Abstract: The correlation functions of Yang-Mills theories formulated in the background field method satisfy linear Slavnov-Taylor identities, which are naive generalizations of simple tree level relations, with no deformations originating from the ghost-sector of the theory. In recent years, a stronger version of these identities has been found to hold at the level of the background gluon self-energy, whose transversality is enforced separately for each special block of diagrams contributing to the gluon Schwinger-Dyson equation. In the present work we demonstrate by means of explicit calculations that the same distinct realization of the Slavnov-Taylor identity persists in the case of the background three-gluon vertex. The analysis is carried out at the level of the exact Schwinger-Dyson equation for this vertex, with no truncations or simplifying assumptions. The demonstration entails the contraction of individual vertex diagrams by the relevant momentum, which activates Slavnov-Taylor identities of vertices and multi-particle kernels nested inside these graphs; the final result emerges by virtue of a multitude of extensive cancellations, without the need of performing explicit integrations. In addition, we point out that background Ward identities amount to replacing derivatives of propagators by zero-momentum background-gluon insertions, in exact analogy to standard properties of Abelian gauge theories. Finally, certain potential applications of these results are briefly discussed.

Abstract: Compton cameras can offer advantages over gamma cameras for some applications, since they are well suited for multitracer imaging and for imaging high-energy radiotracers, such as those employed in radionuclide therapy. While in conventional clinical settings state-of-the-art Compton cameras cannot compete with well-established methods such as PET and SPECT, there are specific scenarios in which they can constitute an advantageous alternative. The combination of PET and Compton imaging can benefit from the improved resolution and sensitivity of current PET technology and, at the same time, overcome PET limitations in the use of multiple radiotracers. Such a system can provide simultaneous assessment of different radiotracers under identical conditions and reduce errors associated with physical factors that can change between acquisitions. Advances are being made both in instrumentation developments combining PET and Compton cameras for multimodal or three-gamma imaging systems, and in image reconstruction, addressing the challenges imposed by the combination of the two modalities or the new techniques. This review article summarizes the advances made in Compton cameras for medical imaging and their combination with PET.

Abstract: Background: The Xe isotopic chain with four valence protons above the Z = 50 shell closure is an ideal laboratory for the study of the evolution of nuclear deformation. At the N = 82 shell closure, 136Xe presents all characteristics of a doubly closed shell nucleus with a spherical shape. In the very neutron-deficient isotopes close to N = 50, the alpha-decay chain of Xe was investigated to probe the radioactive decay properties near the drip-line and the magicity of 100Sn. Additionally, the Xe isotopes present higher order symmetries in the nuclear deformation such as the octupole degree of freedom near N = 60 and N = 90 or O(6) symmetry in stable isotopes.Purpose: The relevance of the O(6) symmetry has been investigated by measuring the spectroscopic quadrupole moment of the first excited states in 124Xe. In the O(6) symmetry limit, the spectroscopic quadrupole moment of collective states is expected to be null.Method: A stable 124Xe beam with energies of 4.03A MeV and 4.11A MeV was used to bombard a natW target at the GANIL facility. Excited states were populated via the safe Coulomb excitation reaction. The collision of the heavy ions with a large Z at low energy make this reaction sensitive to the diagonal E2 matrix element of the excited states. The recoils were detected in the VAMOS++ magnetic spectrometer and the gamma rays in the AGATA tracking array. The least squares fitting code GOSIA was used for the analysis to extract both E2 and M1 transitional and E2 diagonal matrix elements.Results: The rotational ground state band was populated up to the 8+1 state as well as the 2+2 and 4+2 states. Using high precision spectroscopic data to constrain the GOSIA fit, the spectroscopic quadrupole moments of the 2+1 , 4+1 , and 6+1 states were determined for the first time. Conclusions: The spectroscopic quadrupole moments were found to be negative, large, and constant in the ground state band underlining the prolate axially deformed ground state band of 124Xe. The present experimental data confirm that the is broken in 124Xe.