arXiv subjects
Publications and source records attributed to Ulf-G. Meißner.
I review the status of chiral perturbation theory in the one-nucleon sector and give some predictions to be tested. I then discuss various methods to go to higher energies (inclusion of the Delta(1232), dispersion relations) and also to higher precision (virtual photons and isospin violation).
I critically review the status of computations of threshold pion production in proton-proton collisions in the framework of effective field theory approaches or variants thereof. I also present the results of a novel diagrammatic scheme.
The complete renormalization of the generating functional for Green functions of quark currents between one-nucleon states in two flavor heavy baryon chiral perturbation theory is performed to order $q^4$. We show how the heat kernel method has to be extended for operators orthogonal to the heavy fermion four-velocity. A method is developed to treat the multi-coincidence limit arising from insertions of dimension two (and higher) operators on internal baryon propagators in self-energy graphs. As examples, we study the divergences in the isoscalar magnetic moment and the scalar form factor of the nucleon.
We study the parity-violating pion-nucleon coupling $G_π$ in the framework of a realistic three flavor Skryme model. We find a sizeable enhancement of $G_π\simeq 0.8 ... 1.3 \cdot 10^{-7}$ compared to previous calculations in two-flavor models with vector mesons. This strangeness enhancement stems from induced kaon fields of the chiral soliton and the non-monotoneous dependence on symmetry breaking of the nucleon matrix element of the flavor singlet piece of the operator associated with these induced fields. Both features are sensitive to four quark operators including an $\bar s s$ pair.
We reconsider the question of wave function renormalization in heavy fermion effective field theories. In particular, we work out a simple and efficient scheme to define the wave function renormalization with respect to the lowest order heavy fermion propagator. The method presented is free of a set of ambiguities which arise in heavy fermion effective field theories. In this context, we discuss the approaches used in the literature so far. We also calculate the fourth order pion mass contribution to the nucleon mass shift and discuss the tree and loop contributions to the electric Sachs form factor of the nucleon.
We construct the complete effective chiral pion-nucleon Lagrangian to third order in small momenta based on relativistic chiral perturbation theory. We then perform the so-called heavy baryon limit and construct all terms up-to-and-including order $1/m^2$ with fixed and free coefficients. As an application, we discuss in detail pion-nucleon scattering. In particular, we show that the $1/m$ expansion of the Born graphs calculated relativistically can be recovered exactly in the heavy baryon approach without any additional momentum-dependent wave function renormalization. We fit various empirical phase shifts for pion laboratory momenta between 50 and 100 MeV. This leads to a satisfactory description of the phase shifts up to momenta of about 200 MeV. We also predict the threshold parameters, which turn out to be in good agreement with the dispersive analysis. In particular, we can sharpen the prediction for the isovector S-wave scattering length, $0.083 M_π^{-1} \leq a_{0+}^- \leq 0.093 M_π^{-1}$. We also consider the subthreshold parameters and give a short comparison to other calculations of $πN$ scattering in chiral perturbation theory or modifications thereof.
Starting from a precise two-nucleon potential, we use the method of unitary transformations to construct an effective potential that involves only momenta less than a given maximal value. We describe this method for an S-wave potential of the Malfliet-Tjon type. It is demonstrated that the bound and scattering state spectrum calculated within the effective theory agrees exactly with the one based on the original potential. This might open an avenue for the construction of effective chiral few-nucleon forces and for a systematic treatment of relativistic effects in few-body systems.
I discuss low-energy pion-nucleon scattering in the framework of chiral perturbation theory. I argue that using this theoretical method one is able to handle the in some cases tremendous experimental accuracy (for the low partial waves). I then show how strong and electromagnetic isospin violation can be treated simultaneously. Some first results for neutral pion scattering and the $σ$-term are given.
