Speaker
Description
The application of the chiral Lagrangian to results from Lattice QCD simulations played an important role in the early days of the field when it was impossible to generate ensembles at the physical pion mass. With the tremendous improvement of hardware and simulation technologies it is now possible and rather wide spread to do simulations for selected physical quantities at sufficiently small quark masses. Nevertheless, it is still very much desirable to gain a better understanding in how to use the chiral Lagrangian from small quark masses, for which Lattice simulations are still rather expensive, to larger quark masses, for which Lattice simulations are much more economical in energy consumption and budgets. While the chiral Lagrangian with three light flavors was almost declared useless by the community, the two-flavor version with light up and down quark masses is still frequently been used, however mostly for ensembles with rather small quark masses. This reflects an unfortunate and possibly questionable assumption on the applicability domain of the chiral Lagrangian.
In this talk I will discuss a novel development which suggests a much more favorite applicability domain of the chiral Lagrangian with not only two but also three light flavors [1,2]. This would open a new path towards more sustainable approaches to QCD, which is based on Lattice QCD simulation at quark masses significantly larger than the values required to reproduce the physical pion mass and properly combined with a chiral effective field theory. The key observation which may lead to such an avenue is that the use of on-shell hadron masses inside the loop correction terms as implied by chiral Lagrangian does affect its truncation properties. We illustrate our claim at the hand of the chiral Lagrangian as applied to baryon masses and the axial vector form factors [3,4].
There are various technical challenges to be overcome. Firstly, how to organize such a summed chiral perturbation theory without jeopardizing the chiral Ward identities of QCD. This is particularly cumbersome in the presence of a heavy field, which is known to cause power-counting violating terms. They have to be renormalized away in a systematic manner [3]. Secondly, how can we incorporate the effects of isobar fields, which are expected to limit the convergence domain to pion masses smaller than $m_\pi < M_\Delta - M_N \simeq 300$ MeV [2,4]? Here the available Lattice QCD data on flavor SU(2) ensembles are particularly useful. Conclusions on the convergence properties cannot be blurred here by the role of strange quarks.
[1] arXiv:1801.06417
[2] arXiv:2003.10158
[3] arXiv:2309.09695
[4] arXiv:2402.04905
