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Abstract
We extract directly (for the first time) the charmed (C=1) and bottom (B=−1) heavy-baryons (spin 1/2 and 3/2) mass-splittings due to SU(3) breaking using double ratios of QCD spectral sum rules (QSSR) in full QCD, which are less sensitive to the exact value and definition of the heavy quark mass, to the perturbative radiative corrections and to the QCD continuum contributions than the simple ratios commonly used for determining the heavy baryon masses. Noticing that most of the mass-splittings are mainly controlled by the ratio κ≡〈s¯s〉/〈d¯d〉 of the condensate, we extract this ratio, by allowing 1σ deviation from the observed masses of the Ξc,b and of the Ωc. We obtain: κ=0.74(3), which improves the existing estimates: κ=0.70(10) from light hadrons. Using this value, we deduce MΩb=6078.5(27.4) MeV which agrees with the recent CDF data but disagrees by 2.4σ with the one from D0. Predictions of the ΞQ′ and of the spectra of spin 3/2 baryons containing one or two strange quark are given in Table 2. Predictions of the hyperfine splittings ΩQ∗−ΩQ and ΞQ∗−ΞQ are also given in Table 3. Starting for a general choice of the interpolating currents for the spin 1/2 baryons, our analysis favours the optimal value of the mixing angle b≃(−1/5–0) found from light and non-strange heavy baryons.
Highlights
QCD spectral sum rules (QSSR) [1,2] `a la SVZ [3] has been used earlier in full QCD [4,5,6] and in HQET [7] for understanding heavy baryons [charmed, bottom, double charm, double bottom and] masses
The inaccuracy of these results is mainly due to the value of the heavy quark mass and of its ambiguous definition when working to lowest order (LO) in the radiative αs corrections in full QCD and HQET 1, where the heavy quark mass is the main driving term in the QCD expression of the baryon two-point correlator used in the QSSR analysis
We shall concentrate on the analysis of the heavy baryons mass-splittings due to SU (3) breaking using double ratios (DR) of QCD spectral sum rules (QSSR), which are less sensitive to the exact value and definition of the heavy quark mass and to the QCD continuum contributions than the simple ratios used in the literature to determine the absolute value of heavy baryon masses
Summary
QSSR [1,2] `a la SVZ [3] has been used earlier in full QCD [4,5,6] and in HQET [7] for understanding heavy baryons [charmed (cqq), bottom (bqq), double charm (ccq), double bottom (bbq) and (bcq)] masses. QSSR results are in quite good agreement with recent experimental findings but with relatively large uncertainties The inaccuracy of these results is mainly due to the value of the heavy quark mass and of its ambiguous definition when working to lowest order (LO) in the radiative αs corrections in full QCD and HQET 1, where the heavy quark mass is the main driving term in the QCD expression of the baryon two-point correlator used in the QSSR analysis. Another source of uncertainty is the effect of the QCD continuum which parametrizes the higher baryon masses contributions to the spectral function and the ad hoc choices of interpolating baryon currents used in different literatures. We have checked the existing results in [5] obtained in the chiral and SU (2) limits and agree with these ones
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