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28 July 1994

Physics Letters B 333 (1994) 212-214

PHYSICS LETTERS B

An alternative method of extracting Vbu from semi-leptonic B decay Jin Da i 1

Department of Physics 0319, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0319, USA

Received 23 May 1994 Editor: H. Georgi

Abstract

We propose a new method of extracting Vbu from measurements of Semi-leptonic B decay which has much less theoretical uncerUtinties than conventional methods.

The Kobayashi-Maskawa matrix element Vbu is among the least known standard model parameters. Knowing its exact value is very important for under- standing standard model CP violation and radiative corrections. However, extracting Vbu from experiment is difficult due to hadronic physics uncertainties.

At the present time, Vbu is measured in charmless semileptonic B decays, especially from the inclusive lepton spectrum. The advantage of using inclusive de- cay modes is that it can be calculated using the par- ton model approach [ 1 ], and nonperturbative effects can be systematically analysed using heavy quark the- ory [2]. However, in experiment, there is an over- whelming background from the decay process

b ---~ c + l + ~,.

The only way to get a clean measurement is to con- centrate on the kinematic region where b to c decay is not allowed. In charmless B decay, the lepton energy Et is kinematically allowed up to mB/2, and in b to charm decay, Et is allowed up to m B - m2/ 2mn . That leaves available only about 330 MeV of energy near the end point of lepton spectrum.

1 E-mail address: dai@higgs.ucsd.edu.

Unfortunately, it is the endpoint spectrum that is least known theoretically. In the parton model, the maximum El allowed is mb/2, where mb is the b quark mass instead of the B meson mass. For mb ---- 4.8 GeV, this is 240 MeV below the kinematic maximum. QCD radiative corrections have been calculated [3] and contain large logs near the patton model maxi- mum. Beyond the parton model maximum, there is no systematic way of calculating the lepton spectrum, and different models lead to very different results [4].

Instead of thinking of improving the theoretical es- timate of the end point lepton spectrum, we propose an alternative way to get a more precise Vbu: Mea- sure quantities which can be calculated better theo- retically. In this paper, we will assume that the neu- trino momentum can be measured as well as the lepton momentum in semileptonic B decays. This is not un- realistic at electron-positron machines (e.g. CLEO), where missing momentum and missing energy can be measured and the neutrino mass shell condition can be used to reduce backgrounds from particles leaking out of beam pipes. We will show there is a better way to extract Vbu which has few theoretical uncertainties.

First, with the neutrino momentum known, it is much easier to separate the two quark processes b --~

0370-2693/94/$07.00 (~) 1994 Elsevier Science B.V. All rights reserved SSDI 0370-2693 ( 94 ) 0073 2-M

J. Dai / Physics Letters B

clu and b ~ ul~ in semileptonic B decay

B - - - ~ l + ~ + X . (1)

The key observation is that i f the underlying quark decay is b to c, then

M2x > m 2. (2)

On the other hand, for b to u decay, M~ tends to be much smaller.

When the momenta o f the B meson, the lepton and the neutrino are all known, the 4-momentum of X is determined. Therefore we propose the fol lowing cut which corresponds to excluding the kinematic region defined by Eq. (2 ) :

Et + Eu > m~ - m ~ + 2EIE~(1 - c o s 0 ) 2m~ , (3)

where Ez and E~ are lepton and neutrino energies in the rest frame of the B meson and 0 is the angle between the directions of the lepton and the neutrino. This cut will exclude the b to c decay background and keep most of the b to u decay events.

Based on the matrix elements by Al i and Pietari- n e n [ 3 ], we did a numerical calculation o f lepton and neutrino distr ibution including QCD radiative correc- tions. It turns out that about 95% of the b ~ u events will survive the cut mentioned above. Without know- ing 0, you can still exclude b to c decay kinematical ly by using the cut obtained by setting cos 0 = - 1 in Eq. (3 ) , but only around 40% of events are left. Without any knowledge o f the neutrino, as is the way that cur- rent experiments are done, one can use only a small port ion of the events. (For reasons explained above, theory can not predict the exact amount of events near the lepton end point .) Background from charm quark leptonic decay can be excluded by cutting on a high in- variant mass of the the lepton-neutrino pair, i f it turns out to be statist ically favorable.

Theoretical uncertainties of the total semileptonic decay rate is much smaller than that of the end point lepton spectrum, therefore we will have great advan- tage using the cut defined by (3 ) , which essentially let pass all the b ---+ u events while exclude the b c background. Because the parton model differential cross section d~r/dEtdE~ has large logs when El or E~ approach mb/2, theoretical uncertainties may be further reduced by making the cut

333 (1994) 212-214 213

Fig. 1. The phase space plot: x = 2Et/mB, y = 2Ev/mB. Lepton and neutrino energy are kinematically allowed inside the square, however, leading order parton model only allows final states inside the dashed triangle, therefore that is where most of the events are expected to be. The conventional method of extracting Vbu utilizes the narrow region to the right of the dot-dashed line. Cutting on the total final state hadron energy makes use the region above the solid straight line while still excludes b ~ c decay. Knowing both the lepton and neutrino energy but not the angle between them will allow us to use events above the solid curved line. Below the solid curved line, one can still use the angle to distinguish the two types of decay.

mB Et, Ep < ~ - 6, (4)

where 6 should be a few hundred MeV. There are small remaining uncertainty due to uncertainty in mb, which may be determined by studying the shape o f the b to c semi-leptonic decay spectrum.

It is up to experimental physicists to decide whether the neutrino momentum can be reconstructed with a reasonable efficiency, but i f it can be done, we can have a much better measurement o f Vbu. Having good detector coverage will be important on future B fac- tories for using this method.

After this work was completed, we received [5 ] , in which the authors suggest measuring the total final state hadron energy. This corresponds to making the following cut

Et + E~, > mB - m D ,

214 J. Dai / Physics Letters B 333 (1994) 212-214

in which 25% o f the events (accord ing to our calcu-

la t ion) near the end poin t wil l survive.

The Au tho r wou ld l ike to thank A. Manohar for

extens ive discussion, H. Paar for discussion o f C L E O

exper iment , and M. Luke for useful conversat ion.

Work was supported by D O E under grant D E - F G 0 3 -

90ER40546.

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