arXiv subjects
Publications and source records attributed to Thomas D. Cohen.
Exotic baryons have been predicted in the context of the chiral soliton model. These states have been identified with strangeness +1 resonances reported in a number of experiments. In this talk it is pointed out that the technique used to quantize these solitons in most conventional treatments depends on dynamical assumptions beyond those in standard large Nc physics. These additional assumptions have never been justified.
This paper reviews some recent progress on QCD functional integrals at nonzero chemical potentials. One issue discussed is the use of QCD inequalities for this regime. In particular, the positivity of the integrand of particular Euclidean space functional integrals for two-flavor QCD with degenerate quark masses is used to demonstrate that the free energy per unit volume for QCD with a baryon chemical potential $μ_B$ (and zero isospin chemical potential) is necessarily greater than the free energy with isospin chemical potential $μ_I = \frac{2 μ_B}{N_c} $ (and zero baryon chemical potential). This result may be of use in model finite density systems. A corollary to this result is a rigorous {\it ab initio} bound on the nucleon mass. The second major issue addressed is the so-called ``Silver Blaze'' problem: the fact that at zero temperature and chemical potentials less than some critical value the free energy remains as that of the vacuum. This is puzzling in the context of a functional integral since a chemical potential affects the functional determinant of the Dirac operator and any nonzero $μ$ changes every eigenvalue of the Dirac operator compared to the $μ=0$ value. The isospin Silver Blaze problem is solved through the study of the spectrum of the operator $γ_0 (\dslash + m)$. The status of the baryon Silver Blaze problem is briefly discussed.
The problem of describing low-energy two-body scattering for systems with two open channels with different thresholds is addressed in the context of an effective field theory. In particular, the problem where the threshold is unnaturally small and the cross section at low energy is unnaturally large is considered. It is shown that the lowest-order point coupling associated with the mixing of the channels scales as $Λ^{-2}$ rather than $Λ^{-1}$ (the scaling of the same-channel coupling and the scaling in a single-channel case) where $Λ$ is the ultraviolet cutoff. The renormalization of the theory at lowest order is given explicitly. The treatment of higher orders is straightforward. The potential implications for systems with deep open channels are discussed.
A light collective theta+ baryon state (with strangeness +1) was predicted via rigid-rotor collective quantization of SU(3) chiral soliton models. This paper explores the validity of this treatment. A number of rather general analyses suggest that predictions of exotic baryon properties based on this approximation do not follow from large Nc QCD. These include an analysis of the baryon's width, a comparison of the predictions with general large Nc consistency conditions of the Gervais-Sakita-Dashen-Manohar type; an application of the technique to QCD in the limit where the quarks are heavy; a comparison of this method with the vibration approach of Callan and Klebanov; and the 1/Nc scaling of the excitation energy. It is suggested that the origin of the problem lies in an implicit assumption in the that the collective motion is orthogonal to vibrational motion. While true for non-exotic motion, the Wess-Zumino term induces mixing at leading order between collective and vibrational motion with exotic quantum numbers. This suggests that successful phenomenological predictions of theta+ properties based on rigid-rotor quantization were accidental.
A model recently introduced by Jaffe and Wilczek based on the quarks being dynamically bound into diquarks has been used to predict that the recently observed exotic baryons (pentaquarks) fall into a nearly ideally mixed combination of an octer and anti-decuplet representations of SU(3) flavor. The model predicts two states with nucleon quantum numbers which have tentatively been identified with the N*(1440) and the N*(1710). This paper examines the viability of this model by focusing on the decay width of the nucleon members of the multiplet. An inequality relating the partial widths of these nucleon states in the N+nucleon channel to the width of the theta+ is derived for this model under the assuming ideal mixing and that the only significant exact SU(3) symmetry violations are the result of ideal mixing, threshold effects and the masses of pseudo-Goldstone bosons. This inequality is badly violated if the states in the multiplet are the N*(1440) and the N*(1710) and if the recent bounds extracted for the theta+ width are reliable. Thus, the model appears to require a scenario with the existence of at least one presently unknown resonance with nucleon quantum numbers.
