A model for quark exchange in chromodynamics illustrated by a description of meson-meson scattering

Masud, Bilal; Paton, Jack E.; Green, A.M.; Liu, G.Q.

doi:10.1016/0375-9474(91)90247-4

Cited by 19 publications

(47 citation statements)

References 26 publications

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“…With the use of ground state potential v ij in the realistic coulombic plus linear form, it becomes impossible for us to solve the integral equations appearing below in eqs. (21)(22)(23)(24). Therefore we used the parametrization of the static pairwise two quark potential as v ij = Cr 2 ij + C, with i, j = 1, 2, 3, 4.…”

Section: Q 2 Q 2 Potential Model (In the Extended Basis)mentioning

confidence: 99%

“…In this simple harmonic potential, the parameters C is related to size (d) of wavefunction (ξ k ) through the relation C = − 3 16 1 d 4 = − 3 16 mω 2 with ω = 1 md 2 , and for consistency of the diagonal term of the integral eq. (21) C = 3 8 (4m + 3ω − 2M ) GeV [22] with M = 2m = 2.9588GeV being the mass of a charmonium meson. The parameter d is chosen in such a way to reduce the error resulting from a use of this quadratic potential instead of the realistic one.…”

Section: Q 2 Q 2 Potential Model (In the Extended Basis)mentioning

confidence: 99%

“…The kinetic energy in the same form is also used in ref. [22]. The gluonic field overlap factor f, as written in introduction, is suggested by ref.…”

Section: Q 2 Q 2 Potential Model (In the Extended Basis)mentioning

confidence: 99%

“…At the quark level, this model II was noted to much reduce the chisquare of eq.(1). This model has been worked out in [22,23,24] till meson-level transition amplitudes. The dynamical calculations require a kinetic energy term as well.…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper, we have used a formalism of the resonating method as used in [22]. In the resonating group method, the dependence on the internal co-ordinates of the system is specified before solving the problem to integrate out the degrees of freedom corresponding to the internal coordinates of clusters of the system.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical implications of gluonic excitations in meson-meson systems

Akbar¹,

Masud²

2012

Eur. Phys. J. A

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We study meson-meson interactions using an extended q 2q2 (g) basis that allows calculating coupling of an ordinary meson-meson system to a hybrid-hybrid one. We use a potential model matrix in this extended basis which at quark level is known to provide a good fit to numerical simulations of a q 2q2 system in pure gluonic theory for static quarks in a selection of geometries. We use a combination of resonating group method formalism and Born approximation to include the quark motion using wave functions of a qq potential within a cluster. This potential is taken to be quadratic for ground states and has an additional smeared 1 r (Gaussian) for the matrix elements between hybrid mesons. For the parameters of this potential, we use values chosen to 1) minimize the error resulting from our use of a quadratic potential and 2) best fit the lattice data for differences of Σg and Πu configurations of the gluonic field between a quark and an antiquark. At the quark (static) level, including the gluonic excitations was noted to partially replace the need for introducing many-body terms in a multi-quark potential. We study how successful such a replacement is at the (dynamical) hadronic level of relevance to actual hard experiments. Thus we study effects of both gluonic excitations and many-body terms on mesonic transition amplitudes and the energy shifts resulting from the second order perturbation theory (i.e. from the respective hadron loops). The study suggests introducing both energy and orbital excitations in wave functions of scalar mesons that are modelled as meson-meson molecules or are supposed to have a meson-meson component in their wave functions.

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Section: Q 2 Q 2 Potential Model (In the Extended Basis)mentioning

confidence: 99%

Section: Q 2 Q 2 Potential Model (In the Extended Basis)mentioning

confidence: 99%

“…The kinetic energy in the same form is also used in ref. [22]. The gluonic field overlap factor f, as written in introduction, is suggested by ref.…”

Section: Q 2 Q 2 Potential Model (In the Extended Basis)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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