International Journal of Modern Physics A

I summarize what we know of renormalons from the 1970s and 80s: their uses and theoretical status. It is emphasized that renormalons in QCD are closely related to the Wilsonean operator product expansion (OPE) — a setup ideally suited for dealing with the factorially divergent series reflecting infrared dynamics. I discuss a breakthrough proposal due to Uraltsev et al. to use renormalons to evaluate nonperturbative (power) corrections in the processes without OPE. Some fresh ideas which were put forward recently are briefly discussed too, with emphasis on a possible relationship between resurgence via trans-series and OPE.

This article is devoted to the memory of my friend Kolya Uraltsev. I should emphasize that these are my personal recollections. Other people who closely knew Kolya may or may not agree with my opinions.

The CKM matrix elements |V_cb| can be extracted from inclusive semileptonic B decays in a model independent way pioneered by Kolya Uraltsev and collaborators. I review here the present status and latest developments in this field.

Since my return to Austria in the year 2003, I have measured observables in inclusive B meson decays at the Belle experiment and worked together with theorists on the interpretation of these measurements in terms of the Cabibbo–Kobayashi–Maskawa matrix element |V_cb|. And in fact, only this memorial book project made me fully aware of Kolya Uraltsev's ground breaking theoretical contributions to this field. He was not a theorist who talked a lot to an experimentalist like me, and maybe this is not a bad thing for good science. I certainly remember his enthusiasm from conferences, e.g., when I was powerless to keep his presentation to the scheduled time as a session chair at the CKM2005 workshop in San Diego. Still I feel there is some amount of irony in the fact, that I know so little about a person whose work has been so decisive for my career in high energy physics.

To commemorate Kolya Uraltsev's pioneering work on inclusive semileptonic B meson decays B → X_cℓν and on the Heavy Quark Expansion (HQE), which has already been paid tribute to in other articles in this volume, I will review the measurement of the electron energy and the hadronic mass moments in B → X_cℓν decays performed at the Belle experiment. These measurements allow to both test his theoretical calculations and to extract |V_cb| and non-perturbative quantities, such as the b-quark mass, from his formulae.

In this article I pay my tribute to the memory of Kolya Uraltsev. I look back on my experience with him, and focus especially on two joined projects with him on inclusive semi-leptonic decays. This is a field where he had a major impact over the past decades.

Kolya Uraltsev was one of the inventors of the Heavy Quark Expansion (HQE), that describes inclusive weak decays of hadrons containing heavy quarks and in particular lifetimes. Besides giving a pedagogic introduction to the subject, we review the development and the current status of the HQE, which just recently passed several non-trivial experimental tests with an unprecedented precision. In view of many new experimental results for lifetimes of heavy hadrons, we also update several theory predictions: , τ(B_s)/τ(B_d) = 1.001 ±0.002, τ(Λ_b)/τ(B_d) = 0.935 ±0.054 and . The theoretical precision is currently strongly limited by the unknown size of the non-perturbative matrix elements of four-quark operators, which could be determined with lattice simulations.

Working with Kolya Uraltsev was a real 'marvel' for me in general, but in particular about CP and T violation, QCD and its impact on transitions in heavy flavor hadrons and EDMs. The goal was — and still is — to define fundamental parameters for dynamics, how to measure them and compare SM forces with New Dynamics using the best tools including our brains. The correlations of them with accurate data were crucial for Kolya. Here is a review of CP asymmetries in B, D and τ decays, the impact of perturbative and non-perturbative QCD, about EDMs till 2013 — and for the future.

In this article I discuss a few aspects of exclusive decays of heavy mesons from the specific perspective of Kolya Uraltsev's contributions to this field. The selection of topics as well as their presentation reflects my personal view on Kolya's work and also includes some personal remarks related to my collaboration with him.

In the heavy quark limit of QCD, using the Operator Product Expansion and the non-forward amplitude, as proposed by Nikolai Uraltsev, we formulate sum rules that generalize Bjorken and Uraltsev sum rules. We recover the Uraltsev lower bound for the slope of the Isgur–Wise (IW) function, that we generalize to higher derivatives. We show that these results have a clear interpretation in terms of the Lorentz group, since the IW function is given by an overlap between the initial and final light clouds, related by Lorentz transformations. Both the Lorentz group and the Sum Rules approaches are equivalent. Moreover, we formulate an integral representation of the IW function with a positive measure. Inverting this integral formula, we obtain the measure in terms of the IW function, allowing one to formulate criteria to decide if a given ansatz for the IW function is compatible or not with the sum rule constraints. We compare these theoretical constraints to some forms proposed in the literature.

We first discuss Uraltsev's and other sum rules constraining the B → 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 semileptonic decays and non-leptonic ones, based on quark models. We then present in more detail the dynamical approaches: the relativistic quark model à 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.