Recent lattice QCD simulations of the scattering lengths of Nambu-Goldstone bosons off the D mesons are studied using unitary chiral perturbation theory. We show that the Lattice QCD data are better described in the covariant formulation than in the heavy-meson formulation. The D * s0 (2317) can be dynamically generated from the coupled-channels DK interaction without a priori assumption of its existence. A new renormalization scheme is proposed which manifestly satisfies chiral power counting rules and has welldefined behavior in the infinite heavy-quark mass limit. Using this scheme we predict the heavy-quark spin and flavor symmetry counterparts of the D * s0 (2317).

Motivation: In biomedicine, every molecular measurement is relative to a reference point, like a fixed aliquot of RNA extracted from a tissue, a defined number of blood cells, or a defined volume of biofluid. Reference points are often chosen for practical reasons. For example, we might want to assess the metabolome of a diseased organ but can only measure metabolites in blood or urine. In this case the observable data only indirectly reflects the disease state. The statistical implications of these discrepancies in reference points have not yet been discussed. Results: Here we show that reference point discrepancies compromise the performance of regression models like the LASSO. As an alternative, we suggest zero-sum regression for a reference point insensitive analysis. We show that zero-sum regression is superior to the LASSO in case of a poor choice of reference point both in simulations and in an application that integrates intestinal microbiome analysis with metabolomics. Moreover, we describe a novel coordinate descent based algorithm to fit zero-sum elastic nets. Availability: The R-package "zeroSum" can be downloaded at https://github.com/rehbergT/zeroSum. Moreover, we provide all R-scripts and data used to produce the results of this manuscript as supplementary material.

The Bethe-Salpeter equation in unitarized chiral perturbation theory is usually solved with the so-called onshell approximation. The underlying argument is that the off-shell effects can be absorbed by the corresponding coupling constants and physical masses, which has been corroborated by the success of unitarized chiral perturbation theory in describing a variety of physical phenomena. Such an approximation needs to be scrutinized when applied to study the light-quark mass evolution of physical observables, as routinely performed nowadays. In the present work, we propose to solve the Bethe-Salpeter equation with the full off-shell terms of the chiral potentials and apply this formalism to the description of the latest n f ¼ 2 þ 1 lattice QCD (LQCD) data on the scattering lengths of Nambu-Goldstone bosons off D mesons. It is shown that the LQCD data can be better described in this formalism than in the widely used on-shell approximation. On the other hand, no qualitative difference between the on-shell and off-shell approaches is observed for the light-quark mass evolution of the scattering lengths, given the limited LQCD data and their relatively large uncertainties. We also show that the light-quark mass dependence of the D Ã s0 ð2317Þ remains essentially the same in both approaches.

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