The semiclassical SU(3) Skyrme model is traditionally considered as describing a rigid quantum rotator with the profile function being fixed by the classical solution of the corresponding SU(2) Skyrme model. In contrast, we go beyond the classical profile function by quantizing the SU(3) Skyrme model canonically. The quantization of the model is performed in terms of the collective coordinate formalism and leads to the establishment of purely quantum corrections of the model. These new corrections are of fundamental importance. They are crucial in obtaining stable quantum solitons of the quantum SU(3) Skyrme model, thus making the model self-consistent and not dependent on the classical solution of the SU(2) case. We show that such a treatment of the model leads to a family of stable quantum solitons that describe the baryon octet and decuplet and reproduce their masses in a qualitative agreement with the empirical values.
We identify the quantum numbers of baryon exotics in the Quark Model, the Skyrme Model and QCD, and show that they agree for arbitrary colors and flavors. We define exoticness, E, which can be used to classify the states. The exotic baryons include the recently discovered qqqq qbar pentaquarks (E=1), as well as exotic baryons with additional q qbar pairs (E >=1). The mass formula for non-exotic and exotic baryons is given as an expansion in 1/N, and allows one to relate the moment of inertia of the Skyrme soliton to the mass of a constituent quark.
The octet, decuplet and antidecuplet baryon mass spectrum as a function of the Skyrme charge e and the SU(3)_f symmetry breaking parameters is given in tabular form. We also estimate the decuplet-octet and the antidecuplet-octet mass difference. Comparison with existing literature is given.
The bound state extension of Skyrme's topological soliton model for the heavy baryons is quantized canonically in arbitrary reducible representations of the SU(3) flavor group. The canonical quantization leads to an additional negative mass term, which stabilizes the quantized soliton solution. The heavy flavor meson in the field of the soliton is treated with semiclassical quantization. The representation dependence of the calculated spectra for the strange, charm and bottom baryons is explored and compared to the extant empirical spectra.
We review the Skyrme model approach which treats baryons as solitons of an effective meson theory. We start out with a historical introduction and a concise discussion of the original two flavor Skyrme model and its interpretation. Then we develop the theme, motivated by the large $N_C$ approximation of QCD, that the {\it effective} Lagrangian of QCD is in fact one which contains just mesons of all spins. When this Lagrangian is (at least approximately) determined from the meson sector it should then yield a zero parameter description of the baryons. We next discuss the concept of chiral symme…
We outline how one can understand the Skyrme model from the modern perspective. We review the quantization of the SU(3) rotations of the Skyrmion, leading to the exotic baryons that cannot be made of three quarks. It is shown that in the limit of large number of colours the lowest-mass exotic baryons can be studied from the kaon-Skyrmion scattering amplitudes, an approach known after Callan and Klebanov. We follow this approach and find, both analytically and numerically, a strong Theta+ resonance in the scattering amplitude that is traced to the rotational mode. The Skyrme model does predict …
Although it provides a relatively good picture of the nucleons, the Skyrme Model is unable to reproduce the small binding energy in nuclei. This suggests that Skyrme-like models that nearly saturate the Bogomol'nyi bound may be more appropriate since their mass is roughly proportional to the baryon number A. For that purpose, we propose a near-BPS Skyrme Model. It consists of terms up to order six in derivatives of the pion fields, including the nonlinear and Skyrme terms which are assumed to be relatively small. For our special choice of mass term, we obtain well-behaved analytical BPS-type s…
The higher order corrections of SU(3) rotating excited states to the Gell-Mann-Okubo Relations (or GOR) are presented in the standard SU(3) Skyrme model.The Improved GOR (or IGOR) are obtained. The results show the IGOR for decuplet up to the third order and for octet up to the second order are much compatible with the experimental data. But things becomes quite inadequate for the octet to the third order. In order to overcome the inadequacy, a heuristic discussion is presented. The properties of SU(3) rotating excited states 27-let(with spin 1/2 or 3/2),10$^*$-let (with spin 1/2) and 35-let (…
We study a Skyrme-type model with a potential term motivated by Bose-Einstein condensates (BECs), which we call the BEC Skyrme model. We consider two flavors of the model, the first is the Skyrme model and the second has a sixth-order derivative term instead of the Skyrme term; both with the added BEC-motivated potential. The model contains toroidally shaped Skyrmions and they are characterized by two integers P and Q, representing the winding numbers of two complex scalar fields along the toroidal and poloidal cycles of the torus, respectively. The baryon number is B=PQ. We find stable Skyrmi…
We calculate the rotational-vibrational spectrum in the BPS Skyrme model for the hedgehog skyrmion with baryon number one. The resulting excitation energies for the nucleon and delta Roper resonances are slightly above their experimental values. Together with the fact that in the standard Skyrme model these excitation energies are significantly lower than the experimental ones, this provides strong evidence for the conjecture that the inclusion of the BPS Skyrme model is necessary for a successful quantitative description of physical properties of baryons and nuclei.
