Jerrold Franklin
Properties of b-baryon decay matrix elements (amplitudes) have been derived in a nonsymmetric quark model without any use of SU(6), SU(3), or SU(2) (isotopic spin) groups. Equalities between pairs of amplitudes are derived, and $Λ-Σ$ mixing is used to calculate the branching ratio for the transition $Λ_b\rightarrow Σ^0$.
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We study the SU(3) group structure of pentaquark baryons which are made of four quarks and one antiquark. The pentaquark baryons form {1}, {8}, {10}, {10}-bar, {27}, and {35} multiplets in SU(3) quark model. First, the flavor wave functions of all the pentaquark baryons are constructed in SU(3) quark model and then the flavor SU(3) symmetry relations for the interactions of the pentaquarks with three-quark baryons and pentaquark baryons are obtained.
We apply a quark model developed in earlier work to the spectrum of baryons with strangeness -2 and -3. The model describes a number of well-established baryons successfully, and application to cascade baryons allows the quantum numbers of some known states to be deduced.
We review the application of non-relativistic constituent quark models to study one, two and three non-strange baryon systems. We present results for the baryon spectra, potentials and observables of the NN, N$Δ$, $ΔΔ$ and NN$^*(1440)$ systems, and also for the binding energies of three non-strange baryon systems. We make emphasis on observable effects related to quark antisymmetry and its interplay with quark dynamics.
Triggered by experimental prospects to measure electromagnetic dipole moments of baryons containing a bottom quark, we calculate the CP-odd electric dipole moments (EDMs) of spin-1/2 single-bottom baryons. We consider CP-violating dimension-six operators in the Standard Model Effective Field Theory that involve bottom quarks, and apply heavy-baryon chiral perturbation theory to compute the EDMs of several baryons. We discuss the expected size of the EDMs for beyond-the-Standard Model physics appearing at the TeV scale.
We demonstrate in a model independent way that, in the combined heavy quark and large N_c limit, there exists a new contracted U(4) symmetry which connects orbitally excited heavy baryons to the ground states.
We evaluate semileptonic decays of spin-1/2 and spin-3/2 doubly heavy $cb$ baryons. The decays are driven by a $c\to s,d$ transition at the quark level. We check our results for the form factors against heavy quark spin symmetry constraints obtained in the limit of very large heavy quark masses and near zero recoil.
Heavy quark spin symmetry is discussed in the context of single and doubly heavy baryons. A special attention is paid to the constraints/simplifications that this symmetry imposes on the non-relativistic constituent quark model wave functions and on the b->c semileptonic decays of these hadrons.
The recent progress in the investigations on the quark structure of the $Λ$ and $Σ$ baryons are reviewed. It is shown that the quark structure of $Λ$ and $Σ$ hyperons can provide a new domain to test various theories concerning the spin and flavor structure of the nucleon. The $Λ$ and $Σ$ Physics might be new directions to explore the quark distributions of baryons both theoretically and experimentally.
We argue that selected $S$ wave meson-baryon channels may play a key role to match poor baryon mass predictions from quark models with data. The identification of these channels with effective inelastic channels in data analysis allows to derive a prescription which could improve the extraction and identification of baryon resonances.
Using the unified scheme for describing both quark spin and orbital angular momenta in the chiral quark model developed in the previous work, the magnetic moments of octet and decuplet baryons are calculated. The numerical result shows that the overall agreement with data is improved by including the orbital contributions.
We present an unquenched quark model for baryons in which the effects of the quark-antiquark pairs (up, down and strange) are taken into account in an explicit form via a microscopic, QCD-inspired, quark-antiquark creation mechanism. In the present approach, the contribution of the quark-antiquark pairs can be studied for any inital baryon and for any flavor of the pairs. It is shown that, while the inclusion of quark-antiquark pairs does not affect the baryon magnetic moments, it leads to a sizeable contribution of the orbital angular momentum to the spin of the proton and the Lambda hyperon.