Predictions for a light collective $Θ^+$ baryon state (with strangeness +1) based on the collective quantization of chiral soliton models are shown to be inconsistent with large $N_c$ QCD. The lightest strangeness +1 state to emerge from the analysis has an excitation energy which at large $N_c$ scales as $N_c^0$ while collective quantization is legitimate only for excitations which go to zero as $N_c \to \infty$. This inconsistency strongly suggests that predictions for $Θ^+$ properties based on collective quantization of chiral solitons are not valid.
We study excited baryon decay widths in large N_c QCD. It was suggested previously that some spin-flavor mixed-symmetric baryon states have strong couplings of O(N_c^{-1/2}) to nucleons [implying narrow widths of O(1/N_c)], as opposed to the generic expectation based on Witten's counting rules of an O(N_c^0) coupling. The calculation obtaining these narrow widths was performed in the context of a simple quark-shell model. This paper addresses the question of whether the existence of such narrow states is a general property of large N_c QCD. We show that a general large N_c QCD analysis does not predict such narrow states; rather they are a consequence of the extreme simplicity of the quark model.
We show that under a number of rather plausible assumptions QCD spectrum may contain a number of mesons which have not been predicted or observed. Such states will have the quantum numbers of two existing mesons and masses very close to the dissociation threshold into the two mesons. Moreover, at least one of the two mesonic constituents itself must be very close to its dissociation threshold. In particular, one might expect the existence of loosely bound systems of $D$ and $\D$; similarly, $K$ and $\ff$, $\bar{K}$ and $\ff$, $K$ and $å$ and $\bar{K}$ and $å$ can be bound. The mechanism for binding in these cases is the S-wave kaon exchange. The nearness of one of the constituents to its decay threshold into a kaon plus a remainder, implies that the range of the kaon exchange force becomes abnormally long--significantly longer than $1/m_K$ which greatly aids the binding.
A strangeness +1 exotic baryon Theta^+ has recently been seen in a number of experiments. We demonstrate that in large N_c QCD the existence of such a state implies the existence of S = +1 partner states with various spins and isospins but comparable masses. We discuss the spectroscopy of such states and possible channels in which they can be observed, based on the simple assumption that those states with pentaquark quantum numbers are unlikely to be large N_c artifacts.
We demonstrate that the two major complementary pictures of large N_c baryon resonances--as single-quark orbital excitations about a closed-shell core [giving SU(2N_F) x O(3) multiplets], and as resonances in meson-baryon scattering amplitudes--are completely compatible in a specific sense: Both pictures give rise to a set of multiplets of degenerate states, for which any complete spin-flavor multiplet within one picture fills the quantum numbers of complete multiplets in the other picture. This result is demonstrated by: (i) straightforward computation of the lowest multiplets in both pictures; (ii) a study of the nature of quark excitations in a hedgehog picture; (iii) direct group-theoretical comparison of the constraints in the two pictures.
The positivity of the integrand of certain Euclidean space functional integrals implies that the free energy per unit volume for QCD with a baryon chemical potential $μ_B$ (and zero isospin chemical potential) is greater than the free energy with isospin chemical potential $μ_I = (2 μ_B)/N_c$ (and zero baryon chemical potential). This relation implies a bound on the nucleon mass: there exists a particle X in QCD such that $M_N \ge (N_c m_X)/(2 I_X)$ where $m_X$ is the mass and of the particle and $I_X$ is its isospin.
The spin-flavor structure of certain nucleon-nucleon scattering observables derived from the large N_c limit of QCD in the kinematical regime where time-dependent mean-field theory is valid is discussed. In previous work, this regime was taken to be where the external momentum was of order N_c which precluded the study of differential cross sections in elastic scattering. Here it is shown that the regime extends down to order N_c^{1/2} which includes the higher end of the elastic regime. The prediction is that in the large N_c limit, observables describable via mean-field theory are unchanged when the spin and isospin of either nucleon are both flipped. This prediction is tested for proton-proton and neutron-proton elastic scattering data and found to fail badly. We argue that this failure can be traced to a lack of a clear separation of scales between momentum of order N_c^{1/2} and N_c^1 when N_c is as small as three. The situation is compounded by an anomalously low particle production threshold due to approximate chiral symmetry.
