On the spectra of cardinalities of branches of Kurepa trees

We are interested in the possible sets of cardinalities of branches of Kurepa trees in models of ZFC+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+$$\end{document}CH. In this paper we present a sufficient condition (for sets of cardinals) to be consistently the set of cardinalities of branches of Kurepa trees.