sensitivity to certain mechanisms of resonance excitation or decay and the reactions provide novel information on such mechanisms. In particular the γN → N^*(1520) → Δπ process affects all the channels and is a key ingredient in the interpretation of the data. Comparison is made with all available data and the agreement is good in some channels. The remaining discrepancies in some other channels are discussed.     

η in the nuclear medium within a chiral unitary approach

The s-wave η self-energy in the nuclear medium is calculated in a chiral unitary approach. A coupled channel Bethe–Salpeter equation is solved to obtain the effective ηN interaction in the medium. The base model reproduces well the free space πN elastic and inelastic scattering at the ηN threshold or N^*(1535) region. The Pauli blocking on the nucleons, binding potentials for the baryons and self-energies of the mesons are incorporated, including the η self-energy in a self-consistent way. Our calculation predicts about −54−i29 MeV for the optical potential at normal nuclear matter for an η at threshold but also shows a strong energy dependence of the potential.     

The role of meson retardation in the NN interaction above pion threshold

A model is developed for the hadronic interaction in the two-nucleon system above pion threshold which is based on meson, nucleon and Δ degrees of freedom and which includes full meson retardation in the exchange operators. For technical reasons, the model allows maximal one meson to be present explicitly. Thus the Hilbert space contains besides NN and NΔ also configurations consisting of two nucleons and one meson. For this reason, only two- and three-body unitarity is obeyed, and the model is suited for reactions in the two-nucleon sector, where only one pion is produced or absorbed. Starting from a realistic pure nucleonic retarded potential, which had to be renormalized because of the additional π and Δ degrees of freedom, a reasonable fit to experimental NN-scattering data could be achieved.     

Rigorous pion-pion scattering lengths from threshold πN → ππN data

A new evaluation of the universal ππ scattering length relation is used to extract the ππ s-wave scattering lengths from threshold pion production data. Previous work has shown that the chiral perturbation series relating threshold pion production to ππ scattering lengths appears to converge well only for the isospin-2 case, giving a₂ = −0.031 ± 0.007m_π⁻¹. A model-independent and data-insensitive universal curve then implies a₀ = 0.235 ± 0.03m_π⁻¹ for the isospin-0 scattering length.     

Supersymmetric contributions to direct CP violation in K→ππγ decays

We analyze the supersymmetric contributions to direct–CP–violating observables in K→ππγ decays induced by gluino–mediated magnetic–penguin operators. We find that ε′_+−γ and the differential width asymmetry of K^±→π^±π⁰γ decays could be substantially enhanced with respect to their Standard Model values, especially in the scenario where ε′/ε is dominated by supersymmetric contributions. These observables could therefore provide a useful tool to search for New Physics effects in |ΔS|=1 transitions, complementary to ε′/ε and rare decays.     

The large N limit of the O(N) Heisenberg spin system in two dimensions

The large N limit of the O(N) Heisenberg spin system in two dimensions (a lattice version of the non-linear σ-model) is analysed by the collective field technique. A compact expression for the mass gap and the β-function is obtained for arbitrary but fixed gN. The strong and weak coupling limits of this expression correctly reproduce the known results.     

Regge-pole description of γN→πN backward-scattering data

Baryon Regge-pole contributions to u-channel helicity amplitudes for the γN→πN processes are derived, with attention to kinematic singularities and threshold conditions. An N, Nγ and Δδ Regge-exchange model is proposed that describes the backward scattering data on γp→π^op and γp→π⁺n at high energy. The N and Nγ trajectories are found to be nearly degenerate, with residues in the ratio β(Nγ)/β(N)≈0.6. Structure in the differential cross sections is explained as dominance at small u giving way to dominance at large u. An isoscaar-isovector admixture for the γ-coupling to is required by the fits. The solution extrapolates through the mean γp→π^op 180^o differential cross section at intermediate energies, as required by duality.     

