Theoretical status of the B_c meson
Theoretical predictions on the $B_c$ meson properties are reviewed.
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arXiv subjects
V. V. Kiselev
Publications and source records attributed to V. V. Kiselev.
Model for two generations of fermions
In the model with the spontaneous breaking of chiral gauge symmetry, the vacuum structure for the pair of Higgs fields can provide the introduction of two generations of fermions. The mixing matrix of charged currents is determined.
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Nonabelian Nature of Asymmetry for the $B_c$ Meson Production in Gluon-Photon Interaction
Calculations of cross-sections for the gluon-photon production of $B_c$ and $B_c^*$ mesons as well as for the production in $ep$-interactions at HERA are performed in the leading order of perturbative QCD. We show that the nonabelian structure of QCD leads to an essential forward-backward asymmetry in these processes.
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Perturbative Fragmentation of Leptoquark into Heavy Lepto-Quarkonium
The fragmentation function of a scalar leptoquark into possible S-wave bound states with a heavy anti-quark is calculated to the leading order in perturbative QCD for the high energy processes at large transverse momenta. The one-loop equations for the $q^2$-evolution of moments of the fragmentation function due to the hard gluon emission by the leptoquark are derived. The integral probabilities of fragmentation are evaluated.
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Doubly Charmed Baryon Production in Hadronic Experiments
In the leading order of perturbative QCD one calculates the total and differential cross-sections for the hadronic production of doubly charmed baryons $Ξ_{cc}$ and $Ξ_{cc}^*$ in different experiments. The experimental evaluation of cross-sections for the $J/Ψ+D + \bar D$ production would allow one to decrease the uncertainty in the determination of cross-sections for the doubly charmed baryons due to the choice of $α_s$ and $m_c$. One shows that in the HERA-B and E781 experiments with fixed tagets the suppression of the $Ξ_{cc}$ and $Ξ_{cc}^*$ production to the yield of $c \bar c$-pairs is the value of the order of $10^{-6}-10^{-5}$, whereas at the TEVATRON and LHC colliders it is about $10^{-4}-10^{-3}$. In the E781 experiment the observation of $Ξ_{cc}$ and $Ξ_{cc}^*$ is practically unpossible. At the HERA-B and TEVATRON facilities one can expect $10^5$ events with the double charm, and at LHC one has about $10^9$ ones.
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$B_c$ Meson at LHC
In the framework of perturbative QCD and potential models of heavy quarkonium, total cross-sections and differential characteristics of hadronic production for different spin states of the $B_c$-meson family are calculated at energies of LHC. Theoretical predictions for masses and branching ratios of $B_c$ decays are given, which allows one to make estimates for an expected number of reconstructed events with $B_c$.
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Estimate of $α_s(m_Z)$ in sum rules for bottomonium
The value of $α_s(m_Z)=0.106\pm 0.005$ is obtained in a scheme of sum rules for the leptonic constants of the vector $nS$-levels in the heavy $(\bar b b)$-quarkonium.
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Decay of $B_c^{*+}(3S) \to B^+D^0$
The decay constant for the vector state of $3S$-level in the heavy $(\bar b c)$-quarkonium is evaluated in the framework of sum rules for the mesonic currents. A scaling relation for the constants of vector quarkonia with different quark contents is derived. The numerical estime gives $Γ(B_c^{*+}(3S)\to B^+D^0)=90 \pm 35$ MeV.
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Hadronic production of heavy mesons in perturbative QCD
In the framework of perturbative QCD in the fourth order over the $α_s$ coupling constant for the production of two pairs of quarks and in the model of weak binding of the quarks into meson, the analysis of the hadronic production of mesons, containing $b$-quark, is performed, and a minimal transverse momentum is determined, so that at the momenta greater than the found one, the meson differential spectrum can be reliably described in the model of factorization of the hard $b$-quark production and the subsequent fragmentation into the mesons. At low transverse momenta of the meson, nonfragmentational contributions are essential. They are determined by the complete set of QCD diagrams in the given order over $α_s$, so that the latters result in the effect of destructive interference with the diagrams of fragmentation at $z=2E/\sqrt{s}$ close to $1$.
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f_B^{stat} and μ_π^2 in quasiclassical approximation of sum rules
In the framework of sum rules with a use of quarkonium mass spectrum, evaluated in the quasiclassical approximation, estimates of leptonic constant $f_B^{stat}\simeq 320\pm 60$ MeV in a static limit and for the average heavy quark momentum squared $μ_π^2 \simeq 0.5\pm 0.1$ GeV$^2$ are obtained.