We study the effect of representation mixing in the SU(3) Skyme model by diagonalizing exactly the representation-dependent part. It is observed that even without the next-to-leading order symmetry breaking terms the low-lying baryon masses as well as the recently discovered $Θ+$ and $\Cascade_{\bar{10}}$ can be fairly well reproduced within 3% accuracy. It is also demonstrated that the mixing effect is not negligible in decay processes of $\{\bar{10}\}$. In particular the effect of mixing with $\{27\}$ is found to be quite large. These results are compatible with the second-order perturbation…
We investigate and revisit certain aspects of relativistic baryons in the Skyrme model. Starting from static baryons in the helicity eigenstates, we generalize their wavefunctions to the non-static and relativistic regime. A new representation for gamma matrices in the SU(2) collective space is constructed and the corresponding Dirac equation is obtained. Furthermore, we extend the analysis of Adkins et al. concerning vector current vacuum expectation values for baryon states to arbitrary momenta and calculate baryon elastic form factors in a general framework exhibiting vector meson dominance…
We report on the result of some investigations concerning the radiative decays of decuplet baryons and the non-leptonic weak decays of the octet baryons in the context of topological chiral soliton models. Our results are compared with those of alternative baryon models. For the radiative decays we find that the predictions are similar to those of quark models. In the case of the non-leptonic weak decays, we find that although the predicted S-wave amplitudes are in rather good agreement with the observed values, the model is not able to reproduce the empirical P-wave amplitudes. Thus, in contr…
In this paper, I present almost my works performed during my time at VNU. I was interested in the composite Skyrme model proposed by H. Y. Cheung and F. Gursey. The expanding for this model based on results obtained from the original Skyrme model given by T. H. R. Skyrme in 1961 was general and interesting.
We introduce a variation of the Bose-Einstein condensate(BEC)-Skyrme model, with an altered potential for miscible BECs that gives rise to two physical vortex strings. In the ground state of each topological sector, the vortices are linked exactly $B$ times, due to a recently formulated theorem, with $B$ being the baryon number of the solution. The model also possesses metastable states, where the vortices are degenerate and do not lend the interpretation of the baryon number as the linking number of the vortices.
The Skyrme model is reconsidered from an effective theory point of view. From the most general chiral Lagrangian up to including terms of order $p^4$, $N_c$ and $δm^2$ ($δm\equiv m_s-m$), new interactions, which have never been considered before, appear upon collective coordinate quantization. We obtain the parameter set best fitted to the observed low-lying baryon masses, by performing the second order perturbative calculations with respect to $δm$. We calculate the masses and the decay widths of the other members of (mainly) anti-decuplet pentaquark states. The formula for the decay widths i…
The topological Skyrme model is known to give a successful description of baryons. As a consistency check, here it is shown that in view of the recent discovery of charge quantization as an intrinsic and basic property of the Standard Model and the color dependence arising therein, the Skyrme Model is indeed completely consistent with the Standard Model.