In this contribution, we present the unquenched quark model as an extension of the constituent quark model that includes the effects of sea quarks via a $^{3}P_{0}$ quark-antiquark pair-creation mechanism. Particular attention is paid to the spin and flavor content of the proton, magnetic moments and $β$ decays of octet baryons.
We study the baryon-quark phase transition in a molecular dynamics (MD) of quark degrees of freedom at finite temperature and density. The baryon state at low density and temperature, and the deconfined quark state at high density and temperature are reproduced. We investigate the equations of state of matters with different $u$-$d$-$s$ compositions. Then we draw phase diagrams in the temperature-density plane by this simulation. It is found that the baryon-quark transition is sensitive to the quark width.
Single- and double- heavy baryons are studied in the constituent quark model. The model Hamiltonian is chosen as a standard one with two exceptions : (1) The color-Coulomb term depend on quark masses, and (2) an antisymmetric $LS$ force is introduced. Model parameters are fixed by the strange baryon spectra, $Λ$ and $Σ$ baryons. The masses of the observed charmed and bottomed baryons are, then, fairly well reproduced. Our focus is on the low-lying negative-parity states, in which the heavy baryons show specific excitation modes reflecting the mass differences of heavy and light quarks. By chan…
The simple independent quark models have difficulties explaining simultaneously the totality of the known hyperon magnetic moments and hyperon semi-leptonic decay rates. We show that both the Goldstone boson loop contributions and the two-quark effective exchange currents are essential in explaining these observables.
Two topics are briefly reviewed in this talk: the decay of flavored hadrons or quarkonium states involving a baryon--antibaryon pair, and the spectroscopy of heavy baryons containing one, two or three heavy quarks. Some prospects for exotic heavy baryons are also discussed.
We present a model of baryonic matter which contains free constituent quarks in addition to bound constituent quarks in nucleons. In addition to the common linear sigma-model we include the exchange of vector-mesons. The percentage of free quarks increases with baryon density but the nucleons resist a restoration of chiral symmetry.
Model independent sum rules for heavy baryon masses are tested for baryons containing charmed or bottom quarks. The sum rules depend only on the assumption that baryon mass differences are determined by spin-dependent two-body energies of quark pairs that do not depend on which baryon the quark pair is in. No assumption is made about the details of the quark-quark interaction. The sum rules are generally well satisfied, although better experimental accuracy would be required for a quantitative test of some of the sum rules. The success of the sum rules is evidence that "baryon independence" of…
The dynamical fluctuation and correlation of multiplicity distributions of identified baryons and antibaryons produced by the hadronization of the bulk quark system are systematically studied in quark combination model. Starting from the most basic dynamics of quark combination which are necessary for multiplicity study, we analyze moments (variance, skewness and kurtosis) of inclusive multiplicity distribution of identified baryons, two-baryon multiplicity correlations, and baryon-antibaryon multiplicity correlations after the hadronization of quark system with given quark number and antiquar…
Transition decay widths by one-pion emissions for excited heavy-baryons with a single heavy (charm and bottom) quark are investigated by following the heavy-quark symmetry and its breaking effects at ${\cal O}(1/M)$ for a heavy-baryon mass $M$. Based on the heavy-baryon effective theory, interaction Lagrangian for the heavy baryons with axial-vector current induced by a pion is constructed. It is presented that the transition decay widths up to ${\cal O}(1/M)$ in several channels are constrained. The results will be useful in experimental study of excited heavy-baryons.
Mass spectra of baryons consisting of two heavy (b or c) and one light quarks are calculated in the framework of the relativistic quark model. The light quark-heavy diquark structure of the baryon is assumed. Under this assumption the ground and excited states of both the diquark and quark-diquark bound system are considered. The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy quark mass is used revealing the close similarity with the mass spectra of B and D mesons. We find that the relativistic treatment …
A hybrid model for baryons based on a dynamical interplay between relativistic three--quark bound states and soliton configurations of mesons is constructed. The Bethe-Salpeter equation for diquarks and the Faddeev equation for diquark-quark bound states in the background of a soliton is solved. The results show that baryons are very much like hybrids containing both, solitonic meson clouds and three--quark correlations.
