Effective heavy quark theory

The effective theory heavy quark (engl. Heavy quark effective theory or HQET) is an effective theory to describe mesons and baryons with a heavy quark .

Heavy quarks are the b and c quarks in contrast to the light u , d and s quarks; t quarks are usually not taken into account because they are significantly heavier.

General consideration

The typical cutoff in hadron physics is at . A large part of the proton mass does not consist of the mass of the quarks, but of their binding energy ; the bound light quarks are far removed from the mass shell in this energy scale . ${\ displaystyle \ Lambda \ approx m_ {p} / 3 \ approx 330MeV / c ^ {2}}$ ${\ displaystyle m_ {p}}$

The heavy quarks, on the other hand, are of this order of magnitude almost on the mass shell . Their speed changes only negligibly when receiving additional momentum from the light quarks; it can therefore be regarded as identical to the speed of the hadron. In the rest frame of the heavy the heavy hadron curd is provided as a source of static approximately at rest and may be strong interaction are considered, by the Flavor and SU (3) - color charge is characterized.

In contrast, the effective theory does not contain any terms for the spin or the mass of the heavy quark. The coupling constant for a spin interaction is of the order of magnitude , where is the strong coupling constant and the mass of the heavy quark. This can be neglected as well as other terms that depend on the mass of the heavy quark. ${\ displaystyle g_ {s} / m_ {Q}}$ ${\ displaystyle g_ {s}}$ ${\ displaystyle m_ {Q}}$

The latter leads to the fact that B mesons and D mesons do not differ in the effective theory, just as different isotopes can be distinguished chemically - there, too, the mass does not play a role in the effective theory (ie the chemical properties), as long as one does not can resolve the hyperfine structure .

On the other hand, the theory can be developed as a perturbation calculation in powers of . ${\ displaystyle \ Lambda / m_ {Q}}$

Contemplation on the grid

The grid - discretization of the static approximation heavy quark was 1987 by Estia Eichten introduced.

The static effect is given by

{\ displaystyle S_ {static} = a ^ {3} \ sum _ {x} {\ bar {\ psi}} (x) {\ frac {1+ \ gamma _ {4}} {2}} \ left ( (1 + m_ {0} a) \ psi (x) -U_ {4} ^ {\ dagger} (xa {\ hat {e}} _ {4}) \ psi (xa {\ hat {e}} _ {4}) \ right),}

where a is the grid spacing and the unit vector in the time direction. Think of the sum over the grid points. The term can be omitted if the choice of a is sufficiently small (corresponding computing power required). ${\ displaystyle {\ hat {e}} _ {4}}$ ${\ displaystyle m_ {0} a}$

To ensure that the theory can be renormalized , HQET treats the kinetic and chromomagnetic interaction as operator insertions:

{\ displaystyle <\ phi> = {\ frac {1} {Z}} \ int DU \; D \ psi \; D {\ bar {\ psi}} \; \ phi \ left [1 + c_ {2} \ sum _ {x} O_ {2} + c_ {B} \ sum _ {x} O_ {B} \ right] e ^ {- S_ {light} -S_ {static}} \.}

The integration takes place via the link variable as well as the fermion fields and . ${\ displaystyle U}$ ${\ displaystyle \ psi}$ ${\ displaystyle {\ bar {\ psi}}}$

Individual evidence

^ HB Thacker, E. Eichten, JC Sexton: The Three-Body Potential for Heavy Quark Baryons in Lattice QCD

literature

B. Grinstein: An Introduction to the Theory of Heavy Mesons and Baryons , in: Proceedings of the 1994 Theoretical Advanced Studies Institute in Elementary Perticle Physics, Boulder, Colorado, CP Violation and the Limits of the Standard Model, TASI-1994 , ed. : JFDonoghue, World Scientific.
A. Kronfeld, Lectures on HQET on the grid: International Summer School on "Lattice QCD and its applications" (07-2b), Seattle, August 8 - 28, 2007, first (PDF; 153 kB), second (PDF; 208 kB), third (PDF; 428 kB), fourth (PDF; 214 kB) lecture.

[1] HB Thacker, E. Eichten, JC Sexton: The Three-Body Potential for Heavy Quark Baryons in Lattice QCD