Understanding Interquark Force and Quark Masses in Perturbative QCD

Abstract

This lecture note presents a self-contained introduction to the theory of a heavy quark-antiquark ($Q\bar{Q}$) system in terms of perturbative QCD. The lecture is intended for non-experts, such as graduate course students. The heavy $Q\bar{Q}$ system serves as an ideal laboratory for testing various aspects of QCD: We can examine the nature of renormalons in perturbative series; an effective field theory Potential-NRQCD is constructed, whose derivation from full QCD can be traced stepwise; we see absorption of renormalons by non-perturbative matrix elements in OPE clearly; a systematic short-distance expansion of UV contributions can be performed, which predicts a "Coulomb+linear" potential in perturbative QCD; we can test these theoretical formulations by comparison to lattice computations, where we observe a significant overlap with perturbative regime; finally we can test our microscopic understanding by comparing to experimental data for the bottomonium states. These subjects are covered in a concise and elementary manner. Overall, we provide a microscopic description of the main dynamics of a heavy $Q\bar{Q}$ system, as an example for which theoretical framework, practical computations and qualitative understanding have been most advanced.

65 pages, 58 figures; Based on the lecture courses given at Rikkyo Univ., Kyoto Univ., Karlsruhe Univ. and Nagoya Univ., during 2012--2014