Mass spectra of heavy baryons are calculated in the heavy-quark--light-diquark picture in the framework of the QCD-motivated relativistic quark model. The dynamics of light quarks in the diquark as well as the dynamics of the heavy quark and light diquark in the baryon are treated completely relativistically without application of nonrelativistic v/c and heavy quark 1/m_Q expansions. Such approach allows us to get predictions for the heavy baryon masses for rather high orbital and radial excitations. On this basis the Regge trajectories of heavy baryons for orbital and radial excitations are c…
A review of the underlying ideas of the Interacting Quark Diquark Model (IQDM) that asses the baryon spectroscopy in terms of quark diquark degrees of freedom is given, together with a discussion of the missing resonances problem. Some ideas about its generalization the heavy baryon spectroscopy is given.s of freedom is given, together with a discussion of the missing resonances problem. Some ideas about its generalization the heavy baryon spectroscopy is given.The results are compared to the existing experimental data.
The relativistic interacting quark-diquark model, constructed in the framework of point form dynamics, is extended to strange baryons. The strange and nonstrange baryon spectra are calculated and compared with the experimental data.
The implications of the pion (meson) degrees of freedom for baryon properties, taken at the constituent quark and baryon levels are compared. It is shown that there is a dramatic qualitative difference between two approaches.
Mass spectra of strange baryons are calculated in the framework of the relativistic quark model based on the quasipotential approach. Baryons are treated as the relativistic quark-diquark bound systems. It is assumed that two quarks with equal constituent masses form a diquark. The diquark excitations and its internal structure are consistently taken into account. Calculations are performed up to rather high orbital and radial excitations of strange baryons. On this basis the Regge trajectories are constructed. The obtained results are compared with available experimental data and previous pre…
We extend the study of hadron yield correlation in combination models in a recent publication to baryon-anti-baryon flavor correlations in heavy ion collisions. We show that the universal behaviors of the anti-baryon to baryon yield ratios as functions of that of $K^-$ to $K^+$ are naturally explained. We study also the "mixed ratios" and propose other measurements that might be sensitive to the hadronization mechanism.
We study theoretically the baryon spectra in terms of a deformed oscillator quark (DOQ) model. This model is motivated by confinement of quarks and chiral symmetry breaking, which are the most important non-perturbative phenomena of QCD. The minimization of the DOQ hamiltonian with respect to the deformation for each principal quantum number results in deformations for the intrinsic states of excited baryonic states. We find that the resulting baryon spectra agree very well with the existing experimental data. The spatial deformation of the baryonic excited states carry useful information on t…
The spectroscopy of the doubly heavy baryons including different heavy quarks is studied based on the heavy quark symmetry of QCD. We point out that, when the two heavy quarks are in $S$-wave, these baryons with a certain spin $j_l$ of the light cloud can be classified into two sets: a heavy quark singlet with total spin of $j=j_l$ and a heavy quark multiplet with $j= (j_l+1) , j_l ,\ldots \vert j_l-1\vert$, all the baryons in these two sets have the same mass and, the baryons with the same quantum numbers in these two sets do not mix with each other. We finally point out that the strong decay…
The spectrum of the doubly heavy baryons is estimated with respect to the new observation from the LHCb collaboration [Aaij:2017ueg] by using the chiral partner structure and heavy quark spin-flavor symmetry. The effects of heavy quark flavor symmetry breaking and light quark flavor symmetry are considered. The mass splitting of doubly heavy baryons with the same spin but opposite parity arises from the generalized Goldberger-Treiman relation. The intermultiplet one-pion transition and intramultiplet radiative transitions are also be estimated.
