Determination of |Vub|/|Vcb| with DELPHI at LEP

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Abstract

The ratio of the CKM quark-mixing matrix elements |Vub|/|Vcb| has been measured using B hadron semileptonic decays. The analysis uses the reconstructed mass MX of the secondary hadronic system produced in association with an identified lepton. Since B→Xuν̄ transitions are characterised by hadronic masses below those of the D mesons produced in B→Xcν̄ transitions, events with a reconstructed value of MX significantly below the D mass are selected. Further signal enrichments are obtained using the topology of reconstructed decays and hadron identification. A fit to the numbers of decays in the bu enriched and depleted samples with MX above and below 1.6 GeV/c2 and to the shapes of the lepton energy distribution in the B rest frame gives |Vub|/|Vcb|=0.103+0.011−0.012(stat.)±0.016(syst.)±0.010(model) and, correspondingly, a charmless semileptonic B decay branching fraction of BR(B→Xuν̄)=(1.57±0.35(stat.)±0.48(syst.)±0.27(model))×10−3.

Introduction

The measurement of the branching ratio for the decay b→uℓν̄ provides the most precise way to determine the |Vub| element of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix. Evidence for a non-zero value of |Vub| was first obtained 1, 2by observing leptons produced in B decays with momentum above the kinematic limit for b→cℓν̄ transitions. However, extracting |Vub| from the yield of leptons above the b→cℓν̄ endpoint is subject to a large model dependence. More recently, exclusive B→πℓν̄ and B→ρℓν̄ decays were observed and their rates measured 3, 4. But the determination of |Vub| from exclusive semileptonic decays also has a significant model dependence.

The extraction of |Vub| from the distribution of the invariant mass MX of the hadronic system recoiling against the lepton pair in B→Xuν̄ transitions was proposed several years ago [5]and it has recently been the subject of new theoretical calculations 6, 7. There have been two other |Vub| determinations at LEP based on inclusive analysis of semileptonic decays [8]. The method used here starts from the observation that in most B→Xuν̄ decays the hadronic system recoiling against the ν̄ has an invariant mass below the charm mass (see Fig. 1). Because a much larger fraction of the total rate is involved, the model dependence when extracting |Vub| from the decay rate to such states is much smaller than when using the decay rate to leptons above the b→cℓν̄ endpoint or that to exclusive final states 6, 7.

This paper presents the first determination of |Vub|/|Vcb| based mainly on candidate B semileptonic decays with reconstructed hadronic invariant masses below the D mass and enriched in bu transitions using the secondary vertex topology and identified kaons and protons. The shape of the lepton energy spectrum in the B rest frame is also used.

Section 2describes the event preselection, the particle identification, the reconstruction of the hadronic secondary system and of the B energy and direction, and the bu enrichment. Section 3presents the final event sample, the extraction of |Vub|/|Vcb|, the stability checks, and the evaluation of the systematic errors. Section 4summarises.

Section snippets

Data analysis

The analysis was performed using data collected by the DELPHI detector at LEP at centre-of-mass energies around the Z0 pole between 1993 and 1995, corresponding to 2.8 ×106 Z0 hadronic decay candidates. The DELPHI detector was described in detail in [9]and its performance was reviewed in [10]. The backgrounds were estimated using samples of Z0 hadronic decays generated with Jetset 7.3 [11]and passed through the full detector simulation. These simulated events corresponded to 4.9 times the data

Results

Candidate semileptonic B decays were further selected by imposing the following selection in order to remove background and poorly reconstructed decays. The summed energy of the hadronic system and the lepton was required to be larger than 12 GeV and larger than 70% of the jet energy. Decays with an invariant mass of the secondary hadronic system and of the lepton MX below 2.0 GeV/c2 were also removed. Finally, decays in which the lepton charge had a sign equal to that of the hadronic system

Summary and discussion

The value of the ratio |Vub|/|Vcb| was measured using a novel technique. The technique uses the reconstructed mass MX of the secondary hadronic system produced in association with an identified lepton in the semi-leptonic decay of a B hadron and the rest-frame energy spectrum of that lepton. The bu signal is enriched using identified kaons and protons and the lepton impact parameter with respect to the secondary vertex. The result obtained is |Vub|/|Vcb| = 0.103 +0.011−0.012 (stat.)±0.016

Acknowledgements

We would like to thank I. Bigi, N. Uraltsev and M. Neubert for discussions on the modelling of the B→Xuν̄ decays and on the related systematics in the extraction of |Vub|/|Vcb| and D. Lange and A. Ryd for providing an implementation of the ISGW-2 model in the simulation of semileptonic B decays. We are greatly indebted to our technical collaborators, to the members of the CERN-SL Division for the excellent performance of the LEP collider, and to the funding agencies for their support in

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