Harald Fritzsch
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.
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The electromagnetic form factors of the exotic baryons are calculated in the framework of the relativistic quark model at small and intermediate momentum transfer. The charge radii of the E+++ baryons are determined.
The relativistic interacting quark-diquark model of baryons, recently developed, is here extended to introduce a spin-isospin transition interaction into the mass operator. The refined version of the model is used to calculate the non strange baryon spectrum. The results are compared to the present experimental data.
We study the phases of a two-flavor Nambu-Jona-Lasinio model at finite temperature $T$, baryon and isospin chemical potentials: $μ_{B}=(μ_{u}+μ_{d})/2$, $μ_{I}=(μ_{u}-μ_{d})/2$. This study completes a previous analysis where only small isospin chemical potentials $μ_{I}$ were considered
Isospin sum rules in charmed baryon weak decays
本文利用粲夸克弱衰变有效哈密顿量在同位旋降算符下为零的性质，推导单粲与双粲重子两体、三体非轻子衰变的数百条同位旋求和规则，用于检验对称性、寻找新衰变模式及研究奇特强子。
The relativistic five-quark equations are found in the framework of the dispersion relation technique.The five-quark amplitudes for the low-lying exotic baryons including the up and down quarks are calculated.The poles of the five-quark amplitudes determine the masses and the widths of nonstrange exotic baryons(isospin I=5/2). The mass spectrum of the E+++ exotic baryons with JP=1/2+,3/2+, 5/2+ is calculated.
We estimate the isospin breaking contributions to the baryon masses which we analyzed recently using a loop expansion in the heavy baryon approximation to chiral effective field theory. To one loop, the isospin breaking corrections come from the effects of the $d, u$ quark mass difference, the Coulomb and magnetic moment interactions, and effective point interactions attributable to color-magnetic effects. The addition of the first meson loop corrections introduces new structure. We estimate the resulting low-energy, long-range contributions to the mass splittings by regularizing the loop inte…
Baryon mass splittings are analyzed in terms of a simple model with general pairwise interactions. At present, the $Δ$ masses are poorly known from experiments. Improvement of these data would provide an opportunity to make a significant test of our understanding of electromagnetic and quark-mass contributions to hadronic masses. The problem of determining resonance masses from scattering and production data is discussed.
Within the QCD sum-rule approach in an external field, we calculate the baryon matrix element of isovector-scalar current, $H_{\rm B}=\langle B|\overline{u}u- \overline{d}d|B\rangle/2M_{\rm B}$, for octet baryons, which appears in the response of the correlator of baryon interpolating fields to a constant isovector-scalar external field. The sum rules are obtained for a general baryon interpolating field with an appropriate form for the phenomenological ansatz of the spectral density. The key phenomenological input is the response of the quark condensates to the external field. To first order …
Data driven isospin analysis of timelike octet baryons electromagnetic form factors and charmonium decay into baryon-anti-baryon
本文提出一种模型无关的数据驱动同位旋分析方法，利用不同同位旋通道的振荡相位差约束同位旋标量与矢量分量的相对相位，并应用于类时八重态重子电磁形状因子及粲偶素衰变至重子-反重子过程。
The current concepts of isospin and baryon mass groups are only well-adapted to deal with baryon multiplets involving both the u and d quarks, and some other quark k. In this paper, we generalize isospin and mass groups to accommodate baryon multiplets involving quarks of any flavor, and the Gell-Mann--Okubo (GMO) formalism is generalized accordingly. Generalized isospin proves to be a simple and valuable framework when working in non-udk baryon multiplets, and provides new quantum numbers that allows us to distinguish $Λ$-like baryons from $Σ$-like baryons in the non-udk multiplets. The gener…
