arXiv subjects
Publications and source records attributed to A. M. Green.
A brief review is given of attempts to understand the energies of four-quark systems calculated on a lattice in terms of nuclear-physics-inspired many-body techniques involving interquark potentials. Results are given for the next stage of this study where the wavefunctions of heavy-light mesons are also calculated on a lattice.
Recent lattice calculations on the interaction energy of two heavy-light mesons (Q^2\bar{q}^2) are interpreted in terms of the potential of the corresponding single heavy-light meson (Q\bar{q}). This model leads to a large overestimate of the binding compared with the lattice data -- unless the basic Q\bar{q} potential is modified to become a four-quark potential.
The potential between static-light mesons forming a meson-meson or a meson-antimeson system is calculated in quenched and unquenched SU(3) gauge theory. We use the Sheikholeslami-Wohlert action and statistical estimators of light quark propagators with maximal variance reduction. The dependence of the potentials on the light quark spin and isospin and the effect of meson exchange is investigated. Our main motivation is exploration of bound states of two mesons and string breaking. The latter also involves the two-quark potential and the correlation between two-quark and two-meson states.
By comparing lattice data for the two heavy-light meson system (Q^2 qbar^2) with a standard many-body approach employing only interquark potentials, it is shown that the use of unmodified two-quark potentials leads to a gross overestimate of the binding energy.
The coupled pi+N, eta+N, gamma+N systems are described by a K-matrix method. The parameters in this model are adjusted to get an optimal fit to pi+N -> pi+N, pi+N -> eta+N, gamma+N -> pi+N and gamma+N -> eta+N data in an energy range of about 100 MeV each side of the eta-threshold. The coupling of photons to the N(1535) state is extracted and also an alternative to the current S11(gamma+N -> pi+N) amplitudes suggested. Expansions are given for the eta-eta and gamma-eta amplitudes in terms of the eta-momentum. Effects of interference of this state with background potential interactions are discussed and experimental consequences are indicated.
In order to understand the binding of four static quarks, flux distributions corresponding to these binding energies are studied in quenched SU(2) and also related to a model for the energies. The potential relevant to string breaking between two heavy-light mesons is measured in quenched SU(3) using stochastic estimates of light quark propagators with the Sheikholeslami-Wohlert action.
The optical potential for the $η$-meson is calculated. This is based on a new determination of a large $η$-N scattering length and recent experiments of $η$ production in two nucleon collisions. These determine the $η$ - nuclear potential well to be about 45 MeV deep and able to support S, P, D and F quasibound states. Some of the higher angular momentum states are fairly narrow and offer a chance of experimental detection.
We extract pole positions for the N(1535) and N(1650) resonances using two different models. The positions are determined from fits to different subsets of the existing $πN\toπN$, $πN\toηN$ and $γp\toηp$ data and found to be 1515(10)--i85(15)MeV and 1660(10)--i65(10)MeV, when the data is described in terms of two poles. Sensitivity to the choice of fitted data is explored. The corresponding $ππ$ and $ηη$ residues of these poles are also extracted.
A potential model for four interacting quarks is constructed in SU(2) from six basis states -- the three partitions into quark pairs, where the gluon field is either in its ground state or first excited state. With four independent parameters to describe the interactions connecting these basis states, it is possible to fit 100 pieces of data -- the ground and first excited states of configurations from six different four-quark geometries calculated on a 16^3*32 lattice.
The full spatial distribution of the color fields of two and four static quarks is measured in lattice SU(2) field theory at separations up to 1 fm at beta=2.4. The four-quark case is equivalent to a qbar q qbar q system in SU(2) and is relevant to meson-meson interactions. By subtracting two-body flux tubes from the four-quark distribution we isolate the flux contribution connected with the four-body binding energy. This contribution is further studied using a model for the binding energies. Lattice sum rules for two and four quarks are used to verify the results.
As a step towards understanding multi-quark systems abundant in nature we construct a model that reproduces the binding energies of static four-quark systems. These energies have been calculated using SU(2) lattice gauge theory for a set of six different geometries representative of the general case. The model is based on ground and excited state two-body potentials and multi-quark interaction terms.
Action and energy flux-tube profiles are computed, in SU(2) with beta=2.4,2.5, for two quarks up to 1 fm apart and for which the colour fields are in their ground state (A_1g) and the first (E_u) and higher (A'_1g) excited gluonic states. When these profiles are integrated over all space, a scaling comparison is made between the beta=2.4 and 2.5 data. Using sum rules, these integrated forms also permit an estimate to be made of generalised beta-functions giving b(2.4)=-0.312(15), b(2.5)=-0.323(9), f(2.4)=0.65(1) and f(2.5)=0.68(1). When the profiles are integrated only over planes transverse to the interquark line and assuming underlying string features, scaling comparisons are again made near the centres of the interquark line for the largest interquark distances. For the A'_{1g} case, some of the profiles exhibit a 'dip-like' structure characteristic of the Isgur-Paton model.
The spatial distribution of the action and energy in the colour fields of flux-tubes is studied in lattice SU(2) field theory for static quarks at separations up to 1 fm at beta=2.4, 2.5. The ground and excited states of the colour fields are considered. Sum rules are used to get estimates of generalised beta-functions.
The coupled eta N, pi N system is described by a K-matrix method. The parameters in this model are adjusted to get an optimal fit to pi N -> pi N, pi N -> eta N and gamma N -> eta N data in an energy range of about 100MeV each side of the eta threshold. In the notation T^(-1)+iq_(eta) = 1/a + (r_0)/2 q^2_(eta) + s q^4_(eta), q_(eta) being the momentum in the eta N center-of-mass, the resulting effective range parameters for eta N scattering are found to be a(fm) = 0.75(4)-i0.27(3), r_0(fm) = -1.50(13)-i0.24(4) and s(fm^3) = -0.10(2)-i0.01(1)
The spatial distribution of the action and energy in the colour fields of flux-tubes is studied in lattice SU(2) field theory for static quarks at separations up to 1 fm. Special attention is paid to the structure of the colour fields associated with an excited flux-tube with E_u symmetry. We compare our results with hadronic string and flux-tube models. Sum rules are used to extract generalised beta-functions, to describe the expected colour field behaviour and to cross check the methods used.
Sum rules -- relating the static quark potential V(R) to the spatial distribution of the action and energy in the colour fields of flux-tubes -- are applied in three ways: 1) To extract generalised beta-functions: 2) As a consistency check for the use of excited gluon flux-tubes and as an estimate of the quark self-energies: 3) To extract approximate sum rules using a simplified form of V(R). Also the flux-tube profiles are compared with hadronic string and flux-tube models.
We use lattice sum rules for the static quark potential to determine the beta-function for symmetric and asymmetric lattices non-perturbatively. We also study the colour field distributions in excited gluonic states.
Eta-deuteron scattering lengths are calculated. A summation of the multiple scattering series is carried out and the result is checked against more involved calculations. The necessity to go beyond the fixed nucleon approximation is emphasized. It is shown that a quasibound or virtual state in the $η$-deuteron system may occur within the range of $η$-nucleon scattering lengths suggested by other experiments.