The self-consistent chiral quark-soliton model is a relativistic pion mean-field approach in the large $N_c$ limit, which describes both light and heavy baryons on an equal footing. In the limit of the infinitely heavy mass of the heavy quark, a heavy baryon can be regarded as $N_c-1$ valence quarks bound by the pion mean fields, leaving the heavy quark as a color static source. The structure of the heavy baryon in this scheme is mainly governed by the light-quark degrees of freedom. Based on this framework, we evaluate the electromagnetic form factors of the lowest-lying heavy baryons. The ro…
We show that the chiral $SU(n)\otimes SU(n)$ flavor symmetry on the null-plane severely restricts the sea quarks in the baryon octet. It predicts large asymmetry for the light sea quarks $(u,d,s)$, and universality and abundance for the heavy sea quarks. Further it is shown that existence of the heavy sea quarks constrained by the same symmetry reduces the theoretical value of the Ellis-Jaffe sum rule substantially.
We show that $ω_B$ or $ω_{\bar B}$, the squared baryon or antibaryon number fluctuation per baryon or antibaryon, is a possible signature for the quark-gluon plasma that is expected to be created in relativistic heavy ion collisions, as it is a factor of three smaller than in an equilibrated hadronic matter due to the fractional baryon number of quarks. Using kinetic equations with exact baryon number conservation, we find that their values in an equilibrated matter are half of those expected from a Poisson distribution. Effects due to finite acceptance and non-zero net baryon number are also …
The electromagnetic properties of baryon octet are studied in the perturbative chiral quark model (PCQM). The relativistic quark wave function is extracted by fitting the theoretical results of the proton charge form factor to experimental data and the predetermined quark wave function is applied to study the electromagnetic form factors of other octet baryons as well as magnetic moments, charge and magnetic radii. The PCQM results are found, based on the predetermined quark wave function, in good agreement with experimental data.
Longitudinal Transitions Of Baryon Resonances in Constituent Quark Model
在组分夸克模型中引入了满足规范不变性要求的纵向跃迁算符。计算了相应的核子与重子共振之间的纵向跃迁。我们指出，研究纵向耦合对理解重子的结构起着重要的作用。
We show how heavy quark symmetry constraints on doubly heavy baryon semileptonic decay widths can be used to test the validity of different quark model calculations. The large discrepancies in the results observed between different quark model approaches can be understood in terms of a severe violation of heavy quark spin symmetry constraints by some of those models.
Triply heavy baryons are investigated in the framework of the relativistic quark model based on the quark-diquark picture in the quasipotential approach in QCD. Masses of the ground and excited states of the $Ω_{ccc}$, $Ω_{bbb}$, $Ω_{ccb}$ and $Ω_{cbb}$ baryons are calculated. Orbital and radial excitations between the diquark and quark as well as between quarks inside the diquark are considered. The diquark internal structure is consistently taken into account by the form factor of the diquark-gluon interaction expressed through the overlap integral of the diquark wave functions. The detailed…
We describe baryons as quark-diquark bound states at finite temperature and density within the NJL model for chiral symmetry breaking and restoration in quark matter. Based on a generalized Beth-Uhlenbeck approach to mesons and diquarks we present in a first step the thermodynamics of quark-diquark matter which includes the Mott dissociation of diquarks at finite temperature. In a second step we solve the Bethe-Salpeter equation for the baryon as a quark-diquark bound state in quark-diquark matter. We obtain a stable, bound baryon even beyond the Mott temperature for diquark dissociation since…
The interaction energies between two baryons at short distance in different flavor channels are calculated from the constituent quark model (CQM) and are compared with the recent lattice QCD (LQCD) results for baryon-baryon potentials at short distance. We consider the six-quark system with two strange quarks and focus on the quantum numbers, (Flavor,Spin)=(1,0),(8,1),(10,1),($\overline{10}$,1) and (27,0). The interaction energy is defined by subtracting out isolated baryon masses and relative kinetic energy of two baryons from the total energy of a compact six-quark state. We introduce intera…
The magnetic moments of baryon decuplet are studied in vacuum as well as in the symmetric nuclear matter at finite temperature using a chiral SU(3) quark mean field model approach. The contributions coming from the valence quarks, quark sea and the orbital angular momentum of the quark sea have been considered to calculate magnetic moment of decuplet baryons. The decuplet baryon masses decrease, whereas, the magnetic moments increase significantly with the rise of baryonic density of the symmetric nuclear medium. This is because of the reason that constituent quark magnetic moment and the quar…
Mass differences of the flavor octet and decuplet ground-state baryons are studied in the perturbative chiral quark model. We present a way to understand the nontrivial spin- and flavor dependent mass differences, where both pseudoscalar mesons and gluons play a significant role.