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Heavy quark-meson mass gap from spectroscopy
Using a quite accurate flavour-independence of $nS$-level mass differences in heavy quarkonia and a corresponding quasiclassical expression for the heavy quark binding energy, one shows that experimental data on masses of mesons with heavy quarks allow one to make the estimate $\bar Λ= 0.63\pm 0.03$ GeV.
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Hadronic production of S- and P-wave states of (b-bar c)-quarkonium
In the leading $O(α_s^4)$ order of the perturbative QCD, the hadronic production cross-sections of $S$- and $P$-wave states of $B_c$ meson are calculated. The results for the $S$-wave levels are compared with the values given in other papers as well as in the model of the $b$ quark fragmenatation into $B_c$. In the given order, the cross-sections of the hadronic production of the $P$-wave states are calculated for the first time. Their contribution into the $B_c$ meson production is less than 10\%. There is a strong difference between the predictions of the fragmentation model and the exact perturbative calculations. These difeerences are discussed in details for the differential distributions over various kinematical quantities.
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Photonic production of P-wave states of B_c mesons
Numerical calculations for the production of $P$-wave levels of $B_c$ quarkonium in $γγ$ collisions are performed in the leading $O(α_s^2α_{em}^2)$ order of perturbation theory. The total cross-section of $P$-wave state production is about 10 \% of that for the $S$-wave levels. The contribution of fragmentation component ($6+6$ diagrams) is low, and the basic contribution is determined by the recombination mechanism ($8$ Feynman diagrams). The gauge invariant term of the $\bar b\to B_c$ fragmentation ($6$ diagrams) quite accurately reproduces the result of the fragmentation model, whereas there is a strong deviation of the $c\to B_c$ fragmentation term from the predictions of the fragmentation model.
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Hadronic production of baryons, containing two heavy quarks
In the framework of QCD perturbation theory, total and differential cross sections of the $Ξ_{bc}'$, $Ξ_{bc}^{(*)}$ and $Ξ_{cc}^{(*)}$ baryons production in gluon collisions are calculated in the leading order over $α_s$ for the doubly heavy ($b c$) and ($ c c$) diquarks. At both small and large transverse momenta of the baryons, a use of the mechanism of the heavy quark fragmentation into the heavy diquark is shown to underestimate the cross section values in comparison with the exact numerical calculations of complete set of diagrams. The expected in Tevatron experiments yield of baryons with two heavy quarks is evaluated as $(1.3\pm 0.3) \cdot 10^5 \,\, bcq$-baryons and $(1.6\pm 0.3) \cdot 10^4 \,\, ccq$-baryons at $p_T>5$ GeV and $|y|<1$ of the baryon momentum and rapidity cuts, with account for the antiparticle yields.
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Hidden scale dependence in renormalon
In the framework of renormalon consideration, a role of the anomalous dependence of gluon propagator on the scale $μ$ is shown for a large number of quark flavours as well as in the nonabelian theory, where the parameter of the "running" coupling constant evolution has a hidden dependence on the scale. A phenomenological matching between the modified renormalon and the static quark potential is described to fix the renormalon scales.
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Hard-soft factorization in B_c--> psi pi decay
The width of $B_c^+\to ψπ^+$ decay is calculated in the framework of factorization of a hard gluon exchange and a soft binding of quarks in the heavy quarkonium, so that ${\rm BR}(B_c^+\to ψπ^+) = 2.0\pm 0.5$ \%.
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Modified renormalon
In the framework of renormalon consideration in the approximation of a large number of quark flavours, a role of the anomalous dependence of gluon propagator on the scale $μ$ is shown.
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Physics of B_c mesons
In the framework of potential models for heavy quarkonium the mass spectrum for the system ($\bar b c$) is considered. Spin-dependent splittings, taking into account a change of a constant for effective coulomb interaction between the quarks, and widths of radiative transitions between the ($\bar b c$) levels are calculated. In the framework of QCD sum rules, masses of the lightest vector $B_c^*$ and pseudoscalar $B_c$ states are estimated, scaling relation for leptonic constants of heavy quarkonia is derived, and the leptonic constant $f_{B_c}$ is evaluated. The $B_c$ decays are considered in the framework of both the potential models and the QCD sum rules, where the significance of Coulomb-like corrections is shown. The relations, following from the approximate spin symmetry for the heavy quarks in the heavy quarkonium, are analysed for the form factors of the semileptonic weak exclusive decays of $B_c$. The $B_c$ lifetime is evaluated with the account of the corrections to the spectator mechanism of the decay, because of the quark binding into the meson. The total and differential cross sections of the $B_c$ production in different interactions are calculated. The analytic expressions for the fragmentational production cross sections of $B_c$ are derived. The possibility of the practical $B_c$ search in the current and future experiments at electron-positron and hadron colliders is analysed.
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