Heavy Quark Effective Theory

The physics of the mixing and decays of B-mesons is essential for a determination of unknown CKM-matrix elements and thus for our understanding of the violation of CP-symmetry in Nature. It is also still promising for the discovery of physics beyond the standard model of particle physics. Unfortunately, many of the experimental observations can only be related to the standard model parameters if transition matrix elements of the effective weak Hamiltonian are known. These matrix elements between hadron states are only computable in a fully non-perturbative framework. They provide a strong motivation to study B-physics in lattice QCD. However, as the mass of the b-quark is larger than the affordable inverse lattice spacing in Monte Carlo simulations of lattice QCD, the b=quark cannot be treated as a relativistic particle on the lattice. Therefore, effective theories for the b-quark are being developed and used to compute the matrix elements in question. The first effective theory that was suggested is Heavy Quark Effective Theory (HQET). Like other effective theories, it is afflicted by a problem which remained unsolved so far: in general its parameters (the coefficients of the terms in the Lagrangian) themselves have to be determined non-perturbatively. In other words, the theory has to be renormalized non-perturbatively. This fact is simply due to the mixing of operators of different dimensions in the Lagrangian, requiring fine-tuning of their coefficients. If they were determined only perturbatively (in the QCD coupling), the continuum limit of the theory would not exist. The issue is already present in the determination of the b-quark mass in the static approximation, i.e. in the lowest order of the effective theory. In a small finite volume, one may realize lattices fine enough for the b-quark to be treated as a standard relativistic fermion. At the same time the energy scale 1/L = O(1 GeV) is still significantly below m_b and HQET applies quantitatively. Computing the same suitable observables in both theories relates the parameters of HQET to those of QCD. Then one moves to larger and larger volumes by an iterative procedure and computes HQET observables. This yields the connection to a physically large volume (of linear extent O(2 fm)), where eventually the desired matrix elements are accessible. Since in this way the parameters of HQET are determined from those of QCD, the predictive power of QCD is transfered to HQET.

Our strategy is described in

"Nonperturbative heavy quark effective theory",

JHEP 0402:022,2004, hep-lat/0310035

Results at the O(1/m) order can be found in

"Heavy quark effective theory computation of the mass of the bottom quark",

JHEP 0701:007,2007. hep-ph/0609294

"HQET at order 1/m: I. Non-perturbative parameters in the quenched approximation",

DESY-09-153, IFT-UAM-CSIC-09-47, MKPH-T-09-18, SFB-CPP-10-01, arXiv:1001.4783

Tables of results are under

useful tables/results