Three-body forces in nuclear matter from intermediate Δ-states in three-nucleon clusters

Those three-body force contributions in nuclear matter usually generated through a πN scattering amplitude dominated by the Δ(1236) resonance, are here treated as a three-nucleon cluster, in which one of the nucleons becomes, in an intermediate state, a Δ-resonance. All exchange diagrams are calculated and found to significantly reduce the energy per particle from the direct graph. This is contrary to earlier estimates of the exchanges, using more approximate approaches. The resulting attractive contribution is rather small, −1.1 MeV at κ_F = 1.4 fm⁻¹, but the roughly linear density dependence has a crucial effect on the saturation properties. The sensitivity of the results to the correlations used, and to the two-body force spin structure, is displayed. The energy per particle from clusters with three intermediate Δ-resonances is also estimated.     

Renormalization group invariant matrix elements of ΔS=2 and ΔI=3/2 four-fermion operators without quark masses

We introduce a new parameterization of four-fermion operator matrix elements which does not involve quark masses and thus allows a reduction of systematic uncertainties. In order to simplify the matching between lattice and continuum renormalization schemes, we express our results in terms of renormalization group invariant B-parameters which are renormalization-scheme and scale independent. As an application of our proposal, matrix elements of ΔI=3/2 and SUSY ΔS=2 operators have been computed. The calculations have been performed using the tree-level improved Clover lattice action at two different values of the strong coupling constant (β=6/g²=6.0 and 6.2), in the quenched approximation. Renormalization constants and mixing coefficients of lattice operators have been obtained non-perturbatively. Using lowest order χPT, we also obtain ππ|O₇|K^NDR_I=2=(0.11±0.02) GeV⁴ and ππ|O₈|K^NDR_I=2=(0.51±0.05) GeV⁴ at μ=2 GeV.     

Renormalization of N = 2, 4 Yang-Mills theories with soft breaking of an extended supersymmetry by N = 1 mass term

N = 2, 4 Yang-Mills theories with soft breaking of an extended supersymmetry by mass terms are considered. It is proved that for N = 4 there are no ultraviolet divergences in the mass renormalization constants to all orders of perturbation theory. For N = 2 our two-loop calculations show that the charge and mass renormalization constants contain only one-loop divergences and are the same in this order. It is shown by direct calculation that mass terms can acquire finite quantum corrections starting from the two-loop approximation. The renormalization scheme dependence of N = 4 renormalization group functions is investigated. We have found that unlike renormalization schemes with minimal subtractions of divergences other renormalization schemes give a nonzero β-function. At nonzero masses the β-function in MOM schemes is not zero even at the one-loop level. In the massless case β≠0 beginning from the two-loop approximation.     

A superspace action for N = 2 supergravity

The action for N = 2 supergravity can be presented as the invariant volume of the chiral subspaces of the real N = 2 superspace. The invariant volume of the real superspace itself is shown to vanish. The real basis form of the action contains covariant Grassmann δ functions involving N = 2 prepotentials explicitly.     

Interpolating between Ising, XY-, and non-linear σ-models

The β-functions of O(N)-symmetric non-linear σ-models on the lattice were recently discovered to be non-monotonic for N 3. We explain the non-monotonic behaviour as a non-perturbative lattice effect by relating it to the Kosterlitz-Thouless transition of the XY-model. We also relate the latter transition to the phase transition of the Ising model. These relationships are established by interpolating between the O(N)- and the O(N − 1)-symmetric non-linear σ-models by suppression of the Nth component of the N-vector field with a mass term. A critical line in the coupling-mass plane connects the critical point of the Ising model (N = 1) with the critical point of the XY-model (N = 2). This line extends towards the region of non-monotonic behaviour of the β-function of the O(3)-symmetric model. The nature of the transition lines is also investigated.     

The ΔNγ electromagnetic transition form factors GM(q) and GE(q)

A parameter-free, nonperturbative calculation of the ΔNγ electromagnetic transition amplitudes GM*(q2), GE*(q2), and the resonant multipole ratio REM(q2)≡E1+3/2(q2)/M1+3/2(q2) is performed in terms of the well-known nucleon isovector Sachs form factor GMV. Our methods are fully relativistic with conservation of the electromagnetic current guaranteed. We find that GM*(q2) decreases more rapidly than the nucleon dipole form factor when −q21 GeV2/c2 and that REM(q2) remains small even for very high four-momentum transfer implying that the perturbative QCD prediction REM(q2)→1 is purely asymptotic and is valid only for extremely high |q2|.