Spin-flavor Symmetry Research Articles

Low-lying even parity meson resonances and spin-flavor symmetry revisited

We review and extend the model derived in Garcia-Recio et al. [Phys. Rev. D 83, 016007 (2011)] to address the dynamics of the low-lying even-parity meson resonances. This model is based on a coupled-channels spin-flavor extension of the chiral Weinberg-Tomozawa Lagrangian. This interaction is then used to study the $S$-wave meson-meson scattering involving members not only of the $\ensuremath{\pi}$ octet, but also of the $\ensuremath{\rho}$ nonet. In this work, we study in detail the structure of the SU(6)-symmetry-breaking contact terms that respect (or softly break) chiral symmetry. We derive the most general local (without involving derivatives) terms consistent with the chiral-symmetry-breaking pattern of QCD. After introducing sensible simplifications to reduce the large number of possible operators, we carry out a phenomenological discussion of the effects of these terms. We show how the inclusion of these pieces leads to an improvement of the description of the ${J}^{P}={2}^{+}$ sector, without spoiling the main features of the predictions obtained in the original model in the ${J}^{P}={0}^{+}$ and ${J}^{P}={1}^{+}$ sectors. In particular, we find a significantly better description of the ${I}^{G}({J}^{PC})={0}^{+}({2}^{++})$, ${1}^{\ensuremath{-}}({2}^{++})$ and the $I({J}^{P})=\frac{1}{2}({2}^{+})$ sectors, which correspond to the ${f}_{2}(1270)$, ${a}_{2}(1320)$, and ${K}_{2}^{*}(1430)$ quantum numbers, respectively.

Heavy-quark spin symmetry for charmed and strange baryon resonances

We study charmed and strange baryon resonances that are generated dynamically by a unitary baryon-meson coupled-channels model which incorporates heavy-quark spin symmetry. This is accomplished by extending the SU(3) Weinberg-Tomozawa chiral Lagrangian to SU(8) spin-flavor symmetry plus a suitable symmetry breaking. The model generates resonances with negative parity from the s-wave interaction of pseudoscalar and vector mesons with 1/2+ and 3/2+ baryons in all the isospin, spin, and strange sectors with one, two, and three charm units. Some of our results can be identified with experimental data from several facilities, such as the CLEO, Belle, or BaBar Collaborations, as well as with other theoretical models, whereas others do not have a straightforward identification and require the compilation of more data and also a refinement of the model.

Baryon masses and axial couplings in the combined1/Ncand chiral expansions

The effective theory for baryons with combined 1/Nc and chiral expansions is analyzed for non-strange baryons. Results for baryon masses and axial couplings are obtained in the small scale expansion, to be coined as the \xi-expansion, in which the 1/Nc and the low energy power countings are linked according to 1/Nc=O(\xi)=O(p). Masses and axial couplings are analyzed to O(\xi^3) and O(\xi^2) respectively, which correspond to next-to-next to leading order evaluations, and require one-loop contributions in the effective theory. The role of the spin-flavor approximate symmetry in baryons, consequence of the large Nc limit, is manifested in the physical world with Nc=3 in a significant way, as the analysis of its breaking in the masses and the axial couplings shows. Applications to the recent lattice QCD results on baryon masses and the nucleon's axial coupling are presented. It is shown that those results are naturally described within the effective theory at the order considered in the \xi-expansion.

Charmed Mesons in Nuclei with Heavy-Quark Spin Symmetry

We study the properties of charmed pseudoscalar and vector mesons in dense matter within a unitary meson–baryon coupled-channel model which incorporates heavy-quark spin symmetry. This is accomplished by extending the SU(3) Weinberg–Tomozawa Lagrangian to incorporate spin-flavor symmetry and implement a suitable flavor symmetry breaking. Several resonances with negative parity are generated dynamically by the s-wave interaction between pseudoscalar and vector meson multiplets with 1/2+ and 3/2+ baryons. Those states are then compared to experimental data as well as theoretical models. Next, Pauli-blocking effects and meson self-energies are introduced in a self-consistent manner to obtain the open-charm meson spectral functions in a dense nuclear environment. We finally discuss the formation of D-mesic nuclei.

