The Isgur-Wise function from the lattice.

We calculate the Isgur-Wise function by measuring the elastic scattering amplitude of a D meson in the quenched approximation on a 24 3 48 lattice at = 6:2, using an O(a)-improved fermion action. We use this result, in conjunction with heavy-quark symmetry, to extract jV cb j from the experimentally measured B ! D l diierential decay width. Heavy-quark symmetry enables all the non-pertur-bative, strong-interaction physics for semi-leptonic B ! D, D decays to be parametrized in terms of a single universal function, (!), of ! v v 0 , where v and v 0 are the four-velocities of the B and D mesons respectivelyy1, 2]. (!) is known as the Isgur-Wise function and is normalized at zero recoil: (1) = 112]. With (!), one can extract the Cabibbo-Kobayashi-Maskawa matrix element V cb from experimental measurements of the rate for B ! D l decayss3]. We report here on a lattice QCD calculation of the Isgur-Wise function and on the corresponding determination of V cb. We also perform a qualitative test of the avor component of heavy-quark symmetry. To obtain the Isgur-Wise function, we evaluate the elastic scattering matrix element hD(p 0)j c cjD(p)i on the mass shelll4]. Because the electromagnetic current cc c is conserved, this matrix element can be parame-trized in terms of a single form factor: hD(p 0)j c cjD(p)i = m D (v + v 0) h el (!) ; (1) where p (0) = m D v (0) and ! = v v 0 is the four-velocity recoil. In the limit of exact heavy-quark symmetry this form factor is simply (!). There are two sources of corrections to this simple result: h el (!) = 1 + el (!) + el (!) (!) : (2) The rst correction, el (!), stems from perturbative QCD corrections to the heavy-quark current. We obtain this correction from Neubert's short distance expansion of heavy-quark currentss5]. The second correction , el (!), is due to higher-dimension operators with coeecients proportional to inverse powers of the charm quark mass. el (!) is diicult to quantify because it involves the light degrees of freedom and is therefore non-perturbative. Luke's theoremm6], however, guarantees that there is no O ((QCD =(2m c)) correction to h el (!) at zero recoil. Moreover, model estimates of this correction appears to remain well below 3% over the range of experimentally accessible recoilss7]. That this correction is small …