Baryon Mass Differences Research Articles

Comment on “Lattice determination ofΣ−Λmixing”

A recent lattice QCD (LQCD) calculation of $\mathrm{\ensuremath{\Sigma}}\text{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}$ mixing by the QCDSF-UKQCD Collaboration [Phys. Rev. D 91, 074512 (2015)] finds a mixing angle about half of that found from the Dalitz--Von Hippel (DvH) flavor SU(3) mass formula which relates the $\mathrm{\ensuremath{\Sigma}}\text{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}$ mixing matrix element to known octet baryon mass differences and which has been used widely to evaluate charge symmetry breaking effects in $\mathrm{\ensuremath{\Lambda}}$ hypernuclei. We show that the LQCD-calculated $\mathrm{\ensuremath{\Sigma}}\text{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}$ mixing matrix element and octet baryon masses satisfy the DvH mass formula, concluding thereby that a good LQCD evaluation of $\mathrm{\ensuremath{\Sigma}}\text{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}$ mixing requires an equally good reproduction of octet baryon mass differences which is yet to be demonstrated.

Baryon magnetic moments in large-Ncchiral perturbation theory

The baryon magnetic and transition magnetic moments are computed in heavy baryon chiral perturbation theory in the large-N_c limit, where N_c is the number of colors. One-loop nonanalytic corrections of orders m_q^{1/2} and m_q ln m_q are incorporated into the analysis, where contributions of both intermediate octet and decuplet baryon states are explicitly included. Expressions are obtained in the limit of vanishing baryon mass differences and compared with the current experimental data. Furthermore, a comparison with conventional heavy baryon chiral perturbation theory is carried out for three light quarks flavors and at the physical value N_c=3.

Lambda-Sigma Mixing Induced by Condensed Pions in Dense Matter

It has been expected that there appear various hadron phases in dense nuclear matter, such as pion condensation, K condensation, admixture of hyperons and so on. These phases provide us of more excitements in studying nuclear matter under low-temperature high-density extreme conditions. In many of preceding works, each of these phases has been considered separately. Towards an unified understanding of dense matter, we investigate the coexisting phase of hyperon admixture and pion condensation, which have different mechanisms in energy gain. In hyperonic matter, condensed pions would mix Λ with Σ baryons coherently through the ΛΣπ coupling. Recently, this coherent ΛΣ coupling has been applied to solve the long standing problem – consistent understanding of Λ separation energy of three-, four-, and five-body hypernuclei .1) If this coherent coupling is induced by OPEP, it would be equivalent to the pion condensation through the p-wave ΛΣπ coupling. We have included the S = 0,−1 octet and decouplet baryons into the traditional treatment of pion condensation.2) In addition to the p-wave BBπ couplings, we have included the short range repulsion in the form of the Landau-Migdal interaction with a universal parameter g′ = 0.6. The FD ratio parameter for hyperons is selected to be F/(F + D) = 0.35. The left panel of Fig. 1 shows the energy per baryon under charged pion condensation in dense neutral matter. First, we consider those cases without decouplet resonance contributions. At low densities, the energy is lower without hyperons because of the mass difference of nucleons and hyperons. However, at higher densities, hyperon mixed matter becomes more favorable due to the large nucleon Fermi energy and ΛΣπ coupling, and hyperon admixture in the pion condensed phase would emerge. Next, we include the effects of decouplet baryon resonances with S = 0,−1, ∆(1232) and Σ∗(1385). The coupling constants of BB∗π and B∗B∗π are estimated by using the SU(6) quark model. The octet-decouplet couplings in the S = 0 and −1 baryons are given as fN∆π/fNNπ = √ 72/5, fΛΣ∗π/fNNπ = √ 36/5, and fΣΣ∗π/fNNπ = √ 12/5, respectively. In spite of large mass differences of octet and decouplet baryons, the effects of resonance baryons are very large due to these large BB∗π couplings. Especially, since the coupling of N∆π is very large, it generates large energy gain. Although there is also a large energy gain in hyperon mixed matter from ΛΣ∗π coupling, it is smaller than that from N∆π coupling and hyperons cannot appear even at very high densities.

Fields and States of Hadrons Extended in the Microscopic Finslerian Space-Time

From a consideration of extended hadron structure in the microlocal anisotropic space-time, the mesonic and baryonic states with their internal quantum numbers such as strangeness, hypercharge, baryon number are constructed. The SU 3 baryonic multiplets of baryons with spin (j + $${\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}$$ )ħ are generated from the SU 3 mesonic multiplets of mesons with spin jħ. The meson–baryon mass differences are also derived here. The composite particle field of hadrons for the macroscopic space-time are obtained. In particular, the meson field and one particle meson state are considered here. These one particle hadron states of the macroscopic space-time also possess the quantum numbers (strangeness, hypercharge, etc.) which are regarded as the manifestations of the anisotropic nature of the microlocal space-time. The composite fields constructed here are usable in the reduction formulae of the S-matrix approach for strong interaction.

