| from the polarization of vector meson in the semileptonic decay of B and B c meson

Since the degree of polarization of the vector particle in semileptonic decay strongly influences the decay width of the particles, it can be used as a measure of Cabibbo-Kobayashi-Maskawa quark-mixing matrix elements. We show that |Vcb| can be determined from the measurement of polarization of vector meson in B̄, B̄c → V lν̄ decay, where V is vector meson. Typeset using REVTEX Present address: Physics Dept., Hanyang University, Seoul 133-791, Korea. E-mail: [email protected] 1 Exclusive semileptonic decays of hadrons containing a bottom quark provide a means to measure the Cabibbo-Kobayashi-Maskawa(CKM) matrix elements [1]. The decay B̄ → Dlν̄ is a key process for these studies. Neubert proposed the method of model independent determination of |Vcb| from B̄ → Dlν̄ decay within the framework of Heavy Quark Effective Theory (HQET) [2]. He observed that the zero recoil point is especially suitable for the extraction of |Vcb|. His method basically relies on the existence of one universal form factor and the fact that the form factor is unaffected from 1/mQ (Q = b, c) corrections at zero recoil by Luke’s theorem [3]. The decays of the B̄c meson are another source of measurement of CKM element. The B̄c → J/ψlν̄ → (ll)lν̄ decay is, in particular, expected to be a quite suitable mode to measure |Vcb| due to the experimentally clean signature. Based on the fact that the matrix element of B̄c → J/ψlν̄ decay is expressed by only one form factor near zero recoil point due to the spin symmetry of heavy mesons, Sanchis et al. [4] discussed similar procedure as Neubert to extract |Vcb|. In the above method, the value of |Vcb| is extracted from the recoil spectrum of the semileptonic decay, hence complete kinematic reconstruction is required. The decay of neutral B̄ meson has been used because the flight direction of B̄ is unaffected by the magnetic field. In ARGUS and CLEO experiments [5–7], where B̄ is produced almost at rest, the recoil momentum of D to the B̄ meson is easily calculated by reconstructing D and π. The problem comes from the small released energy of decay products of D; since the momentum of pion of the decay is small, the efficiency for reconstructing the charged pion is low, and the combinatorial background for neutral pions from D decays is significant. In ALEPH experiment [8], the B̄ meson is largely boosted. The momentum of ν̄ is calculated from the missing energy in the hemisphere containing the Dl candidate. Although the momentum of the pion from the D decay has large momentum, the momentum of B̄ meson should be reconstructed on an event by event basis: the flight direction of the B̄ meson is measured by reconstructing its production and decay points. There are uncertainties from the missing energy measurement and identification of particles. 2 In this paper, we show that the polarization of the vector particle can be used as a measure of the CKM element. It is based on the fact that the degree of polarization of the vector particle strongly influences the momentum spectrum of the decay particles as well as the decay rate. One advantage of the polarization measurement is no need of full kinematic reconstruction: the polarization of the vector meson is measured only from their decay products regardless of the charge of the original meson(B or B c ). The differential decay rate for B̄ → Dlν̄ is 1 √ y2 − 1 dΓ dy = GF 48π3 mD∗(mB −mD∗)η A1|Vcb| ξ(y) (1) ×4y(y + 1)1− 2yr + r 2 (1− r)2 , B̄ → D ∗ T lν̄, ×(y + 1), B̄ → D∗ Llν̄. (2) Here the variable y is y = v · v′ = m 2 B +m 2 D − q 2mBmD∗ (3) and r = mD∗/mB, q 2 the momentum transfer to the lepton pair, ηA1 the QCD correction factor. The form factor at non-zero recoil point is not predicted from HQET itself, and can be parameterized by various form. Here we compare three different functional form, linear, exponential, and the pole ansatz [2]; ξ(y) = ξ(1)(1− ρ̄(y − 1)), (4) ξ(y) = ξ(1)e 2(y−1), (5) ξ(y) = ξ(1)( 2 y + 1 ) 2 (6) where ξ(1) = 1+ δ(1/mQ). Then |Vcb|ξ(v · v) is fitted to recoil spectrum with |Vcb| and ρ̄ as free parameters in the Neubert’s method. The polarization of D is measured from the angular distribution of their decay products in the rest frame of D. In B̄ → Dlν̄ decay where D decays into two pseudo-scalar particle D and π, the decay amplitude with the helicity λ of the D is given [9] 3