arXiv subjects
Publications and source records attributed to U. -G. Meißner.
We work out the spatial density distributions corresponding to the axial-vector charge density operator for spin-1/2 systems using states described by sharply localized wave packets in arbitrary Lorentz-frames. The static approximation, leading to the frequently assumed Breit-frame distributions, is also considered. We discuss the interpretation of the resulting spatial densities in terms of the axial charge density.
Near-threshold $p\barΛ$ mass spectra for the reactions $e^+e^- \to K^- p\barΛ$ and $J/ψ\to K^- p\barΛ$ are investigated with an emphasis on the role played by the interaction in the $p\barΛ$ system. As guideline for the $p\barΛ$ interaction a variety of $Λ\barΛ$ potential models is considered that have been established in the analysis of data on $p\bar p\to Λ\barΛ$ in the past. Arguments why the properties of the $p\barΛ$ and $Λ\barΛ$ interactions can be expected to be very similar are provided. It is shown that the near-threshold enhancement in the invariant mass observed for the $e^+e^-$ reaction can be reproduced quantitatively by the assumed $p\barΛ$ final-state interaction in the partial wave suggested by an amplitude analysis of the experiment. The effect of the $p\barΛ$ final-state interaction in other decays is explored, including the recently measured reactions $B^- \to J/ψ\, \bar p Λ$ and $B^+ \to J/ψ\, p \barΛ$. It is found that the final-state interaction improves the description of the measured invariant mass near threshold in most cases.
The gravitational form factors of the transition from the proton to the $Δ^+$ resonance are calculated to leading one-loop order using a manifestly Lorentz-invariant formulation of chiral perturbation theory. We take into account the leading electromagnetic and strong isospin-violating effects. The loop contributions to the transition form factors are found to be free of power-counting violating pieces, which is consistent with the absence of tree-level diagrams at the considered order. In this sense, our results can be regarded as predictions of chiral perturbation theory.
We work out details of defining the spatial densities corresponding to the gravitational form factors of spin-0 and spin-1/2 systems using spherically symmetric sharply localized wave packets. The expressions for the spatial densities are provided in the frames with both zero and non-zero expectation values of the momentum operator.
The matrix elements of the electromagnetic current and the energy-momentum tensor for sharply localized states of spin-1 systems are considered. Their interpretation as local spatial densities of various characteristics of the considered system is discussed.
The definition of local spatial densities by using sharply localized one-particle states is applied to spin-3/2 systems. Matrix elements of the electromagnetic current and the energy-momentum tensor are considered and integral expressions of associated spatial distributions in terms of form factors are derived.
The leading one-loop corrections to the gravitational form factors of the delta resonance are calculated in the framework of chiral effective field theory. Various contributions to the energy-momentum tensor and the renormalization of the low-energy constants are worked out. Using the small scale expansion, expressions for static quantities are obtained and the real and imaginary parts of the gravitational form factors are calculated numerically.
The Jülich-Bonn group aims at an extensive study of the baryon-baryon ($BB$) interaction involving strange baryons ($Λ$, $Σ$, $Ξ$) within SU(3) chiral effective field theory. An overview of achievements and new developments over the past few years is provided. The topics covered are: 1) Derivation of the leading charge-symmetry breaking (CSB) interaction for the $ΛN$ system and its application in a study of CSB effects in $A$=$4$ $Λ$-hypernuclei. 2) Updated results for the $ΞN$ interaction at NLO and predictions for $Ξ^- p$ correlation functions. 3) Extension of the $ΛN$-$ΣN$ interaction to next-to-next-to-leading order.
An unambiguous definition of the electromagnetic spatial densities for a spin-1/2 system is proposed and worked out in the zero average momentum frame and in moving frames. The obtained results are compared with the traditional definition of the densities in terms of the three-dimensional Fourier transforms of the electromagnetic form factors in the Breit frame.
The spin-dependent components of the fundamental hyperon-nucleon interactions are largely unknown. We show that under reasonable assumptions, a measurement of the $Σ^+ p$ correlation function in high-energy proton-proton or heavy-ion collisions combined with cross section data allows to separate the singlet and the triplet $S$-wave contributions.
