Orateur
Prof.
Jean-Marc Richard
(LPSC, University of Grenoble, France)
Description
The quark--antiquark confining potential, V2(r)=r (in appropriate units) is generalised to baryons as
V3=min(d1+d2+d3), where di is the distance of the ith quark to a junction whose location is adjusted to minimise the interaction. Hence estimating V3 involves solving the famous Fermat--Torricelli problem.
The extension to the tetraquark problem, initiated by several authors, has been recently revisited in Refs.~[1,2]. It consists of the minimum of (r13}+r24) and (r14+r23) on one side, which is the so-called “flip-flop” potential, and on the other side, (d15+d25+d56+d63+d64), with the junction points r5 and r6 optimised. This latter term is a Steiner minimal tree and it should be computed carefully and efficiently.
This intricate four-body potential, inspired by the flux-tube limit of QCD, has been applied to solve the tetraquark problem for configurations (Q,Qbar,q,qbar)$ and (Q,Q,qbar,qbar) with two different masses M and m.
From a careful variational calculation, it is found that the tetraquark ground-state is slightly bound for M=m, and, while the hidden-flavour state becomes unbound when M/m increases, the state with two units of heavy flavour becomes more stable. See the contribution by A. Valcarce and J. Vijande to this Workshop.
A subtle property of minimal Steiner tree with four terminals gives a rigorous upper bound for the above four-body potential, and the four-body problem is exactly solvable with this upper bound. It is demonstrated that the flavour-exotic tetraquark is stable in the limit of large mass ratio M/m.
[1] J. Vijande, A. Valcarce and J.M. Richard, Phys. Rev. D 76 (2007) 114013
[2] Cafer Ay, Jean-Marc Richard and J. Hyam Rubinstein, in preparation.
Auteur principal
Prof.
Jean-Marc Richard
(LPSC, University of Grenoble, France)
Co-auteur
Prof.
J. Hyam Rubinstein
(Department of Mathematics and Statistics, University of Melbourne, Australia)