We study the color-spin interaction energy of a quark, a diquark and a baryon with their surrounding baryons and/or quark matter. This is accomplished by classifying all possible flavor and spin states of the resulting multiquark configuration in both the flavor SU(2) and SU(3) symmetric cases. We find that while the baryon has the lowest interaction energy when there is only a single surrounding baryon, the quark has the lowest interaction energy when the surrounding has more than three baryons or becomes a quark gas. As the short range nucleon-nucleon interactions are dominated by the color-…
We show that the chiral $SU(n)\otimes SU(n)$ flavor symmetry on the null-plane severely restricts the sea quarks in the baryon octet. It predicts large asymmetry for the light sea quarks $(u,d,s)$, and universality and abundance for the heavy sea quarks. Further it is shown that existence of the heavy sea quarks constrained by the same symmetry reduces the theoretical value of the Ellis-Jaffe sum rule substantially.
We calculate light-front wave functions of mesons, baryons and pentaquarks in a model including constituent mass (representing chiral symmetry breaking), harmonic confining potential, and 4-quark local interaction of 't Hooft type. The model is a simplified version of that used by Jia and Vary. The method used is numerical diagonalization of the Hamiltonian matrix, with certain functional basis. We found that the nucleon wave function displays strong diquar correlations, unlike that for Delta (decuplet) baryon. We also calculate 3-quark-5-quark admixture to baryons, and the resulting antiquark…
Baryon magnetic moments and beta decay ratios ($G_A/G_V$) are calculated in a phenomenological quark model. Non-static effects of pion exchange and orbital excitation are included. Good agreement with experiment is found for a combined fit to all measured baryon magnetic moments and beta decay ratios. The model predicts an antiquark content for the proton that is consistent with the Gottfried sum rule.
Resonating group method for baryon-baryon interactions with unequal oscillator frequencies and its application to the $NΔ$ system in a chiral quark model
本文提出了一种适用于不等振子频率重子-重子相互作用的共振群方法，并应用于楚拉SU(3)夸克模型中的NΔ系统，考虑了标量和伪标量介子交换。
We calculate the magnetic moments of ground state $J^P=\frac{1}{2}^+$ and $J^P=\frac{3}{2}^+$ heavy flavor charm and bottom baryon states employing the concept of effective mass based on single gluon exchange interaction coupling to the spectator quarks in the non-relativistic quark model. We exploit the current experimental information in the heavy flavor sector to estimate the interaction contributions to get the effective masses of the quarks inside the baryons. We study the spin $\frac{1}{2}^{'+} \rightarrow \frac{1}{2}^+$, $\frac{3}{2}^+ \rightarrow \frac{1}{2}^+$, and $\frac{3}{2}^+ \rig…
We present results for exclusive $b\to c$ semileptonic decays of ground state triply-heavy baryons and for semileptonic $c\to s,d$ decays of doubly heavy ground state $cb$ baryons. In both cases, we have derived for the first time heavy quark spin symmetry relations for the hadronic amplitudes near zero recoil. Though strictly valid in the limit of very large heavy quark masses and near zero recoil, they turn out to be reasonable accurate for the whole available phase space in these decays and for the actual heavy quark masses we use. With these relations we have made approximate, but model in…
Light Quark Spin-Flavor Symmetry for Baryons Containing a Heavy Quark in Large N QCD
在大$N$极限下，含有重夸克的重子的耦合和相互作用与轻夸克的自旋味对称性有关。决定所有重夸克重子-π介子耦合的单π耦合常数等于轻夸克重子的π耦合常数。在$1/N^2$阶上，重子耦合之间的轻夸克对称性关系被破坏.利用重夸克自旋味对称性和大$N$轻夸克自旋味对称性来确定重夸克重子简并二重态的耦合。
We discuss some applications of the unquenched quark model which is an extension of the CQM that includes the effects of sea quarks via a 3P0 quark-antiquark pair-creation mechanism. Particular attention is paid to the electromagnetic couplings and beta decays of baryons. It is shown that the observed discrepancies between the experimental data and the predictions of the CQM can be accounted for in large part by the effects of sea quarks in the unquenched quark model.