Studies of the baryon-baryon interaction involving hyperons within chiral effective field theory, so far performed up to next-to-leading order (NLO) in the chiral expansion, have shown that for the strangeness $S=-1$ ($ΛN$, $ΣN$) and $S=-2$ ($ΛΛ$, $ΞN$) sectors a consistent and satisfactory description of the available scattering data and experimental constraints can be achieved based on the assumption of broken SU(3) flavor symmetry. We explore the possible extension of this approach at the NLO level to strangeness $S=-3$ and $S=-4$ baryon-baryon systems where empirical information is rather scarce. Specifically we address the question how measurements of two-body correlation functions in heavy-ion collisions and/or in high-energetic proton-proton collisions can help to constrain the interaction in channels like $ΞΛ$ or $ΞΞ$.
We show that the matrix element of a local operator between hadronic states gives rise to an unambiguous definition of the associated spatial density. As an explicit example, we consider the charge density of a spinless particle in the rest and moving frames and clarify its relationship to the electric form factor. Our results suggest that the interpretation of the spatial densities of local operators and their moments such as the mean square charge radius needs to be revised.
We argue that high-quality data on the reaction $e^+e^-\to π^+π^-η$ will allow one to determine the doubly-virtual form factor $η\to γ^*γ^*$ in a model-independent way with controlled accuracy. This is an important step towards a reliable evaluation of the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. When analyzing the existing data for $e^+e^-\toπ^+π^-η$ for total energies squared $k^2>1\text{GeV}^2$, we demonstrate that the effect of the $a_2$ meson provides a natural breaking mechanism for the commonly employed factorization ansatz in the doubly-virtual form factor $F_{ηγ^*γ^*}(q^2,k^2)$. However, better data are needed to draw firm conclusions.
The low-energy chiral effective field theory of vector mesons and Goldstone bosons in external gravitational field is considered. The energy-momentum tensor is obtained and the gravitational form factors of the $ρ$-meson are calculated up to next-to-leading order in the chiral expansion. This amounts to considering tree-level and one-loop order diagrams. The chiral expansion of the form factors at zero momentum transfer as well as of the slope parameters is worked out. Also, the long-range behaviour of the energy and internal force distributions is obtained and analysed.
The proposed method exploits charged particles confined as a storage ring beam (proton, deuteron, possibly $^3$He) to search for an intrinsic electric dipole moment (EDM) aligned along the particle spin axis. Statistical sensitivities could approach 10$^{-29}$ e$\cdot$cm. The challenge will be to reduce systematic errors to similar levels. The ring will be adjusted to preserve the spin polarisation, initially parallel to the particle velocity, for times in excess of 15 minutes. Large radial electric fields, acting through the EDM, will rotate the polarisation from the longitudinal to the vertical direction. The slow rise in the vertical polarisation component, detected through scattering from a target, signals the EDM. The project strategy is outlined. A stepwise plan is foreseen, starting with ongoing COSY activities that demonstrate technical feasibility. Achievements to date include reduced polarization measurement errors, long horizontal plane polarization lifetimes, and control of the polarization direction through feedback from scattering measurements. The project continues with a proof-of-capability measurement (precursor experiment; first direct deuteron EDM measurement), an intermediate prototype ring (proof-of-principle; demonstrator for key technologies), and finally a high-precision electric-field storage ring.
The complexity of threshold phenomena is exemplified on a prominent and long-known case - the structure in the $Λp$ cross section (invariant mass spectrum) at the opening of the $ΣN$ channel. The mass splitting between the $Σ$ baryons together with the angular momentum coupling in the $^3S_1$-$^3D_1$ partial wave imply that, in principle, up to six channels are involved. Utilizing hyperon-nucleon potentials that provide an excellent description of the available low-energy $Λp$ and $ΣN$ scattering data, the shape of the resulting $Λp$ cross section is discussed and the poles near the $ΣN$ threshold are determined. Evidence for a strangeness $S=-1$ dibaryon is provided, in the form of a deuteron-like (unstable) $ΣN$ bound state. Predictions for level shifts and widths of $Σ^-p$ atomic states are given.
We discuss the formulation of a non-relativistic effective field theory for two-body P-wave scattering in the presence of shallow states and critically address various approaches to renormalization proposed in the literature. It is demonstrated that the consistent renormalization involving only a finite number of parameters in the well-established formalism with auxiliary dimer fields corresponds to the inclusion of an infinite number of counterterms in the formulation with contact interactions only. We also discuss the implications from the Wilsonian renormalization group analysis of P-wave scattering.
We calculate the spin-averaged amplitude for doubly virtual forward Compton scattering off nucleons in the framework of manifestly Lorentz invariant baryon chiral perturbation theory at complete one-loop order $O(p^4)$. The calculations are carried out both in the infinite and in a finite volume. The obtained results allow for a detailed estimation the finite-volume corrections to the amplitude which can be extracted on the lattice using the background field technique.