arXiv subjects
Publications and source records attributed to E. S. Swanson.
The interaction between static quarks is derived by applying many-body techniques to QCD in Coulomb gauge. The result is shown to be exact in the IR and UV limits, and agrees remarkably well with lattice computations.
Modern experiment requires a reliable theoretical framework for low energy QCD. Some of the requirements for constructing a new model of QCD are presented here. Progress toward these requirements are highlighted.
Many of the hadron-hadron cross sections required for the study of the dynamics of matter produced in relativistic heavy-ion collisions can be calculated using the quark-interchange model. Here we evaluate the low-energy dissociation cross sections of $J/ψ$, $ψ'$, $χ$, $Υ$, and $Υ'$ in collision with $π$, $ρ$, and $K$, which are important for the interpretation of heavy-quarkonium suppression as a signature for the quark gluon plasma. These comover dissociation processes also contribute to heavy-quarkonium suppression, and must be understood and incorporated in simulations of heavy-ion collisions before QGP formation can be established through this signature.
We apply a quark interchange model to spin-dependent and exotic meson-meson scattering. The model includes the complete set of standard quark model forces, including OGE spin-orbit and tensor and scalar confinement spin-orbit. Scattering amplitudes derived assuming SHO and Coulomb plus linear plus hyperfine meson wavefunctions are compared. In I=2 pi pi we find approximate agreement with the S-wave phase shift from threshold to 1.5 GeV, where we predict an extremum that is supported by the data. Near threshold we find rapid energy dependence that may reconcile theoretical estimates of small scattering lengths with experimental indications of larger ones based on extrapolation of measurements at moderate kpi^2. In PsV scattering we find that the quark-quark L*S and T forces map into L*S and T meson-meson interactions, and the P-wave L*S force is large. Finally we consider scattering in J^PC-exotic channels, and note that some of the Deck effect mechanisms suggested as possible nonresonant origins of the pi_1(1400) signal are not viable in this model.
In this contribution we summarize experimental information and theoretical results for the dissociation cross sections of charmonium by light hadrons. Theoretical predictions for these RHIC-related processes differ by orders of magnitude over the physically relevant energy range. The results found by the author and collaborators using a constituent interchange model, which predicts cross sections in the mb region near threshold, are discussed in more detail.
We evaluate the cross sections for the dissociation of $J/ψ$ and $ψ'$ by $π$ and $ρ$ at low collision energies, using the quark-interchange model of Barnes and Swanson. The dissociation cross section for $J/ψ$ by $π$ is found to be relatively small with a maximum of about 1 mb and a kinetic energy threshold of 0.65 GeV. The pion-induced $ψ'$ dissociation cross section is found to be much larger, with a maximum of about 5 mb and a lower threshold. Dissociation cross sections for $J/ψ$ and $ψ'$ by $ρ$ mesons are also evaluated and are found to be large near threshold.
Using the quark-interchange model of Barnes and Swanson, we evaluate the dissociation cross sections for $J/ψ$ and $ψ'$ by $π$ and $ρ$ at low collision energies. In collisions with $π$ mesons near threshold the $π+ J/ψ$ dissociation cross section is predicted to be small, but the $π+ψ'$ cross section is found to be quite large, in qualitative agreement with experimental data on $J/ψ$ and $ψ'$ production in high-energy heavy-ion collisions. The $ρ+ J/ψ$ and $ρ+ ψ'$ dissociation cross sections are both predicted to be large numerically and are divergent near threshold. These $ρ+ J/ψ$ and $ρ+ ψ'$ cross sections show considerable sensitivity to the mass of the $ρ$ meson if it is off energy shell.
A quark model calculation of the processes gamma gamma -> pi+ pi- and gamma gamma -> pi0 pi0 is performed. At tree level, only charged pions couple to the initial state photons and neutral pions are not expected in the final state. However, a small but significant gamma gamma -> pi0 pi0 cross section is observed. We demonstrate that this may be accounted for by a rotation in isospin space induced by final state interactions. The resulting pi+ pi- cross section is in good agreement with experiment while the pi0 pi0 cross section is in qualitative agreement with the data.
In this paper we derive quark model results for scattering amplitudes and equivalent low energy potentials for heavy meson pairs, in which each meson contains a heavy quark. This "BB" system is an attractive theoretical laboratory for the study of the nuclear force between color singlets; the hadronic system is relatively simple, and there are lattice gauge theory (LGT) results for V_BB(r) which may be compared to phenomenological models. We find that the quark model potential (after lattice smearing) has qualitative similarities to the LGT potential in the two B*B* channels in which direct comparison is possible, although there is evidence of a difference in length scales. The quark model prediction of equal magnitude but opposite sign for I=0 and I=1 potentials also appears similar to LGT results at intermediate r. There may however be a discrepancy between the LGT and quark model I=1 BB potentials. A numerical study of the two-meson Schrodinger equations in the (bqbar)(bqbar) and (cqbar)(cqbar) sectors with the quark model potentials finds a single "molecule", in the I=0 BB* sector. Binding in other channels might occur if the quark model forces are augmented by pion exchange.
Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.
Continuing our previous QCD Hamiltonian studies in the gluonic and quark sectors, we describe a new renormalization procedure which generates an effective Hamiltonian. The formulation, which is in the Coulomb gauge, provides an improved framework for investigating hadron structure.
The phenomenology of a newly developed model of hybrid meson decay is developed. The decay mechanism is based on the heavy quark expansion of QCD and the strong coupling flux tube picture of nonperturbative glue. A comprehensive list of partial decay widths of a wide variety of light, $s\bar s$, $c\bar c$, and $b \bar b$ hybrid mesons is presented. Results which appear approximately universal are highlighted along with those which distinguish different hybrid decay models. Finally, we examine several interesting hybrid candidates in detail.