Baryon masses at second order in chiral perturbation theory

We analyze the octet baryon mass differences up to second order in chiral perturbation theory, including the effects of decupletintermediate states. We show that the Coleman-Glashow relation has computable corrections of order ( m m − m u ) m s . Thesecorrections are numerically small, and in agreement with the data. We also show that corrections to the Σ equal-spacing rule aredominated by electromagnetic contributions, and that the Gell-Mann-Okubo formula has non-analytic corrections of order m s 2In m s which cannot be computed from known matrix elements. We also show that the baryon masses cannot be used to extractmodel-independent information about the current quark masses.

Breathing mode quantization in an extended SU (3) Skyrme model

Extending the SU (3) Skyrme model of pseudoscalars by adding a massive scalar field improves the predictions for the baryon mass differences when the breathing mode is quantized. The magnetic moments and g a g v ratios of semileptonic hyperon decays are only mildly affected by this additional scalar field. Despite the baryon wavefunctions deviating strongly from SU (3) symmetry the g a g v ratios are compatible with the SU (3) relations.

Photon-cloud effects on isomultiplet mass differences of charmed and uncharmed baryons

Isomultiplet mass differences of ${(1/2}^{+}$ and ${(3/2}^{+}$ baryons are studied in the constituent-quark model. We find that the mass differences of octet and decuplet baryons can be explained well in the presence of photon-cloud contributions. In the charmed sector, only the ${\ensuremath{\Sigma}}_{c}^{0}$-${\ensuremath{\Sigma}}_{c}^{++}$ mass difference has recently been measured. By including the photon-cloud effects, we obtain a negative sign of the ${\ensuremath{\Sigma}}_{c}^{0}$-${\ensuremath{\Sigma}}_{c}^{++}$ mass difference.

Scalar densities and baryon mass differences in lattice QCD with Wilson fermions

We compute the normalization constant and the proton matrix elements of the scalar quark densities on a 10 3 × 20 lattice, at β = 6.0, in the quenched approximation and for three values of the Wilson parameter: K = 0.1515, 0.1530, 0.1545. The normalization constant is in agreement with a new Ward identity derived in this paper. In terms of the usual D and F terms of the baryon octet mass differences, we find D F = −0.4 ± 0.2 , in agreement with the experimental value ( D F ) exp = −0.3 . We observe that D F decreases in absolute value for large quark mass, as suggested by the constituent quark model. Using a previous lattice determination of quark masses, we find M Ξ − M p = 210 ± 60 MeV, to be compared with the measured value ( Ξ − m p = 380 MeV. We also determine the nucleon σ-term to be σ = 15 ± 4 MeV.

Isospin violating mass differences of baryons and hadronic loops

Isospin violating mass splittings of the ground state baryons are discussed within the frame-work of the unitarized quark model. It is shown that the long-distance, nonperturbative unitarity effects are important, and that a good agreement with the observed mass splittings can be retained. The importance of six mass sum rules which hold independently of dynamical assumptions is emphasized.

Quartic confinement, QCD and the nucleon-nucleon interaction

We show that even the quartic qq-potential, the only one that does not imply color Van der Waals forces, fails to produce the attractive intermediate range NN S-state central potential if the parameters are fixed from baryon mass differences.

Baryon masses from deep-inelastic scattering

Nucleon quark wave functions deduced from deep-inelastic scattering are used to calculate baryon mass differences. The Hamiltonian used has a relativistic kinetic-energy operator and spin-dependent two-body oscillator potentials that break SU(6) strongly. With all parameters determined by deep-inelastic scattering fits, the $\ensuremath{\Delta}(1236)\ensuremath{-}N(939)$ mass difference is calculated in good agreement with experiment. The calculation is extended to the low-lying hyperons by introducing a strange-quark mass, fit to the ${\ensuremath{\Omega}}^{\ensuremath{-}}$. Using an SU(3)-breaking spin-spin force determined by the ${\ensuremath{\Lambda}}^{0}$ magnetic moment (as suggested by quantum chromodynamics), good agreement is found for all low-lying baryon masses.

Chiral-symmetry breaking, the Dashen mass formula, and the decayη→3π

The recently proposed extended partially conserved axial-vector current (EPCAC) hypothesis is used in order to obtain the chiral-SU(3) x SU(3) -symmetry-breaking corrections to (a) the Dashen mass formula, (b) the soft-meson theorem relevant to the eta ..-->.. 3..pi.. decay, and (c) the ..delta..I = 1 baryon mass differences. It is found that the EPCAC hypothesis together with current algebra and an epsilon/sub 3/u/sub 3/ term in the chiral Hamiltonian provides a working explanation for the eta ..-->.. 3..pi.. puzzle in the framework of the (3,3*) + (3*,3) model.

