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A. M. Green

Publications and source records attributed to A. M. Green.

45 records · Page 3Linked to original sources
arXiv1995

Perturbative Static Four-Quark Potentials

A first attempt to understand hadron dynamics at low energies in terms of the fundamental quark and gluon degrees of freedom incorporates the effects of the gluonic field into a potential depending only on the spatial positions of the quarks, which are considered in the infinite mass limit. A suitable framework for calculating such potentials between static quarks, i.e.\ a generalization of the Wilson loop will be discussed. Making a connection with recent Monte Carlo lattice simulations for the lowest two energies of a system of two quarks and two antiquarks, the static $qq\bar{q}\bar{q}$-potential will be calculated in perturbation theory to fourth order. The result will be shown to be exactly equal to the prediction of a straightforward two-body approach, which in Monte Carlo lattice simulations has been found to be a reasonable approximation for very small interquark distances.

hep-ph↗
arXiv1995

A Study of Degenerate Four-quark states in SU(2) Lattice Monte Carlo

The energies of four-quark states are calculated for geometries in which the quarks are situated on the corners of a series of tetrahedra and also for geometries that correspond to gradually distorting these tetrahedra into a plane. The interest in tetrahedra arises because they are composed of {\bf three } degenerate partitions of the four quarks into two two-quark colour singlets. This is an extension of earlier work showing that geometries with {\bf two} degenerate partitions (e.g.\ squares) experience a large binding energy. It is now found that even larger binding energies do not result, but that for the tetrahedra the ground and first excited states become degenerate in energy. The calculation is carried out using SU(2) for static quarks in the quenched approximation with $β=2.4$ on a $16^3\times 32$ lattice. The results are analysed using the correlation matrix between different euclidean times and the implications of these results are discussed for a model based on two-quark potentials.

hep-lat↗
arXiv1995

Are there eta-Helium bound states?

Using multiple scattering theory the scattering lengths of $η$ mesons on helium nuclei are calculated and checked against final state $η$ interactions from the $pd \rightarrow η^3$He and $dd \rightarrow η^4$He reactions. The existence of an $η^4$He quasibound state is indicated.

nucl-th↗
arXiv1994

An Analysis of Four-quark Energies in SU(2) Lattice Monte Carlo using the Flux-tube Symmetry:

Energies of four-quark systems calculated by the static quenched SU(2) lattice Monte Carlo method are analyzed in $2\times 2$ bases for square, rectangle, tilted rectangle, linear and quadrilateral geometry configurations and in $3\times 3$ bases for a non-planar geometry configuration. For small interquark distances, a lattice effect is taken into account by considering perimeter dependent terms which are characterized by the cubic symmetry. It is then found that a parameter $f$ - that can be identified as a gluon field overlap factor - is rather well described by the form $exp(-[b_sE{\cal A}+\sqrt{b_s}F{\cal P}])$, where ${\cal A}$ and ${\cal P}$ are the area and perimeter mainly defined by the positions of the four quarks, $b_s$ is the string constant in the 2-quark potentials and $E,F$ are constants.

hep-lat↗
arXiv1994

Four-Quark Binding Energies from SU(2) Lattice Monte Carlo

Energies of four-quark systems have been extracted in a static quenched SU(2) lattice Monte Carlo calculation for six different geometries, both planar and non-planar, with $β=2.4$ and lattice size $16^3\times 32$. In all cases, it is found that the binding energy is greatly enhanced when the four quarks can be partitioned in two ways with comparable energies. Also it is shown that the energies of the four-quark states cannot be understood simply in terms of two-quark potentials.

hep-lat↗
arXiv1993

The Production of the Exotic Atoms $π^+π^-$, $K^+π^-$ and $K^+K^-$

Estimates are made of the signals to be expected in the production of the exotic atoms Pionium ($π^+π^-$), Kaonium ($K^+K^-$) and also $K^+π^-$ in pp, pd and $e^+e^-$ reactions. Such experiments are now being undertaken or contemplated at CELSIUS, COSY, Indiana and SATURNE.

hep-ph↗
arXiv1993

Multi-Quark Energies in SU(2) Lattice Gauge Theory

Energies of four-quark systems have been extracted in a quenched SU(2) lattice Monte Carlo calculation for two different geometries, rectangular and colinear, with $β=2.4$ and lattice size $16^3\times 32$. Also, by going to a lattice $24^3\times 32$ and to $β=2.5$, the effect of the finite lattice size and scaling are checked. An attempt is made to understand these results in terms of a model based on interquark two-body potentials but modified very significantly by a phenomenological gluon-field overlap factor.

hep-lat↗
arXiv1992

Multi-quark energies in QCD

Four-quark potentials for $SU(2)$ are evaluated in the static limit with the quenched approximation -- using a lattice of $16^3\times 32$ and $β=2.4$. The four quarks are restricted to the corners of rectangles with sides upto seven lattice spacings long. The results are analysed in terms of a strategy based on interquark two-body potentials -- as advocated earlier by the authors. This shows that a standard two-body approach overestimates the four-quark binding energy by upto a factor of about three for the largest rectangles.

hep-lat↗