The properties of the two-flavored Gross-Neveu model in the (1+1)-dimensional spacetime are investigated in the presence of the isospin $μ_I$ as well as quark number $μ$ chemical potentials both at zero and nonzero temperatures. The consideration is performed in the limit $N_c\to\infty$, i.e. in the case with an infinite number of colored quarks. In the plane of parameters $μ_I,μ$ a rather rich phase structure is found, which contains phases with and without pion condensation. Moreover, we have found a great variety of one-quark excitations of these phases, including gapless and gapped quasipa…
We construct bi-local interpolating field operators for baryons consisting of three quarks with two flavors, assuming good isospin symmetry. We use the restrictions following from the Pauli principle to derive relations/identities among the baryon operators with identical quantum numbers. Such relations that follow from the combined spatial, Dirac, color, and isospin Fierz transformations may be called the (total/complete) Fierz identities. These relations reduce the number of independent baryon operators with any given spin and isospin. We also study the Abelian and non-Abelian chiral transfo…
Magnetic Moment of Octet Baryons in Isospin Asymmetric Magnetized Strange Matter
结合手征SU(3)夸克平均场模型和手征组分夸克模型，研究强磁场下同位旋不对称奇异强子物质中八重态重子的磁矩，发现狄拉克海效应导致磁催化，重子有效质量随磁场单调增加，真空极化效应在确定重子电磁性质中起关键作用。
In this paper, the electromagnetic mass differences of heavy hadrons are discussed, while ignoring the relevant hyperfine interactions. The effects of one-photon exchange interaction and up-down quark mass difference are parameterized. Two mass difference equations 2Σ_c^+ - (Σ_c^{++} + Σ_c^0) = 2Σ_b^0 - (Σ_b^+ + Σ_b^-) and (Ξ_{cc}^+ - Ξ_{cc}^{++}) + (Ξ_{bb}^- - Ξ_{bb}^{0}) =2(Ξ_{bc}^0 - Ξ_{bc}^{+}) for the heavy baryons are obtained. In addition, the masses of Σ_b^0, Ξ_b^0, and Ξ_{cc}^{++} are predicted based on the known experimental data.
A study of the meson-baryon interaction in the $S=-1$ sector is performed, employing a chiral SU(3) lagrangian up to next-to-leading order (NLO) and implementing unitarization in coupled channels. The model is constrained by a large set of experimental data, paying a especial attention to processes that are sensitive to the NLO contributions, such as the $K^- p\to K^+Ξ^-, K^0Ξ^0$ reactions. The consideration of additional cross sections in single isospin channels, $K^-p\to ηΛ, ηΣ$, has been found to provide more homogeneous and reliable values of the low-energy constants, the stability of whic…
Current measurements of isospin splittings in mesons and baryons are sufficiently precise that they allow estimates of the mass difference between constituent up and down quarks. Some previous results are updated in the light of these new measurements, and the importance of better measurements of some observables such as $M(K^{*\pm})$, $M(B^{*0})-M(B^0)$, and isospin splittings in bottom baryons is noted.
The properties of the two-flavored Gross-Neveu model with nonzero current quark mass are investigated in the (1+1)-dimensional spacetime at finite isospin $μ_I$ as well as quark number $μ$ chemical potentials and zero temperature. The consideration is performed in the limit $N_c\to\infty$, i.e. in the case with an infinite number of colored quarks. In the plane of parameters $μ_I,μ$ a rather rich phase structure is found, which contains phases with and without pion condensation. We have found a great variety of one-quark excitations of these phases, including gapless and gapped quasiparticles.…
Magnetic moments of decuplet baryons in isospin asymmetric magnetized strange matter
在统一手征有效框架下，研究有限温度同位旋不对称磁化奇异物质中十重态重子的介质质量和磁矩，采用手征SU(3)夸克平均场模型和手征组分夸克模型，考虑狄拉克海效应和反常磁矩。
We study the isospin symmetry breaking and mass splittings of the eight lowest-lying baryons. We consider three kinds of baryon mass terms, including the bare mass term, the electromagnetic terms and the spontaneous chiral symmetry breaking terms. We include the mixing term between flavor-octet and flavor-decuplet baryons. This assumes that the lowest-lying Sigma and Xi baryons contain a few decuplet components and so are not purely flavor-octet. We achieve a good fitting that the difference between every fitted mass and its experimental value is less than 0.2 MeV.