The quark cluster model approach to the baryon-baryon interaction is reviewed and recent application to the charge symmetry breaking in nuclear force is discussed.
Baryons made of heavy quarks are extremely interesting and could be seen at the LHC.
We derive covariant baryon wave functions for arbitrary Lorentz boosts. Modeling baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to a covariant 3-dimensional form by projecting on the relative quark-diquark energy. Guided by a phenomenological multigluon exchange representation of a covariant confining kernel, we derive for practical applications explicit solutions for harmonic confinement and for the MIT Bag Model. We briefly comment on the interplay of boosts and center-of-mass corrections in relativistic quark models.
We establish a holographic bottom-up model which covers both the baryonic and quark matter phases in cold and dense QCD. This is obtained by including the baryons using simple approximation schemes in the V-QCD model, which also includes the backreaction of the quark matter to the dynamics of pure Yang-Mills. We examine two approaches for homogeneous baryon matter: baryons as a thin layer of noninteracting matter in the holographic bulk, and baryons with a homogeneous bulk gauge field. We find that the second approach exhibits phenomenologically reasonable features. At zero temperature, the va…
This paper explores properties of baryons and finite density baryonic matter in an artificial world in which Nc, the number of colors, is large and the quarks of all species are degenerate and much larger than Λ_QCD. It has long been known that in large Nc QCD, baryons composed entirely of heavy quarks are accurately described in the mean-field approximation. However, the detailed properties of baryons in the combined large Nc and heavy quark limits have not been fully explored. Here some basic properties of baryons are computed using a variational approach. At leading order in both the large …
Heavy Quark Fragmentation into Baryons in a Quark-Diquark Model
在非相对论QCD和重子的夸克-双夸克模型框架下，我们得到了重夸克分裂成自旋为1/2和3/2的重子的碎裂函数。预测了LEP对撞机上$Z^o$峰区的$cc-$和$bc-$重子的产生率和能谱形状。
Baryon and quark superfluidity in the cooling of neutron stars are investigated. Observations could constrain combinations of the neutron or Lambda-hyperon pairing gaps and the star's mass. However, in a hybrid star with a mixed phase of hadrons and quarks, quark gaps larger than a few tenths of an MeV render quark matter virtually invisible for cooling. If the quark gap is smaller, quark superfluidity could be important, but its effects will be nearly impossible to distinguish from those of other baryonic constituents.
By analogy with pNRQCD, we construct Effective Field Theories suitable to describe the heavy-quark sector of baryons made of two and three heavy quarks. A long-standing discrepancy between the hyperfine splitting of doubly heavy baryons obtained in the HQET and potential models is solved. The one-loop matching of the 4-quark operators of dimension 6 is provided.
Fluctuations of conserved charges such as baryon number, electric charge and strangeness may provide a test for completeness of states in lattice QCD for three light flavors. We elaborate on the idea that the corresponding susceptibilities can be saturated with excited baryonic states with an underlying quark-diquark structure with a linearly confining interaction. Using Polyakov-loop correlators we show that in the static limit, the quark-diquark potential coincides with the quark-antiquark potential in marked agreement with recent lattice studies. We thus study in a quark-diquark model the b…
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