Electromagnetic properties of charmed hadrons

The electromagnetic properties of charmed hadrons are discussed in the framework ofSU6 ⊗Uc. Magnetic moments and mass differences between variousI-spin multiplets have been calculated both for baryons and mesons. Our results are consistent with those obtained by other authors with different methods. It is shown indeed that electromagnetic mass differences of uncharmed baryons are in very good agreement with the theory. As to the mesons we find satisfactory results for the D+-D0 mass difference, while the calculated D*+-D*0 mass difference is far from the experimental one.

Hadron and quark mass differences

An estimate D/sup +/ - D/sup 0/ approx. = 5 MeV is made on the basis of a phenomenological quark model in which baryon mass differences are fitted exactly and simple corrections are made for the looser structure of bosons. The other boson fits are satisfactory except for predicting rho/sup +/ - rho/sup 0/ approx. = 0.3 MeV. An incidental quark mass difference is obtained: m/sub d/ - m/sub u/ approx. = 10 MeV from sources other than ordinary QED. It is suggested that weak interactions with the heavy charmed quark are responsible, so that ((m/sub d/ - m/sub u/)/(m/sub s/ - m/sub u/))/sup 1///sup 2/ approx. = theta/sub C/, the Cabibbo angle.

Baryon mass differences in a hybrid gauge model of strong and electromagnetic interactions

We calculate all the baryon mass differences in the single-loop approximation in a gauge model of strong and electromagnetic interactions. The model is a hybrid version of the Georgi-Goldman model. We obtain good agreement with experimental values.

Sum Rules for Mass Differences Within the Baryon Decuplet and the Meson Nonets

A group-theoretic approach, previously used to derive a precise hybrid formula relating electromagnetic mass differences of pseudoscalar mesons and baryons, is extended here to the barycn decuplet and the vector- and tensor-meson nonets. We derive three sum rules relating mass differences within isotopic-spin multiplets of the decuplet, as well as a hybrid formula relating baryon-octet and -decuplet electromagnetic mass differences. Using the present experimental average for the Ξ*−−Ξ*0 mass difference, the hybrid formula can be used to predict MY−−MY+=3.2±0.5 MeV, MΔ0−MΔ+=−0.24±0.16 MeV, and MΔ++−MΔ−=0.72±0.48 MeV. No assumptions concerning U-spin symmetry are required in obtaining these results. With the 27-dimensional part of the SU(2)-breaking interaction taken to be a U-spin singlet, two additional predictions follow: MY−−MY0=3.4±0.6 MeV and MΔ++−MΔ+=3.9±0.9 MeV. Hybrid mass formulas are also derived for meson nonets. Using the present experimental average for the K*0−K*+ mass difference, we predict the neutral ρ meson to be heavier than its charged counterparts by approximately 5 ± 2 MeV.

Precise Hybrid Formula for Electromagnetic Mass Differences

We present the derivation of a mass formula which relates electromagnetic mass differences of baryons and pseudoscalar mesons and is experimentally accurate within \ensuremath{\sim} 2%. The derivation reveals that the new formula is the appropriate hybrid analog to the Coleman-Glashow formula.

Deep-Inelastic Scattering, the Subtraction of Divergent Sum Rules, and Chiral-Symmetry Breaking in the Gluon Model

The formal light-cone properties of commutators involving current divergences are studied in the gluon model. Relations are derived which make it possible (in principle) to distinguish the vector- from the (pseudo) scalar-gluon model. In the vector-gluon model these relations provide an experimental determination of the bare quark masses. The additional assumption that the residues of any $\ensuremath{\alpha}=0$ fixed poles in current scattering amplitudes are polynomials in ${q}^{2}$ makes it possible to relate the $\ensuremath{\sigma}$ term in pion-nucleon scattering to convergent integrals over neutrino-scattering structure functions; the polynomial assumption dictates a prescription for subtracting a (linearly) divergent sum rule derived previously. The same technique generates subtracted sum rules for the (neutrino- and spin-dependent) structure functions ${W}_{3}$ and ${G}_{2}$. With the parton-model assumption that the leading scaling behavior of current-divergence and divergence-divergence scattering is given by free-field theory, it is possible to relate fixed-pole residues in $\mathrm{ep}$, $\mathrm{en}$, $\ensuremath{\nu}p$, and $\ensuremath{\nu}n$ scattering, deep-inelastic data, the $\ensuremath{\sigma}$ term, baryon mass differences, and the bare quark masses; approximate values for the bare quark masses and the parameter ${\ensuremath{\mu}}_{0}$ can be obtained.

Baryon Mass Differences in a Gauge Model of Strong and Electromagnetic Interactions

Baryon Mass Differences in a Gauge Model of Strong and Electromagnetic Interactions

Duality and nonlinear SU 3

Dual ideas when applied to the algebraic realisation of nonlinear unitary symmetry predict the F/D ratio for the helicity non-flip A 2BB̄ vertex, and relate a ratio of meson and baryon mass differences to experimental total cross-sections.