Basis light-front quantization approach to $Λ$ and $Λ_c$ and their isospin triplet baryons
本研究采用基矢光前量子化方法，通过含三维禁闭势和单胶子交换的有效哈密顿量，计算了$Λ$、$Λ_c$及其同位旋三重态重子的质量、电磁性质和部分子分布函数，结果与实验、格点QCD等相符。
Medium modification of the magnetic moments of octet baryons in the isospin asymmetric nuclear medium at finite temperature has been calculated using medium modified quark and baryon masses derived in chiral SU(3) quark mean field model. The magnetic moments of baryons are found to vary significantly as a function of density of nuclear medium as well as with the increase in isospin asymmetry of the medium. The rise of temperature is found to decrease the effect of isospin asymmetry on masses and magnetic moments of baryons. The results of present investigation may be helpful to understand the …
The mass splittings of the pseudoscalar and vector D and B light-heavy quark systems have been calculated using the method of QCD sum rules. Electromagnetic, quark mass, and nonperturbative QCD effects are all included. The results are in good agreement with experiment. A measurement of isospin splitting for the vector B mesons would give valuable information about quark mass splittings.
The isospin mass splittings of the pseudoscalar and vector D and B light-heavy quark system have been calculated using the method of QCD sum rules. Nonperturbative QCD effects are shown to be very small, so that mass splittings arise almost completely from current quark mass splitting and electromagnetic effects, for which a new gauge invariant QED treatment is used. The results are consistent with experiment. A measurement of the isospin splitting of the vector B mesons would give valuable information about quark mass splittings.
We discuss the isospin-breaking mass differences among baryons, with particular attention in the charm sector to the $Σ_c^{+}-Σ_c^0$, $Σ_c^{++}-Σ_c^0$, and $Ξ_c^+-Ξ_c^0$ splittings. Simple potential models cannot accommodate the trend of the available data on charm baryons. More precise measurements would offer the possibility of testing how well potential models describe the non-perturbative limit of QCD.
Isospin sum rules for bottom-baryon weak decays
本研究利用底夸克弱衰变有效哈密顿量在同位旋降算符下为零的性质，无需 Wigner-Eckart 不变量即可推导数百条底重子两体及三体非轻子衰变的同位旋求和规则，为新衰变模式和五夸克态同位旋伙伴提供线索。
A recent general analysis of light-baryon isospin splittings is updated and extended to charmed baryons. The measured $Σ_c$ and $Ξ_c$ splittings stand out as being difficult to understand in terms of two-body forces alone. We also discuss heavy-light mesons; though the framework here is necessarily less general, we nevertheless obtain some predictions that are not strongly model-dependent.
We discuss the isospin-breaking mass differences among baryons, with particular attention in the charm sector to the $Σ_c^{+}-Σ_c^0$, $Σ_c^{++}-Σ_c^0$, and $Ξ_c^+-Ξ_c^0$ splittings. Simple potential models cannot accommodate the trend of the available data on charmed baryons. More precise measurements would offer the possibility of testing how well potential models describe the non-perturbative limit of QCD.
In this paper we investigate the phase structure of a (1+1)-dimensional schematic quark model with four-quark interaction and in the presence of baryon ($μ_B$), isospin ($μ_I$) and chiral isospin ($μ_{I5}$) chemical potentials. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one. The role and influence of this property on the phase structure of the model are studied. Moreover, it is shown that the chemical potential $μ_{I5}$ promotes th…
Generation of isospin sum rules in heavy hadron weak decays
提出一种无需Wigner-Eckhart不变量、利用同位旋下降算符生成重强子弱衰变同位旋求和规则的系统方法，并以D和B介子非轻子衰变为例详细阐述，同时推广至V/U自旋求和规则。
We investigate the QCD phase diagram of isospin asymmetric matter using the Polyakov loop extended quark meson (PQM) model with vector interaction. The critical point temperature is found to decrease in isospin asymmetric matter and disappear at large isospin chemical potential. We also discuss the QCD phase transition in the neutron star core. From comparison of the QCD phase diagram in PQM and corresponding baryon and isospin chemical potentials of neutron star matter in relativistic mean field models, we show that the order of the chiral phase transition in the neutron star core could be cr…
In this work we extend our formalism to study meson-baryon interactions by including $s$- and $u$-channel diagrams for pseudoscalar-baryon systems. We study the coupled systems with strangeness $-1$ and focus on studying the isospin-1 resonance(s), especially in the energy region around 1400 MeV. By constraining the model parameters to fit the cross section data available on several processes involving relevant channels, we find resonances in the isoscalar as well as the isovector sector in the energy region around 1400 MeV.
