Perturbative HQET

Methods of calculation of loop diagrams in Heavy Quark Effective Theory (HQET) are presented. 1 Hadrons with a Heavy Quark B meson is the hydrogen atom of Quantum Chromodynamics (QCD), its simplest nontrivial object. In the leading approximation, the b quark in it just seats at rest at the origin and creates chromoelectric field. Light constituents (gluons, light quarks and antiquarks) move in this external field. Their motion is relativistic; the number of gluons and light quark-antiquark pairs in this light cloud is undetermined and varying. Therefore, there are no reasons to expect that a nonrelativistic potential quark model describes B meson well. Similarly, Λb baryon can be called the helium atom of QCD. Unlike in atomic physics, where the hydrogen atom is much simpler than helium, B and Λb are equally difficult. Both have a light cloud with a variable number of relativistic particles. The size of this cloud is the confinement radius 1/ΛQCD; its properties are determined by the large-distance nonperturbative QCD. The analogy with atomic physics can tell us a lot about hadrons with a heavy quark. The usual hydrogen and tritium have identical chemical properties, despite the fact that the tritium nucleus is 3 times heavier than the proton. Both nuclei create identical electric fields, and both stay at rest. Similarly, D and B mesons have identical “hadro-chemical” properties, despite the fact that b quark is 3 times heavier than c. The proton magnetic moment is of the order of the nuclear magneton e/(2mp), and is much smaller than the electron magnetic moment e/(2me). Therefore, the energy difference between the states of the hydrogen atom with the total spins 0 and 1 (hyperfine splitting) is small (of the order me/mp times the fine structure). Similarly, the b quark chromomagnetic moment is proportional to 1/mb by dimensionality, and the hyperfine splitting between B and B mesons is small (proportional to 1/mb). In the limit m → ∞, the heavy quark spin does not interact with gluon field. Therefore, it may be rotated at will, without changing physics. Such rotations can transform B and B into each other; they are degenerate and have identical properties in this limit. This heavy quark spin symmetry yields many useful relations among heavy-hadron form factors. Not only the orientation, but also the magnitude of the heavy quark spin is irrelevant in the infinite mass limit.