0 v 1 1 5 Ju l 1 99 4 The Inclusive Semileptonic B Decay Lepton Spectrum from B → Xeν ∗

In this talk, we review the QCD calculations of the lepton spectrum from inclusive semileptonic B decay. We compare this prediction to that of the ACCMMmodel. This latter work was done in collaboration with Csaba Csaki. Invited Talk, Presented at WHEPP-3 Workshop in Madras This work is supported in part by funds provided by the U.S. Department of Energy (DOE) under contract #DE-AC02-76ER03069 and in part by the Texas National Research Laboratory Commission under grant #RGFY92C6. National Science Foundation Young Investigator Award. Alfred P. Sloan Foundation Research Fellowship. Department of Energy Outstanding Junior Investigator Award. CTP#2333, hep-ph/9407300 June 1994 In this talk we discuss the calculation of the inclusive semileptonic decay lepton spectrum from B → Xeν. We first discuss the motivation for renewed interest in this calculation, and discuss the use of the OPE and HQET to determine this spectrum. We then compare this prediction to that of heavy quark models, in particular that of Altarelli, Cabbibo, Corbo, Maiani, and Martinelli [1] (hereafter referred to as ACCMM). I will concentrate on B → Xceν and not the detailed questions of the endpoint of the spectrum which are important for B → Xueν. There are several reasons for renewed interest in this prediction. First of all is the copious production of b quarks at LEP and CLEO. A good understanding of the decay spectrum is necessary for understanding fundamental b quark parameters, which are being precisely studied, such as the b width and the forward–backward asymmetry at LEP and those couplings relevant to the rare decays studied by CLEO. Furthermore, with a good understanding of the spectrum one can do detailed measurements of heavy quark fragmentation, which could give interesting tests of heavy quark theory and QCD predictions [2, 3]. Furthermore, in order to do high statistics measurements, one needs to do inclusive measurements. On the theoretical side, it is of interest to study the inclusive decays because they are under much better control theoretically than predictions for exclusive modes, where one needs to know hadronic matrix elements. An understanding of the lepton spectrum is therefore crucial to extracting fundamental parameters. In the seminal paper of Chay, Georgi, and Grinstein [4] it was shown that one can treat the decay spectrum with the operator product expansion and heavy quark methods. They showed the leading Λ/m corrections to the free quark result vanish in the matrix elements. Subsequently, Bigi, Blok, Koryakh, Shifman, Uraltsev, and Vainshtein [5] studied (Λ/m)2 corrections. They compared the results to a free quark, ACCMM model where they did not see the vanish-