We present a study of the 1+1 flavor system of strongly interacting matter in terms of the Polyakov$-$Nambu$-$Jona-Lasinio model. We find that though the small isospin symmetry breaking brought in through unequal light quark masses is too small to affect the thermodynamics of the system in general, it may have significant effect in baryon-isospin correlations and have a measurable impact in heavy-ion collision experiments.
We calculate the mass splittings within the heavy baryon isospin multiplets Σ_{c(b)} and Ξ_{c(b)}' in chiral perturbation theory to leading one-loop order. The pattern of the mass splittings in the Σ_c iso-triplet, which is different from that of any other known isospin multiplet, can be explained. We predict m_{Ξ_c'^+} - m_{Ξ_c'^0}=-0.2\pm0.6 MeV, m_{Ξ_b'^0} - m_{Ξ_b'^-}=-4.0\pm1.9 MeV and the mass of the Σ_b^0 to be 5810.3\pm1.9 MeV.
The extraction of meson-baryon scattering parameters from lattice QCD is complicated by the necessity, in some channels, of including annihilation diagrams. We consider a strategy to avoid the need for these extremely costly and noisy contributions. The strategy is based on simulations with an isospin chemical potential which, contrary to a baryon chemical potential, has no sign problem. When the isospin chemical potential is larger than a critical value, a charged pion condensate forms. Baryons propagating in the pion condensate will have their masses modified by pion-baryon scattering parame…
We study the posibility of large isospin fluctuations in high-energy heavy-ion collisions by assuming that pions are produced semiclassically both directly and in pairs through the isovector channel. The leading-particle effect and the factorization property of the scattering amplitude in the impact parameter space are used to define the classical pion field. In terms of the joint probability function $P_{II_{3}}(n_{0},n_{\_})$ for producing $n_{0}$ neutral and $n_{\_}$ negative pions from a definite isospin state $II_{3}$ of the incoming leading-particle system we calculate the two pion corre…
We explore the phase diagram of two-flavor QCD at imaginary values of baryon and isospin chemical potentials analyzing the thermodynamic potential of QCD analytically and that of the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model numerically. QCD has no pion condensation at imaginary baryon and isospin chemical potentials, and therefore has discrete symmetries that are not present at real baryon and isospin chemical potentials. The PNJL model possesses all the discrete symmetries. The PNJL model can reproduce qualitatively lattice QCD data presented very lately.
We use the Nambu--Jona-Lasinio model to study the effects of the isospin chemical potential on the QCD phase diagram at nonzero temperature and baryon chemical potential. We find that the phase diagram is qualitatively altered by a small isospin chemical potential. There are two first order phase transitions that end in two critical endpoints, and there are two crossovers at low baryon chemical potential. These results have important consequences for systems where both baryon and isospin chemical potentials are nonzero, such as heavy ion collision experiments. Our results are in complete agree…
This paper has been withdrawn by the author since it is too simple and naive.
We consider charge-symmetry violations in the nucleon-nucleon force which result from isospin-violating meson-baryon coupling constants. The vector mesons are assumed to couple to the nucleon's electromagnetic current, which we decompose into isoscalar and isovector quark components. We compute these currents in the context of a constituent quark model. The isospin violations in the meson-baryon couplings arise from the difference in the up and down constituent quark masses. We show that class IV charge-symmetry-breaking potentials arise in the resulting $ω$ and $ρ$ exchange contributions to t…
Isospin splittings in baryons with two heavy quarks and a $u$ or $d$ quark are calculated using simple methods proposed previously by the authors. The results are $M(Ξ_{cc}^{++})-M(Ξ_{cc}^+) = 1.41 \pm 0.12^{+0.76}$ MeV, $M(Ξ_{bb}^0) - M(Ξ_{bb}^-) = - 4.78 \pm 0.06^{+0.03}$ MeV, and $M(Ξ_{bc}^+)-M(Ξ_{bc}^0)=-1.69 \pm0.07 ^{+0.39}$ MeV, where the statistical errors reflect uncertainties in input mass splittings, and the systematic errors are associated with the choice of constituent-quark masses.
