Form Factors for Semileptonic Decays of Heavy-Light Hadrons

In the quark mass M → ∞ limit, QCD has an exact SU(2Nf) spin-flavour symmetry. This symmetry relates many matrix elements and form factors of hadrons containing heavy quarks [2,3]. In particular, the semileptonic weak decay form factors of s−wave hadrons containing a single infinitely heavy quark can be reduced to two unknown functions, one for mesons (ξ) and another for baryons (ζ). The knowledge of these IsgurWise functions is of practical importance in a precise determination of the quark mixing matrix element Vcb: the experimentally measured B → D semileptonic decay rates can be fitted to a leading term involving ξ plus phenomenological estimates of corrections suppressed by powers of 1/M . In the M → ∞ limit, it is convenient to scale all variables so as to explicitly separate the factors of heavy quark mass, e.g. a heavy hadron state is characterised by its four-velocity vμ and the Isgur-Wise functions depend only on the Lorentz invariant v · v. In the static geometry, the light QCD degrees of freedom decouple from the dynamics of the heavy quark, and flavour independence of QCD fixes the absolute normalisation of the form factors: ξ(v · v = 1) = 1 = ζ(v · v = 1). As an explicit case, consider the form factor for semileptonic weak decay B → Dlν, and its behaviour as mb and mc go to infinity. Only the partially conserved vector current contributes: