303 research outputs found

    The Instantaneous Bethe-Salpeter Equation and Its Analog: the Breit-like Equation

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    We take (μ±e∓\mu^\pm e^\mp) systems and consider the states with quantum number JP=0−J^P=0^- as examples, to explore the different contents of the instantaneous Bethe-Salpeter (BS) equation and its analog, Breit equation, by solving them exactly. The results show that the two equations are not equivalent, although they are analogous. Furthermore, we point out that the Breit equation contains extra un-physical solutions, so it should be abandoned if one wishes to have an accurate description of the bound states for the instantaneous interacting binding systems.Comment: 5 pages, no figur

    Hadronic production of the PP-wave excited BcB_c-states (BcJ,L=1∗B_{cJ,L=1}^*)

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    Adopting the complete αs4\alpha_s^4 approach of the perturbative QCD (pQCD) and updated parton distribution functions, we have estimated the hadronic production of PP-wave excited BcB_c-states (BcJ,L=1∗B_{cJ,L=1}^*). In the estimate, special care on the relation of the production amplitude to the derivative of wave function at origin of the potential model is payed. For experimental references, main uncertainties are discussed, and the total cross sections and the distributions of the production with reasonable cuts at the energies of Tevatron and LHC are computed and presented. The results show that PP-wave production may contribute to the BcB_c-meson production indirectly by a factor about 0.5 of the direct production, and with such a big cross section, it is worth further to study the possibility to observe the PP-wave production itself experimentally.Comment: 23 pages, 9 figures, to replace for revising the misprints ec

    Decays of the Meson BcB_c to a PP-Wave Charmonium State χc\chi_c or hch_c

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    The semileptonic decays, Bc⟶χc(hc)+ℓ+νℓB_{c}{\longrightarrow}{\chi_c}(h_c)+{\ell}+{{\nu}}_{\ell}, and the two-body nonleptonic decays, Bc⟶χc(hc)+hB_{c}{\longrightarrow}{\chi_c}(h_c)+h, (here χc\chi_c and hch_c denote (ccˉ[3PJ])(c\bar c[^3P_J]) and (ccˉ[1P1])(c\bar c[^1P_1]) respectively, and hh indicates a meson) were computed. All of the form factors appearing in the relevant weak-current matrix elements with BcB_c as its initial state and a PP-wave charmonium state as its final state for the decays were precisely formulated in terms of two independent overlapping-integrations of the wave-functions of BcB_c and the PP-wave charmonium and with proper kinematics factors being `accompanied'. We found that the decays are quite sizable, so they may be accessible in Run-II at Tevatron and in the foreseen future at LHC, particularly, when BTeV and LHCB, the special detectors for B-physics, are borne in mind. In addition, we also pointed out that the decays Bc→hc+...B_c\to h_c+... may potentially be used as a fresh window to look for the hch_c charmonium state, and the cascade decays, Bc→χc[3P1,2]+l+νlB_c\to \chi_c[^3P_{1,2}]+l+\nu_l (Bc→χc[3P1,2]+hB_c\to \chi_c[^3P_{1,2}]+h) with one of the radiative decays χc[3P1,2]→J/ψ+γ\chi_c[^3P_{1,2}] \to J/\psi+\gamma being followed accordingly, may affect the observations of BcB_c meson through the decays Bc→J/ψ+l+νlB_{c}\to {J/\psi}+{l}+\nu_{l} (Bc→J/ψ+hB_c\to J/\psi+h) substantially.Comment: 24 pages, 3 figures, the replacement for improving the presentation and adding reference

    The meson BcB_c annihilation to leptons and inclusive light hadrons

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    The annihilation of the BcB_c meson to leptons and inclusive light hadrons is analyzed in the framework of nonrelativistic QCD (NRQCD) factorization. We find that the decay mode, which escapes from the helicity suppression, contributes a sizable fraction width. According to the analysis, the branching ratio due to the contribution from the color-singlet component of the meson BcB_c can be of order (10^{-2}). We also estimate the contributions from the color-octet components. With the velocity scaling rule of NRQCD, we find that the color-octet contributions are sizable too, especially, in certain phase space of the annihilation they are greater than (or comparative to) the color-singlet component. A few observables relevant to the spectrum of charged lepton are suggested, that may be used as measurements on the color-octet and color-singlet components in the future BcB_c experiments. A typical long distance contribution in the annihilation is estimated too.Comment: 26 pages, 5 figures (6 eps-files), submitted to Phys. Rev.

    The Color-Octet Contributions to PP-wave BcB_c Meson Hadroproduction

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    The contributions from the color-octet components ∣(cbˉ)8(1S0)g>|(c\bar b)_{\bf 8}(^{1}S_{0}) g> and ∣(cbˉ)8(3S1)g>|(c\bar b)_{\bf 8}(^{3}S_{1}) g> to the hBch_{B_c} or χBcJ\chi_{B_c}^J (the PP-wave BcB_c meson) hadroproduction are estimated in terms of the complete O(αs4){\cal O}(\alpha_s^4) calculation. As necessary inputs in the estimate, we take the values of the octet matrix elements according to the NRQCD scaling rules, and as a result, we have found that the contributions to the PP-wave production may be the same in order of magnitude as those from the color-singlet ones, ∣(cbˉ)1(1P1)>|(c\bar b)_{\bf 1}(^{1}P_{1})> and ∣(cbˉ)1(3PJ)>|(c\bar b)_{\bf 1}(^{3}P_{J})> (J=1,2,3J=1,2,3). Especially, our result indicates that the observation of the color-octet contributions to the PP-wave production in the low transverse momentum region is not very far from the present experimental capability at Tevatron and LHC.Comment: 14 pages, 4 figures (8 eps-files for figures), add references and correct typo
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