Ulf-G. Meißner

Modern theory of nuclear forces

Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.

Chiral dynamics of the two Lambda(1405) states

Using a chiral unitary approach for the meson--baryon interactions, we show that two octets of J^{\pi}=1/2^- baryon states, which are degenerate in the limit of exact SU(3) symmetry, and a singlet are generated dynamically. The SU(3) breaking produces the splitting of the two octets, resulting in the case of strangeness S=-1 in two poles of the scattering matrix close to the nominal \Lambda(1405) resonance. These poles are combinations of the singlet state and the octets. We show how actual experiments see just one effective resonance shape, but with properties which change from one reaction to another.

The Two-nucleon system at next-to-next-to-next-to-leading order

Abstract We consider the two-nucleon system at next-to-next-to-next-to-leading order (N 3 LO) in chiral effective field theory. The two-nucleon potential at N 3 LO consists of one-, two- and three-pion exchanges and a set of contact interactions with zero, two and four derivatives. In addition, one has to take into account various isospin-breaking and relativistic corrections. We employ spectral function regularization for the multi-pion exchanges. Within this framework, it is shown that the three-pion exchange contribution is negligibly small. The low-energy constants (LECs) related to pion–nucleon vertices are taken consistently from studies of pion–nucleon scattering in chiral perturbation theory. The total of 26 four-nucleon LECs has been determined by a combined fit to some np and pp phase shifts from the Nijmegen analysis together with the nn scattering length. The description of nucleon–nucleon scattering and the deuteron observables at N 3 LO is improved compared to the one at NLO and NNLO. The theoretical uncertainties in observables are estimated based on the variation of the cut-offs in the spectral function representation of the potential and in the regulator utilized in the Lippmann–Schwinger equation.

Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

Abstract 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 for this process andto third order, 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 Mπ−1 ⩽ a0+− ⩽ 0.093 Mπ−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.

Nuclear forces from chiral Lagrangians using the method of unitary transformation I : Formalism

Abstract 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.

Chiral Expansion of Baryon Masses andσ-Terms

We analyze the octet baryon masses and the pion/kaon--nucleon

Axial structure of the nucleon

\sigma

Aspects of chiral pion - nucleon physics

--terms in the framework of heavy baryon chiral perturbation theory. We include {\it all} terms up-to-and-including quadratic order in the light quark masses,

Ab initio calculation of the Hoyle state

m_q

The Chiral effective pion nucleon Lagrangian of order p**4

. We develop a consistent scheme to estimate low--energy constants related to scalar--isoscalar operators in the framework of resonance exchange involving one--loop graphs. The pertinent low--energy constants can only be estimated up to some finite coefficients. Including contributions from loop graphs with intermediate spin--3/2 decuplet and spin--1/2 octet states and from tree graphs including scalar mesons, we use the octet baryon masses and the pion--nucleon