Lattice Results for Heavy Light Matrix Elements

Lattice results for heavy light matrix elements are reviewed and some of their implications are very briefly discussed [1]. Despite the fact that in most cases the lattice results for weak matrix elements at the moment have only a modest accuracy of about 20–30% they already have important phenomenological repercussions; e.g. for Vtd/Vts, xs/xd and B → K ∗γ. I. As samples of “new” projects, I briefly discuss four projects a. The NRQCD group [2] reports a preliminary result on the mass splitting mB∗ S −mBS . They use 100 configurations on a 16 × 32 lattice of the HEMCGC group (dynamical, staggered nf = 2, am = .01 and β = 5.6). Their very preliminary result is mB∗ S −mBS = [50± 5(statistical)± 10(am) ±15(scale)]MeV (1) Since rough phenomenological estimates for the splitting invariable yield about 50 MeV, such a lattice calculation will be very interesting if the errors can be brought down to 0 (5 MeV). b. The LANL collaboration [3] is acquiring many interesting results via their large scale simulations on the CM-5. So far they have analyzed 58 configurations of size 32 × 64 at β = 6.0. This lattice has the distinction of having the largest physical volume used so far for weak matrix element calculations. Comparison with results previously obtained on smaller lattices will therefore be very valuable. Here are some of their preliminary findings: (1) fK/fπ = 1.163± .023; (2) f + (q =0) f + (q2=0) = 0.86± .08; (2) (3) A ∗ eν 2 (0) A eν 1 (0) = .77± .22. c. The Fermilab Static Group (FSG) [4] is now finishing a comprehensive study with the use of their static method. They reported interesting results on fB, fBS/fBu andmBS−mBu . With their method they find a significant lattice spacing (a) dependence for fB whereas the other two quantities appear insensitive to a. Their key results are: fB = 188± 23(stat)± 15(sys) +27 −0 (extr)± 14(a) (3) fBS/fBu = 1.216± .041± .016 (4) mBS −mBu = 86± 12± 7(MeV) (5) d. MILC collaboration [5] is undertaking a dedicated study of fB using primarily the Intel Paragon machine. They have analyzed so far 40 configurations (24 × 80, β = 6.3). Their preliminary results for the decay constants are given below: fB = 174± 7 MeV fBS = 198± 7 MeV fD = 205± 5 MeV (6) fDS = 228± 5 MeV