Abstract: In calculations of the elementary scalar spectra of spontaneously broken gauge theories there are a number of subtleties which, though it is often unnecessary to deal with them in the order-of-magnitude type of calculations, have to be taken into account if fully consistent results are sought for. Within the “canonical” effective-potential approach these are, for instance: the need to handle infinite series of nested commutators of derivatives of field-dependent mass matrices, the need to cope with spurious IR divergences emerging in the consistent leading-order approximation and, in particular, the need to account for the fine interplay between the renormalization effects in the one-and two-point Green functions which, indeed, is essential for the proper stable vacuum identification and, thus, for the correct interpretation of the results. In this note we illustrate some of these issues in the realm of the minimal Abelian Higgs model and two of its simplest extensions including extra heavy scalars in the spectrum in attempt to exemplify the key aspects of the usual “hierarchy problem” lore in a very specific and simple setting. We emphasize that, regardless of the omnipresent polynomial cut-off dependence in the one-loop corrections to the scalar two-point function, the physical Higgs boson mass is always governed by the associated symmetry-breaking VEV and, as such, it is generally as UV-robust as all other VEV-driven masses in the theory.

Abstract: Motivated by the observation of the first hidden charm pentaquarks by the LHCb collaboration in 2015 and the updated analysis with an order-of-magnitude larger data set in 2019, we estimate their cross sections for the prompt production as well as their heavy quark spin partners, in the Sigma(()(c)*()) (D) over bar (()*()) hadronic molecular picture, at the center-of-mass energy 7 TeV in the pp collision. Their cross sections are several nb and we would expect several tens hidden charm pentaquark events in the LHC based on its current integrated luminosity. The cross sections show a sizable deviation of the cross sections for hidden charm pentaquarks with the third isospin component Iz = + 1/2 (P-c(+)) from those with Iz = – 1/2 (P-c(0)). The cross sections decrease dramatically with the increasing transverse momentum. Our study can also tell where to search for the missing hidden charm pentaquarks. The confirmation of the complete hidden charm pentaquarks in the heavy quark symmetry would further verify their Sigma(()(c)*()) (D) over bar (()*()) molecular interpretation. In addition, the relative strength among these cross sections for pentaquarks can help us to identify the quantum numbers of the P-c(4440) and P-c(4457).