Abstract: A method to find relations between the operators in the mesonic Lagrangian of Chiral Perturbation Theory at order p(6) is presented. The procedure can be used to establish if the basis of operators in the Lagrangian is minimal. As an example, we apply the method to the two-flavor case in the absence of scalar and pseudo-scalar sources (s = p = 0), and conclude that the minimal Lagrangian contains 27 independent operators.

Abstract: Purpose: There are perineal templates for interstitial implants such as MUPIT and Syed applicators. Their limitations are the intracavitary component deficit and the necessity to use computed tomography (CT) for treatment planning since both applicators are non-magnetic resonance imaging (MRI) compatibles. To overcome these problems, a new template named Template Benidorm (TB) has been recently developed. Titanium needles are usually reconstructed based on their own artifacts, mainly in T1-weighted sequence, using the void on the tip as the needle tip position. Nevertheless, patient tissues surrounding the needles present heterogeneities that complicate the accurate identification of these artifact patterns. The purpose of this work is to improve the titanium needle reconstruction uncertainty for the TB case using a simple method based on the free needle lengths and typical MRI pellets markers. Material and methods: The proposed procedure consists on the inclusion of three small A-vitamin pellets (hyper-intense on MRI images) compressed by both applicator plates defining the central plane of the plate's arrangement. The needles used are typically 20 cm in length. For each needle, two points are selected defining the straight line. From such line and the plane equations, the intersection can be obtained, and using the free length (knowing the offset distance), the coordinates of the needle tip can be obtained. The method is applied in both T1W and T2W acquisition sequences. To evaluate the inter-observer variation of the method, three implants of T1W and another three of T2W have been reconstructed by two different medical physicists with experience on these reconstructions. Results and conclusions: The differences observed in the positioning were significantly smaller than 1 mm in all cases. The presented algorithm also allows the use of only T2W sequence either for contouring or reconstruction purposes. The proposed method is robust and independent of the visibility of the artifact at the tip of the needle.

Abstract: We demonstrate how to realize within supergravity a novel chaotic-type inflationary scenario driven by the radial parts of a conjugate pair of Higgs superfields causing the spontaneous breaking of a grand unified gauge symmetry at a scale assuming the value of the supersymmetric grand unification scale. The superpotential is uniquely determined at the renormalizable level by the gauge symmetry and a continuous R symmetry. We select two types of Kahler potentials, which respect these symmetries as well as an approximate shift symmetry. In particular, they include in a logarithm a dominant shift-symmetric term proportional to a parameter c together with a small term violating this symmetry and characterized by a parameter c(+). In both cases, imposing a lower bound on c, inflation can be attained with subplanckian values of the original inflaton, while the corresponding effective theory respects perturbative unitarity for r +/- = c(+)/c_ <= 1. These inflationary models do not lead to overproduction of cosmic defects, are largely independent of the one-loop radiative corrections and accommodate, for natural values of r +/-, observable gravitational waves consistently with all the current observational data. The inflaton mass is mostly confined in the range (3.7 – 8.1) x 10(10) GeV.