Within the class of field theories with the field contents of the Skyrme model, one submodel can be found which consists of the square of the baryon current and a potential term only. For this submodel, a Bogomolny bound exists and the static soliton solutions saturate this bound. Further, already on the classical level, this BPS Skyrme model reproduces some features of the liquid drop model of nuclei. Here, we investigate the model in more detail and, besides, we perform the rigid rotor quantization of the simplest Skyrmion (the nucleon). In addition, we discuss indications that the viability…
We study two-dimensional, large $N$ field theoretic models (Gross-Neveu model, 't Hooft model) at finite baryon density near the chiral limit. The same mechanism which leads to massless baryons in these models induces a breakdown of translational invariance at any finite density. In the chiral limit baryonic matter is characterized by a spatially varying chiral angle with a wave number depending only on the density. For small bare quark masses a sine-Gordon kink chain is obtained which may be regarded as simplest realization of the Skyrme crystal for nuclear matter. Characteristic differences …
A consistent ansatz for the Skyrme model in (3+1)-dimensions which is able to reduce the complete set of Skyrme field equations to just one equation for the profile in situations in which the Baryon charge can be arbitrary large is introduced: moreover, the field equation for the profile can be solved explicitly. Such configurations describe ordered arrays of Baryonic tubes living in flat space-times at finite density. The plots of the energy density (as well as of the Baryon density) clearly show that the regions of maximal energy density have the shape of a tube: the energy density and the B…
The ${\bf 27}_{J=3/2}$-plet mass spectrum and the ${\bf 27}_{3/2}$-$\bar{\bf 10}$ mass splittings are computed in the framework of the minimal SU(3)$_f$ extended Skyrme model. As functions of the Skyrme charge $e$ and the SU(3)$_f$ symmetry breaking parameters the predictions are presented in tabular form. The predicted mass splitting ${\bf 27}_{3/2}$-$\bar{\bf 10}$ is the smallest among all SU(3)$_f$ baryonic multiplets.
We construct the first analytic self-gravitating Skyrmions with higher Baryon charge in four dimensions for the $SU(3)$-Skyrme-Einstein-$Λ$ theory by combining the generalized hedgehog ansatz with the approach developed by Balachandran et al. to describe the first (numerical) example of a non-embedded solution. These are genuine $SU(3)$ analytic solutions instead of trivial embeddings of $SU(2)$ into $SU(3)$ and its geometry is that of a Bianchi IX Universe. The Skyrme ansatz is chosen in such a way that the Skyrme field equations are identically satisfied in the sector with Baryon charge 4. T…
In the heavy quark and large Nc limits, ordinary (exotic) heavy baryons can be considered as bound states of heavy mesons (anti-mesons)and chiral solitons. In these limits, the heavy mesons (or anti-mesons) and the chiral solitons are extremely heavy and are presumed to fall to the bottom of the effective potential. Previous studies have approximated the effective potential as harmonic about the minimum. However, when realistic masses for the heavy meson and chiral soliton are considered, longer range parts of the effective potential can become relevant. In this paper, we show that these longe…
We continue the investigation of thermodynamical properties of the BPS Skyrme model. In particular, we analytically compute the baryon chemical potential both in the full field theory and in a mean-field approximation. In the full field theory case, we find that the baryon chemical potential is always exactly proportional to the baryon density, for arbitrary solutions. We further find that, in the mean-field approximation, the BPS Skyrme model approaches the Walecka model in the limit of high density - their thermodynamical functions as well as the equation of state agree in this limit. This f…
The mass spectrum and magnetic moments of Ξand Ωbaryon resonances are investigated in the bound state approach of the Skyrme model. The empirical hyperon spectrum shows that several hyperon resonances share a pattern of (approximately) equal mass spacings between the states of same spin but of opposite parity. It is found that this pattern can be explained mostly by the energy difference between the P-wave and S-wave kaons bound to the soliton. Although one cannot exclude the possibility that these states can be described as pion-hyperon resonances, the present approach predicts that Ξ(1620) a…
A Skyrme type Lagrangian for a skyrmion imbedded in a baryon rich environment is proposed. The dependence of static nucleon properties and nucleon - nucleon tensor interaction on nuclear density is investigated.
We construct a spherical domain wall which has baryon charge distributed on a sphere of finite radius in a Skyrme model with a sixth order derivative term and a modified mass term. Its distribution of energy density likewise takes the form of a sphere. In order to localize the domain wall at a finite radius we need a negative coefficient in front of the Skyrme term and a positive coefficient of the sixth order derivative term to stabilize the soliton. Increasing the pion mass pronounces the shell-like structure of the configuration.
In this paper we investigate an SU(3) extension of the chiral quark-meson model. The spectra of baryons with strangeness, charm and bottom are considered within a "rigid oscillator" version of this model. The similarity between the quark part of the Lagrangian in the model and the Wess-Zumino term in the Skyrme model is noted. The binding energies of baryonic systems with baryon number B=2 and 3 possessing strangeness or heavy flavor are estimated. The results obtained are in good qualitative agreement with those obtained previously in the topological soliton (Skyrme) model.