The SELEX Collaboration has reported a very large isospin splitting of doubly charmed baryons. We show that this effect would imply that the doubly charmed baryons are very compact. One intriguing possibility is that such baryons have a linear geometry Q-q-Q where the light quark q oscillates between the two heavy quarks Q, analogous to a linear molecule such as carbon dioxide. However, using conventional arguments, the size of a heavy-light hadron is expected to be around 0.5 fm, much larger than the size needed to explain the observed large isospin splitting. Assuming the distance between tw…
We present initial results of a numerical investigation of the chiral symmetry restoring transition in the (3+1)-dimensional Nambu -- Jona-Lasinio model with both non-zero baryon chemical potential (mu_B) and isospin chemical potential (mu_I). With non-zero isospin chemical potential, the model suffers from a sign problem. We proceed in two ways: (i) We perform ``partially quenched'' simulations in which mu_I is made non-zero only during the measurement of chiral observables; (ii) We perform full simulations with imaginary isospin chemical potential with the aim to analytically continue result…
We study the two-color QCD matter within two fundamental quark flavors via both chiral perturbation theory and Nambu--Jona-Lasinio model methods. The effective Lagrangian described by low lying meson and baryon, i.e., diquark, is derived, where the excitations locate in the extended $\mathrm{SU}(4)$ flavor symmetry space. We determine the leading order terms on the dependence of the baryon and axial isospin densities. Then, the two-color NJL model is employed to run the numerical simulation and the phase diagram in the plane of $μ-ν_{5}$ is plotted.
We study the Kondo effect for a $Σ_{c}$ ($Σ_{c}^{\ast}$) baryon in nuclear matter. In terms of the spin and isospin ($\mathrm{SU}(2)_{\mathrm{spin}} \times \mathrm{SU}(2)_{\mathrm{isospin}}$) symmetry, the heavy-quark spin symmetry and the S-wave interaction, we provide the general form of the Lagrangian for a $Σ_{c}$ ($Σ_{c}^{\ast}$) baryon and a nucleon. We analyze the renormalization equation at the one-loop level, and find that the coexistence of spin exchange and isospin exchange magnifies the Kondo effect in comparison with the case where the spin-exchange interaction and the isospin-exc…
The self-consistent mean field approximation of two-flavor NJL model with introducing a free parameter $α$ to reflect the competition between "direct" channel and the "exchange" channel, is employed to study QCD phase structure at finite isospin chemical potential $μ_I$, finite baryon chemical potential $μ_B$ and finite temperature $T$, especially the location of the QCD critical point. It is found that, for fixed isospin chemical potentials the lower temperature of phase transition is obtained with $α$ increasing in the $T-μ_I$ plane, and the largest difference of the phase transition tempera…
In this paper the phase structure of dense quark matter has been investigated in the presence of baryon, isospin and chiral isospin chemical potentials in the framework of (3+1)-dimensional Nambu--Jona-Lasinio model with two quark flavors. It has been shown that in the large-$N_{c}$ limit ($N_{c}$ is the number of colors of quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation one. The key conclusion of our studies is the fact that chiral isospin chemical potential generates charged pion condensation in dense quark matter wit…
We use a hadron resonance gas model to study the QCD phase diagram at nonzero temperature, baryon, isospin and strangeness chemical potentials. We determine the temperature of the transition from the hadronic phase to the quark gluon plasma phase using two different methods. We find that the critical temperatures derived in both methods are in very good agreement. We find that the critical surface has a small curvature. We also find that the critical temperature's dependence on the baryon chemical potential at zero isospin chemical potential is almost identical to its dependence on the isospin…
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 …
Baryonic Vortex Phase and Magnetic Field Generation in QCD with Isospin and Baryon Chemical Potentials
该研究在含有限重子与同位旋化学势的低能致密QCD中提出重子涡旋相，证明其携重子数且高密下负张力可自发形成，为理解QCD相图和中子星磁场提供新思路。
For baryons composed by the light quarks ($q=u,d$) we write spectral integral equation using the notion of two diquarks: (i) axial--vector state, $D^{1}_{1}$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii) scalar one, $D^{0}_{0}$, with the spin $S_D=0$ and isospin $I_D=0$. We present spectral integral equations for the $qD^{0}_{0}$ and $qD^{1}_{1}$ states taking into account quark--diquark confinement interaction.