Using heavy baryon chiral perturbation theory to one loop, we derive an analytic and parameter-free expression for the momentum dependence of the strange magnetic form factor of the nucleon $G_M^{(s)} (Q^2)$ and its corresponding radius. This should be considered as a lower bound. We also derive a model-independent relation between the isoscalar magnetic and the strange magnetic form factors of the nucleon based on chiral symmetry and SU(3) only. This gives an upper bound on the strange magnetic form factor. We use these limites to derive bounds on the strange magnetic moment of the proton from the recent measurement of $G_M^{(s)} (Q^2=0.1 GeV^2)$ by the SAMPLE collaboration. We stress the relevance of this result for the on-going and future experimental programs at various electron machines.
We examine the role of the elementary isoscalar pion--nucleon scattering amplitude in the description of the processes $pp \to ppπ^0$ and $pp\to dπ^+$ at threshold. We argue that the presently used tree level dimension two approximation used in chiral perturbation theory is insufficient as input by direct comparison with the $π$N scattering data. We also show that a successful semi--phenomenological boson--exchange model does better in the description of these data. The influence of the violation of crossing symmetry in the meson--exchange model has to be studied in more detail. We stress that further investigations of the process $pp\to dπ^+$ can pave the way to a deeper understanding of the pion dominated part of the transition operator.
We study the low energy expansion of the nucleon's electroweak form factors in the framework of an effective chiral Lagrangian including pions, nucleons and the $Delta (1232)$. We work to third order in the so-called small scale expansion and compare the results with the ones previously obtained in the chiral expansion. In addition, these calculations serve as a first exploratory study of renormalization and decoupling within the small scale expansion.
We construct the two- and three-nucleon potential based on the most general chiral effective pion-nucleon Lagrangian using the method of unitary transformations. For that, we develop a power counting scheme consistent with this projection formalism. In contrast to previous results obtained in old-fashioned time-ordered perturbation theory, the method employed leads to energy-independent potentials. We discuss in detail the similarities and differences to the existing chiral nucleon-nucleon potentials. We also show that to leading order in the power counting, the three-nucleon forces vanish lending credit to the result obtained by Weinberg using old-fashioned time-ordered perturbation theory.
These lectures give an introduction to baryon chiral perturbation theory. I show in detail how to construct the chiral effective pion-nucleon Lagrangian in the one loop approximation. Particular emphasis is put on the physics related to electromagnetic probes, as manifest in pion photo- and electroproduction, Compton scattering off nucleons and the electroweak form factors of the nucleon. Other topics discussed in some detail are the meaning of low-energy theorems, pion-nucleon scattering, the reaction $πN \to ππN$ and isospin violation in the pion-nucleon system. The chiral predictions are confronted with the existing data. Some remaining problems and new developments are outlined.
This is the summary of the working group on $ππ$ and $π$N interactions of the Chiral Dynamics Workshop in Mainz, September 1-5, 1997. Each talk is represented by an extended one page abstract. Some additional remarks by the convenors are added
I review recent progress made in the description of pion-nucleon scattering, the $σ$--term, the scalar form factor and the strangeness content of the nucleon in the framework of heavy baryon chiral perturbation theory. Other topics are single pion production by real and virtual photons as well as in proton-proton collisions.
We construct the complete effective chiral pion-nucleon Lagrangian in the presence of virtual photons to one loop. As an application, we consider strong and electromagnetic isospin violation for scattering of neutral pions off nucleons. We show that for the scattering lengths these isospin violating terms are of the same size as the purely hadronic ones. We also analyze isospin-violating effects for the $σ$--term. These can be as large as 10% for the absolute value but are negligible for the shift to the Cheng-Dashen point.
I review the present status of three flavor baryon chiral perturbation theory in the heavy fermion formalism. It is argued that precise calculations have to include all terms quadratic in the quark masses. As examples, I consider the chiral expansion of the octet baryon masses, the baryon magnetic moments and kaon photoproduction off nucleons.
We consider constraints on the isoscalar S-wave pi-N scattering length a+ from pi-deuteron scattering, to third order in small momenta and pion masses in chiral perturbation theory. To this order, the pi-deuteron scattering length is determined by a+ together with three-body corrections that involve no undetermined parameters. We extract a novel value for a combination of dimension two low-energy constants which is in agreement with previous determinations.