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Register a new userThe mass spectra and wave functions for the doubly heavy baryons with $J^P=1^+$ heavy diquark core
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The mass spectra and wave functions for the doubly heavy baryons are computed under the picture that the two heavy quarks inside a doubly heavy baryon, such as two $c$-quarks in $Xi_{cc}$, combine into a heavy `diquark core in color anti-triplet firstly, then the diquark core turns into a color-less doubly heavy baryon via combining the light $q$-quark inside the baryon. Namely both of the combinations, the two heavy quarks inside the baryon into a diquark core in color anti-triplet and the heavy diquark core with the light quark into the baryon, are depicted by relativistic Bethe-Salpeter equations (BSEs) with an accordingly QCD inspired kernel respectively, although in the paper only the heavy diquark cores with the quantum numbers $J^P=1^+$ are considered. Since the `second combination is of the heavy diquark core and the light quark, so the structure effect of the diquark core to the relevant kernel of the BSE is specially considered in terms of the diquark-core wave functions. The mass spectra and wave functions for the `low-laying doubly heavy baryons in the flavors $(ccq)$, $(bcq)$ and $(bbq)$ and in the quantum numbers $J^P=frac{1}{2}^+$, $J^P=frac{3}{2}^+$, achieved by solving the equations under the so-called instantaneous approximation, are presented properly and some comparisons with the others results under different approaches in the literature are made.
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We construct a leading-order effective field theory for both scalar and axial-vector heavy diquarks, and consider its power expansion in the heavy diquark limit. By assuming the transition from QCD to diquark effective theory, we derive the most general form for the effective diquark transition currents based on the heavy diquark symmetry. The short-distance coefficients between QCD and heavy diquark effective field theory are also obtained by a tree level matching. With the effective currents in the heavy diquark limit, we perform a reduction of the form factors for semi-leptonic decays of doubly heavy baryons, and find that only one nonperturbative function is remaining. It is shown that this soft function can be related to the Isgur-Wise function in heavy meson transitions. As a phenomenological application, we take a single pole structure for the reduced form factor, and use it to calculate the semi-leptonic decay widths of doubly heavy baryons. The obtained results are consistent with others given in the literature, and can be tested in the future.
The excitation energy spectra are investigated by using diquark models in order to discuss the possibility of the existence of the diquark as a constituent of the single heavy baryons. We consider two diquark models in which the diquark is treated as a constituent of baryons together with a heavy baryon. In model A the diquark is a point-like particle, while it is a spatially extended object in model B. We determine the masses of scalar and axial vector diquarks by the ground state masses of the charmed baryons. We find that both models reproduce well the excitation energy spectra of the charmed and bottomed baryons, whereas the string tension of the confinement potential in model A should be a half of that of the charmonium and Model B overestimates the 2s excitation energy.
The radiative decays of the p-wave charmed heavy baryons to the ground state baryon states are studied in the framework of the light cone QCD sum rules method. Firstly, the transition form factors that describe these transitions are estimated, and then using these form factors the corresponding decay widths are calculated. A comparison of our results on the decay widths with those predicted by the other approaches existing in literature is performed.
Baryons with one or more heavy quarks have been shown, in the context of a nonrelativistic description, to exhibit mass inequalities under permutations of their quarks, when spin averages are taken. These inequalities sometimes are invalidated when spin-dependent forces are taken into account. A notable instance is the inequality $2E(Mmm) > E(MMm) + E(mmm)$, where $m = m_u = m_d$, satisfied for $M = m_b$ or $M = m_c$ but not for $M = m_s$, unless care is taken to remove effects of spin-spin interactions. Thus in the quark-level analog of nuclear fusion, the reactions $Lambda_b Lambda_b to Xi_{bb}N$ and $Lambda_c Lambda_c to Xi_{cc}^{++}n$ are exothermic, releasing respectively 138 and 12 MeV, while $Lambda Lambda to Xi N$ is endothermic, requiring an input of between 23 and 29 MeV. Here we explore such mass inequalities in the context of an approach, previously shown to predict masses successfully, in which contributions consist of additive constituent-quark masses, spin-spin interactions, and additional binding terms for pairs each member of which is at least as heavy as a strange quark.
In this paper we present in greater detail previous work on the Born-Oppenheimer approximation to treat the hydrogen bond of QCD, and add a similar treatment of doubly heavy baryons. Doubly heavy exotic resonances X and Z can be described as color molecules of two-quark lumps, the analogue of the H_2 molecule, and doubly heavy baryons as the analog of the H_2^+ ion, except that the two heavy quarks attract each other. We compare our results with constituent quark model and lattice QCD calculations and find further evidence in support of this upgraded picture of compact tetraquarks and baryons.
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