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Register a new userMass inequalities for baryons with heavy quarks
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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.
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We discuss the mass differences for isospin multiplets of the charmed and b-flavored baryons. The mass of the neutral b-flavored sigma baryon, which is not measured, is calculated. We point out, that the measurements of the mass differences between the charmed sigma and chi baryons might be wrong.
In this work, we compute masses and magnetic moments of the heavy baryons and tetraquarks with one and two open heavy flavors in a unified framework of MIT bag model. Using the parameters of MIT bag model, we confirm that an extra binding energy, which is supposed to exist between heavy quarks ($c$ and $b$) and between heavy and strange quarks in literatures, is required to reconcile light hadrons with heavy hadrons. Numerical calculations are made for all light mesons, heavy hadrons with one and two open heavy flavors, predicting the mass of doubly charmed baryons to be $M(Xi _{cc})=3.604$ GeV, $M(Xi _{cc}^{ast })=3.714$ GeV, and that of the strange isosinglet tetraquark $udbar{s}bar{c}$ with $J^{P}=0^{+}$ to be $Mleft( udbar{s}bar{c},0^{+}right) =2.934$ GeV. The state mixing due to chromomagnetic interaction is shown to be sizable for the strange scalar tetraquark $nnbar{s}bar{c}$.
We study the isospin mass differences of singly heavy baryons, based on a pion mean-field approach. We consider both the electromagnetic interactions and the hadronic contributions that arise from the mass difference of the up and down quarks. The relevant parameters have been already fixed by the baryon octet. In addition, we introduce the strong hyperfine interactions between the light quarks inside a chiral soliton and the Coulomb interactions between the chiral soliton and a heavy quark. The numerical results are in good agreement with the experimental data. In particular, the results for the neutral mass relations, which contain only the electromagnetic contributions, are in remarkable agreement with the data, which implies that the pion mean field approach provides a good description of the singly heavy baryons.
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