Sensitivity of predictions in an effective model -- application to the chiral critical end point position in the Nambu--Jona-Lasinio model

Understand

The measurement of the position of the chiral critical end point (CEP) in the QCD phase diagram is under debate.

• While it is possible to predict its position by using effective models specifically built to reproduce some of the features of the underlying theory (QCD), the quality of the predictions (\textit{e.g.}, the CEP position) obtained by such effective models, depends on whether solving the model equations constitute a well- or ill-posed inverse problem.
• Considering these predictions as being inverse problems provides tools to evaluate if the problem is ill-conditioned, meaning that infinitesimal variations of the inputs of the model can cause comparatively large variations of the predictions.
• If it is ill-conditioned, it has major consequences because of finite variations that could come from experimental and/or theoretical errors.