Strangeness and charm in nuclear matter

The properties of strange ($K$, $\bar K$ and $\bar K^*$) and open-charm ($D$, $\bar D$ and $D^*$) mesons in dense matter are studied using a unitary approach in coupled channels for meson-baryon scattering. In the strangeness sector, the interaction with nucleons always comes through vector-meson exchange, which is evaluated by chiral and hidden gauge Lagrangians. For the interaction of charmed mesons with nucleons we extend the SU(3) Weinberg-Tomozawa Lagrangian to incorporate spin-flavor symmetry and implement a suitable flavor symmetry breaking. The in-medium solution for the scattering amplitude accounts for Pauli blocking effects and meson self-energies. On one hand, we obtain the $K$, $\bar K$ and $\bar K^*$ spectral functions in the nuclear medium and study their behaviour at finite density, temperature and momentum. We also make an estimate of the transparency ratio of the $\gamma A \to K^+ K^{*-} A^\prime$ reaction, which we propose as a tool to detect in-medium modifications of the $\bar K^*$ meson. On the other hand, in the charm sector, several resonances with negative parity are generated dynamically by the s-wave interaction between pseudoscalar and vector meson multiplets with $1/2^+$ and $3/2^+$ baryons. The properties of these states in matter are analyzed and their influence on the open-charm meson spectral functions is studied. We finally discuss the possible formation of $D$-mesic nuclei at FAIR energies.

Neutron Star Properties in the Chiral Quark–Meson Coupling Model

We study the properties of neutron stars using the chiral quark–meson coupling model, in which the quark–quark hyperfine interaction due to the exchanges of gluon and pion based on chiral symmetry is considered. We also examine the effects of hyperons and Δ-isobars in a neutron star. Extending the SU(6) spin-flavor symmetry to more general SU(3) flavor symmetry in the vector–meson couplings to baryons, the maximum mass of neutron star can reach the recently observed massive pulsar mass, $${1.97 \pm 0.04 M_{\odot}}$$ . In this calculation, Λ and Ξ are generated in a neutron star, while Σ and Δ-isobars do not appear.

Renormalization of the baryon axial vector current in large-Ncchiral perturbation theory: Effects of the decuplet-octet mass difference and flavor symmetry breaking

The baryon axial vector current is computed at one-loop order in large-N_c baryon chiral perturbation theory, where N_c is the number of colors. Loop graphs with octet and decuplet intermediate states are systematically incorporated into the analysis and the effects of the decuplet-octet mass difference and SU(3) flavor symmetry breaking are accounted for. As expected, large-N_c cancellations between different one-loop graphs are observed as a consequence of the large-N_c spin-flavor symmetry of QCD baryons. Fitting our analytical formulas against experimental data on baryon semileptonic decays and the strong decays of decuplet baryons, a detailed numerical analysis regarding the determination of the basic parameters of large-N_c baryon chiral perturbation theory as well as the extraction of the baryon axial vector couplings is performed. The large-N_c baryon chiral perturbation theory predictions are in very good agreement both with the expectations from the 1/N_c expansion and with the experimental data.

One-loop corrections to the baryon axial vector current

The symmetry breaking corrections to the pion–baryon couplings vanish to first order in 1/Nc, where Nc is the number of colours. Loop graphs with octet and decuplet intermediate states cancel to various orders in Nc as a consequence of the large-Nc spin-flavour symmetry of QCD baryons. The baryon axial vector current is computed at one-loop order in heavy baryon chiral perturbation theory in the large Nc limit. 1/Nc corrections in the case of gA in QCD are presented here.

Analysis of baryon properties in large-Nc chiral perturbation theory

We discuss how to compute corrections to one-loop order to the baryon axial-vector current and magnetic moments in heavy baryon chiral perturbation theory in the large-Nc limit, where Nc is the number of colors. Loop graphs with octet and decuplet intermediate states cancel to various orders in Nc as a consequence of the large-Nc spin-flavor symmetry of QCD baryons. These cancellations are explicitly shown for the general case of Nf flavors of light quarks. We also indicate how to compare our resultant expressions with the corresponding ones obtained within conventional heavy baryon chiral perturbation theory at the physical values Nc = 3, Nf = 3. We observe an excellent agreement order by order.

Charmed and strange baryon resonances with heavy-quark spin symmetry

We study charmed and strange baryon resonances that are generated dynamically by a unitary baryon-meson coupled-channel model which incorporates heavy-quark spin symmetry. This is accomplished by extending the SU(3) Weinberg-Tomozawa chiral Lagrangian to SU(8) spin-flavor symmetry plus a suitable symmetry breaking. The model produces resonances with negative parity from s-wave interaction of pseudoscalar and vector mesons with $1/2^+$ and $3/2^+$ baryons. Resonances in all the isospin, spin, and strange sectors with one, two, and three charm units are studied. Our results are compared with experimental data from several facilities, such as the CLEO, Belle or BaBar Collaborations, as well as with other theoretical models. Some of our dynamically generated states can be readily assigned to resonances found experimentally, while others do not have a straightforward identification and require the compilation of more data and also a refinement of the model. In particular, we identify the $\Xi_c(2790)$ and $\Xi_c(2815)$ resonances as possible candidates for a heavy-quark spin symmetry doublet.