We investigate the thermodynamics of a thermal field theory in presence of both a baryon and an isospin chemical potential. For this we consider a probe of several D7-branes embedded in the AdS-Schwarzschild black hole background. We determine the structure of the phase diagram and calculate the relevant thermodynamical quantities both in the canonical and in the grand canonical ensemble. We discuss how accidental symmetries present reflect themselves in the phase diagram: In the case of two flavors, for small densities, there is a rotational symmetry in the plane spanned by the baryon and iso…
We present a study of the isospin-violating one-pion strong decays of single heavy tetraquarks $X_Q = X(s q \bar q \bar Q)$, $Q=c, b$, and $q=u, d$ with spin-parity $J^P = 0^+$. We assume that the tetraquarks have the configuration of a color diquark and a antidiquark. Three mechanisms of isospin violation can contribute to the decay rate: (1) mixing of the $X(s u \bar u \bar Q)$ and $X(s d \bar d \bar Q)$ tetraquark currents, (2) an explicit $m_d-m_u$ quark mass difference in the quark diagrams describing the corresponding decay transitions and (3) $π^0-η$ mixing in the final state. Our main …
The pentaquark $P_c^+(4450)$ recently discovered by LHCb has been interpreted as a bound state of $Ψ(2S)$ and nucleon. The charmonium-nucleon interaction which provides the binding mechanism is given, in the heavy quark limit, in terms of charmonium chromoelectric polarizabilities and densities of the nucleon energy-momentum tensor (EMT). In this work we show in model-independent way, by exploring general properties of the effective interaction, that $Ψ(2S)$ can form bound states with nucleon and $Δ$. Using the Skyrme model to evaluate the effective interaction in the large-$N_c$ limit and est…
Equation of state of isospin asymmetric QCD with small baryon chemical potentials
本文通过首阶泰勒展开系数将同位旋不对称QCD状态方程扩展至小重子和奇异数化学势，并首次给出沿电荷化学势轴的状态方程结果，对研究大轻子味不对称下早期宇宙演化具有潜在意义。
QCD phase diagram in a magnetic field with baryon and isospin chemical potentials
本文基于楚拉斯基扰动理论，研究了在磁场中考虑重子和等旋化学位移的QCD相图，揭示了不同相结构及它们在中子星中的物理意义。
We introduce a random matrix model with the symmetries of QCD at finite temperature and chemical potentials for baryon number and isospin. We analyze the phase diagram of this model in the chemical potential plane for different temperatures and quark masses. We find a rich phase structure with five different phases separated by both first and second order lines. The phases are characterized by the pion condensate and the chiral condensate for each of the flavors. In agreement with lattice simulations, we find that in the phase with zero pion condensate the critical temperature depends in the s…
Lattice QCD simulations are now reaching a precision where isospin breaking effects become important. Previously, we have developed a program to systematically investigate the pattern of flavor symmetry beaking within QCD and successfully applied it to meson and baryon masses involving up, down and strange quarks. In this Letter we extend the calculations to QCD + QED and present our first results on isospin splittings in the pseudoscalar meson and baryon octets. In particular, we obtain the nucleon mass difference of $M_n-M_p=1.35(18)(8)\,\mbox{MeV}$ and the electromagnetic contribution to th…
So far, the masses of excited states of mixed orbital symmetry and in particular those of nonstrange $[{\bf 70},1^-]$ baryons derived in the $1/N_c$ expansion were based on the separation of a system of $N_c$ quarks into a symmetric core and an excited quark. Here we avoid this separation and show that an advantage of this new approach is to substantially reduce the number of linearly independent operators entering the mass formula. A novelty is that the isospin-isospin term becomes as dominant in $Δ$ as the spin-spin term in $N$ resonances.
Hadronic structure on the light-front IX . Orbital-spin-isospin wave functions of baryons
该文作为光前强子结构系列研究的第九篇，分析了重子质心系波函数的置换群对称性、构造了各壳层波函数并计算相关矩阵元，还研究了光前重子波函数的对称性质与激发态组合。
The coupled Bethe--Salpeter bound state equations for a $Q\bar Q$ system, where $Q=(U,D)$ is a degenerate, fourth generation, super--heavy quark doublet, are solved in several ladder approximation models. The exchanges of gluon, Higgs and Goldstone modes in the standard model are calculated in the ultra--heavy quark limit where weak $γ, W^\pm$ and $Z^0$ contributions are negligible. A natural $I=0$ and $I=1$ multiplet pattern is found, with large splittings occuring between the different weak iso--spin states when $M_Q$, the quark masses, are larger than values in the range $0.4 TeV<M_Q<0.8 Te…
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