Hybrid meson energies are calculated in the static quark limit with the Dynamical Quark Model (DQM). In the DQM, transverse gluons are represented as effective constituents with a dynamically generated mass. Hybrid masses are determined within the Tamm-Dancoff approximation for the resulting relativistic Salpeter equation. Although the general features of the adiabatic potential surfaces correspond with lattice data, the results disagree on level orderings. Similar problems appear to exist in all constituent glue models of hybrids. We conclude that constituent gluons do not accurately represent soft gluonic degrees of freedom. The steps necessary to correct this deficiency are discussed.
It has become traditional to assume that the Dirac structure of the phenomenological quark confinement potential is scalar $\otimes$ scalar. We use the heavy quark expansion of the Coulomb gauge QCD Hamiltonian and the Flux Tube model to demonstrate that this is true but in the effective sense only. The demonstration contains some surprises: confinement is actually vector $\otimes$ vector and it is nonperturbative mixing between ordinary and hybrid $Q \bar Q$ states which generates the scalar-like spin dependent potential at order $1/m_q^2$. Thus the existence of hybrids is crucial to establishing well-known spin splitting phenomenology. Finally, the resolution also indicates that the gluonic degrees of freedom in a hybrid must be of a collective nature.
A model which combines the perturbative behavior of QCD with low energy phenomenology in a unified framework is developed. This is achieved by applying a similarity transformation to the QCD Hamiltonian which removes interactions between the ultraviolet cutoff and an arbitrary lower scale. Iteration then yields a renormalization group improved effective Hamiltonian at the hadronic energy scale. The procedure preserves the standard ultraviolet behavior of QCD. Furthermore, the Hamiltonian evolves smoothly to a phenomenological low energy behavior below the hadronic scale. This method has the benefit of allowing radiative corrections to be directly incorporated into nonperturbative many-body techniques. It is applied to Coulomb gauge QCD supplemented with a low energy linear confinement interaction. A nontrivial vacuum is included in the analysis via a Bogoliubov-Valatin transformation. Finally, the formalism is applied to the vacuum gap equation, the quark condensate, and the dynamical quark mass.
We discriminate gluonic hadrons from conventional $q\bar q$ states by surveying radial and orbital excitations of all I=0 and I=1 $n\bar n$ systems anticipated up to 2.1 GeV. We give detailed predictions of their quasi-two-body branching fractions and identify characteristic decay modes that can isolate quarkonia. Several of the ``missing mesons'' with L$_{q\bar q}=2$ and L$_{q\bar q}=3$ are predicted to decay dominantly into certain S+P and S+D modes, and should appear in experimental searches for hybrids in the same mass region. We also consider the topical issues of whether some of the recently discovered or controversial meson resonances, including glueball and hybrid candidates, can be accommodated as quarkonia.
Open-flavor strong decays are mediated by $q\bar q$ pair production, which is known to occur dominantly with \3p0 quantum numbers. The relation of the phenomenological \3p0 model of these decays to ``microscopic" QCD decay mechanisms has never been clearly established. In this paper we investigate $q\bar q$ meson decay amplitudes assuming pair production from the scalar confining interaction (sKs) and from one gluon exchange (OGE). sKs pair production predicts decay amplitudes of approximately the correct magnitude and D/S amplitude ratios in $b_1\toωπ$ and $a_1\toρπ$ which are close to experiment. The OGE decay amplitude is found to be subdominant in most cases, a notable exception being $^3$P$_0\to{}^1$S$_0+{}^1$S$_0$. The full sKs~+~OGE amplitudes differ significantly from \3p0 model predictions in some channels and can be distinguished experimentally, for example through an accurate comparison of the D/S amplitude ratios in $b_1\toωπ$ and $a_1\toρπ$.
We present results from analytical and numerical studies of a flux tube model of hybrid mesons. Our numerical results use a Hamiltonian Monte Carlo algorithm and so improve on previous analytical treatments, which assumed small flux tube oscillations and an adiabatic separation of quark and flux tube motion. We find that the small oscillation approximation is inappropriate for typical hadrons and that the hybrid mass is underestimated by the adiabatic approximation. For physical parameters in the ``one-bead" flux tube model we estimate the lightest hybrid masses (${}_ΛL = {}_1 P$ states) to be 1.8-1.9~GeV for $u\bar u$ hybrids, 2.1-2.2~GeV for $s\bar s$ and 4.1-4.2~GeV for $c\bar c$. We also determine masses of conventional $q\bar q$ mesons with $L=0$ to $L=3$ in this model, and confirm good agreement with experimental $J$-averaged multiplet masses. Mass estimates are also given for hybrids with higher orbital and flux-tube excitations. The gap from the lightest hybrid level (${}_1P$) to the first hybrid orbital excitation (${}_1D$) is predicted to be $\approx 0.4$~GeV for light quarks $(q=u,d)$ and $\approx 0.3$~GeV for $q=c$. Both ${}_1P$ and ${}_1D$ hybrid multiplets contain the exotics $1^{-+}$ and $2^{+-}$; in addition the ${}_1P$ has a $0^{+-}$ and the ${}_1D$ contains a $3^{-+}$. Hybrid mesons with doubly-excited flux tubes are also considered. The implications of our results for spectroscopy are discussed, with emphasis on charmonium hybrids, which may be accessible at facilities such as BEPC, KEK, a Tau-Charm Factory, and in $ψ$ production at hadron colliders.