Formula omitted] breaking corrections to the D, [formula omitted], B, and [formula omitted] decay constants

We report on a first next-to-next-to-leading order calculation of the decay constants of the D (D⁎) and B (B⁎) mesons using a covariant formulation of chiral perturbation theory. It is shown that, using the state-of-the-art lattice QCD results on fDs/fD as input, one can predict quantitatively the ratios of fDs⁎/fD⁎, fBs/fB, and fBs⁎/fB⁎ taking into account heavy-quark spin-flavor symmetry breaking effects on the relevant low-energy constants. The predicted relations between these ratios, fDs⁎/fD⁎<fDs/fD and fBs/fB>fDs/fD, and their light-quark mass dependence should be testable in future lattice QCD simulations, providing a stringent test of our understanding of heavy quark spin-flavor symmetry, chiral symmetry and their breaking patterns.

Total nucleon-nucleon cross sections in largeNcQCD

We use contracted spin-flavor symmetry which emerges in the large ${N}_{c}$ limit of QCD to obtain relations between proton-proton and proton-neutron total cross sections for both polarized and unpolarized scattering. The formalism used is valid in the semiclassical regime in which the relative momentum of the incident nucleons is much larger than the inverse size of the nucleon, provided that certain technical assumptions are met. The relations should be phenomenologically useful provided that ${N}_{c}=3$ is sufficiently large so that the large ${N}_{c}$ results have at least semiquantitative predictive power. The relations are model independent in the sense that they depend on properties of large ${N}_{c}$ QCD only and not on any particular model-dependent details of the nucleon-nucleon interaction. We compare these model-independent results to the experimental data. We find the relation for spin-unpolarized scattering works well empirically. For the case of polarized scattering, the data are consistent with the relations, but the cross sections are too small to make sharp predictions.

Odd-parity light baryon resonances

We use a consistent SU(6) extension of the meson-baryon chiral Lagrangian within a coupled channel unitary approach in order to calculate the T-matrix for meson-baryon scattering in s-wave. The building blocks of the scheme are the pion and nucleon octets, the rho nonet and the Delta decuplet. We identify poles in this unitary T-matrix and interpret them as resonances. We study here the non exotic sectors with strangeness S=0,-1,-2,-3 and spin J=1/2, 3/2 and 5/2. Many of the poles generated can be associated with known N, Delta, Sigma, Lambda and Xi resonances with negative parity. We show that most of the low-lying three and four star odd parity baryon resonances with spin 1/2 and 3/2 can be related to multiplets of the spin-flavor symmetry group SU(6). This study allows us to predict the spin-parity of the Xi(1620), Xi(1690), Xi(1950), Xi(2250), Omega(2250) and Omega(2380) resonances, which have not been determined experimentally yet.

The strangeness form factors of the proton within nonrelativistic constituent quark model revisited

We reexamine, within the nonrelativistic constituent quark model (NRCQM), a recent claim that the current data on the strangeness form factors indicates that the uudss¯ component in the proton is such that the uuds subsystem has the mixed spatial symmetry [31]X and flavor spin symmetry [4]FS[22]F[22]S, with s¯ in S state (configuration I). We find this claim to be invalid if corrected expressions for the contributions of the transition current to GAs and GEs are used. We show that, instead, it is the lowest-lying uudss¯ configuration with uuds subsystem of completely symmetric spatial symmetry [4]X and flavor spin symmetry [4]FS[22]F[22]S, with s¯ in P state (configuration II), which could account for the empirical signs of all form factors GEs, GMs, and GAs. Further, we find that removing the center-of-mass motion of the clusters will considerably enhance the contributions of the transition current. We also demonstrate that it is possible to give a reasonable description of the existing form factors data with a tiny probability Pss¯=0.025% for the uudss¯ component. We further see that with a small admixture of configuration I, the agreement of our prediction with the data for GAs at low-q2 region can be markedly improved. We find that without removing CM motion, Pss¯ would be overestimated by about a factor of four in the case when transition current dominates. We also explore the consequence of a recent estimate reached from analyzing the existing data on d¯−u¯, s+s¯, and u¯+d¯−s−s¯, that Pss¯ lies between 2.4–2.9%. It would lead to a large size for the five-quark system and a small bump in both GEs+ηGMs and GEs in the region of q2⩽0.1 GeV2 within the considered model.

