Dispersion relation for hadronic light-by-light scattering: theoretical foundations

In this paper we make a further step towards a dispersive description of the hadronic light-by-light (HLbL) tensor, which should ultimately lead to a data-driven evaluation of its contribution to (g − 2) μ . We first provide a Lorentz decomposition of the HLbL tensor performed according to the general recipe by Bardeen, Tung, and Tarrach, generalizing and extending our previous approach, which was constructed in terms of a basis of helicity amplitudes. Such a tensor decomposition has several advantages: the role of gauge invariance and crossing symmetry becomes fully transparent; the scalar coefficient functions are free of kinematic singularities and zeros, and thus fulfill a Mandelstam double-dispersive representation; and the explicit relation for the HLbL contribution to (g − 2) μ in terms of the coefficient functions simplifies substantially. We demonstrate explicitly that the dispersive approach defines both the pion-pole and the pion-loop contribution unambiguously and in a model-independent way. The pion loop, dispersively defined as pion-box topology, is proven to coincide exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors.

Molecular-Based Magnetism in Bimetallic Two-Dimensional Oxalate-Bridged Networks. An X-ray and Neutron Diffraction Study

Bimetallic, oxalate-bridged compounds with bi- and trivalent transition metals comprise a class of layered materials which express a large variety in their molecular-based magnetic behavior. Because of this, the availability of the corresponding single-crystal structural data is essential to the successful interpretation of the experimental magnetic results. We report in this paper the crystal structure and magnetic properties of the ferromagnetic compound {[N(n-C3H7)4][MnIICrIII(C2O4)3]}n (1), the crystal structure of the antiferromagnetic compound {[N(n-C4H9)4][MnIIFeIII(C2O4)3]}n (2), and the results of a neutron diffraction study of a polycrystalline sample of the ferromagnetic compound {[P(C6D5)4][MnIICrIII(C2O4)3]}n (3). Crystal data:  1, rhombohedral, R3c, a = 9.363(3) Å, c = 49.207(27) Å, Z = 6; 2, hexagonal, P63, a = 9.482(2) Å, c = 17.827(8) Å, Z = 2. The structures consist of anionic, two-dimensional, honeycomb networks formed by the oxalate-bridged metal ions, interleaved by the templating cations. Single-crystal field dependent magnetization measurements as well as elastic neutron scattering experiments on the manganese(II)−chromium(III) samples show the existence of long-range ferromagnetic ordering behavior below Tc = 6 K. The magnetic structure corresponds to an alignment of the spins perpendicular to the network layers. In contrast, the manganese(II)−iron(III) compound expresses a two-dimensional antiferromagnetic ordering.

Hadronic light-by-light scattering and the muon g−2

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g − 2)μ come from hadronic contributions. In particular, it can be expected that in a few years the subleading hadronic light-by-light (HLbL) contribution will dominate the theory uncertainty. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. Such a model-independent Approach opens up an avenue towards a data-driven determination of the HLbL contribution to the (g − 2)μ.

Scintillation efficiency of liquid argon in low energy neutron-argon scattering

Experiments searching for weak interacting massive particles with noble gases such as liquid argon require very low detection thresholds for nuclear recoils. A determination of the scintillation efficiency is crucial to quantify the response of the detector at low energy. We report the results obtained with a small liquid argon cell using a monoenergetic neutron beam produced by a deuterium-deuterium fusion source. The light yield relative to electrons was measured for six argon recoil energies between 11 and 120 keV at zero electric drift field.