In Memoriam Nikolai Uraltsev : Uraltsev's and other Sum Rules, Theory and Phenomenology of $D^{**}$'s

TL;DR

This paper reviews sum rules and theoretical models for $D^{**}$ meson decays, compares predictions with experimental data, and discusses discrepancies and future prospects for clarification.

Contribution

It provides a comprehensive comparison of sum rules, quark models, and lattice QCD results for $D^{**}$ decays, highlighting discrepancies and analyzing the applicability of the infinite mass limit.

Findings

Predictions at infinite mass agree with experiments for non-leptonic decays.

Large discrepancies exist between different experimental measurements.

Semileptonic decay predictions show less agreement with experimental data.

Abstract

We first discuss Uraltsev's and other sum rules constraining the $B \to D^{**}(L=1)$ weak transitions in the infinite mass limit, and compare them with dynamical approaches in the same limit. After recalling these well established facts, we discuss how to apply infinite mass limit to the physical situation. We provide predictions concerning semi-leptonic decays and non-leptonic ones, based on quark models. We then present in more detail the dynamical approaches: the relativistic quark model \`a la Bakamjian-Thomas and lattice QCD. We summarise lattice QCD results in the infinite mass limit and compare them to the quark model predictions. We then present preliminary lattice QCD results with finite $b$ and $c$ quark masses. A systematic comparison between theory and experiment is performed. We show that some large discrepancies exist between different experiments. Altogether the predictions at infinite mass are in fair agreement with experiment for non-leptonic decays contrary to what happens for semileptonic decays. We conclude by considering the prospects to clarify both the experimental situation, the theoretical one and the comparison between both.