Spin of ground state baryons

We calculate the quark spin contribution to the total angular momentum of flavor octet and flavor decuplet ground state baryons using a spin-flavor symmetry based parametrization method of quantum chromodynamics. We find that third order SU(6) symmetry breaking three-quark operators are necessary to explain the experimental result ${\ensuremath{\Sigma}}_{1}=0.29(09)$. For spin $3/2$ decuplet baryons, we predict that the quark spin contribution is ${\ensuremath{\Sigma}}_{3}=3.93(22)$, i.e. considerably larger than their total angular momentum.

Low-lying even-parity meson resonances and spin-flavor symmetry

A study is presented of the $s-$wave meson-meson interactions involving members of the $\rho-$nonet and of the $\pi-$octet. The starting point is an SU(6) spin-flavor extension of the SU(3) flavor Weinberg-Tomozawa Lagrangian. SU(6) symmetry breaking terms are then included to account for the physical meson masses and decay constants, while preserving partial conservation of the axial current in the light pseudoscalar sector. Next, the $T-$matrix amplitudes are obtained by solving the Bethe Salpeter equation in coupled-channel with the kernel built from the above interactions. The poles found on the first and second Riemann sheets of the amplitudes are identified with their possible Particle Data Group (PDG) counterparts. It is shown that most of the low-lying even parity PDG meson resonances, specially in the $J^P=0^+$ and $1^+$ sectors, can be classified according to multiplets of the spin-flavor symmetry group SU(6). The $f_0(1500)$, $f_1(1420)$ and some $0^+(2^{++})$ resonances cannot be accommodated within this SU(6) scheme and thus they would be clear candidates to be glueballs or hybrids. Finally, we predict the existence of five exotic resonances ($I \ge 3/2$ and/or $|Y|=2$) with masses in the range 1.4--1.6 GeV, which would complete the $27_1$, $10_3$, and $10_3^*$ multiplets of SU(3)$\otimes$SU(2).

Excited nucleon electromagnetic form factors from broken spin-flavor symmetry

A group theoretical derivation of a relation between the N → Δ A charge quadrupole transition and neutron charge form factors is presented.

The Chiral and Angular Momentum Content of the ρ-Meson

It is possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark Fock component of a meson in the infrared, where mass is generated. Using the variational method and a set of interpolators that span a complete chiral basis we extract in a lattice QCD Monte Carlo simulation with two dynamical light quarks the orbital angular momentum and spin content of the rho-meson. We obtain in the infrared a simple 3S1 component as a leading component of the rho-meson with a small admixture of the 3D1 partial wave, in agreement with the SU(6) flavor-spin symmetry.

All you need isN: Baryon spectroscopy in two largeNlimits

The generalization of QCD to many colors is not unique; each distinct choice corresponds to a distinct $1/{N}_{c}$ expansion. The familiar 't Hooft ${N}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit places quarks in the fundamental representation of $\mathrm{SU}({N}_{c})$, while an alternative approach places quarks in its two-index antisymmetric representation. At ${N}_{c}=3$ these two $1/{N}_{c}$ expansions coincide. We compare their predictions for certain observables in baryon spectroscopy, particularly mass combinations organized according to SU(3) flavor breaking. Each large ${N}_{c}$ limit generates an emergent spin-flavor symmetry that leads to the vanishing of particular linear combinations of baryon masses at specific orders in the expansions. Experimental evidence shows that these relations hold at the expected orders regardless of which large ${N}_{c}$ limit one uses, suggesting the validity of either limit in the study of baryons. We also consider a hybrid large ${N}_{c}$ limit in which one flavor is taken to transform in the two-index antisymmetric representation and the rest of the flavors are in the fundamental representation. While this hybrid large ${N}_{c}$ limit is theoretically attractive, we show that for a wide class of observables it faces some phenomenological difficulties.

Photoproduction of excited baryons in the 1 /Nc expansion of QCD

Baryon photo-couplings have been the subject of many studies over the last forty years, and are key elements in the understanding of baryon structure and dynamics. In this talk I will present the results of the photoproduction helicity amplitudes for excited baryons in the context of the 1=Nc expansion of QCD [1]. Such an expansion has been shown to provide a useful and systematic framework for the analysis of various baryon properties. This is mostly due to the existence of a contracted spin-flavor symmetry in the large Nc limit[2, 3]. Although SU(2N f) is not an exact symmetry in the excited baryon sector[4], its N 0 c breaking is small as several analyses of the baryon spectrum have shown[5‐7]. In this context the photoproduction helicity amplitudes for the negative parity excited baryons have been first analyzed in [8]. Here we report on an extension of such analysis which includes a systematic building of a complete basis of current operators to sub-leading order in the 1=Nc expansion, for both negative and positive parity resonances[9, 10].