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A bstract A three-particle quantization condition on the lattice is written down in a manifestly relativistic-invariant form by using a generalization of the non-relativistic effective field theory (NREFT) approach. Inclusion of the higher partial waves is explicitly addressed. A partial diagonalization of the quantization condition into the various irreducible representations of the (little groups of the) octahedral group has been carried out both in the center-of-mass frame and in moving frames. Furthermore, producing synthetic data in a toy model, the relativistic invariance is explicitly demonstrated for the three-body bound state spectrum.

A bstract A manifestly relativistic-invariant Lellouch-Lüscher formalism for the decays into three identical particles with no two-to-three transitions is proposed. Similarly to [1], the formalism is based on the use of the non-relativistic effective Lagrangians. Manifest Lorentz invariance is guaranteed, as in [2], by choosing the quantization axis along the total four-momentum of the three-particle system. A systematic inclusion of the higher-order derivative couplings, as well as higher partial waves is addressed.

A bstract We derive the modified Lüscher equation in the presence of the long-range force caused by the exchange of a light particle. It is shown that the use of this equation enables one to circumvent the problems related to the strong partial-wave mixing and the t -channel sub-threshold singularities. It is also demonstrated that the present method is intrinsically linked to the so-called modified effective-range expansion (MERE) in the infinite volume. A detailed comparison with the two recently proposed alternative approaches is provided.

A bstract We propose a systematic method to block-diagonalize the finite volume effective Hamiltonian for two-particle systems with arbitrary spin in both the rest and moving frame. The framework is convenient and efficient for addressing the left-hand cut issue arising from long-range potential, which are challenging in the framework of standard Lüscher formula. Furthermore, the method provides a foundation for further extension to three-particle systems. We first benchmark our method by examining several toy models, demonstrating its consistency with standard Lüscher formula in the absence of long-range potential. In the presence of long-range potential, we investigate and resolve the effects and issues of left-hand cut. As a realistic application, we calculate the finite volume spectra of isoscalar D D ¯ ∗ system, where the well-known exotic state χ c 1 (3872) is observed. The results are qualitatively consistent with the lattice QCD calculation, highlighting the reliability and potential application of our framework to the study of other exotic states in hadron physics.

A bstract Since 1959, singularities in single-loop diagrams have been a subject of extensive study, as they are believed to play a crucial role in shaping our understanding of experimental observables. In this work, we investigate the singularities arising from box diagrams in decay processes, which can be categorized into two distinct types. We present a comprehensive analysis of these box singularities, deriving explicit conditional expressions that determine their occurrence and discussing the corresponding physical scenarios.

The systematic molecular associations between the peripheral blood cells and brain in Alzheimer's disease (AD) remains unclear, which hinders our understanding of AD pathological mechanisms and the exploration of new diagnostic biomarkers. Here, we performed an integrated analysis of the brain and peripheral blood cells transcriptomics to establish peripheral biomarkers of AD. By employing multiple statistical analyses plus machine learning, we identified and validated multiple regulated central and peripheral network in patients with AD. By bioinformatics analysis, a total of 243 genes were differentially expressed in the central and peripheral systems, mainly enriched in three modules: immune response, glucose metabolism and lysosome. In addition, lysosome related gene ATP6V1E1 and immune response related genes (IL2RG, OSM, EVI2B TNFRSF1A, CXCR4, STAT5A) were significantly correlated with Aβ or Tau pathology. Finally, receiver operating characteristic (ROC) analysis revealed that ATP6V1E1 showed high-diagnostic potential for AD. Taken together, our data identified the main pathological pathways in AD progression, particularly the systemic dysregulation of the immune response, and provided peripheral biomarkers for AD diagnosis.

A bstract We derive an explicit expression for the Lellouch-Lüscher (LL) factor in the K → 3 π decays at leading order (without derivative couplings). Several important technical details are addressed, like a proper decomposition into the isospin amplitudes, the choice of a minimal set of effective couplings and the renormalization, as well as the algorithm for the solution of the pertinent Faddeev equations in the infinite volume which is based on the contour deformation method. Most importantly, our numerical results demonstrate that the three-body force contributes very little to the LL factor. This result paves the way for the study of the K → 3 π decays on the lattice.

A bstract The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the energy-dependent behaviour of these phase shifts. The existing implementations of the quantization condition at finite boosts rely on momentum transformations between rest and moving frames, defined directly in terms of the energy eigenvalues. This energy dependence is unsuitable in the formulation of a Hamiltonian. In this work, we introduce a novel approach to generalise the three-momentum boost prescription, enabling the incorporation of energy-independent finite-volume Hamiltonians within moving frames. We demonstrate the application of our method through numerical comparisons, employing a phenomenological ππ scattering example.

Acute respiratory distress syndrome (ARDS) is a common life-threatening condition in critically ill patients. Itis also an important public health issue because it can cause substantial mortality and health care burden worldwide. The objective of this study was to investigate therisk factors that impact ARDS mortality in a medical center in Taiwan. This was a single center, observational study thatretrospectively analyzed data from adults in 6 intensive care units (ICUs) at Taichung Veterans General Hospital in Taiwan from 1st October, 2018to30th September, 2019. Patients needing invasive mechanical ventilation and meeting the Berlin definition criteria were included for analysis. A total of 1,778 subjects were screened in 6 adult ICUs and 370 patients fulfilled the criteria of ARDS in the first 24 hours of the ICU admission. Among these patients, the prevalenceof ARDS was 20.8% and the overall hospital mortality rate was 42.2%. The mortality rates of mild, moderate and severe ARDS were 35.9%, 43.9% and 46.5%, respectively. In a multivariate logistic regression model, combination of driving pressure (DP) > 14cmH2O and oxygenation (P/F ratio)≤150 was an independent predictor of mortality (OR2.497, 95% CI 1.201-5.191, p = 0.014). Patients with worse oxygenation and a higher driving pressure had the highest hospital mortality rate(p<0.0001). ARDS is common in ICUs and the mortality rate remains high. Combining oxygenation and respiratory mechanics may better predict the outcomes of these ARDS patients.

A bstract In hadron spectrum physics, the partial wave analysis is a primary method used to extract properties of hadronic resonances. The covariant orbital-spin coupling scheme holds unique advantages over other partial wave methods due to its Lorentz covariant form and determined orbital-spin quantum numbers. This paper presents a general form of the covariant orbital-spin coupling scheme based on the irreducible tensor of the homogeneous proper Lorentz group and its little groups. A systematic procedure for constructing partial wave amplitude in a Lorentz covariant way is provided, which can be applied to both massive and massless particles. Specific examples are also included.