We illustrate the exotic SU(3) baryon sub-multiplets in the SU(4) baryon multiplets predicted from the flavor SU(4) collective-coordinate quantization, and investigate the exotic states with charm number $C=\pm1$ up to leading order of $1/N_c$ under chiral $SU(3)_L\times SU(3)_R$ symmetry and the heavy quark limit from bound state approach. We find that there exist the $\bar{15}$-plets and 24-plets with C=1 and the $\bar{6}$-plets, 15-plets and $15^{\prime}$-plets with $C=-1$ bounded in this approach, qualitatively consistent with predictions from the flavor SU(4) collective-coordinate quantiz…
We present a procedure to calculate 1-loop graphs in the soliton sector of chiral Lagrangians and use it to calculate quantum corrections to certain baryon observables in Skyrme-type models. Results generally show an improvement over the values obtained in tree approximation except for the case of the axial coupling g_A.
We study a Skyrme-type model with a quadratic potential for a field with $S^2$ vacua. We consider two flavors of the model, the first is the Skyrme model and the second has a sixth-order derivative term instead of the Skyrme term; both with the added quadratic potential. The model contains molecules of half Skyrmions, each of them is a global (anti-)monopole with baryon number 1/2. We numerically construct solutions with baryon numbers one through six, and find stable solutions which look like beads on rings. We also construct a molecule with fractional Skyrmions having the baryon numbers 1/3 …
Normally, standard (ungauged) skyrmion masses are proportional to the coupling of the Skyrme term needed for stability, and so can grow to infinite magnitude with increasing coupling. In striking contrast, when skyrmions are gauged, their masses are bounded above for any Skyrme coupling, and, instead, are of the order of monopole masses, O(v/g), so that the coupling of the Skyrme term is not very important. This boundedness phenomenon and its implications are investigated.
The traditional approach to fixing the parameters of the Skyrme model requires the energy of a spinning Skyrmion to reproduce the nucleon and delta masses. The standard Skyrme parameters, which are used almost exclusively, fix the pion mass to its experimental value and fit the two remaining Skyrme parameters by approximating the spinning Skyrmion as a rigid body. In this paper we remove the rigid body approximation and perform numerical calculations which allow the spinning Skyrmion to deform and break spherical symmetry. The results show that if the pion mass is set to its experimental value…
Analytical treatment of skyrmions given by rational map (RM) ansaetze proposed recently for the Skyrme model is extended to the model including the 6-th order term in chiral fields derivatives in the lagrangian (the SK6 variant of the model) and used for calculation of different properties of multiskyrmions. For special class of profile functions approximating the true profile and the domain wall behaviour at the same time, the masses and other static properties of multiskyrmions are expressed in terms of the Euler-type integrals. An upper bound is obtained for the masses of RM multiskyrmions …
The equation of state and phase diagram of strongly interacting matter composed of $α$ particles are studied in the mean-field approximation. The particle interactions are included via a Skyrme-like mean field, containing both attractive and repulsive terms. The model parameters are found by fitting known values of binding energy and baryon density in the ground state of $α$ matter, obtained from microscopic calculations by Clark and Wang. Thermodynamic quantities of $α$ matter are calculated in the broad domains of temperature and baryon density, which can be reached in heavy-ion collisions a…
The analogy between the Skyrme and Higgs field leads to the conjecture that all fermions are skyrmions and thus always carry conserved quantum numbers, which are identified with baryon or lepton quantum numbers. This connection between spin and quantum numbers, which parallels the connection between spin and statistics due to the Pauli principle, may explain why supersymmetry has not been observed. Creation of s-particles at higher than present energies due to a breakdown of the Skyrme mechanism might imply the violation of the exclusion principle.
We offer the Skyrme model on a lattice as an effective field theory - fully quantized - of baryon-meson interactions at temperatures below the chiral phase transition. We define a local topological density that involves the volumes of tetrahedra in the target space S^3 and we make use of Coxeter's formula for the Schlafli function to implement it. This permits us to calculate the mean-square radius of a skyrmion in the three-dimensional lattice Skyrme model, which may be viewed as a Ginzburg-Landau effective theory for the full quantum theory at finite temperature. We find that, contrary to ex…
We use the method of QCD Sum Rules to estimate the masses of the charm baryon, $Λ^+_c$, bottom baryon $Λ^0_b$, strange baryon $Λ^0_s$ and compare them to their experimental values.