We analyze excited baryon properties via a 1/N_c expansion from two perspectives: as resonances in meson-nucleon scattering, and as single-quark excitations in the context of a simple quark model. For both types of analysis one can derive novel patterns of degeneracy that emerge as N_c --> \infty, and that are shown to be compatible with one another. This helps justify the single-quark excitation picture and may give some insight into its successes. We also find that in the large N_c limit one of the S_{11} baryons does not couple to the pi-N channel but couples to the eta-N channel. This is empirically observed in the N(1535), which couples very weakly to the pi-N channel and quite strongly to the eta-N channel. The comparatively strong coupling of the N(1650) to the pi-N channel and weak coupling to eta-N channel is also predicted. In the context of the simple quark model picture we reproduce expressions for mixing angles that are accurate up to O(1/N_c) corrections and are in good agreement with mixing angles extracted phenomenologically.
We show that excited baryons in large N_c QCD form multiplets, within which masses are first split at O(1/N_c). The dominant couplings of resonances to various mesons are highly constrained: The N(1535) decays at leading 1/N_c order exclusively to eta-N rather than pi-N, and vice versa for the N(1650). This multiplet structure is reproduced by a simple large N_c quark model, well studied in the literature, that describes resonances as single-quark excitations.
The large $N_c$ nuclear potential puzzle arose because three- and higher-meson exchange contributions to the nucleon-nucleon potential did not automatically yield cancellations that make these contributions consistent with the general large $N_c$ scaling rules for the potential. Here it is proposed that the resolution to this puzzle is that the scaling rules only apply for energy-independent potentials while all of the cases with apparent inconsistencies were for energy-dependent potentials. It is shown explicitly how energy-dependent potentials can have radically different large N behavior than an equivalent energy-independent one. One class of three-meson graphs is computed in which the contribution to the energy-independent potential is consistent with the general large N rules even though the energy-dependent potential is not.
We study certain physical observables of isoscalar heavy baryons using potential models based on hadronic degrees of freedom. The goal is to compare these results with those from an effective theory obtained in a combined heavy quark and large $N_{c}$ expansion and thereby test the convergence of the effective theory. We study the excitation energy of $Λ_{b}$ and semileptonic decay form factors. The models tend to confirm the usefulness of the effective theory for most observables.
Nucleon-nucleon scattering observables are considered in the context of the large $N_c$ limit of QCD for initial states with moderately high momenta ($p \sim N_c$). The scattering is studied in the framework of the time-dependent mean-field approximation. We focus on the dependence of those observables on the spin and isospin of the initial state which may be computed using time-dependent mean-field theory. We show that, up to corrections, all such observables must be invariant under simultaneous spin and isospin flips ({\it i.e.} rotations through $π/2$ in both spin and isospin) acting on either particle. All observables of this class obtained from spin unpolarized measurements must be isospin independent up to $1/N_c$ corrections. Moreover, it can be shown that the leading correction is of relative order $1/N_c^2$ rather than $1/N_c$.
The nature of the nonrelativistic nucleon-nucleon potential in the large N_c limit is discussed. In particular, we address the consistency of the meson exchange picture of nucleon interactions. It is shown that the nonrelativistic nucleon-nucleon potential extracted from the Feynmann graphs up to and including two-meson exchange diagrams satisfies the spin-flavor counting rules of Kaplan and Savage, and Kaplan and Manohar, provided the nucleon momenta is of order N_{c}^{0}. The key to this is a cancelation of the retardation effect of the box graphs against the contributions of the crossed-box diagram. The consistency requires including $Δ$ as an intermediate state.