Determination of |$V_{ub}$|/|$V_{cb}$| with DELPHI at LEP

The ratio of the CKM quark-mixing matrix elements |V_{ub}|/|V_{cb}|has been measured using B hadron semileptonic decays.The analysis is based on a novel technique, recently proposed by theoreticians, that uses the reconstructed mass M_X ofthe secondary hadronic system produced in association with an identified lepton.Since B rightarrow X_u \ell \bar \nu transitions are characterisedby hadronic masses below those of the $D$ mesons produced inB \rightarrow X_c \ell \bar \nu transitions, events with a reconstructed value of M_X significantly below the D massare selected.Further signal enrichments are obtained using thetopology of reconstructed decays and hadron identification.A fit to the numbers of decays in the b\to u enriched and depleted samples with M_X above and below 1.6 GeV/c^2and to the shapes of the lepton energy distribution in the Brest frame gives |V_{ub}|/|V_{cb}|= \mathrm{0.103^{+0.011}_{-0.012}~(stat.)\pm0.016~(syst.)\pm0.010~(mo del)}%The model dependance of $b \rightarrow u \ell \bar \nu$%is significantly reduced with this method.and, correspondingly, a charmless semileptonic $B$ decay branching fractionof BR($B \rightarrow X_u \ell \bar \nu) = \mathrm{(1.57 \pm 0.35~(stat.)\pm0.48~(syst.)\pm0.27~(model))\times 10^{-3}}$.