Beauty Quark Fragmentation Into Strange B Mesons

Using the recent measurement of the total production rate for Bs and B ∗ s mesons in electron-positron annihilation to determine the strange quark mass parameter in the b̄ → Bs, B ∗ s fragmentation functions we calculate the momentum distributions of the Bs and B ∗ s mesons. Internet address: [email protected] Internet address: [email protected] Recently the probability for a heavy quark to hadronize into a strange B or D meson has been measured at LEP by the DELPHI Collaboration [1]. These data can be used to determine the strange quark mass parameter,ms, in the heavy quark fragmentation functions and, therefore, to predict the momentum distributions of the Bs and B ∗ s mesons produced in the fragmentation process. Using the heavy quark fragmentation functions calculated in perturbative QCD at the scale of the heavy quark [2] for the initial condition we have numerically integrated the Altarelli-Parisi equation to obtain the momentum distributions of the Bs and B ∗ s mesons at the scale of the Z mass. The resulting distributions are only moderately sensitive to the value of ms, which we find to be about 300 MeV/c . The fragmentation function for the process b̄ → Bs at the scale of the b mass is easily obtained from the b̄ → Bc fragmentation functions calculated using perturbative QCD by Braaten, Cheung, and Yuan [2]: Db̄→Bs(z, μ0) = 2αs(2ms) |R(0)| 81πm3s rz(1− z) (1− (1− r)z) × [6− 18(1− 2r)z + (21− 74r + 68r)z −2(1− r)(6− 19r + 18r)z + 3(1− r)(1− 2r + 2r)z] . (1) Here z is the fraction of the b̄ quark momentum carried by the Bs meson, r = ms/(mb+ms), and R(0) is the Bs meson S-wave radial wavefunction at the origin. The corresponding fragmentation function for b̄ → B s is Db̄→B∗ s (z, μ0) = 2αs(2ms) |R(0)| 27πm3s rz(1− z) (1− (1− r)z) × [2− 2(3− 2r)z + 3(3− 2r + 4r)z −2(1− r)(4− r + 2r)z + (1− r)(3− 2r + 2r)z] , (2) The wavefunction at the origin, R(0), can be determined from the Bs meson decay constant, fBs , from the Van Royen-Weisskopf [3] relation, modified for color: f 2 Bs = 3 π |R(0)| MBs . (3)